\r\n\t2) Human sexual disorders in males and females. \r\n\t3) Psychological aspects of the human sexual response cycle and its disorders. \r\n\t4) The therapeutic aspects.
\r\n
\r\n\tThe human sexual response cycle and human sexual behavior are interrelated. How this inter-relationship and its association to normal sexual health need to be delineated. In a world torn between sex and sexually transmitted disease, clear-cut scientific information in the form of a monograph is required to educate.
\r\n
\r\n\tHuman sexuality, gender identity, and sexuo-erotic orientation play great roles in human health and disease. Sex education is the need of the hour and a reflection will be timely.
",isbn:"978-1-80355-151-7",printIsbn:"978-1-80355-150-0",pdfIsbn:"978-1-80355-152-4",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,isSalesforceBook:!1,hash:"13af09c4cf93ae89789a3db597972cf6",bookSignature:"Dr. Dhastagir Sultan Sheriff",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/11267.jpg",keywords:"Master and Johnson's Cycle, Sex Education, Premature Ejaculation, Orgasmic Disorders, Sexual Aversion Disorders, Dyspareunia, Vaginismus, Sex Hormones, Sexually Transmitted Diseases, Impotence, Low Libido, Blood Analyses",numberOfDownloads:100,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"August 18th 2021",dateEndSecondStepPublish:"March 3rd 2022",dateEndThirdStepPublish:"May 2nd 2022",dateEndFourthStepPublish:"July 21st 2022",dateEndFifthStepPublish:"September 19th 2022",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Dr. Sheriff is a life counselor, sex educationist, and researcher with over 35 years of teaching experience, five authored books, and editorials written in the British Journal of Sexology and the Journal of Royal Society of Medicine. 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1. Introduction
Recombination of excess (nonequilibrium) electrons and holes in semiconductors through impurity recombination centers (traps) referred to in this chapter as trap-assisted (Shockley-Read-Hall) recombination is in many cases the dominant process [1-9]. Hall [10] and Shockley and Read [11] have proposed the theory of trap-assisted recombination as early as 1952. Further, the theory of trap-assisted recombination has been developed in many aspects and details [1-5, 12-14]. At the same time, due attention was not paid to study dependences of lifetimes of excess electrons τn(N) and holes τp(N) on concentration of traps N. In some cases, traps are produced intentionally by doping semiconductor (e.g., by bombarding with high-energy ions [15, 16]) to reduce time of transient processes. It seems that lack of attention is caused by traditional understanding that the larger the concentration of traps N, the greater the capture rate of excess charge carriers on impurity level traps and, therefore, the shorter the lifetimes of excess charge carriers.
That reasonable understanding is incompletely adequate to reality. As shown below, lifetimes of excess electrons and holes (see our definition of τn and τp in Section 2) may grow strongly (in order of magnitude and more) with increase of concentration N.
In this chapter, we generalize the theory and give systematic mathematical and detailed physical analysis of dependences τn(N) and τp(N) on concentration of recombination centers.
2. Preliminaries
Let’s consider the case of small deviation of free charge carriers’ concentrations from equilibrium values. This situation occurs often in semiconductors used for registration of low-level signals, for example, optical signals. It will be shown that both τn(N) and τp(N), under certain conditions, will grow very strongly with increasing N in a particular interval of N values. Completely different physical mechanism causes this increase in lifetimes. It differs from mechanisms available for many years [4], as well as proposed in [17]. We analyze extreme points (corresponding formulas are derived) of dependences τn(N) and τp(N) as functions of semiconductor parameters and temperature. We give detailed physical interpretation of obtained results. In particular, it is shown that physical mechanisms responsible for strong non-monotonic dependences τn(N) and τp(N) differ from each other.
It is reasonable to expect that the growth of lifetimes τn(N) and τp(N) with increasing N will lead to the growth of photoresponse of semiconductor sample (including photoelectric gain G). However, specificity of dependences τn(N) and τp(N) does not determine the type of dependence G(N) in total. As it follows from [18, 19], G increases with increasing charge carriers’ lifetime, if ambipolar mobility [2, 13] μa=0 or there is no recombination at current contact electrodes (x=0 and x=W ; see insert in Figure 1a). In reality, recombination at current contact electrodes is always happening to some extent [5-9]. Therefore, in normal conditions (μa≠0), increase in lifetimes, after reaching some values, does not lead to an increase in photocurrent Iph [5, 9, 18, 19]. Saturation of Iph becomes apparent in the case of high-rate recombination at the contact electrodes (sweep-out effect [5, 9, 18, 19]) when
Δn(0)=Δp(0)=Δn(W)=Δp(W)=0,E1
\n\t\t\t
where Δn(x)=n(x)−ne and Δp(x)=p(x)−pe are deviations of electron n and hole p concentrations from their equilibrium values ne and pe, respectively. In trap-assisted recombination, function μ(N) can vanish at the same (up to small corrections) concentration N, at which dependences τn(N) and τp(N) reach points of maximal extremum τ^n and τ^p (Figure 1b and 1c). Therefore G and, hence, Iph grow to the extent of increase in τn(N) and τp(N). These are physical grounds of giant splash of photoelectric gain with increasing N (Figure 1a).
It was first reported in [20] that vanishing μ(N) in points of maximal extremum of dependences τn(N) and τp(N) allows avoiding highly undesirable effect – saturation of G in intrinsic photoconductors, when applied bias voltage V increases [5, 9, 18, 19, 21, 22]. As is known [19], this disadvantage is the most evident in photoconductors with sweep-out effect on contact electrodes, i.e., when relations (1) are fulfilled. Result presented in Ref. [20] was obtained in approximation of quasi-neutrality [1-9, 13, 18, 19, 21, 22], which was usually used at moderate electric fields, i.e., when we neglect in Poisson equation by term Δρ≡(ε×ε0)×divΔE, which determines the density of photoinduced space charge Δρ.
In our case, ΔE≡E(x)−E0 is the variation of electric field caused by deviation of concentrations of free charge carriers and their traps from equilibrium values by reason of band-to-band absorption of radiation, E(x) and E0 are the electric field intensity in the presence and absence of illumination, ε is the relative dielectric permittivity of semiconductor, and ε0 is the vacuum permittivity. However, even at moderate electric fields (≈ 1÷10 V/cm), approximation of quasi-neutrality is not always acceptable [23].
Below, in case of single recombination level, we consider in detail the impact of photoinduced space charge Δρ on value G^ of photoelectric gain G in semiconductors with sweep-out effect on contact electrodes at the point of maximal extremum of function G(N) (Figure 1a). Considering semiconductor as base material for making intrinsic photoconductors with threshold electro-optical performance, we assume that photocarriers are excited by photons of low-intensity optical radiation with wavelength range responding to fundamental absorption band of semiconductor. Figure 2a shows that we cannot use approximation of quasi-neutrality, when voltage V across the sample becomes larger than some particular value.
Also, ignoring approximation of quasi-neutrality, we study, at low-level illumination, the effectiveness of band-to-band photoexcitation of charge carriers and photo-emf Vph in semiconductors with dominant trap-assisted recombination. Analytical expressions for photo-emf Vph and mean, with respect to light propagation length, concentrations of photoelectrons <Δn> and photoholes <Δp> are given. It is shown that target values of Vph, <Δn>, and <Δp> can be improved radically by increasing concentration of recombination centers; moreover, approximation of quasi-neutrality can lead to errors of several orders of magnitude.
Analyzing above-mentioned problems, we do not use conventional (Shockley-Read) expression-based form [1-5, 9, 11-14] of generation-recombination rate. This form does not allow to express explicitly dependences τn and τp and, even more, Iph and Vph on N. And therefore, because of the need for solving complex transcendental equations, conventional (Shockley-Read) expression-based form leads to serious mathematical difficulties in study (especially analytical) dependences τn,p(N) and, even more, Iph(N) and Vph(N).
These difficulties are dramatized by the fact that under certain conditions, τn,p, Iph and Vph are dependent very strongly on concentration N in a particular interval of N (Figure 1а, 1b, 7). Perhaps, it was the main reason for longtime absence of complete theoretical analysis of lifetime dependences τn,p(N), while detailed analysis of lifetime dependences on concentrations of free charge carriers was made in pioneering paper by Shockley and Read [11] concerning the theory of recombination through impurity level trap. In present chapter, we use the method of calculation assuming that N is expressed in terms of the ratio of the number of filled recombination level states to the number of empty. This allows to avoid transcendental equations, in other words, to avoid the need to solve inverse problem. As a result, the described above approach simplifies greatly the mathematical analysis and physical interpretation of calculations of desired parameters.
3. Model and basic relations
Consider nondegenerated semiconductor doped by shallow fully ionized single type impurity (for definition donors) with concentration ND. Recombination of excess charge carriers occurs in said semiconductor through the energy level of acceptor impurity atoms with concentration N, which can be in two charge states (assume in neutral and singly negatively charged). Concentration of recombination impurity atoms in neutral state corresponds to concentration of acceptor atoms N0, which are simultaneously centers of electron capture and centers of thermal emission of holes. Concentration of recombination impurity atoms in negatively charged state corresponds to concentration of atoms N−=N−N0, which are capture centers of holes and, at the same time, centers of thermal emission of electrons. Described above is recombination through single-level trap [10-13] (Figure 5b), which is often dominant [1-5, 9, 14] and called Shockley-Read-Hall recombination.
Figure 1.
Dependences on concentration of single-level recombination centers N (сm – 3): (a)\n\t\t\t\t\t\tG− photoelectric gain; (b)\n\t\t\t\t\t\tτ− lifetime of electrons (curve 1) and holes (curve 2) (s); (c)\n\t\t\t\t\t\tμ− ambipolar mobility of charge carriers (in units of hole mobility). Adopted: room temperature, W=10−1cm, θ≡wp/wn=102, wn=10−8cm3/s, ni/nt=104, ND=1015cm-3, E0=10V/cm. Solid curves, GaAs, and dashed curves, Si. Physical parameters of semiconductors are obtained from monograph [3]. Schematic view of photoconductor on insert in Figure 1a
Let either band-to-band excitation (Figure 5b) or injection on the contacts produce excess electrons and holes. Then, in stationary case, equation
Rn=RpE2
\n\t\t\t
determines the charge state of recombination impurity atoms.
Recombination-generation rates of electrons Rn and holes Rp due to capture of charge carriers by acceptor impurity traps and their thermal emission from recombination level states into permitted conduction or valence bands are equal to
Rn=(n×N0−δ−1×ne×N−)×wn,Rp=(p×N−−δ×pe×N0)×wp.E3
\n\t\t\t
Here, wn and wp are electron and hole capture probabilities, respectively, at appropriate recombination level state, δ=N−e/N0e (superscript indicates equilibrium values of concentration of recombination impurity atoms N in relevant charge states).
For small deviation of charge carriers’ and their capture centers’ concentrations ΔN0=N0−N0e=−ΔN−=N−e−N− from equilibrium values, we can linearize relations (2) and (3) with respect to proper deviations. Then taking into account Poisson equation
ΔE is change in electric field caused by deviation of charge carriers’ and capture centers’ concentrations from equilibrium values, and q is absolute electron charge value and θ=wp/wn. First terms in (5) and (6) mean recombination rates of excess electrons and holes (and therefore, symbols τn and τp mean their lifetimes) in quasi-neutrality with respect to electric field ΔE, i.e., at sufficiently small values divΔE [1-3, 5, 9-14, 18, 24, 25]. We will use the same terminology for τn and τp in the case of failure to comply quasi-neutrality (see below); therefore values τn and τp will not depend on value divΔE in the present study.
High-performance photoconductors operate with extremely low-level illumination. Therefore, linear for g approximation, usually used in the theory of high-performance photodetectors [5-7, 9, 21, 22, 26], is correct in calculation of photoelectric gain G, where g is density of charge carriers’ photoexcitation rate.
In view of the above provision, we can write expressions for the density of photocurrent components as follows:
ΔIn=q×μn×(E0×Δn+ne×ΔE)+q×Dn×∂Δn∂x,E12
\n\t\t\t
ΔIp=q×μp×(E0×Δp+pe×ΔE)−q×Dp×∂Δp∂x.E13
\n\t\t\t
where μn and μp are electron and hole mobility and Dn and Dp are electron and hole diffusion constants. The density of electron ΔIn and hole ΔIp components of photocurrent
Iph=ΔIn+ΔIpE14
\n\t\t\t
must satisfy continuity equations:
∂ΔIn∂x=q×(Rn−g),E15
\n\t\t\t
∂ΔIp∂x=q×(g−Rp),E16
\n\t\t\t
and also
∂Iph∂x=0.E17
\n\t\t\t
Let limit voltage be applied to sample by value
V=E0×WE18
\n\t\t\t
that allows to neglect by the dependence of μn and μp on electric field, where W is distance between current contact electrodes (see insert in Figure 1a).
Figure 2.
Dependences: (a), photoelectric gain G = G^ in point of maximal extremum of function G(N) (see Figure 1a) on bias voltage across the sample V (distance between current contacts W=10−1 cm); (b), ratio ζ≡G^appr/G^exact on V at W = 10−1 cm, where G^appr and G^exact are approximate and exact values G^, respectively; (c), value G^max on W, where G^max is maximal value G^ for given W (see Figure 2a); (d), value Vop on W, where Vop is optimal voltage, at which G^ = G^max (see Figure 2c). Voltage V in V; length W in cm. Physical parameters of semiconductors and temperature are the same as in Figure 1. Solid curves GaAs, dashed curves Si
4. Lifetime of excess charge carriers
Using distribution function of electrons over acceptor level states [12, 27], we can write neutrality equation
ne+N−e=pe+NDE19
\n\t\t\t
for nondegenerated semiconductor at thermodynamic equilibrium as follows:
N=nt×1+δ2×δ2×f(δ),E20
\n\t\t\t
where
δ=N−eN0e,f(δ)=B+A×δ−δ2,E21
\n\t\t\t
A=2×NDnt,B=4×ptnt=(2×nint)2,E22
\n\t\t\t
nt and pt are equilibrium concentrations of electrons and holes when Fermi level energy coincides with recombination level energy Et, and ni is intrinsic charge carriers’ concentration. When derived (20), we have adopted that spin degeneracy factor of acceptor state is equal to 1/2 [2, 12, 14, 27]. In considered conditions
ne=δ2×nt,pe=2δ×pt.E23
\n\t\t\t
From expressions (8), (9), (20), and (23), it follows that
Expressions (20), (24), and (25) determine dependences τn(N) and τp(N) in parametric form. Figure 1b shows that, as usual, dependences τn(N) and τp(N) fall with increased N, but in some interval of concentration N, dependences can rise up sharply. Further, we give analytical solution of extremum problem for dependences τn(N) and τp(N) at θ≥1, because hole is captured on attractive center and electron – on neutral.
4.1. Mathematical analysis of hole lifetime
The analysis of equation
∂∂δ×1τp=0,E26
\n\t\t\t\t
which determines extremum points of dependence τp(N), shows that well-defined non-monotonic behavior of this function occurs at
ξ1≡3θ×B<<1<<1ξ2≡A24×B,ξ3≡1A<<1.E27
\n\t\t\t\t
To determine minimum point, let us set out equation (26) into the form
It means that the first root of equation (26)\n\t\t\t\t\tδ1p can be found by the method of successive iterations using Λ1p(δ1p) as small parameter. Zeroth-order approximation (30) leads to the formula for concentration of recombination centers N=N1p, where dependence τp(N) reaches its minimum τ⌣p (Figure 1b):
N1p=ND+2×θ×pt−2×θ×pt×(ND+2×θ×pt).E31
\n\t\t\t\t
It follows from this formula that ratio N1p/ND increases from ½ when ND<<2×θ×pt to (1−2×θ×pt)≅1 when ND>>2×θ×pt with increased ND (Figure 3a). Further, it will be demonstrated that extremum, like the maximum of dependence τp(N) as well as τn(N), can occur only at values N closer to ND. Therefore, in expression for upper limit of value N1p, small correction has been remained, which is primal.
To determine maximum point of dependence τp(N), let us set out equation (26) into the form
It means that the second root of equation (26)\n\t\t\t\t\tδ2p can be found by the method of successive iterations using Λ2p(δ2p) as small parameter. It follows from relations (20) and (34) that concentration of recombination centers N=N2p, where dependence τp(N) reaches its maximum τ^p (Figure 1b), is determined in first-order approximation for small parameter Λ2p(δ2p) by expression
N2pND=1−1A+B−A+BA×Λ2p×(A+B)≅1.E35
\n\t\t\t\t
Figure 3.
Dependences: point of minimum N1 of functions τp(N) и τn(N)\n\t\t\t\t\t\t\t(a) and ratio K between maximal to minimal charge carriers’ lifetimes (b) on concentration of shallow donors ND at different locations of recombination level. Solid curves, holes; dashed curves, electrons. Ratio nt/ni values: curve 1, 10-4; curve 2, 10-2; curve 3, 1; curve 4, 102. Concentration N1 is measured in units ND, concentration ND in units ni. Adopted: θ=102
Relation (37) shows that function Kp(ND) is non-monotonic and can vary by several orders of magnitude (Figure 3b). Value
τ^p=(1+2×θ×ptND×nt+2×ni2)×(ND×wp)−1E38
\n\t\t\t\t
increases with decreasing recombination level energy Et (Figure 4a).
The dependence of τ^p on temperature T is determined by the location of recombination level in forbidden gap of semiconductor (Figure 4b). Value τ^p decreases with lowering temperature if Et≥Eg/2 and increases if Et≤Eg/3 (value Et is measured from top of valence band and Eg is the energy gap of semiconductor). If Eg/3<Et<Eg/2, then dependence τ^p has maximum value at
T=T˜≡Etk×ln−1(2×NvND×Eg−2×Et3×Et−Eg),E39
\n\t\t\t\t
where k is Boltzmann constant and Nv is effective density of states in valance band.
4.2. Mathematical analysis of electron lifetime
The analysis of equation
∂∂δ×1τn=0,E40
\n\t\t\t\t
which determines extremum points of dependence τn(N), shows that well-defined non-monotonic behavior of this function occurs at
2×ξ3<<1,ξ4=2×BA<<1.E41
\n\t\t\t\t
To determine minimum point let us set out equation (40) into the form
It means that the first root of equation (40)\n\t\t\t\t\tδ1n can be found by the method of successive iterations using Λ1n(δ1n) as small parameter. Zeroth-order approximation (44) leads to the formula for concentration of recombination centers N=N1n where dependence τn(N) reaches its minimum τ⌣n :
N1n=ND+2×θ×ptθ−1×(θ×(ND+2×pt)−ND+2×θ×pt).E45
\n\t\t\t\t
It follows, from this formula, that ratio N1n/ND decreases from ½ when ND<<2×θ×pt to 1/(θ+1) when ND>>2×θ×pt with increased ND (Figure 3a).
We can transform equation (40) to form (32) where Λ2p(δ) will be replaced by function:
At value δ=δ2n, where dependence τn(N) has its maximum τ^n, absolute value |Λ2n(δ)|<<1. Therefore, in zeroth-order approximation for small parameter Λ2n(δ2n), value δ2n=δ2p(0) and concentration N=N1n, where τn(N)=τ^n equals to ND (as for holes). And
where κ=4 at θ=1 and κ=1 at θ>>1. It follows from relation (47) that function Kn(ND), in contrast to Kp(ND), grows monotonically with increased ND and this growth can be many orders of magnitude (Figure 4b).
Value
τ^n=ND+2×pt2×ni×(ND×wn)−1E48
\n\t\t\t\t
increases, as for τ^p, with the decrease of recombination level energy (Figure 4a) and, in contrast to τ^p, always falls with temperature rise (Figure 4b).
4.3. Physical interpretation
Let’s explain physical mechanisms of the above regularities.
Figure 4.
Dependences of maximal lifetime of holes τ^p(N) (solid lines) and electrons τ^n(N) (dashed lines) on recombination level energy Et (eV) for Ge (1), Si(2), and GaAs (3) at T=300 K (a) and on temperature T (K) for Si at different values Et\n\t\t\t\t\t\t\t(b): curve 1, 0; curve 2, (-101/152); curve 3, (-3/4). Recombination level energy is reckoned from the middle of forbidden gap. Physical parameters for Ge, Si, and GaAs are obtained from monograph [3]. Adopted: ND= 1015 сm-3, wn=10−8cm3 /s, θ=102
4.3.1. Hole lifetime
Reciprocal hole lifetime
τp−1=τp1−1+τp2−1+τp3−1E49
\n\t\t\t\t\t
consists of three partial components.
First component
τp1−1=wp×N−e=wp×nt2×B+A×δ−δ2δE50
\n\t\t\t\t\t
corresponds to the change of capture rate of holes Δp×wp×N−e=Δp/τp1 caused only by deviation of hole concentration from its equilibrium value (capture of excess holes Δp at equilibrium trapping centers N−e).
corresponds to the change of capture rate of holes pe×wp×ΔN−=Δp/τp2 caused only by deviation of concentration of hole trapping centers from its equilibrium value (capture of equilibrium holes pe at nonequilibrium trapping centers ΔN−).
Third component
τp3−1=δ×τp2−1E52
\n\t\t\t\t\t
corresponds to the change of thermal emission rate of holes from impurity level states into valence band 2×pt×wp×ΔN0=Δp/τp3 caused by deviation of concentration of hole generation centers from its equilibrium value (thermal emission of holes from nonequilibrium centers ΔN0).
Lifetime τp1 can be interpreted as capture time of excess holes by equilibrium traps, lifetime τp2 can be interpreted as relaxation time of excess holes due to capture of equilibrium holes by nonequilibrium traps, and lifetime τp3 can be interpreted as time of thermal emission of holes from nonequilibrium centers.
If conditions (27) are fulfilled and N<ND, then recombination centers are almost completely filled with electrons (δ≡N−e/N0e>1). For this reason, even if θ≡wp/wn=1, capture time of hole τp1 is much shorter than capture time of electron τn1 for the relevant equilibrium trapping centers. In other words, equilibrium traps capture holes much more intensively than electrons. Therefore, the generation of excess free charge carriers initiates the formation of additional nonequilibrium centers of thermal generation of holes and, simultaneously, reducing concentration of trapping centers of electrons (ΔN0=−ΔN−>0). This change of charge state of recombination impurity atoms results in negative values of components 1/τp2 and 1/τp3 in expression (36); moreover |τp3|<<|τp2|, because δ>>1 at N<ND. This means that hole lifetime τp exceeds capture time of holes τp1 at equilibrium traps due to dominating thermal emission of holes from relevant nonequilibrium centers. As long as N<ND, concentration N−e≅N of equilibrium capture centers of holes grows with increased N, but concentration N0e<<N of capture centers of electrons still remains low. Therefore, concentration ΔN0 of nonequilibrium centers of hole thermal emission increases as well. This increase causes faster decreasing |τp3| than decreasing τp1. As a result, starting with concentration N=N1p, the rate of hole thermal emission from nonequilibrium centers and the capture rate of nonequilibrium holes at equilibrium traps become closer to each other. For this reason, τp starts to grow (Figure 1b).
When N becomes larger than ND, the concentration N−e of equilibrium hole capture centers practically stabilizes, while concentration N0e of equilibrium electron capture centers grows with the increase of recombination centers’ concentration (N−e≅\n\t\t\t\t\t\tND,N0e\n\t\t\t\t\t\t≅N−\n\t\t\t\t\t\tND at nt/2<<\n\t\t\t\t\t\tN−\n\t\t\t\t\t\tND << ND2/2pt). This means that the ratio τp1/τn1 increases with increasing N. For this reason, concentration of nonequilibrium hole thermal emission centers decreases, and concentration of hole traps N− increases. As a result, τp(N) decreases with increased N (Figure 1b). When N prevails ND2/2pt, the concentration N−e of equilibrium hole capture centers grows again with increased N due to thermal emission of electrons from valence band to impurity level (N−e≅2N×pt). However, concentration of equilibrium capture centers of electrons grows much faster (N0e≅N). Therefore, the decrease of τp(N) continues. As it is seen from (36)-(39), τp becomes less than τp1, when product δ×θ becomes less than unity.
As shown above, minimum point N=N1p of dependence τp(N) shifts toward ND with growth ND (Figure 3a). The main reason is that equilibrium electrons are being captured at centers of hole thermal emission and decreased concentration ΔN0 of these centers. The higher the concentration of equilibrium electrons ne, the more ΔN0 decreases. Concentration ne grows with increased ND. When N ascends, then ne descends and N−e increases that causes increased ΔN0 at N<ND. In other words, decreased ΔN0 with increased ND is compensated by increased ΔN0 with increased N. This is the reason why the greater the ND, the closer the N1p to ND.
For the same reasons, non-monotonic dependence τp on N cancels out, as shown above (Figure 3b), at ND>2×(θ×pt)2/nt (increased ΔN0 with increasing N is not able to compensate decreasing ΔN0 with increasing ND).
Non-monotonic character of dependence τp on N does not occur and at low concentrations ND {see inequities (27), expressions (22), and Figure 3b}, when equilibrium electron population at recombination level is determined mostly by electron-hole transitions between that level and free bands. In this case, values δ cannot provide prevailing growth of hole thermal emission rate from nonequilibrium centers over the growth of capture rate of nonequilibrium holes at equilibrium hole traps with increasing N.
Maximal value of ratio Kp≡τ^p/τ⌣p is achieved at ND≅2×θ×pt and equals to approximately
(Kp)max≅θ×ptnt.E53
\n\t\t\t\t\t
Note that with increasing energy Et of recombination level, non-monotonicity of dependence τp(N) fades out (Figure 3b) and then cancels out absolutely. This is caused by the increase in concentration ne of equilibrium electrons and decrease in value δ and fall of the probability of hole thermal emission from recombination level into valence band with increasing energy of recombination level referred to the top of valence band. For the same reason, value τ^p decreases with increasing Et (Figure 4a).
The character of dependence τ^p on temperature (Figure 4b) is determined by the following dependences on temperature:
Values pt(T) and ne(T) increase always with temperature T rise. Increased pt means increasing probability of thermal emission of hole from recombination center into valence band. Therefore, the above-mentioned process facilitates increasing τ^p with T rise. At the same time, growth ne(T) facilitates decreasing τ^p with T rise due to decreasing concentration of nonequilibrium centers ΔN0 of hole thermal emission.
Value δ2p decreases with T rise at Et≤Eg/3 due to approaching N2p closer and closer to ND (see expression (36)). Value δ2p decreases also at Et≥Eg/2 up to temperature at which non-monotonic dependences τp and τn on N cancel out. Falling δ2p decreases ΔN0 that facilitates decreasing τ^p with T rise. When Et≥Eg/2, then pt(T) increases faster and δ2p(T) falls and ne(T) grows. As a result, τ^p increases with temperature rise (Figure 4b). If Et≤Eg/3, then increased pt with temperature rise cannot compensate decreased δ2p(T) and growth ne(T). As a result, τ^pdecreases with temperature rise (Figure 4b). If Eg/3<Et<Eg/2, then at T<T˜, dependence τ^p(T) will be increasing, and at T>T˜ dependence τ^p(T) will be falling for the same reasons that in previous cases (see expression (39) and insert in Figure 4b).
4.3.2. Electron lifetime
By analogy with hole lifetime, reciprocal electron lifetime consists of three partial components:
τn−1=τn1−1+τn2−1+τn3−1E56
\n\t\t\t\t\t
First component
τn1−1=wn×N0e=wn×nt2×B+A×δ−δ2δ2E57
\n\t\t\t\t\t
corresponds to the change of electron capture rate Δn×wp×N0e=Δn/τn1 caused by deviation of electron concentration from equilibrium value (capture of excess electrons Δn on equilibrium traps N0e).
corresponds to the change of electron capture rate ne×wn×ΔN0=Δn/τn2 caused solely by deviation of concentration of electron capture centers from equilibrium value (capture of equilibrium electrons ne on nonequilibrium capture centers ΔN0).
Third component
τn3−1=(δ×τn2)−1E59
\n\t\t\t\t\t
corresponds to the change of thermal emission rate of electrons from impurity level into valence band (1/2)×nt×wn×ΔN−=−Δn/τn3 caused by deviation of concentration of electron thermal emission centers from equilibrium value (thermal emission of electrons from nonequilibrium centers ΔN−).
Times τn1, τn2 and (−τn3) have physical sense similar to times τp1, τp2 and (−τp3), respectively.
Value δ>>1 as long as N<ND, and hence ratio τp1/τn1<<1. Therefore, the occurrence of excess free charge carriers leads to the formation of additional (nonequilibrium) capture centers of electrons and, at the same time, decrease in concentration (ΔN0=−ΔN−>0) of electrons’ generation centers. Partial components 1/τn2 and 1/τn3 are positive values at such change of charge state of recombination centers; moreover τn2<τn3, because of δ>1 at N<ND. It means that, due to preferable capture of equilibrium electrons on nonequilibrium traps, lifetime of electrons τn is shorter, than capture time of electrons on equilibrium traps. With further increased N, the number of equilibrium capture centers of holes grows, but the number of equilibrium capture centers of electrons remains still small. As a result, concentration ΔN0 of nonequilibrium capture centers of electrons increases. For this reason, starting from concentration N=N1n, capture rate of equilibrium electrons on nonequilibrium traps becomes higher than capture rate of nonequilibrium electrons on equilibrium traps. In other words, partial component 1/τn2 becomes critical component defining reciprocal lifetime of electrons 1/τn. Component 1/τn2 falls with growth N due to the decrease in concentration ne of equilibrium electrons, so τn≈τn2 and increases with growth N (Figure 1b).
At values N greater than ND, the ratio τp1/τn1 increases with increasing N. This, again, leads to decreasing concentration of nonequilibrium capture centers of electrons with increasing N. Value ne continues to fall as well. As a result, partial component 1/τn1 becomes critical component defining reciprocal electron lifetime 1/τn, and therefore, τn(N) falls with increasing N (Figure 1b).
As shown above, in contrast to dependence τp(N), ratio N1n/ND decreases (Figure 3a) and ratio Kn≡τ^n/τ⌣n always increases monotonically with increasing ND (Figure 3b). Such regularities are caused by increased ne with increasing ND. Because of this, capture rate of equilibrium electrons at nonequilibrium traps becomes greater than capture rate of nonequilibrium electrons at equilibrium traps at lower concentrations ΔN0, i.e., at lower values of ratio N/ND. In contrast to the situation with holes, here, decreasing ΔN0 with increased ND is compensated by increasing ne.
Similar to the behavior of hole lifetime, non-monotonic dependence τn(N) fades gradually and then cancels out (Figure 3b) with decreasing ND or increasing Et. First regularity is caused by decreased ne and δ=2ne/nt with decreasing ND. Second regularity is caused by decreasing δ and, hence, ΔN0, with increasing energy Et of recombination level. In this case, however, due to growth ne, non-monotonicity of dependence τn(N) cancels out at larger values Et than in the case of holes.
Due to decreasing δ2n with increasing Et, value τ^n decreases as well (Figure 4a). The type of dependence τ^n on temperature (Figure 4b) is determined only by dependence δ2n(T), because in maximum point τn=τn1/2∼1/N0e∼δ2n. In zeroth approximation, δ2n(T) coincides with δ2p(T), determined by expression (56). Therefore, τ^n decreases always with temperature rise (Figure 4b).
5. Relation between concentrations of photoholes and photoelectrons outside approximation of quasi-neutrality
Note first, from formulas (10), (11), (20), and (23) follow
Recall that ΔE≡E(x)−E0 is the change of electric field intensity caused by deviation of concentrations of free charge carriers and their capture centers from equilibrium values by reason of band-to-band absorption of optical radiation: E(x) and E0 are electric field intensities with and without illumination.
Eliminating ∂ΔE∂x from equations (7) and (64) and taking into account expressions (23) and (65), we find that relation between concentrations of excess holes Δp and electrons Δn is determined by the following formula:
Formulas (73) and (74) are, none other than, well-known (in quasi-neutrality approximation) expressions for ambipolar diffusion constant Dna, and ambipolar mobility μna of electrons and dimensionless parameter
ξ=an+apμn×ne+μp×pe=2×(an+ap)×δ(δ2×μn+B×μp)×ntE75
\n\t\t\t
is much less than unity (see below). On the other hand, as it follows from equations (63) and (64),
Equation (81) is the desired equation. It depicts adequately the continuity of electron, hole, and total currents [see (15)-(17)].
7. Solitary Illuminated Sample
In this section, we will consider opportunities for improving photoexcitation of charge carriers and photo-emf Vph by increasing concentration N of recombination centers.
7.1. Preliminaries: Basic relations
We will call the sample as solitary, if it is not in external electric field and external electrical circuit is open.
For simplicity, we will characterize effectiveness of charge carriers’ photoexcitation by light-propagation-length averaged concentrations of photoelectrons <Δn> and photoholes <Δp> (Figure 5).
Figures 6 and 7 show calculated dependences <Δn>(N) and Vph(N).
We have not used in study quasi-neutrality approximation [2-9, 13, 18, 21, 22, 28-31] because it can lead to unacceptable errors in calculation of dependences <Δn>(N), <Δp>(N) (Figures 8 and 9), and Vph(N) (Figures 10 and 11) due to the fundamental contribution of photoexcited space charge into photoelectric effects in semiconductors. In other words, even in solitary sample, photoexcited electron-hole plasma in semiconductor may not always be quasi-neutral.
Let’s consider a homogeneous semiconductor sample (Figure 5) with no voltage applied, i.e., in absence of illumination and intensity of electric field E0=0. The density of photogeneration rate of charge carriers, in view of multiple internal reflections, is determined by the following expression:
g(x)=γ×[a−×exp(−γx)+a+×exp(γx)],E85
\n\t\t\t\t
in which
a−=(1−R)×F01−R2×exp(−2γW˜),a+=a−×R×exp(−2γW˜),E86
\n\t\t\t\t
where R and γ are coefficients of light reflection and absorption, F0 is density of incident photon flux, and W˜ is sample thickness along incident light direction (Figure 5a). As is clear from (66) and (81), in discussed conditions, relation between concentrations of excess holes Δp and electrons Δn is as follows:
Δp=τpτn×Δn+χ×(τpτn×Δn−g×τp−Dn×τp×∂2Δn∂x2),E87
\n\t\t\t\t
and function Δn(x) obeys the equation
Q×∂4Δn∂x4−D×∂2Δn∂x2+Δnτn=g(x)−ξ×τp×Dp×∂2g∂x2,E88
\n\t\t\t\t
where
D=Dna+Dξ.E89
\n\t\t\t\t
Figure 5.
Layout of sample illumination (а) and generation-recombination processes in semiconductor (b). F0, density of incident photon flux; Vph, photo-emf; ϕ(x), electric potential; W˜, thickness of sample along light propagation; Ec and Ev, energy of conduction band bottom and valence band top
Figure 6.
Dependences of mean concentration of photoelectrons <Δn> in GaAs for levels with energy (eV): Et=\n\t\t\t\t\t\t\tEt1 = –0.42 (curve 1) and Et=Et2=–0.24 (curve 2) on concentration of recombination impurity N ; layout of sample illumination and axis x are shown on insert. Adopted: light absorption coefficient γ=104 cm-1, diffusion constants of electrons Dn=221 cm3/s and holes Dp =10.4 cm3/s [2-9]; W˜=10−3 cm; F0=1 cm-2×s-1; T=300 К; concentration of shallow donors ND=1015 cm-3; θ≡wp/wn=102, wn=10−8 cm3/s [1-9], where wp and wn are capture probabilities of hole and electron
Denote: τn and τp are electron (24) and hole (25) lifetimes; Dn,p are their diffusion constants and values Dna, Dξ and Q and dimensionless parameters χ and ξ<<1 are determined by expressions (73), (84), (67), and (75), respectively.
Figure 7.
Dependence of photo-emf Vph (arbitrary units) in GaAs for levels with energy Et1 (curve 1) and Et2 (curve 2) on concentration of recombination impurity N. Parameters are the same as in Figure 6
Ln=Dn×τn and Lp=Dp×τp are electron and hole diffusion lengths, Dpa is quasi-neutral ambipolar hole diffusion constant, and La is quasi-neutral ambipolar diffusion length of charge carriers.
In quasi-neutrality approximation, parameters ξ, ξn and ξp are equal to zero; therefore, in this approximation, the distribution of excess electrons’ concentration is determined by equation
Dna×∂2Δn∂x2−Δnτn=−g(x).E95
\n\t\t\t
7.2. Effectiveness of charge carriers’ photoexcitation
We define the mean value <y> of variable y(x) as
<y>=1W˜∫0W˜y(x)dx.E96
\n\t\t\t\t
Let’s analyze the worst case, when recombination of excess charge carriers on illuminated (x=0) and unilluminated (x=W˜) surfaces of the sample (Figure 5a) is so intensive that
Outside quasi-neutrality approximation, expressions (20)–(25), (60), (61), (75), (80), (91)–(94), and (104)–(110) determine, in parametric form (value δ=N−e/N0e is used as parameter), dependences <Δn>(N) and <Δp>(N). We will call found dependences (see Figures 6, 8, and 9) as exact, because, in linear approximation with respect to F0, dependences are exact in contrast to quasi-neutrality approximation case.
Denote desired dependences in quasi-neutrality approximation as <Δn˜(N)> and <Δp˜(N)>. In quasi-neutrality approximation,
Figure 6 shows that the effectiveness of charge carriers’ photoexcitation may grow significantly with increasing N. Up to small corrections, dependences <Δn>(N) and <Δp>(N) reach maximums <Δn>max and <Δp>max at the same concentration N=N^=ND as for lifetimes (Figure 1b) and after that fall very strongly. Figures 8 and 9 illustrate the influence of photoexcited space charge in point N=N^ on the validity of results. It is clear from Figures 8 and 9 that with thinning W˜ of sample, using quasi-neutrality approximation leads to error up to several orders of magnitude. Let’s clarify Figures 6, 8, and 9.
Lengths L and L1≡1/k1, up to small corrections, equal to La ; moreover
Ln>L1>L2≡1k2.E114
At W˜<<La, we have
<Δn˜>=ψ(W˜,γ)Dna,<Δp˜>=ψ(W˜,γ)Dpa,E115
\n\t\t\t\t
where function ψ(W˜,γ) is independent on τn and τp. On the other hand, if inequality W˜<<L2 is sufficiently strong, and when Lp>>W˜ as well, from expressions (104), (105), and (108)–(110), it follows that
<Δn>=ψ(W˜,γ)Dn,<Δp>=ψ(W˜,γ)Dp.E116
\n\t\t\t\t
This means that diffusion of photoelectrons and photoholes is independent from each other.
Therefore, L2 has physical meaning as shielding length of photoinduced space charge.
Length L2<<La,W˜ in the vicinity of the point N=N^, i.e. quasi-neutrality is valid. At values N<N^, length La<W˜ due to small value Dna. When N passing through the point N^ toward larger values N, then Dna increases very strongly (by several orders of magnitude), and after that it is remaining substantially constant. As a result, length La>W˜ at values N higher N^. This explains the asymmetry of dependence <Δn>(N) about point N=N^, and “plateau,” when N>N^ as well (Figure 6).
At point N=N^ and about it, length L2 is so long that even at W˜ ∼ 0.1 cm, solution in quasi-neutrality approximation is unacceptable; moreover, with decreasing W˜\n\t\t\t\t
When γ−1<<W˜ and inequity W˜<<Ln are sufficiently strong, then the total quantity of photoelectrons is proportional to W˜ due to reducing loss on unilluminated surface. Therefore, there is a “plateau” on dependence <Δn>max on W˜. For the same reason, at γ−1<<W˜<<La, dependence <Δn˜>max on W˜ has a “plateau” as well. However, in the last case, “plateau” height is much higher, and its width is much wider than true “plateau” (Figure 8, curve 1).
Moreover, shielding length of photoinduced space charge L2≈La when impurity level energy equals to Et2. Therefore, solution obtained in quasi-neutrality approximation, even when W˜→∞, differs from exact solution at least by several times (Figures 8 and 9, curve 2).
7.3. Effectiveness of photo-emf excitation
In view of the fact that under considered conditions
Iph=0,E119
\n\t\t\t\t
from expressions (12)–(14) and (87), we obtain that photo-emf
Vph=∫0W˜ΔE(x)dx=ϕ(0)−ϕ(W˜),E120
\n\t\t\t\t
i.e. potential ϕ(x) of illuminated surface with respect to unilluminated (Figure 5а) expressed by formula
It is clear from expression (121) that at infinite surface recombination rate, i.e., when conditions (97) are fulfilled, illumination produces no photo-emf. In this regard, assume that photoexcited charge carriers are not captured on surfaces and there is no charge on surfaces. In these conditions, photoexcited electric field intensity
ΔE(0)=ΔE(W˜)=0E124
\n\t\t\t\t
And densities of electron ΔIn and hole ΔIp photocurrents
ΔIn(0)=ΔIp(0)=ΔIn(W˜)=ΔIp(W˜)=0.E125
\n\t\t\t\t
Figure 8.
Dependences of <Δn>max in the point of maximum functions <Δn>(N) and <Δp>(N) on thickness W˜ for GaAs. Curves 1 and 2, recombination level energy Et equals to Et1 and Et2, respectively; solid lines - exact solutions; dashed lines - solutions in approximation of quasi-neutrality. Adopted parameters and other symbols are the same as in Figure 6
Figure 9.
Dependences of ratio <Δp>max/<Δn>max in the point of maximum functions <Δn>(N) and <Δp>(N) on thickness W˜ for GaAs. Curves 1 and 2, recombination level energy Et equals to Et1 and Et2, respectively; solid lines - exact solutions; dashed lines - solutions in approximation of quasi-neutrality. Adopted parameters and other symbols are the same as in Figure 6
Therefore, we may write boundary conditions, in view of relation (87), as
We refer to the dependences (141) of photo-emf Vph on N and W˜ as exact. The reason is that, in contrast to the case of quasi-neutrality approximation, said dependences are exact in linear approximation with respect to flux density F0.
Figures 7, 10, and 11 show these dependences and solution in quasi-neutrality approximation as well. It is clear in Figures 10 and 11 that, in quasi-neutrality approximation, maximal value Vph(N) far exceeds the “true” value; moreover, exceedance may be several orders of magnitude.
We can explain results by the fact that very long shielding length (114) of photoexcited space charge L2 in the point of maximum N=N^≡ND and nearby will cause diffusion of photoelectrons independently on photoholes (see Section 6.2) at W˜ ∼ 0.1 cm. In other words, electron diffusion constant Dn determines the distribution of photoelectron concentration Δn(x). Aside from that, at N≅N^, due to charge coupled to impurities, inequity Dn>>Dna is fulfilled. It means that true effectiveness of photoelectrons’ spreading is much higher, than that given by quasi-neutrality approximation. Therefore, ratio (Vph)max/(V˜ph)max<<1, when W˜>>L2 (Figure 11).
Evidently, with thinning W˜, spreading area of photoexcited charge carriers becomes wider, i.e., values Δn=Δn(0)−Δn(W˜) и Δp=Δp(0)−Δp(W˜) decrease. Therefore, values (Vph)max and (V˜ph)max fall with thinning W˜ (Figure 10).
Note that for impurity level energy equal to Et2, the solution obtained in quasi-neutrality approximation, even when W˜→∞, differs from the exact solution more than two times (Figure 10). This is due to the fact that in considered case the shielding length of photoexcited space charge L2=1/k2≈La, where La is ambipolar diffusion length of charge carriers.
8. Photoelectric gain
We will consider uniform spatial distribution of density of charge carriers’ photoexcitation rate g and ignore surface recombination of photoexcited charge carriers.
We will facilitate mathematical description of photoelectric gain (see Figures 1а and 2)
G(N,V)≡Iphq×W×gE146
\n\t\t\t
through utilizing small dimensionless parameter (75) ξ<<1, which will characterize the degree of deviation of semiconductor from local neutrality under illumination. Here N is concentration of recombination centers; Iph is photocurrent density (14); q is absolute value of electron charge; V is bias voltage applied across the sample; Wis distance between current electrodes (see insert in Figure 1a).
Using linearized expressions for electron (12) and hole (13) components of photocurrent Iph and expressions (60) and (61), we may rewrite equations (5)–(7) as follows:
E0=V/W, and dimensionless small parameters ξn<<1 and ξp<<1 as defined in (80). Relations (147) show that, by dimensionless small parameter ξ, we may really characterize the degree of deviation of semiconductor from local neutrality under illumination. If there is no external load (inset in Figure 1a), then illumination does not change voltage V across the sample.
Therefore, expressions (4), (5), (8), and (9) with boundary conditions (1) allow us to write
Values of parameters Q, Dξ, μξ, and DE are dictated by photoexcitation of space charge Δρ (4). Analysis shows that inequality ξ<<1, which is typically fulfilled with large margin, allowing to omit in equation (151) terms with parameters Q, Dξ and μξ. However, term with parameter DE must be retained, because, even at moderate electric fields, DE may exceed Dna due to square-law dependence DE on E0. For the same reason, we can omit in equation (149) terms including small parameter ξ. Thus, we arrive at relations
(Dna+D)E×∂2Δn∂x2−μna×E0×∂Δn∂x−Δnτn+g=0,E152
\n\t\t\t
Iph=q×(μn+τpτn×μp)×〈Δn〉×E0.E153
\n\t\t\t
Figure 10.
Dependences of maximal value Vph(N) in GaAs on thickness W˜. Curves 1 and 2, recombination level energy Et equals to Et1 and Et2, respectively; solid curves, exact solutions; dashed curves, solutions in approximation of quasi-neutrality. Adopted parameters and other symbols are the same as in Figure 6
Figure 11.
Dependence of ratio rt=V˜ph/Vph in the point of maximal value Vph(N) in GaAs on thickness W˜. Curves 1 and 2 – recombination level energy Et equals to Et1 and Et2. Vph, exact solutions; V˜ph, solutions in approximation of quasi-neutrality. Adopted parameters and other symbols are the same as in Figure 6
Equation (152), with boundary condition (1), and relation (153) allow us to obtain the formula for photoelectric gain:
where quasi-neutral ambipolar drift length of charge carriers
da=μna×τn×E0,E155
\n\t\t\t
effective diffusion length of charge carriers
Lef=(Dna+DE)×τn,E156
\n\t\t\t
and effective reciprocal diffusion-drift lengths L1 and L2 are defined by expressions
1L1,2=±da2Lef2+(da2Lef2)2+1Lef2.E157
\n\t\t\t
Relations (18), (20)–(22), (24), (25), (73)–(75), (83), and (153)–(157) determine, in parametric form dependence G(N,V) (see Figures 1a and 2а). Ratio δ=N−e/N0e is used as parameter in said relations.
It can be shown that equation μna(N)=0, where μna is given by expression (74), has a solution when inequalities (27) and (41) are fulfilled. In zeroth-order with respect to small parameters (27) and (41), the root of this equation coincides with maximal extrema of functions τn(N) and τp(N) and equals to ND (Figure 1b and 1c).
Let’s explain dependence μna on N shown in Figure 1c.
Product
μna×τn=μpa×τpE158
\n\t\t\t
determines drift length and direction in electric field of concentrational perturbation – quasi-neutral cloud of positive and negative charges [2, 31], including bound at deep impurity (here μna and μpa are electron and hole ambipolar mobility). Last mentioned bounding explains dependence μna on ratio τp(N)/τn(N) in trap-assisted recombination. It would appear reasonable that charge carriers, which prevail in quantity, can easily shield photoexcited space charge, i.e., they are adjusted to drift of charge carriers of another type. That is why, in the case of band-to-band recombination (τn=τp), quasi-neutral cloud of positive and negative charges drifts in electric field with the same velocity and in the same direction as minority charge carriers, whereas in intrinsic material, cloud is out of control by electric field at all [2, 31] (μna\n\t\t\t\t=μpa\n\t\t\t\t≅μp>0 at ne>>pe, μna=μpa≅−μn<0 at ne<<pe and μna\n\t\t\t\t=μpa=0 at ne=pe). Similar situation, but not exactly identical, happens in the case of trap-assisted recombination.
In this case, due to the fact that τp<τn (Figure 1c), vanishing μna occurs in n-type material (for specified parameters in Figure 1, at ne≅10×pe in silicon and ne≅104×pe in gallium arsenide). Positive sign of perturbation charge bound at deep impurities (ΔN−<0) causes such behavior. Ratio pe/ne begins to increase significantly, and very sharply, only when N≅ND. At the same time, ratio τp/τn may not have so many orders of smallness as ratio pe/ne may have. Therefore, μna vanishes when N≅ND, if deep level, according to conditions (27) and (41), lies in lower half of bandgap. If that level lies in upper half of bandgap, then, again, due to the fact that τp/τn may not have so many orders of smallness as ratio pe/ne may have, function μna(N) is always positive for actual values N, wherein lifetimes τp and τn decrease always with increasing N (see Section 3). We denote solution based on relations (152) and (153) as approximate. Parameter ξ(N), still remaining small, reaches its global maximum near point N=N^=ND, where function G(N) reaches maximal extremum G^ (Figure 1a). Deviation of approximate value G^=G^appr from exact value G^=G^exact {calculated with due regard for all terms in relation (149) and equation (151)} is shown in Figure 2b. Exact solution at N=N^ is not so difficult to find, because at this point μna=0. It is clear from Figure 2b that agreement G^appr with G^exact is quite good.
Value L^a is conventional ambipolar diffusion length at maximal extremum of function G(N) (Figure 1a) calculated in quasi-neutrality approximation, i.e., when parameter ξ is set to zero.
From expression (159), it follows that function G^ depends non-monotonically on applied bias voltage V (Figure 2a). This is caused by increased L^ef with increasing E0=V/W that provides progressive loss of photoexcited charge carriers resulting from increasing diffusive inflow of photocarriers to current contacts’ electrodes with follow-up recombination.
Increase in effective ambipolar diffusion constant Def=Dna+DE (coefficient before second derivative in equation (152)) causes elongation L^ef with increasing E0. In turn, photoinduced space charge Δρ (4) causes monotonic increased Def with increasing E0. The analysis of expressions (159)–(163) shows that function G^(V) reaches its maximum value (Figure 2c)
Threshold value G=G^maxmax (for given physical parameters of semiconductor) and electric field intensity E0=E˜0, at which L^ef=2×L^a, are defined by the following expressions:
G^maxmax=(μn×τ^n+μp×τ^p)×3×E˜025×L^a,E166
\n\t\t\t
E˜=8π×kT×niε×(1+AB)1/4.E167
8. Summary
Capture rate of excess charge carriers increases with increasing concentration N of deep impurity levels, i.e., recombination centers (traps). However, as shown in this chapter on the example of single-level acceptor, this increase does not lead to unavoidable decrease in lifetime of excess electrons τn and holes τp, when nonequilibrium filling of recombination level states is very low. The matter is that lifetimes are determined not only by capture of excess charge carriers at equilibrium traps but also by bound-to-free transitions of electrons and holes from nonequilibrium capture centers due to thermal emission and by capture of equilibrium charge carriers at nonequilibrium traps as well. Therefore, lifetimes of excess charge carriers can be either more or less than the time of their capture at equilibrium traps and can be strongly non-monotonic functions of recombination center concentration (Figure 1b). In the case of acceptor recombination level, it can happen if recombination level is located in lower half of forbidden gap. In the case of donor recombination level, it must be located in upper half of forbidden gap. It is essential that the ratio of lifetimes in maximum and minimum of functions τn(N) and τp(N) can be several orders of magnitude (Figures 1b and 3b).
It seems, authors of article [25] have reported first about the availability of minimum and portion of weak growth (up to 24 %) on experimental dependence of excess charge carriers’ lifetime on recombination center concentration, which increased because of bombarding sample by high-energy electrons. Many years later, increase in lifetime, presumably, caused by increasing N, but already gained in several times, was observed experimentally [32].
The main reason for giant splash of photoresponse in semiconductors with increasing recombination center concentration N (Figures 1a, 6, and 7) is the growth of charge carriers’ lifetime in orders of magnitude.
This reason is also sufficient to provide increase, in order of magnitude and more, in efficiency of charge carriers’ photoexcitation with increasing N (Figure 6).
At and about point N=N^≅ND, where charge carriers’ lifetime is maximal, equilibrium concentration of charge carriers becomes small, where ND is shallow dopant concentration. Therefore, increase in Dember photo-emf Vph in several orders of magnitude (Figure 7) is caused by both strongly non-monotonic dependences τn(N) and τp(N) (Figure 1b) and highly non-monotonic dependence of sample dark resistance on concentration N [1-3, 8, 30, 31].
However, increase in orders of magnitude in charge carriers’ lifetime with increasing N (Figure 1b) is not a good reason for the development of giant splash in photoelectric gain G with increasing N (Figure 1a). As follows from [18, 19], G increases with increasing charge carriers’ lifetime, if ambipolar mobility μa (see (74), (158), [2]) is equal to zero, or if there is no recombination on current contact electrodes (x=0 and x=W ; see inset in Figure 1a).
In reality, recombination on contact electrodes occurs always to more or less extent [5, 9]. Therefore, under normal conditions (μa≠0), increase in lifetimes, beginning from some lifetime values, does not increase in photocurrent density Iph [5, 18, 19].
Saturation in Iph is most clear in the case of high-rate recombination at contact electrodes (sweep-out effect on contacts [5, 18, 19]), when there are no photocarriers at contacts, i.e., conditions (1) are fulfilled. At trap-assisted recombination, function μ(N), under the same conditions (27) and (41), when there are non-monotonic dependences τn(N) and τp(N), vanishes at the same, up to small, correction value N≅N^, at which functions τn(N) and τp(N) reach their maximal extrema τ^n and τ^p (Figure 2b and 2c). Therefore, Iph and, consequently, G increase to the extent of increasing τ^n and τ^p. These are physical grounds of giant splash in photoelectric gain G with increasing N (Figure 2a). Above mentioned results of strict analytical calculations (i.e., outside commonly used local approximation of quasi-neutrality) show that photoinduced local space charge affects substantially on giant splash of semiconductor photoelectric response with increasing concentration of recombination centers.
Strict solutions of problems concerning the quantity of photoexcited electrons Nph and holes Pph and Dember photo-emf Vph may be fundamentally different from solutions obtained in approximation of quasi-neutrality N˜ph, P˜ph, and V˜ph, respectively.
It may be that Pph/Nph>>1 even if hole lifetime τp is much less than electron lifetime τn (Figure 2b). At the same time, in approximation of quasi-neutrality, P˜ph/N˜ph=τp/τn<<1 (Figure 2b). At point N=N^, at which functions Nph(N), Pph(N), and Vph(N) reach maximum values, and for thin samples (with thickness along light propagation W˜<0.1 cm), in surroundings of point N=N^, solutions obtained in quasi-neutrality approximation may differ from solution outside quasi-neutrality in several orders of magnitude (Figures 8–11). Moreover, even W˜→∞, neglecting by photoinduced space charge is not always possible, i.e., it is not always possible to solve problem in quasi-neutrality approximation. The reason is that when recombination level is deep enough, then shielding length of photoexcited space charge may be of the order of ambipolar diffusion length of charge carriers.
At sweep-out effect on contact electrodes, splash of G(N) with increasing N depends non-monotonically on applied voltage V across the sample (Figure 2a). That non-monotonic behavior is not related to heating of charge carriers or lattice and charge carriers injecting contacts. The reason is the increase in effective ambipolar diffusion constant D (coefficient before second derivative in equation (81) determining the distribution of photocarriers) with increasing V, leading to huge loss of photocarriers due to faster diffusion to contacts and subsequent recombination. In turn, increase in D ~ V2 is caused by photoinduced local space charge. What is important is that, at optimum voltage Vop (Figure 2d), value G can have several orders of magnitude (Figure 2c) at high concentrations of recombination centers.
As shown in [33], when recombination impurity N has three charged states (two-level recombination center), then, again, strong increase in τn(N) and τp(N) with increasing N may occur; moreover dependences τn(N) and τp(N) may have two charged states and two minimums and maximums. Opposite to single-level recombination center, in the case of two-level recombination center, maximum G(N), as shown in [34], can be reached at lower concentrations N and have greater peak value. Photoelectric gain G, to the left of maximum value G(N), is larger in the case of two-level recombination center, than in single level. The reason is the low ambipolar mobility of charge carriers in the case of two-level recombination center.
As shown in [35], significant growth of charge carriers’ lifetimes with increase in concentration of recombination impurity in certain range could be stimulated by uncontrolled (background) doping by deep impurities. Even two maximums can occur.
Above-mentioned regularities occur at arbitrarily low-level photoexcitation and they become the more evident, the wider the semiconductor bandgap.
The theory of giant splash of photoresponse in semiconductors at low-level illumination with increasing concentration of recombination centers could develop further through the generalization of boundary conditions on semiconductor surfaces and current contact electrodes, accounting for nonuniformity of charge carriers’ photoexcitation along the line of current flow and fluctuation processes. The study of nonstationary (frequency domain and transient) characteristics is of particular interest.
From physical essence of considered effects, it follows that similar effects can occur in other mediums with recombination of dissociative or ion-ion type, for example, in multicomponent plasma [36]. More details about topic are given in [37-46].
Acknowledgments
Authors are grateful to Prof. Sergey A. Nikitov for valuable support of publication.
\n',keywords:"Impurity recombination center (trap), Trap-assisted (Shockley-Read-Hall) recombination, Excess (nonequilibrium) charge carriers, Band-to-band photogeneration of excess charge carriers, Electron lifetime, Hole lifetime, Photoresponse, Photoelectric gain, Photo-emf, Small deviation from equilibrium state in semiconductor, Photoinduced space charge, Approximation of quasi-neutrality, Giant splash of photoresponse",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/49081.pdf",chapterXML:"https://mts.intechopen.com/source/xml/49081.xml",downloadPdfUrl:"/chapter/pdf-download/49081",previewPdfUrl:"/chapter/pdf-preview/49081",totalDownloads:1097,totalViews:87,totalCrossrefCites:0,totalDimensionsCites:0,totalAltmetricsMentions:0,impactScore:0,impactScorePercentile:12,impactScoreQuartile:1,hasAltmetrics:0,dateSubmitted:"October 5th 2014",dateReviewed:"June 10th 2015",datePrePublished:null,datePublished:"October 7th 2015",dateFinished:"September 7th 2015",readingETA:"0",abstract:"Recombination of excess (nonequilibrium) electrons and holes in semiconductors through impurity recombination centers (traps) known as trap-assisted (Shockley-Read-Hall) recombination is in many cases the dominant process. In this chapter, we develop the general theory of trap-assisted recombination and study in detail two key characteristics: (1) dependences of excess charge carriers’ lifetime and photoelectric gain on concentration N of recombination centers and (2) effectiveness of band-to-band photoexcitation of charge carriers and photo-emf in semiconductors at low-level illumination considered outside quasi-neutrality approximation.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/49081",risUrl:"/chapter/ris/49081",book:{id:"4607",slug:"optoelectronics-materials-and-devices"},signatures:"Viacheslav A. Kholodnov and Mikhail S. Nikitin",authors:[{id:"16374",title:"Dr.",name:"Mikhail",middleName:null,surname:"Nikitin",fullName:"Mikhail Nikitin",slug:"mikhail-nikitin",email:"nikiboxm@yandex.ru",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/16374/images/5077_n.jpg",institution:null},{id:"151470",title:"Prof.",name:"Viacheslav",middleName:null,surname:"Kholodnov",fullName:"Viacheslav Kholodnov",slug:"viacheslav-kholodnov",email:"vkholodnov@mail.ru",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Preliminaries",level:"1"},{id:"sec_3",title:"3. Model and basic relations",level:"1"},{id:"sec_4",title:"4. Lifetime of excess charge carriers",level:"1"},{id:"sec_4_2",title:"4.1. Mathematical analysis of hole lifetime",level:"2"},{id:"sec_5_2",title:"4.2. Mathematical analysis of electron lifetime",level:"2"},{id:"sec_6_2",title:"4.3. Physical interpretation",level:"2"},{id:"sec_6_3",title:"4.3.1. Hole lifetime",level:"3"},{id:"sec_7_3",title:"4.3.2. Electron lifetime",level:"3"},{id:"sec_10",title:"5. Relation between concentrations of photoholes and photoelectrons outside approximation of quasi-neutrality",level:"1"},{id:"sec_11",title:"6. Derivation of equation for distribution function of photoexcited charge carriers’ concentration outside quasi-neutrality",level:"1"},{id:"sec_12",title:"7. Solitary Illuminated Sample",level:"1"},{id:"sec_12_2",title:"7.1. Preliminaries: Basic relations",level:"2"},{id:"sec_13_2",title:"7.2. Effectiveness of charge carriers’ photoexcitation",level:"2"},{id:"sec_14_2",title:"7.3. Effectiveness of photo-emf excitation",level:"2"},{id:"sec_16",title:"8. Photoelectric gain",level:"1"},{id:"sec_17",title:"8. Summary",level:"1"},{id:"sec_18",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Milns A. Deep Impurities in Semiconductors. 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Statistics of the recombination of holes and electrons. Phys. Rev. 1952; 87(5) 835-842.'},{id:"B12",body:'Blackmore J. Semiconductor Statistics. Oxford: Pergamon Press; 1962.'},{id:"B13",body:'Ryvkin S. Photoelectric Effects in Semiconductors. New York: Consultants Bureau; 1964.'},{id:"B14",body:'Blackmore J. Solid State Physics. London: Cambridge University Press; 1985.'},{id:"B15",body:'Downey P.; Martin R.; Nahory R. & Lorimor O. High speed, ion bombarded InGaAs photoconductors. Appl. Phys. Lett. 1985; 46(4) 396.'},{id:"B16",body:'Schaelin A.; Loepfe R; Melchior H.; Suter M. & Woelfli W. Beryllium-bombarded In0.53Ga0.47As and InP photoconductors with response times below 3 ps. Mater. Sci. Eng. B 1989; 2(1-3) 81-85.'},{id:"B17",body:'Balberg I. & Naidis R. Sensitization of the minority carriers lifetime in a photoconductor. Phys. Rev. B 1998; 57(12) R6783-6787.'},{id:"B18",body:'Rittner E. Electron processes in photoconductors. 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Giant burst of photoconductivity in semiconductors upon an increase in the concentration of recombination centers. JETP Lett. 1998; 67(9) 685-691.'},{id:"B24",body:'Osipov V. & Kholodnov V. Theory of the diodes with radiative and unradiative impurity recombination. Sov. Phys. Semicond. 1970; 4(12) 1932-1937.'},{id:"B25",body:'Wertheim G. Transient recombination of excess carriers in semiconductors. Phys. Rev. 1958; 109(4) 1086-1091.'},{id:"B26",body:'Tsang W., editor. Lightwave Communication Technology: Photodetectors. Semiconductors and Semimetals v. 22, Part D, Willardson R. & Beer A. (eds.), New York: Academic Press; 1985.'},{id:"B27",body:'Kireev P. Physics of Semiconductors (in Russian). Moscow: Higher School; 1969.'},{id:"B28",body:'Moss T. Optical Properties of Semiconductors. London: Butterworth; 1959.'},{id:"B29",body:'Pikus G. Foundations of the Semiconductor Devices Theory (in Russian). Moscow: Nauka; 1965.'},{id:"B30",body:'Auth J.; Genzow D. & Herrmann K. Photoelektrische Erscheinungen (in German). Berlin: Akademie-Verlag 1977.'},{id:"B31",body:'Bonch-Bruevich V. & Kalashnikov S. Semiconductor Physics (in Russian). Moscow: Nauka; 1990.'},{id:"B32",body:'Basheleishvili Z.; Garnyk V.; Gorin S. & Pagaeva T. Change of the minority carrier lifetime under irradiation of high-ohmic p-type silicon. Sov. Phys. Semicond. 1984; 18(9) 1074-1075.'},{id:"B33",body:'Kholodnov V. & Serebrennikov P. Critical importance of the single-level approximation to account for the highly non-monotonic dependences of carrier lifetimes on recombination impurity concentration. Tech. Phys. Lett. 1997; 23(4) 268-270.'},{id:"B34",body:'Kholodnov V. & Serebrennikov P. Effect of photo-induced space charge on dependence of intrinsic threshold photoresistor amplification on two-level recombination impurity concentration. Proceedings SPIE, v. 5126, 352-356, Bellingham: SPIE Press; 2003.'},{id:"B35",body:'Kholodnov V. & Serebrennikov P. Dependence of electron and hole lifetimes on the majority recombination impurity concentration in the presence of auxiliary carrier trapping centers. Tech. Phys. Lett. 1997; 23(12) 969-971.'},{id:"B36",body:'Rayzer Yu. Physics of Gas Discharge (in Russian). Moscow: Intellect; 2009.'},{id:"B37",body:'Drugova A. & Kholodnov V. Character of the dependences of non-equilibrium electron and hole lifetimes on the concentration of recombination centers in impurity-type recombination semiconductors. Solid-St. Electron. 1995; 38(6) 1247-1252.'},{id:"B38",body:'Kholodnov V. Contribution to the Hall-Shockley-Read theory of recombination. Semiconductors 1996; 30(6) 538-544.'},{id:"B39",body:'Kholodnov V. Giant splash of photoelectric amplification in photoconductors with increasing of recombination centers’ concentration under weak optical radiation from the region of intrinsic absorption (in Russian). XV International Scientific and Engineering Conference on Photoelectronics and Night Vision Devices, Abstracts, p. 14, October 1998, Moscow, Russia.'},{id:"B40",body:'Kholodnov V. Super non-monotonic dependence of gain in threshold intrinsic photoresistors on the concentration of recombination centers (in Russian). International Conference "Applied Optics-98", Abstracts, p. 88, December 1998, Sankt-Petersburg, Russia.'},{id:"B41",body:'Kholodnov V. Gigantic splash of the weak optical radiation gain in intrinsic threshold photoconductive devices (photoresistors) upon an increase in the concentration of recombination centers. Proceedings of SPIE v. 3819, 98-115, Bellingham: SPIE Press; 1999.'},{id:"B42",body:'Kholodnov V. & Drugova A. On impact of the photo-induced space charge upon semiconductor photoresponse dependence on the concentration of recombination centers under weak optical radiation. Proceedings of SPIE v. 4340, 186-212, Bellingham: SPIE Press; 2000.'},{id:"B43",body:'Kholodnov V. & Drugova A. The influence of a photoinduced volume charge on the weak-radiation-induced interband photoproduction of carriers in semiconductors with impurity recombination centers. Tech. Phys. Lett. 2002; 28(9) 714-718.'},{id:"B44",body:'Kholodnov V. & Drugova A. The principal role of non-quasi-neutrality of semiconductor photoexcited plasma in effect a giant splash the photoresponse of homogeneous semiconductors with increasing of recombination centers concentration (in Russian). VI Russian Conference on Semiconductor Physics, Abstracts, p. 204-205, October 2003, Sankt-Petersburg, Russia.'},{id:"B45",body:'Kholodnov V. & Drugova A. On the degree to which the increase in the concentration of the recombination centers raises the efficiency of inter-band photoexcitation of carriers under weak optical radiation. Proceedings of SPIE v. 5126, 367-380, Bellingham: SPIE Press; 2003.'},{id:"B46",body:'Kholodnov V. & Drugova A. The degree of efficiency enhancement of interband photoexcitation of the electromotive force of Dember at the cost of increasing the recombination centers concentration at weak optical radiation. XIX International Scientific and Engineering Conference on Photoelectronics and Night Vision Devices. Abstracts, p. 190, May 2006, Moscow, Russia.'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Viacheslav A. Kholodnov",address:null,affiliation:'
V.A. Kotelnikov Institute of Radio Engineering and Electronics Russian Academy of Sciences, Moscow, Russia
Moscow Institute of Physics and Technology (MIPT), Dolgoprudny town, Moscow Region, Russia
'},{corresp:"yes",contributorFullName:"Mikhail S. Nikitin",address:"nikiboxm@yandex.ru",affiliation:'
JSC Shvabe-Photodevice, Moscow, Russia
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Krasilenko",slug:"vladimir-g.-krasilenko"},{id:"153819",title:"Dr.",name:"Aleksandr",middleName:null,surname:"Nikolskyy",fullName:"Aleksandr Nikolskyy",slug:"aleksandr-nikolskyy"},{id:"153820",title:"Dr.",name:"Alexander",middleName:null,surname:"Lazarev",fullName:"Alexander Lazarev",slug:"alexander-lazarev"}]},{id:"38213",title:"All-Optical Autonomous First-in–First-out Buffer Managed with Carrier Sensing of Output Packets",slug:"all-optical-autonomous-first-in-first-out-buffer-managed-with-carrier-sensing-of-output-packets",signatures:"Hiroki Kishikawa, Hirotaka Umegae, Yoshitomo Shiramizu, Jiro Oda, Nobuo Goto and Shin-ichiro Yanagiya",authors:[{id:"4400",title:"Professor",name:"Nobuo",middleName:null,surname:"Goto",fullName:"Nobuo Goto",slug:"nobuo-goto"},{id:"133356",title:"Prof.",name:"Hiroki",middleName:null,surname:"Kishikawa",fullName:"Hiroki Kishikawa",slug:"hiroki-kishikawa"}]},{id:"40008",title:"A Method and Electronic Device to Detect the Optoelectronic Scanning Signal Energy Centre",slug:"a-method-and-electronic-device-to-detect-the-optoelectronic-scanning-signal-energy-centre",signatures:"Moisés Rivas, Wendy Flores, Javier Rivera, Oleg Sergiyenko, Daniel Hernández-Balbuena and Alejandro Sánchez-Bueno",authors:[{id:"24227",title:"Dr.",name:"Moises",middleName:null,surname:"Rivas-Lopez",fullName:"Moises Rivas-Lopez",slug:"moises-rivas-lopez"},{id:"154068",title:"MSc.",name:"Wendy",middleName:null,surname:"Flores F.",fullName:"Wendy Flores F.",slug:"wendy-flores-f."}]},{id:"38891",title:"Opto-Electronic Packaging",slug:"opto-electronic-packaging",signatures:"Ulrich H. 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Fischer",authors:[{id:"35000",title:"Prof.",name:"Ulrich H.P",middleName:"H.P.",surname:"Fischer",fullName:"Ulrich H.P Fischer",slug:"ulrich-h.p-fischer"}]},{id:"37760",title:"III-V Multi-Junction Solar Cells",slug:"iii-v-multi-junction-solar-cells",signatures:"Gui jiang Lin, Jingfeng Bi, Minghui Song, Jianqing Liu, Weiping Xiong and Meichun Huang",authors:[{id:"31275",title:"Prof.",name:"Meichun",middleName:null,surname:"Huang",fullName:"Meichun Huang",slug:"meichun-huang"},{id:"153850",title:"Dr.",name:"Guijiang",middleName:null,surname:"Lin",fullName:"Guijiang Lin",slug:"guijiang-lin"},{id:"163182",title:"Dr.",name:"Jingfeng",middleName:null,surname:"Bi",fullName:"Jingfeng Bi",slug:"jingfeng-bi"},{id:"163303",title:"Dr.",name:"Minghui",middleName:null,surname:"Song",fullName:"Minghui Song",slug:"minghui-song"},{id:"163304",title:"Dr.",name:"Jianqing",middleName:null,surname:"Liu",fullName:"Jianqing Liu",slug:"jianqing-liu"},{id:"163305",title:"Dr.",name:"Weiping",middleName:null,surname:"Xiong",fullName:"Weiping Xiong",slug:"weiping-xiong"}]},{id:"40009",title:"Use of Optoelectronic Plethysmography in Pulmonary Rehabilitation and Thoracic Surgery",slug:"use-of-optoelectronic-plethysmography-in-pulmonary-rehabilitation-and-thoracic-surgery",signatures:"Giulia Innocenti Bruni, Francesco Gigliotti and Giorgio Scano",authors:[{id:"54030",title:"Dr",name:"Giulia",middleName:null,surname:"Innocenti Bruni",fullName:"Giulia Innocenti Bruni",slug:"giulia-innocenti-bruni"}]}]}],publishedBooks:[{type:"book",id:"2478",title:"Optical Communication",subtitle:null,isOpenForSubmission:!1,hash:"f8af14196b5429d6bf9fcb7db0a39199",slug:"optical-communication",bookSignature:"Narottam Das",coverURL:"https://cdn.intechopen.com/books/images_new/2478.jpg",editedByType:"Edited by",editors:[{id:"15357",title:"Dr.",name:"Narottam",surname:"Das",slug:"narottam-das",fullName:"Narottam Das"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"2992",title:"Current Trends in Short- and Long-period Fiber Gratings",subtitle:null,isOpenForSubmission:!1,hash:"7ea3b8fc542d07312526928ba5bac062",slug:"current-trends-in-short-and-long-period-fiber-gratings",bookSignature:"Christian Cuadrado-Laborde",coverURL:"https://cdn.intechopen.com/books/images_new/2992.jpg",editedByType:"Edited by",editors:[{id:"29543",title:"Dr.",name:"Christian",surname:"Cuadrado-Laborde",slug:"christian-cuadrado-laborde",fullName:"Christian Cuadrado-Laborde"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3360",title:"Current Developments in Optical Fiber Technology",subtitle:null,isOpenForSubmission:!1,hash:"834b9a9593a62b116d2101815fd94dd3",slug:"current-developments-in-optical-fiber-technology",bookSignature:"Sulaiman Wadi Harun and Hamzah Arof",coverURL:"https://cdn.intechopen.com/books/images_new/3360.jpg",editedByType:"Edited by",editors:[{id:"17617",title:"Dr.",name:"Sulaiman Wadi",surname:"Harun",slug:"sulaiman-wadi-harun",fullName:"Sulaiman Wadi Harun"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4494",title:"Advances in Optical Communication",subtitle:null,isOpenForSubmission:!1,hash:"8cd5ba4d56db55598d255b1d4f9e9519",slug:"advances-in-optical-communication",bookSignature:"Narottam Das",coverURL:"https://cdn.intechopen.com/books/images_new/4494.jpg",editedByType:"Edited by",editors:[{id:"15357",title:"Dr.",name:"Narottam",surname:"Das",slug:"narottam-das",fullName:"Narottam Das"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],publishedBooksByAuthor:[{type:"book",id:"4607",title:"Optoelectronics",subtitle:"Materials and Devices",isOpenForSubmission:!1,hash:"0e72724ec0d3faf1ec705cb92fa03c32",slug:"optoelectronics-materials-and-devices",bookSignature:"Sergei L. 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1. Introduction
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The need to control interactions between materials and their surrounding environment is mainly concerned with the surface properties of these materials. In this sense, the sol-gel process is being increasingly used to surface modify a wide range of materials such as metals, organic polymers, inorganic particles, and glasses, where wettability, biocompatibility, porosity, corrosion, catalytic activity, and selective adsorption of analytes can be controlled at the required substrate surfaces. For this reason, sol-gels have gained attention in different scientific and technological fields, including metallurgy, biomaterials, analytical chemistry, and photocatalysts. In this chapter, an overview of sol-gel chemistry and its applicability to modifying the surfaces of metals and their alloys for anticorrosion and biomedical purposes will be presented.
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2. Sol-gel chemistry
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The sol-gel technology is a technique that has been widely employed in the synthesis of inorganic polymers or advanced organic-inorganic hybrids due to versatile and simplicity. Two chemical reactions are involved, hydrolysis and condensation, and these produce a variety of organic-inorganic networks from precursor monomers such as silicon alkoxide or metals alkoxides [1, 2]. This technique permit to obtain materials in any form and to it is possible to produce homogeneous materials with the desirable properties of toughness, high purity, optical transparency, chemical stability, controlled porosity, and thermal resistance at room temperature and low cost [3].
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The sol-gel process, as the name implies, is the transition of a liquid colloidal solution (sol) to a solid three-dimensional matrix (gel). The precursors for the synthesis of these colloids consist of a metal or metalloid element surrounded by several reactive ligands. Metal alkoxides are the most popular, since they react easily with water. The most extensively used are the metal alkoxides and the alkoxysilanes, such as tetramethoxysilane (TMOS) and tetraethoxysilane (TEOS). Nevertheless, other alkoxides such as aluminates, titanates, and borates are also commonly used in the sol-gel process, where they are often mixed with TEOS [1].
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The most widely used method is the organic approach, which generally starts with a solution of monomeric metal or metalloid alkoxide precursors, M(OR)n, in an alcohol or another low-molecular-weight organic solvent. Here, M represents a network-forming element such as Si, Ti, Zr, Al, Fe, and B, while R is typically an alkyl group (CxH2x+1) [4].
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The sol-gel process involves a transition from a liquid colloidal solution (sol) to a solid three-dimensional matrix (gel). The precursors for the synthesis of these colloids consist of a metal or metalloid element surrounded by several reactive ligands. Metal alkoxides are the most popular due to their affinity with water. Among the most used alkoxylated agents are tetramethoxysilane (TMOS), tetraethoxysilane (TEOS), and alkoxides such as aluminates, titanates, and borates mixed with TEOS [1].
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Figure 1.
General schematic of the hydrolysis and condensations of alkoxides.
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In the hydrolysis reactions (\nFigure 1\n\n(1)), alkoxide groups (▬OR) are replaced with hydroxyl groups (▬OH) through the addition of water. Subsequent condensation reactions (\nFigure 1\n\n(2a) and (2b)) involve the silanol groups (Si▬OH), which create siloxane linkages (Si▬O▬Si) and subproducts such as water and alcohol. The condensation reaction starts before the hydrolysis has been completed. However, conditions such as the pH, H2O/Si R and catalyst can force the hydrolysis to end before the condensation starts [3].
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The use of an alcohol favors hydrolysis, causing the miscibility of the alkoxide and the water [3]. As the number of siloxane linkages increases, the individual molecules are joined to one another and aggregated into the sol. When the sol’s particles are interlocked into a network, a gel is formed. A drying stage in which volatile components such as water and alcohol are extracted from the network is necessary, causing the gel to shrink while condensation occurs. It should be noted, however, that the addition of solvents and certain reaction conditions can promote esterification and depolymerization reactions, in accordance with the reverse reactions (\nFigure 1\n\n\n(2a)\n and \n(2b)\n) [1, 3]. More specifically, factors such as the pH, nature and concentration of the catalyst, and H2O/Si R play the most important parts in the final structure and properties of the obtained hybrid polymeric network [1]. In this section, the effect of pH will be described, as controlling the pH of sol-gel media is generally used to obtain either coatings or powders; however, readers can find a detailed mechanism in specialized reviews or books on sol-gel chemistry.
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Drying involves the loss of water, alcohol, and other volatile components. During drying, the gel initially shrinks due to the loss of pore fluid that maintains the liquid-vapor interface on the outer surface of the gel, this occurs always under atmospheric conditions. The liquid-vapor meniscus recedes toward the interior of the gel, in the final stage of drying [5]. When the drying is under supercritical conditions, the surface tension disappears with a gradient of capillary pressure accumulated in the walls of the pores, which avoids the possible collapse of the volume of the pores due to the capillary forces. Under these conditions, the materials are left with a wet porous texture that prevents the collapse of the pores of the gel, and the resulting materials are generally hydrophobic, because their surfaces are covered with alkoxy groups [6].
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2.1 Sol-gel coatings
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For anticorrosion and biomedical applications, several techniques are used to surface modify metals to improve their mechanical properties, enhance their corrosion resistance or, in some cases, give biological, osteoconductive, or antibacterial activity. Among these techniques are physical vapor deposition (PVD), chemical vapor deposition (CVD), and electrophoresis, and sol-gels can be used to surface modify metal [7]. However, the versatile methodology of sol-gel synthesis generates diverse types of materials that have found applications in several scientific and technical fields [8]. It is precisely this versatility that has generated great interest in using sol-gel techniques to develop coatings that are applied in areas such as analytical chemistry to develop more efficient, specific sorbents that allow the concentration of desired analytes [9, 10, 11]. In biomedical fields, sol-gel coatings have gained attention in controlling the surface interactions between medical implants/devices and biological environments [12, 13]. In the field of photocatalysis, sol-gel coatings have been developed for applications such as for organic compound degradation [14]. Anticorrosion sol-gel coatings have been applied to avoid degradation of materials and metallic structures to prevent or preserve the surface and bulk integrity of metallic materials [15].
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The sol-gel coating technique consists of the immersion of a substrate that is to be coated in the “sol” solution and the vertical extraction of this substrate at a controlled speed [13]. A very fine coating of gel is thus formed, since there is rapid evaporation of the solvent during the extraction of the substrate. The thickness depends on the viscosity of the liquid, the surface tension, and especially the speed of removal; the higher the speed of removal is, the greater the thickness of the coating [16]. Once the first coating layer is obtained, the process can be repeated to form a multilayer structure. The drying step also influences the final structure of the film, and there are thickness limits that must be obeyed to avoid the cracking of films or their detachment from the substrate [17].
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3. Sol-gel coatings for anticorrosion purposes
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According to the standard ISO8044:2015, corrosion is defined as a spontaneous degradation of metals due to their physicochemical interaction with the surrounding environment, which changes the properties of the metal and can lead to its functional destruction. The main cause of the corrosion of metals is their thermodynamic instability in outdoor conditions. As a result, metals are converted into compounds (oxides, hydroxides, carbonates, sulfides, etc.) that, as corrosion products, are the most stable forms of the metal. In this way, corrosion leads to a decrease in Gibbs free energy and therefore occurs spontaneously. Generally, coatings are designed to stop corrosion of metals by one of the following mechanisms: cathodic protection, anodic passivation, electrolytic inhibition, environmental modification, plating, painting, and active corrosion inhibition [18, 19].
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Using coatings to protect metallic substrates from corrosion is an active and important research area in materials science and industry. Through the application of coatings, corrosion can be minimized and controlled; the coating acts as a barrier preventing contact between the corrosive medium and the metallic substrate and preventing ion migration among the coatings; in addition, in cathodic protection, the coating material acts as a sacrificial anode. The use of species for inhibition/passivation, including cases of anodic and/or cathodic protection, inhibits the action of external corrosive agents. The sol-gel process stands out among the many other coating methods, e.g., CVD [20], PVD [21], electrochemical deposition [22], plasma spraying, and others [23]. The sol-gel coating process generally involves temperatures close to room temperature; thus, thermal volatilization and degradation of entrapped species, such as organic inhibitors, is minimized. Since liquid precursors are used, it is possible to cast coatings in complex shapes and to produce thin films without the need for machining or melting. The sol-gel films are formed by “green” coating technologies, which use compounds that do not introduce impurities into the product; this method is waste free and lacks a washing stage. The interest in this type of material has increased exponentially in recent decades.
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3.1 Organic-inorganic hybrid coatings
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Organic-inorganic hybrid (OIH) coatings created by the sol-gel process are very suitable for resisting corrosion. Inorganic sols in hybrid coatings not only increase adhesion by forming chemical bonds between metals and hybrid coatings but also improve the comprehensive performance of polymers in the coatings. Different organic polymers or organic functionalities are introduced into the gel network to produce tailored properties such as hydrophobicity and increased crosslink density. For corrosion protection of metals, organic components of hybrid coatings are selected to repel water, form dense thick films, and reduce coating porosity. Factors such as the ratio between inorganic and organic components in hybrid coatings, cure temperature, and pigment-related parameters need to be optimized as a function of the specific metal for the production of hybrid films with maximum corrosion resistance [24].
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Sol-gel OIH coatings are macromolecular matrices where the intermolecular interactions (such as porosity, rigidity and adhesion to the substrate, among others) between its structure and the metal surface are very relevant for the final properties of the material. The better it is combination between OIH coatings and the substrate results in materials with improved protection against corrosion, oxidation and erosion, and good electrical and thermal insulation properties. Sol-gel OIH coatings are commonly produced by gels obtained from the gelation of colloidal solutions, hydrolysis and polycondensation of precursors, and their subsequent aging and drying [25].
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Sol-gel OIHs based on siloxanes (Si▬O-metal oxide), alkoxysilanes and alkoxides of zirconium, titanium, cerium, tin, and aluminum are potential candidates for the treatment of steel surfaces, allowing covalent bonding between the inorganic parts of the OIHs and the metallic substrate.
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For iron-based alloys, steel is the most common and versatile metal, and the corrosion resistance behavior of sol-gel coatings deposited on these substrates has been extensively studied. Publications have mostly focused on the use of TEOS, 3-glycidoxypropyl-trimethoxysilane (GPTMS), methacryloxypropyl trimethoxysilane (MAPTS), and methyltriethoxysilane (MTES) and have sometimes included the performance of coating materials with embedded corrosion inhibitor species. For example, Santana et al. used clay nanoparticles to improve mechanical and barrier properties and Ce as an inhibitor for OIH sol-gel coatings [26]. Generally, the reported studies show that those OIH coatings exhibit a promising performance against corrosion in iron-based alloys [27]. The use of different organosilica sol-gel coatings on steel substrates has been reported. The results indicate that it is possible to tailor the sol-gel composition to modify coating properties such as hydrophobicity, wettability, adhesion, and corrosion prevention. Precise selection of organically modified sol-gel compositions has yielded coatings that are adhesive, water-repellent, and effective at preventing corrosion of coated steel panels.
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OIH sol-gel coatings are an excellent choice for aluminum-based alloys because in addition to the OIH properties; these materials can provide a stable Si▬O▬Al bond between the inorganic functionality of these materials and the formed passivation layer. Previous work in the literature focuses on the use of TEOS and GPTMS, the performance of coating materials with encrusted corrosion inhibitor species, and the deposition of multilayers by several cycles of deposition curing [25, 28]. Cambon et al. investigated modifications of OIH sol-gel coatings using different amounts of cerium, studied how these coatings protected different aluminum-based alloys from corrosion with electrochemical methods, and reported improvements in the anticorrosion process by increasing the concentration of cerium in OIH sol-gel coatings [29].
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For copper and copper-based alloys, the use of OIH coatings did not give very good results with respect to corrosion, but the use of TEOS and GPTMS with 1,2,3-benzotriazole resulted in a corrosion inhibitor effective in different environmental media. For zinc-based alloys, few studies have used OIH sol-gel coatings, and GPTMS, TEOS and MTES have been used as precursors to focus on new green conversion coatings based on molybdate, permanganate, silicate, titanate, rare earth salt, tungsten, and vanadate compounds. Finally, for magnesium-based alloys with OIH coatings, the reported literature mainly focuses on the use of GPTMS in combination with other reagents, especially (3-aminopropyl) triethoxysilane (APTES). For this material, the inorganic component is selected to form the network for the film, while the organic component is selected to repel water and fill the porosity shortly. These hybrid coatings have excellent mechanical strength and adhesion to metal substrates. Hybrid coatings doped with slow release corrosion inhibitors provide long-term metal anticorrosion. Superhydrophobic coatings are an excellent option to resist corrosion, and their properties are derived from the low surface tension and roughness of the surface of hybrid coatings, although it is necessary to prolong their durability. It is obvious that the combination of these techniques can provide superior anticorrosive properties [24].
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Despite the advantages of combining different properties in these materials, synthesis constraints remain. The major limitations of sol-gel processing for coating metals are delamination, crackability, adhesion, and thickness limits. Assuring a uniform distribution on the substrate and optimizing thermal treatments (curing/drying) are crucial factors to ensure the quality of anticorrosive coatings.
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3.2 Smart coatings
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Active corrosion inhibition addresses the unavoidable failure of coatings and includes the introduction of components that release selectively during damage to the coating to reconstruct a protective barrier at the metal-environment interface. Such active corrosion inhibition is different from the broader concept of “self-healing,” which also includes the introduction of materials that are released within the coating that allow for reformation of polymeric organic coatings even without direct protection from corrosion [18].
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Functional coatings (organic, inorganic, or hybrid) are a new class of materials that can be adapted for many applications in which they should be able to perform well-defined arrays of functions. The concept of a smart coating is more recent and has been applied to functional coatings that can respond to certain stimuli generated by surroundings [30]. Functional and smart coatings have been regularly reviewed for various applications, including active corrosion protection and inhibition. However, summarizing the progress in this area requires a concise review of the latest trends. The application of functional and smart coatings is one of the most promising routes to developing active corrosion protection and inhibition systems. Two main strategies have been pursued to introduce the required functionalities into coatings: encapsulation/loading of functional active species in host carriers and manipulation of the coating matrix composition for inclusion of bulk and/or surface functional groups. In this case, intelligent self-healing coatings are coatings whose suitable repair agents are safely stored but can be released on demand, i.e., when corrosion occurs and only then [31].
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3.3 Self-healing coatings by sol-gel methods
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Self-healing materials are well known as materials that are capable of autonomously restoring their properties in such a manner that they can function longer than similar materials without self-healing abilities. Self-healing coatings are required for the total or partial repair of coated areas damaged by aging or unexpected aggressive events. Two main strategies have been pursued regarding self-healing coatings for corrosion protection: (i) mending defects formed in the polymeric coating matrix via addition of polymerizable agents and (ii) inhibition of corroding areas due to the presence of corrosion inhibitors [32, 33]. Usually, the self-healing agent is released because of mechanical damage. However, not all mechanical damage leads to corrosion, and corrosion is not necessarily initiated at mechanical cracks. Ideally, the release of self-healing agents should take place only when corrosion is initiated. Triggers for sensing the corrosion of a metal system that have been investigated in depth are pH and ionic strength changes. However, the most reliable and case-selective trigger is a change in the electrochemical potential, as it always decreases when corrosion occurs [31].
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Currently, the literature exhibits many reports of the encapsulation of agents for protection against corrosion that have self-healing capacity activated by different extrinsic or intrinsic stimuli, which can be local pH gradients, capsule rupture induced by mechanical stress, ion exchange processes, water trapping, electrochemical potential changes, light irradiation, thermal variations, and others; in some cases, neither the kinetics of healing nor the mechanisms are completely understood [30]. Below, some self-healing coatings for corrosion protection that were obtained by the sol-gel technique and have been applied on aluminum substrates are presented.
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Snihirova and coworkers investigated inhibitor-doped hydroxyapatite (HAp) microparticles that were used as reservoirs, storing corrosion inhibitors to be released on demand. Release of the entrapped inhibitor was triggered by redox reactions associated with the corrosion process. HAp was used as reservoirs for several inhibiting species, Ce(III), La(III), salicylaldoxime, and 8-hydroxyquinoline, which are effective corrosion inhibitors for 2024 aluminum alloy (AA2024). Dissolution of the microparticles and release of the inhibitor were triggered by local acidification resulting from an anodic half-reaction during corrosion of AA2024. Calculated and experimentally measured local acidification at the aluminum anode (down to pH = 3.65) were presented. The anticorrosion properties of inhibitor-doped HAp were assessed using electrochemical impedance spectroscopy. Microparticles impregnated with corrosion inhibitors were introduced into a hybrid silica-zirconia sol-gel film, which acted as a thin protective coating for AA2024, an alloy used for aeronautical applications. The protective properties of the sol-gel films were improved by the addition of Hap microparticles, proving their applicability as submicrometer-sized reservoirs of corrosion inhibitors for active anticorrosion coatings. The synthesis of HAp from solutions of calcium nitrate and ammonium hydrophosphate was carried out with the addition of citric acid to modulate its morphology. The obtained solution was placed in a water bath at 37°C for 24 h, allowing the precipitation of HAp. Once the HAp particles were obtained, they were immersed in solutions containing Ce(III), La(III), salicylaldoxime, and 8-hydroxyquinoline. Hybrid silica-zirconia sol-gel films were obtained by combining an organosiloxane alkosol with another alkosol containing a zirconia. The silane-based alkosol was prepared through hydrolysis of GPTMS in 2-propanol by adding a diluted aqueous solution of HNO3 at room temperature for 1 h. The second alkosol, containing zirconia nanoparticles, was prepared through controlled stoichiometric acidic hydrolysis of a 70 wt% 2-propanol solution of Zr(IV) tetrapropoxide in ethyl acetoacetate under ultrasonic agitation. Finally, the two alkosols were mixed in a 2:1 volume ratio, ultrasonically agitated for 1 h and then aged for another 1 h at room temperature [34]. According to their results, HAp presents a good chemical stability and compatibility with the sol-gel matrix, sufficient loading capacity, an ability to sense corrosion onset (local acidification), and an ability to release the inhibitor on demand [34].
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Li and coworkers have reported the incorporation of environment-responsive properties into tube-like nanomaterials in self-healing coatings for corrosion protection. Stimulus-responsive silica/polymer double-walled hybrid nanotubes with a controlled aspect ratio (length/diameter) were synthesized by surface-graft precipitation polymerization. The surface grafts on the hybrid nanotubes consisted of pH-, temperature-, or redox-responsive polymers that can confer a smart stimulus-responsive property upon the hybrid nanotubes. In addition to their well-defined morphology, uniform size, and wall thickness, the as-prepared silica/polymer hybrid nanotubes exhibited release in response to these different environmental stimuli. The silica/polymer double-walled hybrid nanotubes serve as intelligent nanocontainers of the anticorrosion agent benzotriazole.
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The silica/polymer double-walled hybrid nanotubes served as smart nanocontainers, which is very important for applications in self-healing coatings [35]. Self-healing coatings were prepared by dispersing the as-obtained nanotube containers into SiOx/ZrOy hybrid films at room temperature. The SiOx/ZrOy hybrid films doped with benzotriazole-loaded SiO2/PMAA nanocontainers were prepared by a sol-gel process. In this case, a zirconium oxide sol was prepared from a tetra-n-propoxy zirconium (TPOZ) solution (70 wt% 2-propanol) in ethylacetoacetate at room temperature. The second organosiloxane sol was prepared by hydrolyzing 3-chloropropyltrimethoxysilane (CPTMS) in 2-propanol by the addition of acidified water (HNO3, pH 0.5). Then, the zirconia sol and organosiloxane sol were mixed, stirred and aged at room temperature. BTA-loaded nanotube containers were mixed with the SiOx/ZrOy films at a concentration of 10 mg/mL by sonication. Self-healing films were fabricated on carbon steel by a dip-coating procedure. The carbon steel was immersed into the sol-gel mixtures and then withdrawn, and the samples were cured at 130°C [35].
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As you will see in detail later, corrosion is an important factor in the design and selection of alloys for application in vivo. Because toxic species might be released to the body during corrosion and various corrosion mechanisms can lead to implant loosening and failure, biomaterials are often required to be tested for corrosion and solubility before they are approved by regulatory organizations.
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4. Sol-gel coatings applied to biomaterials
\n
A biomaterial is any substance that has been engineered to interact with biological systems for a medical purpose, such as a therapeutic (which treats, augments, repairs, or replaces a tissue function of the body) [36, 37, 38]. Metals [23], polymers [39], ceramics [40], and their combinations [41] can be used as biomaterials. Among the different kinds of biomaterials, metal implants have been used with success in orthopedic applications, as well as temporary appliances such as pins, screws, and bone plates and permanent implants such as total joint substitutions.
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An implanted material could have a desired or undesired biological response depending on its surface characteristics such as wettability, charge, topography, and surface chemistry [42]. These surface properties are the major factors that ultimately determine the rejection or acceptance of a biomaterial in the body because the surface is the interface where the biomaterials meet and interact with the biological environment (i.e., bone, soft tissue, and blood). For this reason, surfaces of these metals must be modified; otherwise, the body will recognize those implants as foreign and isolate them in a fibrotic capsule, compromising their overall performance [43]. Surface modification of these metallic surfaces is engineered and designed to improve tissue tolerance, osseointegration, and corrosion [44]. Among the different surface modification technologies, such as grist blast [45], chemical etching [46], and plasma surface modification [47], the application of sol-gels has also been shown to improve the biocompatibility of metal implants [48].
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Osseointegration is defined as “the direct structural and functional connection between the ordered, living bone and the surface of a load-carrying implant” [49]. The sol-gel process allows the chemical composition of its products to be controlled, resulting in greater bioactivity than those materials with the same composition but prepared with different methods [13]. The intrinsic bioactivity of sol-gel materials together with their possibility of being coupled with a range of coating techniques, e.g., dip, spin, and spray coating, makes sol-gels an ideal technology in the making of bioactive and biocompatible coatings [13].
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In this section, TiO2, HAp, bioactive glasses, and hybrid composite coatings synthetized by the sol-gel technique to surface-modify metals of biomedical interest for implants will be described.
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4.1 Hydroxyapatite (HAp) as a sol-gel coating
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HAp (Ca10(PO4)6(OH)2) is a biocompatible and bioactive material that can be used to restore bony defects [50, 51, 52]. Because of its chemical and structural similarities to the inorganic phase of human bone, HAp shows excellent biocompatibility. Most of the relevant applications of this material take advantage of its biological influence on tissues and especially its biodegradation behavior. Conventionally, HAp powders are synthesized via precipitation from an aqueous solution, solid-state reactions, and hydrothermal methods. However, these powders are sometimes unsuitable for the preparation of HAp ceramics with controlled biocompatibility and bioactivity because of their chemical and phase heterogeneity [53, 54, 55, 56, 57, 58].
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One of the most important issues when considering HAp for biological coatings is its dissolution rate in human body fluids. Plasma-sprayed HAp coatings dissolve and degrade quickly, resulting in the weakening of the coating-substrate bonding or implant fixation to host tissues [59, 60].
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Sol-gel synthesis of HAp ceramics has recently attracted much attention because of its advantages: it provides a molecular-level mixing of the calcium and phosphorus precursors and is capable of improving the chemical homogeneity of the resulting mineral composite in comparison with the products from conventional solid-state reactions, wet precipitation, and hydrothermal synthesis [55, 56, 57, 61, 62].
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The sol-gel process provides an alternative to conventional synthesis methods. The metal alkoxides, M(OR)n, convert to amorphous gels of metal oxides through hydrolysis and condensation reactions. The sol-gel materials are transformed into ceramics by heating at relatively low temperatures and have better chemical and structural homogeneity than ceramics obtained by conventional methods.
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Pathway alkoxide-based considers an anhydrous medium, where precipitation of unwanted calcium phosphate phases can be slowed down, and the molar concentration of the reactive species can be heightened relative to a point that benefit the mineral development before the start of the reaction. Likewise, chelation-based sol-gel methods preserve a good degree of control, preventing the precipitation.
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The synthesis of pure HAp requires the same molar ratio between calcium and phosphate as in the final product. The temperature required to form the apatite structure depends on the chemical nature of the substrate. Low-temperature synthesis particularly benefits the metal substrates (temperatures below 500°C).
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The conditions to obtain the best coatings have been related to the pH decrease that occurs in aqueous sols during aging, which is based on the polymerization reaction between calcium and phosphorous. To obtain homogeneous, crack-free coatings, the annealing temperature and thickness of the coatings should also be controlled. Film roughness is related to the viscosity of the sol-precursor used for deposition and the number of coating layers. Thus, depending on the exact application, various parameters of the applied coating can be adequately controlled.
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Prepared HAp sols and Ag-doped HAp sols have been coated on passivated Ti surfaces by spin coating at 5000 rpm for 50 s. The coated Ti surfaces were immediately dried at 70°C for 12 h and then heat-treated at 650°C for 3 h. HAp without Ag doping was used as controls in this study. All samples were autoclaved prior to material characterization and all culture experiments [63].
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Overall, it was concluded that the material AgHA1.0 has similar biological activity as HAp with respect to bone cell proliferation and differentiation. In addition, AgHAp 1.0 also minimizes the initial bacteria adhesion [63].
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Caution should also be taken in applying HAp-coated materials to patients, since an HAp coating was found to have negative effects on bone formation. Reports in the literature [64, 65] have suggested that HAp coatings are unstable, susceptible to bacterial infection, possibly predisposed to rapid osseous breakdown, and absent of significant advantages over titanium implants [66].
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To obtain bioactive materials with high mechanical strength, metal implants (titanium and stainless steel (SS) alloys) are usually coated with a thin layer of HAp using plasma spray techniques [67, 68, 69]. The main problem associated with this technique is a lack of exact stoichiometry control and the occurrence of glassy phases in the ceramic layer. Some of these additional phases do not show bioactive behavior or do not dissolve in biological environments [69].
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For the above, various techniques have been described as effective means of surface treatment and corrosion resistance enhancement of NiTi implants, including chemical passivation, electropolishing, anodization, thermal oxidation, laser surface melting, nitriding, plasma ion implantation, and coating with sol-gels [70, 71, 72, 73, 74, 75].
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Out of these, the sol-gel route for surface modification of Ti implants is of particular interest because of simple and inexpensive methodology, low temperature processing, and suitability for coating substrates of irregular shapes, such as implants [76, 77, 78].
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4.2 Titanium dioxide (TiO2) as a sol-gel coating
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TiO2 is a very interesting material due to its technological applications in biomaterials. An example of this is sol-gel-derived titania and its coatings, which are bioactive materials, and are used in applications as diverse as biomaterials [79, 80]. Advantages of sol-gel processes over other methods are their controlled transformation of the microstructure of the deposited film. Today microstructure control is needed for many applications and the use of sol-gel routes opens up new possibilities.
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In common sol-gel methods for preparing TiO2 materials, highly reactive alkoxide titanium precursors are violently hydrolyzed and further condense to form a Ti▬O▬Ti network. Unfortunately, this route can lead to precipitation of amorphous particles with uncontrolled structures. To overcome many of the specific problems of sol-gel methods employing water as the hydrolysis agent and to control hydrolysis and polycondensation reactions, the application of nonhydrolytic methods, ionic liquids, organic additives, and coordination chemistry have been attempted [81, 82, 83].
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On the other hand, it has been reported that TiO2 films can effectively improve corrosion resistance and biocompatibility [84, 85, 86]. An example of this is given in titania films on biomedical steel exhibit anticorrosion properties in physiological solutions [87, 88]. At present, resistant sol-gel TiO2 coatings synthesized by heat treatment under low temperature have received good results for the preparation of anticorrosive and bioactive coatings to protect metal implants.
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The desired properties can be obtained by careful control of reaction conditions or by the use of suitable additives [89]. Moreover, sol-gel processing offers a unique opportunity to prepare layers at low temperatures so that an essential part of the sol-gel preparation process is the thermal treatment that is necessary to form pure TiO2 films.
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Conventional metal implants can be surface modified with sol-gel coatings, but organic synthetic polymers such as polyether-ether-ketone (PEEK) can also be surface modified with TiO2 sol-gel-derived coatings to overcome low bioactivity due to their chemical inertness, which is characteristic of most synthetic organic polymers. These sol-gel-derived TiO2 coatings showed greater bone bonding ability than PEEK [90].
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However, to avoid corrosion, a TiO2 dip-coating method and its variants are commonly used for the deposition of TiO2 sol-gel-derived coatings onto metal implants [91]. For example, an NiTi surgical alloy was surface modified with thin films of TiO2 to improve corrosion resistance, but these films also showed blood compatibility in vitro [92]. Avoiding corrosion and improving biocompatibility with surrounding tissues are not the only ultimate goals of sol-gel-coating metals of biomedical interest, avoiding the release of toxic ions, possibly through degradation, that some alloys may contain is another such goal [92].
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With respect to annealing time and temperature in sol-gel coatings, both parameters exhibit a dependence with the degradation rate, as studied in the TiO2 sol-gel deposited onto a magnesium alloy (AZ31), where the treatment with low annealing temperatures decreased the corrosion rate. Long-time treatment of annealing helped to enhance corrosion resistance [93].
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TiO2 sol-gel coatings doped with a high calcium ion concentration showed better corrosion resistance for M30NW biomedical alloy substrates in a simulated body fluid (SBF) test than similar coatings with low calcium ions concentrations [94].
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4.3 Sol-gel-derived bioactive glass coatings
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Bioglasses are a family of materials that have shown bioactivity for bone repair and can bond with living bone [95]. In 1971, the first bioglass named 45S5 was discovered by Hench, and since then, many other glass compositions have been developed. Bioglass 45S5 is composed of 45 wt% SiO2, 24.5 wt% CaO, 24.5 wt% Na2O, and 6.0 wt% P2O5, but other similar composition has been used and in some cases enhancing components can be added [96]. Bioglass 45S5 compositions have been shown to be optimal for biomedical applications because it is similar to that of HAp, the mineral component of bone. Ca/P ratios in SiO2·CaO·P2O5 glasses coatings can be controlled with stoichiometric control of TEOS, calcium nitrate tetrahydrate (Ca(NO3)2·4H2O), and triethyl phosphate (TEP) as sol-gel precursors [97]. Coatings with higher Ca/P ratios showed that greater cell proliferation, however, growth inhibition was observed in response to a low Ca/P-ratio in coating compositions [98].
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The surface of a bioglass implant, when subjected to an aqueous solution or body fluids, converts to a silica-CaO/P2O5-rich gel layer that subsequently mineralizes into hydroxycarbonate in hours [99, 100, 101]. Bone tissue growth improved with increasing dissolution [102]. This gel layer resembles the HAp matrix so much that osteoblasts were differentiated and new bone was deposited [103].
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Bioglasses are the most promising materials for bone grafting in several clinical applications such as orthopedic, dental, maxillofacial, and otolaryngological applications [104].
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From a synthetic point of view, bioglasses can be prepared either by melting or sol-gel methods, which affect their physical and biological properties [105], but it is also important to define the methods of coating preparation or deposition affecting the ultimate performance of the coatings. Bioglass coatings are usually deposited onto metals or alloys using sol-gel [106], electrophoretic deposition [107], laser cladding [108], and thermal spraying (plasma spraying and high-velocity oxy-fuel) techniques [109]. The technique most employed to spray bioglass since 1980 is thermal spraying and specifically atmospheric plasma spraying, due to its low cost and industrial feasibility [110, 111].
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Sol-gel-derived bioglasses are excellent materials for use in tissue engineering applications, such as covering prosthetic metallic implants. Recently, porous bioactive glasses have been derived through sol-gel processing in an attempt to increase the specific surface area and thus the surface reactivity and degradability of the material. This approach allows the material to be replaced ultimately by natural tissue while stimulating bone regeneration [97].
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The sol-gel technique can be used to coat 316 L SS [112], titanium [4], and magnesium biomedical alloys [106] with bioactive glass or derived glass-ceramic.
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For example, the formation of an apatite layer assures the bioactivity of the bioglass coating, which also improves the corrosion resistance of 316 L SS substrates. Bioactive glass-coated 316 L SS showed greater pitting corrosion resistance than pristine samples. It was concluded that by using the bioactive glass-coated 316 L SS as a human body implant, improvement of corrosion resistance, as an indication of biocompatibility, and bone bonding could be obtained simultaneously [112]. Uncoated 316 L SS possesses high corrosion current density (Icorr = 265 nA/cm2) and thus low corrosion resistance in normal saline solution [112].
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Relatively dense sol-gel coatings can be obtained with postheat treatment, causing a substantial volume contraction. In parallel, residual stress gradually accumulates at the interface between the coating and the substrate [113], remarkably affecting bond strength and the corrosion resistance of samples [114]. Therefore, heat treatments must be carefully controlled and optimized to obtain favorable bonding properties as well as corrosion resistance for sol-gel-derived coatings on magnesium alloy implants [106].
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The sol-gel process is carried out at much lower temperatures than traditional melting methods. Because of the low fabrication temperatures used in this method, the composition and homogeneity of the product are greatly controlled. Higher mesoporosity and surface areas are obtained in sol-gel-derived bioglasses than in melt-derived bioglasses, which exhibit high glass transition temperatures [105].
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4.4 Organic-inorganic composite hybrid coatings
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Inorganic sol-gel coatings are brittle, which can compromise their performance. To overcome this drawback, an organic polymer can be entrapped in an inorganic sol-gel glassy matrix to form an OIH sol-gel nanocomposite coating that can be deposited onto different metals and their alloys of biomedical interest. Poly-ε-caprolactone (PCL) [13], poly(dl-lactic-glycolic acid) [115], silica-polyethylene glycol hybrids [116], chitosan [117], and collagen type I have been incorporated into sol-gel coatings.
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Sol-gel coatings that can release silicon compounds under in vivo conditions have been shown to promote fast and good osseointegration. For this reason, hybrid composites can be prepared through acid-catalyzed sol-gel methods using methyl-trimethoxysilane (MTMOS) and GPTMS as alkoxide precursors, which allows the degradation kinetics and Si release of the coatings to be controlled by adjusting the amount of GPTMS. Although these coatings showed osteoinduction ability in vivo, coatings with some alkoxide proportions did not demonstrate strong cellular results [118].
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Another way to control the degradation profiles of HAp coatings is to incorporate silver ions, which are effective in inhibiting microbial infection [119].
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For example, type I collagen layers can be assembled into a sol-gel composite coating to cover magnesium alloys such as AZ31 and ZE41 to allow the release of growing factors, enhancing cell adhesion for tissue integration. This effect is due to the high biocompatibility and cytocompatibility that type I collagen has as well as the its positive effects on cell activity [120].
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Another bioactive composite coating, one composed of a silica xerogel and chitosan hybrid, was used to surface modify Ti at room temperature through a sol-gel process to obtain crack-free thin layers (<2 μm) with a chitosan content of >30 vol.%. These hybrid coatings showed bioactivity, and their properties suggested applicability to titanium-based medical implants [121].
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From a biological perspective, titanium is classified as a biologically inert material that does not promote adverse reactions and is well tolerated by human tissues. However, the formation of peri-implant fibrosis may isolate the implant from the surrounding bone and induce the mobilization of prostheses, thus reducing their performance [122].
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Surface hydroxy groups enhance the bioactivity of sol-gel glasses due to their promotion of calcium phosphate deposit nucleation, causing osseointegration when these materials are implanted [76].
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Commercially pure (CP) Ti grade 4 substrates were dip coated with an OIH crack-free coating consisting of a sol-gel-derived ZrO2−based matrix in which different PCL percentages (between 20 and 30 wt%) were incorporated. These films showed bioactivity and induced HAp formation when they were soaked in SBF. Biological evaluation with human mesenchymal stem cells (hMSCs) demonstrated that compared to pristine Ti, the coatings were nontoxic, supported cell proliferation at all compositions, and did not hamper hMSC differentiation in an osteogenic medium [122].
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Although further investigation is needed to fully describe the osseointegration potential of the developed OIH, such a material may find application in the surface coatings of Ti dental implants [122].
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The addition of an organic polymer such as PEG onto SiO2 in a hydric composite can affect its biocompatibility and bioactivity, as cell growth and the proliferation of NIH 3T3 cells depend on the PEG amount and exposure time. The formation of a HAp layer was indeed observed on the material’s surface by scanning electron microscopy (SEM)/energy-dispersive X-ray (EDX) analysis after the samples were soaked in SBF. Their effects were superior to those exerted from SiO2, whose ceramics are already widely used in medical applications [123].
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Homogeneous, porous and crack-free titania-based coatings can be obtained when PCL is added to a TiO2 inorganic matrix to make pure grade 4 titanium (CP Ti-4) disks more bioactive, as demonstrated by the ability to induce the formation of HAp when soaked in SBF, which is a crucial property for the osseointegration of metal implants in vivo [13].
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Hybrid inorganic-organic ZrO2/PCL composite films showed HAp formation on their surface when the hybrid coating was exposed to SBF, implying their osteointegration ability once implanted in vivo. In addition, a WST-8 colorimetric assay shows that the coating makes Ti-4, which is generally bioinert and biocompatible [124].
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Finally, it has been demonstrated that biodegradability can be controlled by adjusting the composite sol-gel hybrid coating composition, resulting in the ultimate material performance.
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5. Conclusions
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Sol-gel coatings provide excellent corrosion protection by providing a protective barrier layer for the reduced permeation of corrosive entities, providing a water repellent surface, chemically modifying the surface of a metal to make it more inert, and altering the electrical potential of surface sites. This review has presented an overview of new approaches to generate self-healing behavior in smart coatings. Extending the working life of structural and industrial metallic surfaces might depend on the fabrication of novel self-healing protective smart coatings that are able to repair scratches and eliminate corrosion. Additional development of materials with self-healing properties will reduce the loss that results from corrosion of metallic materials that are used in chemical plants, automobile parts, building structures, and home appliances.
\n
The factors most limiting the use of sol-gel processing for coating metals are delamination, crackability, adhesion, and thickness limits. Assuring a uniform distribution on the substrate and optimizing thermal treatments (curing/drying) are crucial factors in ensuring the quality of anticorrosive coatings.
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Although other processes such as plasma spraying, CVD, and electrochemical methods can be used to obtain thin film coatings of TiO2, HAp or bioglass on metallic substrates for biomedical purposes, the sol-gel process has remarkable advantages over those techniques, including better control of composition, structures, and porosity, which results in greater bioactivity than materials with the same composition but prepared with other techniques. Sol-gel coatings, due to their low processing temperatures, can also be applied onto nonmetallic implant substrates, such as organic polymers such as PEEK, or nonpermanent metallic implants such as those made of magnesium alloys. In addition, the sol-gel process can perfectly enable the integration of organic polymers with an inorganic glassy matrix.
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\n\n',keywords:"surface modification, coatings, sol-gel, corrosion, biomaterials",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/65990.pdf",chapterXML:"https://mts.intechopen.com/source/xml/65990.xml",downloadPdfUrl:"/chapter/pdf-download/65990",previewPdfUrl:"/chapter/pdf-preview/65990",totalDownloads:1370,totalViews:0,totalCrossrefCites:6,dateSubmitted:"October 8th 2018",dateReviewed:"December 20th 2018",datePrePublished:"March 6th 2019",datePublished:"October 2nd 2019",dateFinished:"March 6th 2019",readingETA:"0",abstract:"Sol-gel synthesis is used to obtain coatings that can modify the surfaces of metals to avoid corrosion or to enhance the biocompatibility and bioactivity of metals and their alloys that are of biomedical interest. Anticorrosion coatings composed of smart coatings and self-healing coatings will be described. TiO2, hydroxyapatite, bioglass, and hybrid coatings synthetized by sol-gel technology will be briefly introduced with regard to their role in surface-modifying metals for biomedical purposes. Finally, although there are other approaches to surface-modifying metals for either anticorrosion or biomedical purposes, sol-gel methods have several advantages in controlling surface chemistry composition and functionality.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/65990",risUrl:"/chapter/ris/65990",signatures:"Cristian Carrera-Figueiras, Yamile Pérez-Padilla, Manuel Alejandro Estrella-Gutiérrez, Erbin G. Uc-Cayetano, Juan Antonio Juárez-Moreno and Alejandro Avila-Ortega",book:{id:"8242",type:"book",title:"Applied Surface Science",subtitle:null,fullTitle:"Applied Surface Science",slug:"applied-surface-science",publishedDate:"October 2nd 2019",bookSignature:"Gurrappa Injeti",coverURL:"https://cdn.intechopen.com/books/images_new/8242.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-78984-098-8",printIsbn:"978-1-78984-097-1",pdfIsbn:"978-1-78984-745-1",isAvailableForWebshopOrdering:!0,editors:[{id:"12369",title:"Dr.",name:"Gurrappa",middleName:null,surname:"Injeti",slug:"gurrappa-injeti",fullName:"Gurrappa Injeti"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"280088",title:"Dr.",name:"Alejandro",middleName:null,surname:"Avila",fullName:"Alejandro Avila",slug:"alejandro-avila",email:"alejandro.avila@correo.uady.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null},{id:"288815",title:"Dr.",name:"Critian",middleName:null,surname:"Carrera-Figueiras",fullName:"Critian Carrera-Figueiras",slug:"critian-carrera-figueiras",email:"cristian.carrera@correo.uady.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null},{id:"288816",title:"Dr.",name:"Juan Antonio",middleName:null,surname:"Juárez-Moreno",fullName:"Juan Antonio Juárez-Moreno",slug:"juan-antonio-juarez-moreno",email:"juan.juarez@correo.uady.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null},{id:"288817",title:"Dr.",name:"Yamile",middleName:null,surname:"Pérez-Padilla",fullName:"Yamile Pérez-Padilla",slug:"yamile-perez-padilla",email:"yamile.perez@correo.uady.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null},{id:"288818",title:"Dr.",name:"Erbin Guillermo",middleName:null,surname:"Uc-Cayetano",fullName:"Erbin Guillermo Uc-Cayetano",slug:"erbin-guillermo-uc-cayetano",email:"erbin.uc@correo.uady.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null},{id:"288821",title:"Dr.",name:"Manuel Alejandro",middleName:null,surname:"Estrella-Gutiérrez",fullName:"Manuel Alejandro Estrella-Gutiérrez",slug:"manuel-alejandro-estrella-gutierrez",email:"alejandro.estrella@correo.uady.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Sol-gel chemistry",level:"1"},{id:"sec_2_2",title:"2.1 Sol-gel coatings",level:"2"},{id:"sec_4",title:"3. Sol-gel coatings for anticorrosion purposes",level:"1"},{id:"sec_4_2",title:"3.1 Organic-inorganic hybrid coatings",level:"2"},{id:"sec_5_2",title:"3.2 Smart coatings",level:"2"},{id:"sec_6_2",title:"3.3 Self-healing coatings by sol-gel methods",level:"2"},{id:"sec_8",title:"4. Sol-gel coatings applied to biomaterials",level:"1"},{id:"sec_8_2",title:"4.1 Hydroxyapatite (HAp) as a sol-gel coating",level:"2"},{id:"sec_9_2",title:"4.2 Titanium dioxide (TiO2) as a sol-gel coating",level:"2"},{id:"sec_10_2",title:"4.3 Sol-gel-derived bioactive glass coatings",level:"2"},{id:"sec_11_2",title:"4.4 Organic-inorganic composite hybrid coatings",level:"2"},{id:"sec_13",title:"5. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'\nBrinker CJ, Scherer GW. Sol-Gel Science, the Physiscs and Chemistry of Sol-Gel Processing, Advanced Materials. Vol. 3. Deerfield Beach, Fla: Academic Press; 1990. 1-908 p\n'},{id:"B2",body:'\nLevy D, Zayat M. The Sol-Gel Handbook. David Levy, Zayat M, editors. Vols. 1-3, USA: Wiley-VCH; 2015. 1-1508 p\n'},{id:"B3",body:'\nSchaefer DW, Keefer KD, Brinker CJ. Structure of silica condensation polymers. In: Zeigler JM, FWG F, editors. American Chemical Society, Polymer Preprints, Division of Polymer Chemistry, Advances in Chemistry. Vol. 24. Washington, DC: American Chemical Society; 1983. pp. 239-240\n'},{id:"B4",body:'\nDurán A, Conde A, Coedo AG, Dorado T, García C, Ceré S. Sol–gel coatings for protection and bioactivation of metals used in orthopaedic devices. Journal of Materials Chemistry. 2004;14(14):2282-2290\n'},{id:"B5",body:'\nSmitha S, Shajesh P, Aravind PR, Kumar SR, Pillai PK, Warrier KGK. Effect of aging time and concentration of aging solution on the porosity characteristics of subcritically dried silica aerogels. Microporous and Mesoporous Materials. 2006;91(1-3):286-292\n'},{id:"B6",body:'\nPierre AC, Pajonk GM. Chemistry of aerogels and their applications. Chemical Reviews. 2002;102(11):4243-4266\n'},{id:"B7",body:'\nGuglielmi M. Sol-gel coatings on metals. Journal of Sol-Gel Science and Technology. 1997;8(1/2/3):443-449\n'},{id:"B8",body:'\nWright JD. NAJMS. Sol-gel materials: Chemistry and applications. 1st Edition. John D. Wright NAJMS, editor. London: CRC Press; 2001. 136 p\n'},{id:"B9",body:'\nChong SL, Wang D, Hayes JD, Wilhite BW, Malik A, Chong SL, et al. Sol-gel coating technology for the preparation of solid-phase microextraction fibers of enhanced thermal stability. Analytical Chemistry. 1997;69(19):3889-3898\n'},{id:"B10",body:'\nJillani SMS, Alhooshani K. Urea functionalized surface-bonded sol-gel coating for on-line hyphenation of capillary microextraction with high-performance liquid chromatography. Journal of Chromatography. A. 2018;1543:14-22\n'},{id:"B11",body:'\nBurgos-Tan MJ, Pérez-Padilla Y, Avila-Ortega A, Barrón-Zambrano JA, Vilchis-Néstor AR, Carrera-Figueiras C, et al. Preparation, characterization and evaluation of a hybrid polymeric coating with sorbent properties. Chemical Papers. 2017;71(7):1205-1215\n'},{id:"B12",body:'\nOwens GJ, Singh RK, Foroutan F, Alqaysi M, Han C-M, Mahapatra C, et al. Sol-gel based materials for biomedical applications. Progress in Materials Science. 2016;77:1-79\n'},{id:"B13",body:'\nCatauro M, Papale F, Bollino F. Characterization and biological properties of TiO2/PCL hybrid layers prepared via sol-gel dip coating for surface modification of titanium implants. Journal of Non-Crystalline Solids. 2015;415:9-15\n'},{id:"B14",body:'\nYu J, Zhao X, Zhao Q. 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Facultad de Ingeniería Química, Universidad Autónoma de Yucatán (UADY), Mérida, Yucatán, Mexico
Facultad de Ingeniería Química, Universidad Autónoma de Yucatán (UADY), Mérida, Yucatán, Mexico
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