Molecular Beam Epitaxy of Si, Ge, and Sn and Their Compounds

Abstract

In the past decade, the increasing need for high-performance micro- and nanoelectronics has driven the research on group IV heterostructure devices, which utilize quantum effects as dominant working principle. The compound semiconductor SiGeSn has presented itself as promising material system for group IV heterostructures due to its unique properties. Prominent applications range from the Si-integrated laser to tunneling field effect transistors for the next complementary metal oxide semiconductor generations. However, the epitaxy of heterostructures requires atomic sharp material transitions as well as high crystal quality, conditions where molecular beam epitaxy is the method of choice since it can take place beyond the thermodynamic equilibrium. Besides the numerous opportunities, the molecular beam epitaxy of SiGeSn poses various challenges, like the limited solid solubility of Sn in Si and Ge and the segregation of Sn. In this chapter, we discuss the molecular beam epitaxy of SiGeSn at ultra-low temperatures to suppress these effects.

1. Introduction

Since its inception in the 1950s, the microelectronics market has grown to one of the world’s most important industries. The upcoming end of Moore’s law and the steady need for faster and higher-performing devices have driven the research on novel device concepts. Particularly for devices that functionalize quantum effects and heterostructures, atomic sharp structures in the nanometer regime become more and more important and attract the interest of research.

In this context, molecular beam epitaxy (MBE) is a beloved technique since it allows atomically precise deposition control as well as the process procedure beyond the thermodynamic equilibrium. Although MBE is not the best-suited tool for mass production, its uniqueness makes MBE the method of choice for research applications.

Due to the highly developed Si-based complementary metal oxide semiconductor (CMOS) technology, the MBE of Si and other group IV compounds has become more and more important in the last few decades. Possible research topics are the Si-integrated laser [1, 2, 3], the last missing key component for optical on-chip communication, as well as novel transistor concepts for future CMOS generations [4, 5, 6].

Although the beginnings of Si-MBE reached into the late 1970s and early 1980s [7, 8, 9, 10], its number of possible applications increased rapidly since the first synthesis of Sn-containing group IV compounds [11, 12, 13, 14, 15]. However, generally, the epitaxy of Sn-containing group IV compounds has proven itself quite challenging due to undesirable effects, like the temperature and strain intensified segregation of Sn [16, 17], the limited solid solubility of Sn in Ge and Si of less than 1% [18, 19], and the low melting point of Sn of 231.9°C [20]. Altogether, this reasons the necessity for the execution of the MBE of group IV compounds at ultra-low substrate temperatures in the range of approximately 160°C.

In this chapter, we not only lay the basics but also discuss the particularities of the MBE of group IV compounds. For this, Section 2 deals with the physical processes on the substrate and undesired effects during the MBE process as well as the various growth modes of heteroepitaxy. Afterwards, Section 3 presents the requirements for the basic components of a group IV MBE system. Finally, Section 4 highlights some of the most important insights of the MBE of SiGeSn.

2. Basics of molecular beam epitaxy

In a typical MBE experiment, several molecular or atomic beams are directed toward a well-oriented single crystalline substrate with beam flux densities $J$ in the order of 10¹⁵ cm⁻² s⁻¹ for matrix elements (group IV elements in our case) and lower 10¹² cm⁻² s⁻¹ for doping elements (group III for p-doping, group V for n-doping). The technical solutions for beam sources are described in the next section.

The molecules or atoms on a beam have a velocity $v_L$ of several hundred to thousand meters per second. That velocity defines two time scales. A variation of the beam intensity (on/off) is transferred to the substrate, which is typically in a distance of 10 to 50 cm, within a millisecond. In most cases, the transfer of beam on/off is defined by the technical design of the beam shutter construction. However, beam on/off switching is obtained within subnanometer and nanometer dimensions of growth, routinely. This exact control of beam fluxes makes MBE a valued method for research on nanometer heterostructures.

Another important time scale is defined by the length of interaction between the arriving beam atoms and the growing layer. Very close to the surface (nanometers or less), the atoms are attracted and accelerated toward the surface. The time scale for this interaction is in the picosecond (10⁻¹² s) range.

Elastic scattering would result in a reflection of the atomic beam. The transfer of energy, momentum, and angular momentum to phonons within the picosecond time frame would result in adsorption of the atom on the surface. For single atoms with strong bonding, as in the case of group IV epitaxy, the sticking probability is near unity. This is important for good control of alloy mixing and doping with calibrated beam flux densities.

The thermal velocities $v_B$ are given by mean energy considerations as

$$v_B^2=\frac{3k_B}{M_P}·\frac{T_B}{M}$$E1

with the constants, the Boltzmann constant $k_B=1.38·{10}^{-23}\mathrm{J}/\mathrm{K}$ and the proton mass $M_P=1.67·{10}^{-27}\mathrm{kg}$ and the variables, the beam source temperature $T_B$ and the atomic weight $M$. For a Si beam, one will get $v_B=1300\mathrm{m}/\mathrm{s}$ with $T_B=2000\mathrm{K}$ and $M=28$.

2.1 Sticking, adsorption, and desorption of atoms

The sticking of atoms from group IV elements on a diamond-type lattice with strong bonds is unity. This is proven for Si [21] but can reasonably also be assumed for other group IV systems. The same conclusion is valid for the doping atoms from groups III and V, which are strongly bonded on lattice sites. Complete sticking allows the realization of complex designs with heterostructures and doping transitions using calibrated beam fluxes.

The arriving atom sticks on the surface as an isolated adatom which is weaker bonded to the crystal than a bulk atom.

$$W=W_{\mathrm{ad}}+W_S$$E2

The evaporation energy $W$ of a bulk material is composed of the adsorption energy $W_{\mathrm{ad}}$ and the additional surface energy $W_S$, which is gained from the incorporation of an adatom on the kink of a surface step, as seen in the left part of Figure 1. The value of $W$ can be extracted from the temperature-dependent vapor pressure of the matrix element. At equilibrium, the incoming flux of the vapor equals the desorbing flux density $F_{\mathrm{eq}}$ of the epitaxial surface. The typical value of $W$ amounts to several electronvolts per atom (Si: $W=4.55\mathrm{eV}/\text{atom}$).

Figure 1.

Adsorption and incorporation of an atomic beam. Left: Schematic view of a substrate surface with an adatom (striped), a surface step, and an incorporated adatom at a kink side of an atomic step (checked). Right: Binding energy diagram for the movement of an adatom in x-direction with the adsorption energy $W_{\mathrm{ad}}$, the bulk crystal binding energy $W$, and the surface diffusion barrier $U_S$.

The adsorption energy $W_{\mathrm{ad}}$ depends on the surface orientation and on the reconstruction of the surface. For model calculations, often a value of $2/3W$ is assumed. The impinging flux $F_S$ of atoms is usually much higher than the desorbing flux because MBE conditions are preferably in the lower growth temperature regime. That means the supersaturation $\sigma$ is high. We define here the supersaturation as

$$\sigma =\frac{F_S}{F_{\mathrm{eq}}}=1$$E3

Sometimes, the value of $ln\sigma$ is also called supersaturation. It must be considered that supersaturation under growth conditions causes an increase in the concentration of adatoms from the equilibrium value $n_{s0}$ to an $n_s$, which is dependent on the distance to the next step.

Steps on the surface, mainly of mono-atomic or bi-atomic height $h$, stem from three sources.

• Slight surface misorientation of the nominal surface with low index planes (Miller index: (001) planes perpendicular to the cubic axes, (111) planes perpendicular to the cubic diagonals). The preferred surface orientation for Si substrates is (001) because the interface quality between dielectrics and semiconductors is the best. Commercially available substrates typically have a misorientation angle $i$ below $i<0.25°\left(\mathrm{arc}i\le 4·{10}^{-3}\right)$

  $$\mathrm{arc}i=\frac{h}{L}$$E4

  with the atomic step height $h$ and the length of the terrace to the next step $L$. With $h=0.14\mathrm{nm}$, the mono-atomic step height on Si(001), one obtains terrace lengths of $L>35\mathrm{nm}$. That means commercial substrates already deliver a dense sequence of steps. The microscopic picture of the macroscopic growth in vertical direction is, therefore, a lateral movement of step trains. The steps move in the downward direction by the repeated incorporation of adatoms to the kink position on steps.

• Dislocations generate a step at their point of intersection with the surface. These steps are pinned to the dislocation position. Under the supersaturation of adatoms, they wind up as spirals. These sources are available in substrates of lower quality than Si or in virtual substrates formed by relaxed layers on Si, for example, Ge virtual substrates. Burton-Cabrera-Frank [22] developed their early atomic theory of growth from step movement under this assumption.

• Two-dimensional nucleation generates additional steps. This mechanism operates if the concentration of adatoms is very high. This concentration depends on the supersaturation of the incoming flux and the diffusion of adatoms toward the steps. The diffusion of adatoms is described by a diffusion coefficient $D_S$ which results from a Brownian motion across an energy barrier $U_S$ (see right part of Figure 1) between the lattice sites for adatoms. One should consider the surface as populated with very mobile adatoms. Epitaxy by MBE is, therefore, possible at low temperatures when bulk atoms are frozen into their respective positions. However, adatoms become less mobile at lower temperatures. Finally, the adatom flux to preexisting steps does not counterbalance the incoming atom flux. The resulting increasing adatom density promotes nucleation processes, as seen in Figure 2, mainly by reducing the needed size for the so-called critical nucleus.

Figure 2.

Schematic presentation of the two-dimensional nucleation. Top: Development of a stable nucleus. Bottom: Decay of a critical nucleus.

The critical nucleus forms by a dynamic process counterbalancing the incoming adatom flux, which is proportional to the adatom density, and the leaving adatom flux which is dependent on the nucleus size. In effect, this means an increase of steps when the surface adatom supersaturation ${\sigma }_S$ surpasses a value necessary for the formation of critical nuclei.

$${\sigma }_S=\frac{n_S}{n_{S0}}-1$$E5

There is an important difference of these nuclei steps and steps from misorientation. The step trains from misorientation follow the inclination direction. The steps from adjacent nuclei move forward and become extinct when they meet. For each mono-atomic step, a new nuclei must be formed. The caused periodic modulation of the step density may be observed with sensitive methods like RHEED (reflection high energy electron diffraction).

2.2 Growth modes of strained heteroepitaxy

The macroscopic growth mode models, as seen in Figure 3, predict two-dimensional (2D) growth (Frank v. d. Merve), three-dimensional (3D) growth (Volmer-Weber), or mixed 2D/3D growth (Stranski-Krastanov) from a balance of surface energies of the substrate $E_S$ and the film $E_f$ and the interface energy $E_i$ densities

Figure 3.

Monocrystalline growth models on a crystalline substrate (checked). Left: Two-dimensional (2D) growth according to Frank van der Merve. Middle: Three-dimensional (3D) growth according to Volmer-Weber. Right: Mixed two-three-dimensional growth according to Stranski-Krastanov.

$$E_S-E_i=E_f·cos\mathrm{\Theta }$$E6

The inclination angle $\mathrm{\Theta }\ge 0$ of a 3D island is given by Eq. (6). Solutions with $cos\mathrm{\Theta }\ge 1$ deliver 2D growth. Mixed 2D/3D growth mode is only possible for a thickness-dependent $E_i$ term

Microscopic theories explain the thickness dependence of the interface energy by contributions from the elastic film strain and from the interface misfit-dislocation network. Table 1 gives the lattice constants of the diamond-type lattice cell for the group IV elements C, Si, Ge, and Sn.

	C	Si	Ge	Sn
$a_0\left(\AA \right)$	3.56683 [23]	5.43102 [23]	5.64613 [23]	6.4912 [24]

Table 1.

Lattice constants of the group IV elements C, Si, Ge, and Sn.

For the group IV compound SiGeSn, the lattice constant $a_{0,\text{SiGeSn}}$ depends on the compound composition and follows the relationship in Eq. (7):

$$a_{0,\text{SiGeSn}}=c_{\mathrm{Si}}·a_{\mathrm{Si}}+c_{\mathrm{Ge}}·a_{\mathrm{Ge}}+c_{\mathrm{Sn}}·a_{\mathrm{Sn}}$$E7

In heteroepitaxy, two materials, hence the film and the substrate, with different electrical and mechanical properties but the same crystal structure, are grown on each other. Therefore, the lattice constant of the grown film $a_f$ usually differs from the lattice constant of the substrate $a_S$. The relative lattice constant difference, according to Eq. (8), is called lattice mismatch $f$:

$$f=\frac{a_f-a_S}{a_S}$$E8

Due to the lattice mismatch, three possible cases, as shown in Figure 4, are conceivable: For pseudomorphic, also known as coherent, growth, the atomic rows of the film fit exactly to the underlying rows of the substrate. In other words, the in-plane lattice constant of the film $a_{\Vert ,f}$ adapts to the lattice constant of the substrate $a_S$ (see left part of Figure 4). However, due to the different lattice constants of the two materials, this can only take place under the formation of elastic strain of the film with the in-plane strain ${\epsilon }_{\Vert }=-f$.

Figure 4.

Comparison of the growth modes of heteroepitaxy with the grown film (brown) on the substrate (blue) left: Pseudomorphic growth. Middle: Partial-relaxed growth. Right: Strain-relaxed growth.

The elastic strain energy of a pseudomorphic film is proportional to the film thickness. This pseudomorphic state holds only up to a critical thickness $t_C$ of the film. Above this critical thickness for strained films, dislocations are nucleated and bend to the interface for a partial relief of strain. Nanometer films and structures may be strained to much higher values, for example 1% strain in 10 nm thickness, than bulk material. This high tolerance of high strain values in nanometer structures is the base of strain engineering in electronics and photonics. Films with a thickness above the critical thickness, but which exhibit residual strain, are referred to as partially relaxed (see middle part of Figure 4).

In the case of complete relief of strain, the resulting film is called completely strain relaxed. The corresponding growth mode is thus called strain-relaxed growth.

A special case of heteroepitaxy can be performed with SiGeSn. The mixing of Si and Sn with Ge allows a decrease of the lattice constant with Si and an increase with Sn. Therefore, SiGeSn allows the decoupling of its electrical and mechanical properties from its lattice constant. Consequently, SiGeSn can be grown lattice-matched on Ge and even on GeSn. In order to achieve this so-called lattice-matching on Ge, a constant ratio of the Si and Sn concentration, according to Eq. (9), has to be fulfilled:

$$\frac{c_{\mathrm{Si}}}{c_{\mathit{Sn}}}=\frac{a_{\mathrm{Ge}}-a_{\mathrm{Sn}}}{a_{\mathrm{Si}}-a_{\mathrm{Ge}}}=3.67$$E9

2.3 Limits of single crystalline growth

Considering a strongly magnified picture of the epitaxy process reveals that approx. ${10}^{15}\text{atoms}/\left({\mathrm{cm}}^2,\mathrm{s}\right)$ are impinging on the surface. In the MBE regime without desorption, the growth rate $R$ is determined by Eq. (10):

$$R=F_S·\mathrm{\Omega }$$E10

with the beam flux density $j$ and the atomic volume $\mathrm{\Omega }=2·{10}^{-23}\mathrm{c}{\mathrm{m}}^3$ for Si.

The growth rate equals a coverage of approx. one monolayer (ML) per second. This means each atom out of the ${10}^{15}\text{atoms}/\left(\mathrm{c},{\mathrm{m}}^2,\mathrm{s}\right)$ have to find their position on a lattice site within roughly 1 s; otherwise, the next monolayer flux would cover and fix them on unwanted sites, producing interstitials and vacancies. Exactly that is happening at very low growth temperatures of approx. 20–100°C, resulting in a growth start with single crystalline layers of high crystal defect density and subsequently an alteration to amorphous material after a critical thickness of crystalline growth at low temperatures. It has to be considered that this low-temperature growth critical thickness is not the same as that of the coherent growth of mismatched structures. This defect-rich growth regime is not applicable for working devices but is useful as a nucleation starter for dislocations [25] and amorphous structures.

2.4 Segregation

Through the usage of MBE, the influences of the volume diffusion of doping or alloy atoms within the Si or SiGeSn crystal can be remarkably reduced. However, the effect of surface segregation, which results in a broadening or smearing of doping profiles, can also be observed in these epitaxial layers. In order to suppress this effect, special epitaxial strategies are needed. The basic mechanism of surface segregation is an exchange of atoms from subsurface states to surface states due to the energetically favorable surface adatom position (see Figure 5). The segregation is quantified by the segregation length $\mathit{\Delta s}$ [9], which is the ratio of the impurity surface concentration $n_S$ and the bulk concentration $n_B$. The segregation length $\mathit{\Delta s},$ thus defined, can be converted into the dimensionless segregation coefficient $S$ by dividing it by the thickness of a monolayer. Segregation leads, therefore, to an increasing impurity surface concentration $n_S$, which saturates at an equilibrium where the number of segregating adatoms equals the number of incorporating adatoms. Therefore, the resulting doping profile shows an exponential increase after the beginning of the co-evaporation of dopant and lattice atoms. Consequently, the segregation length $\mathit{\Delta s}$ describes the length in the growth direction from the beginning of co-evaporation to reaching equilibrium. The segregation length is typically in the order of a few nanometers but can, outside of the optimum growth parameter window, increase to several tenth to hundred nanometers.

Figure 5.

Left: Dopant atom (blue) in subsurface state. Middle: Dopant atom swaps its place with a surface crystal adatom (gray striped). Right: Further overgrowth leads to the same situation as before.

Generally, the perfect abruptness of transitions may be obtained by a growth interruption, in which the equilibrium adatom concentration of the doping or alloy element is adjusted. These techniques are called prebuild-up for ramp-up and flash-off for an abrupt ramp-down.

The surface segregation of Sb in Si and Ge is strongly dependent on the growth temperature [9, 26, 27, 28]. In order to achieve an atomic sharp doping profile, the growth strategy, which is known as prebuild-up, can be used. For this, the adatom concentration required for equilibrium, which is typically less than a monolayer, is evaporated onto the surface before the co-evaporation begins. At the beginning of the subsequent co-evaporation, the number of incorporated adatoms per monolayer is already at the desired value.

The biggest disadvantage of the prebuild-up technique to counteract surface segregation is the remaining surface concentration of segregated atoms. Following the segregation mechanism, the surface concentration decreases linearly subsequently to the co-evaporation of dopant and matrix atoms, which leads in turn to a nonideal doping profile. Therefore, special methods are needed to get rid of the segregated surface concentration such as the flash-off method. Here, a growth interruption is used for an increase of the substrate temperature to a value where the remaining segregated atoms are being desorbed from the epitaxial surface. However, depending on the element to be desorbed, the necessary temperature for this can be relatively high and in an unfavorable range for the already grown crystal. In order to avoid the disadvantages of high temperature flash-off, the “freeze out” method may be used by which growth rate and temperature are reduced to form a delta-doping structure from the adlayer. This is specially of advantage in device structures with highly doped regions in contacts, in buried layers, and in modulation-doped quantum wells.

Besides the described prebuild-up technique, other methods can be used to suppress or counteract surface segregation. A possibility is the doping by secondary implantation (DSI) [29, 30]. In the example of Si, which is being evaporated using an electron beam evaporator (see Section 3.1.2), the molecular beam contains Si atoms as well as Si⁺ ions. These Si⁺ ions can then be accelerated toward the substrate using an electric field. Once these accelerated ions hit the substrate surface, they can drive segregated atoms further into the crystal and, therefore, counteract the segregation. Furthermore, special effusion cells are conceivable in which the evaporated atoms are ionized in an additional stage, whereby the dopants themselves can be accelerated toward the substrate surface [31, 32].

The presence of a third species of adatoms also influences the segregation length because the species with higher binding energy occupies the crystal positions faster. We call the third species a surfactant if it is added only to reduce the segregation length of the second species.

Particularly in the MBE of group IV compounds such as SiGeSn, segregation has a huge influence on the incorporation of Sn [16, 33]. In this case, segregation not only leads to a smearing out of the alloy composition but also to a disturbance of the epitaxy process. The consequences of Sn segregation range from an increased point defect concentration within the crystal over the formation of Sn precipitates on the surface and finally to the complete breakdown of the epitaxial process (see Section 4). Consequently, many of the previously described methods to counteract the surface segregation are not applicable for the MBE of SiGeSn which in turn justifies the necessity of ultra-low-temperature MBE of these group IV compounds.

3. Molecular beam epitaxy of group IV compounds and low-dimensional structures

3.1 Molecular beam sources

3.1.1 Theory of molecular beam sources

Different types of molecular beam sources are used in MBE systems depending on the physical properties of the material to be evaporated or sublimated. The equilibrium vapor pressure $p_0$ as a function of the absolute temperature $T$ of the vaporization material plays an important role. From this dependency, the particle flux $F_0$ emitted by a surface is calculated with Eq. (11) as follows:

$$F_0=p_0\sqrt{\frac{N_A}{2\pi M_r{k}_{B}T}}$$E11

with the surface temperature $T$, the molecular weight $M_r$ of the considered element or molecule, the Avogadro constant $N_A$, and the Boltzmann constant $k_B$. From the evaporation rate ${\Gamma }_0$ at the surface of a melt, the area-specific particle flux can be calculated, which vaporizes an area $A$ at a distance $r$ and at an angle $\vartheta$. The flux $F_S$ arriving there is inversely proportional to the square of the distance $r$ and has the same characteristics as the evaporation rate to a first approximation. At some distance, the effusion cell acts like a point source of flux with a cosine distribution. The particle flux $F_S$ impinging on the substrate is then given with Eq. (12) as follows:

$$F_S=\frac{{\mathrm{\Gamma }}_0}{r^2}cos\vartheta =\frac{F_{0}A}{r^2}cos\vartheta$$E12

The required working temperatures can be determined with these formulas. For this purpose, the vapor pressures as a function of the temperature for the corresponding elements are taken from the literature. It is additionally assumed that the typical evaporation area is 1 cm², and the distance between the evaporation surface and the substrate is $r=30\mathrm{cm}$. Furthermore, perpendicular incidence is assumed $\left(\vartheta =0\right)$.

The left graph in Figure 6 shows the results of the calculations for the matrix materials of group IV. Therefore, the necessary temperature range to achieve the required growth rates for the respective molecular beam sources can be seen in this diagram. The growth rate $R$ corresponds to the right scale on the example of a Si(100) surface.

Figure 6.

Particle flux on the substrate as a function of the inverse surface temperature $1/T$ of the evaporation material. Left: Typical group IV matrix materials. Right: Typical doping materials for Si-based devices. (data source: [34]).

For a Si molecular beam source, a working temperature range between $1460°\mathrm{C}\le T\le 1820°\mathrm{C}$ results in growth rates of $0.1\AA /s\le R\le 10\AA /s$. Using the melting point of Si ($T_{\text{melt},\mathrm{Si}}=1410°\mathrm{C}$), it follows that Si is evaporated instead of sublimated, which means that a crucible must be used.

In case of the growth of carbon, the working range of a molecular beam source is between $2270°\mathrm{C}\le T\le 2630°\mathrm{C}$ for growth rates of $0.1\AA /s\le R\le 10\AA /s$. However, since the melting point of carbon ($T_{\text{melt},\mathrm{C}}=3550°\mathrm{C}$) is significantly higher, carbon is only sublimated under MBE conditions. Therefore, carbon can be used directly as a filament material.

The right-hand graph of Figure 6 shows the particle fluxes on the substrate as a function of the surface temperature of the material to be evaporated for typical group IV doping materials. In Si-based technology, only the element B is used for p-type doping. For a large variation of the doping concentration between ${10}^{16}\mathrm{c}{\mathrm{m}}^{-3}\le N_A\le {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$, the resulting typical working temperature of a B source in the range of $1200°\mathrm{C}\le T\le 1600°\mathrm{C}$, as it can be read in the vapor pressure curve. Since the melting point of B is $T_{\text{melt},\mathrm{B}}=2076°\mathrm{C}$, B belongs to the sublimated materials under MBE conditions.

The typical n-type dopants in Si technology are P and As, although Sb is also used. The respective vapor pressure curves are also shown in the right graph of Figure 6. The typical temperatures for the evaporation of the element P for doping concentrations between ${10}^{16}\mathrm{c}{\mathrm{m}}^{-3}\le N_D\le {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$ are in this regard in the range of $33°\mathrm{C}\le T\le 97°\mathrm{C}$. This is very problematic in an ultra-high vacuum (UHV) chamber, since an effusion cell coats not only the substrate but also the rest of the chamber, specifically the chamber walls. However, these P deposits evaporate again at low temperatures, resulting in a continuous flow of P throughout the growth chamber. The result is a tremendous background doping in the epitaxial layer.

Things are looking a little better for the next group V element, As. The typical temperature range here is between $81°\mathrm{C}\le T\le 172°\mathrm{C}$. For the conditioning of the UHV, the entire chamber is heated at $T\ge 200°\mathrm{C}$. In the case of residual As in the chamber, it would be distributed evenly in the chamber during this conditioning, leading to a similarly increased background doping.

Consequently, the group V element Sb is typically used as n-type dopant in a Si-MBE system. The resulting working range of an Sb beam source is between $240°\mathrm{C}\le T\le 380°\mathrm{C}$. Since the melting point of Sb is $T_{\text{melt},\mathrm{Sb}}=630°\mathrm{C}$, Sb is being sublimated under MBE condition.

The choice of the appropriate molecular beam source is based on the vapor pressure curve and the melting point of the material to be evaporated. The possibilities include electron beam evaporators (EBE), effusion cells, and high-temperature sublimation cells.

3.1.2 Electron beam evaporators

Although any material can be evaporated using an EBE, their technical realization is very challenging. A schematic drawing of the main components and the functionality of a Si EBE is shown in the left part of Figure 7.

Figure 7.

Left: Schematic drawing of the main components and the functionality of an electron beam evaporator (EBE) for the evaporation of Si. Right: Marangoni convection caused turbulence in the Si melt.

A W filament emits electrons which are accelerated in an electric field with typical energies between 8 and 12 keV. Since metallic impurities in the Si melt are undesirable, the electrons, emitted from the filament, are thereupon deflected at an angle of 270° using a magnetostatic field, which does not manipulate the also emitted W atoms. Due to the high reactivity of molten Si, it would attack any crucible material, which in turn leads to an excessive contamination of the melt and the molecular beam with the crucible material itself. Therefore, Si acts in an EBE as its own crucible material. For this purpose, a high-purity Si ingot is used, which is placed in a water-cooled Cu crucible. The electron beam melts the Si only partially on the surface. By using an additional electromagnetic field, the electron beam can be scanned over the entire crucible to adjust the molten area. Due to the thermal properties of Si, the molten area is limited to the area directly heated by the electron beam.

The EBE is controlled using a quadrupole mass spectrometer (QMS), which directly measures the intensity of the Si isotope with the mass number 30 in the Si molecular beam. The measurement signal is proportional to the flux or the growth rate on the substrate surface and can be used as a control parameter. A problem of heating with electrons is the Marangoni convection in the Si melt, as seen in the right part of Figure 7.

Since there are subareas of different temperatures with different surface tensions in the molten Si, turbulent flows arise in the melt, leading to high flux fluctuations. Although this effect can be compensated by the regulation using a QMS, the flux of an EBE underlies higher fluctuations compared to an effusion cell. However, the biggest advantage of an EBE in comparison to effusion cells is the high rate of change of the desired Si flux. The disadvantage, on the other hand, is the already mentioned fluctuation of the Si rate, which is in the range of approx. 10%.

3.1.3 Effusion cells

In an effusion cell, the crucible is heated from the outside and from below by thermal radiation. For this purpose, the crucible is surrounded by an electric heater. The production of uniform layers requires a constant flux over time. The flux from an effusion cell is determined indirectly based on the cell temperature and can be regulated by the applied heating power. The task of controlling a cell is to keep the cell temperature as constant as possible at a specified value, or to reach a new nominal temperature as quickly as possible. The regulation of the temperature of an effusion cell by the heating power must be very precise since the evaporated flux increases exponentially with the temperature.

The thermal properties of an effusion cell are the static and dynamic relationships between the conversion of electrical energy into heat, the propagation and dissipation of the thermal energy, and its effect on the evaporated flux. The material flux can only be controlled precisely if its reaction to the electrical power input is known. Since the heating element is located inside the effusion cell, the electrical heating power is initially transferred to the cell. If one neglects delays due to heat capacities, a power balance can be drawn up at any point in time: The sum of all power losses corresponds to the electrical power input. Thermal energy can be transported between two bodies by the following three mechanisms:

1. Thermal radiation

2. Conduction

3. Convection

This results in the following heat loss mechanisms for a typical effusion cell:

1. Thermal radiation through opening the shutter

2. Thermal radiation through the shield

3. Heat conduction via fortifications

4. Evaporation energy and kinetic energy of the molecular beam

The ratio of the parts in the total power depends on the temperature of the cell and, thus on the induced electrical power. For the most thermally stable operation possible, the power loss must be minimized.

A schematic drawing of the structure of an effusion cell can be seen in the left part of Figure 8. The evaporating material is placed in a pyrolytic BN crucible (PBN). This crucible is heated using a meander-shaped graphite heater. Side and bottom shields made of Ta minimize the thermal losses of the effusion cell. A water-carrying cooling shroud is used for a further reduction of the thermal radiation into the MBE chamber. The temperature of the crucible is measured using a thermocouple, which has to be calibrated to the actual temperature of the melt. The molecular flux can be switched on or off with a shutter.

Figure 8.

Left: Schematic scheme of an effusion cell. Right: Real Ge effusion cell on a 150 mm flange. The crucible has a volume of 100 cm³. The meander-shaped heater is made of graphite.

The illustration on the right part of Figure 8 shows a technical realization of a Ge effusion cell. The effusion cell is built on a flange with a diameter of 150 mm and has a crucible with a volume of 100 cm³. The built-in thermocouple of an effusion cell is used to monitor and control it. Besides that, it is also possible to directly measure and control the atomic or molecular flux using a QMS. The advantage of an effusion cell is the very stable molecular flux. However, due to the good thermal isolation of the cell, the rate of change in the molecular flux is very limited, in comparison with an EBE.

3.2 In situ reflectometry

The in situ analysis describes the measurement of various process parameters during the epitaxy process in an MBE chamber. In addition to measuring the composition of the residual gas, the actual surface temperature of the substrate, a measurement of the reflectivity of the epitaxial layers can also be carried out directly during the process. The so-called in situ reflectometry is interesting when the optical properties of the epitaxial layer change compared to the underlying substrate or layer stack. For example, a change from monocrystalline to amorphous growth can be observed. In the case of heteroepitaxial growth, the thickness of the growing layer can also be measured using in situ reflectometry.

The perpendicularly incident light beam is reflected both at the growth surface and at the interface between the substrate and the heterolayer, as it can be seen in the left part of Figure 9, which leads to the interference of the respective parts.

Figure 9.

Left: Schematic drawing of the reflectometry measurement principle. Right: Exemplary in situ reflection measurements at the wavelengths of 670 and 950 nm during the growth of an Si buffer and a SiGe layer on a Si substrate.

A typical measurement of the reflectivity during a growth process is shown in the right part of Figure 9. The growth typically begins with a Si buffer on the Si substrate. Since the optical properties do not change between the film and the substrate, the reflectivity measurements remain constant at both used wavelengths. At a time $t=0\mathrm{s}$, the heteroepitaxial growth of a SiGe layer begins. Therefore, the reflectivity of the epitaxial layer changes from $n_{\mathrm{epi}}=n_{\mathrm{sub}}=n_{\mathrm{Si}}$ to then $n_{\mathrm{epi}}=n_{\text{SiGe}}$ immediately with increasing thickness of the SiGe layer. Therefore, the already mentioned thickness interference can be observed. Using the positions of the arising maxima and minima, the corresponding thickness $d$ of the epitaxial SiGe layer can be calculated using Eq. (13) and Eq. (14), respectively.

For $n_{\mathrm{epi}}>n_{\mathrm{sub}}$ the following Eq. (13) applies for the maxima:

$$n_{\mathrm{epi}}·d=\frac{\lambda }{4}·\left(2m+1\right)$$E13

and Eq. (14) applies for the minima:

$$n_{\mathrm{epi}}·d=\frac{\lambda }{2}·m\text{with}m\in \mathbb{N}$$E14

with the wavelength $\lambda$ of the used light.

Besides that, a weakening of the oscillations for the wavelength of 670 nm is measured. This is due to the absorption behavior of the SiGe layer. Consequently, the absorption behavior of the epitaxial-grown material can be determined from these measurements. On the other hand, at a wavelength of 950 nm, the absorption is negligible.

The technical implementation of an in situ reflection measurement is shown in Figure 10. In order to enable the necessary perpendicular incidence of light, a flange with a window is mounted directly under the substrate on the growth chamber. The measurement head contains several light sources at different wavelengths and a corresponding detector. For an optimal homogeneity of the layer thickness over the entire wafer, the substrate is rotated during growth. In order to compensate for slight wobbling movements, the reflectivity measurement is synchronized with the rotation.

Figure 10.

Schematic drawing of the setup for in situ measurement of the reflectivity of the growing layer. The measuring system is attached to the growth chamber in such a way that the reflectivity can be measured under vertical incidence of light.

3.3 Substrate heating and temperature measurement

Heating of the substrate surface during the epitaxy process is necessary due to various reasons. As mentioned in Section 2.1, heating provides not only enough energy for adatoms to reach their preferred destination on the crystal surface. Furthermore, heating of the substrate prevents the adsorption of undesired elements of the residual gas and, therefore, the concentration of impurities.

As described in Section 3.1, thermal energy can be transported by three different mechanisms. Due to the lack of a transport medium as well as the necessity for substrate rotation, the mechanism of choice for the transport of thermal energy under MBE conditions is thermal radiation. The typical temperature regime for the substrate heating for the epitaxy of group IV compounds is in the range of $100°\mathrm{C}\le T_S\le 1200°\mathrm{C}$. According to Planck’s radiation law, the corresponding radiation is, as seen in the left part of Figure 11, in the wavelength range of $\lambda \ge 1100\mathrm{nm}$. However, the absorption of typically used Si substrates is due to the bandgap of Si of $E_g=1.12\mathrm{eV}$ limited to wavelengths $\lambda <1100\mathrm{nm}$ (see the absorption border of Si in the left part of Figure 11). Therefore, the heating of Si substrates in a group IV MBE system is based not on the fundamental absorption but on the free carrier absorption.

Figure 11.

Left: Thermal emission of a radiative heater according to Planck’s radiation law. Right: Schematic drawing of a graphite meander-based electrical heater and the used thermocouple for measurement and control of the substrate temperature.

The necessary infrared radiation for the heating of the substrates is generated using a graphite meander-based electrical heater. A schematic drawing of such a heater is shown in the right part of Figure 11. The measurement and control of the substrate temperature is generally performed using a thermocouple, which is located behind the graphite heater. Due to the heating via free carrier absorption, the measurement of the thermocouple is calibrated once to the actual substrate surface temperature using a second thermocouple mounted to the surface of a calibration wafer. Since the amount of free carriers in a semiconductor can be manipulated via doping, the resulting calibration is dependent on the substrate doping concentration.

Despite the necessity of substrate heating, too high substrate temperatures promote undesired, epitaxy disturbing effects, especially the already in Section 2.4 described segregation. In particular, the MBE of group IV compounds suffers from the segregation of Sn [16, 33], which causes its often-reported temperature sensitivity. Furthermore, the limited solid solubility of Sn in Ge of less than 1%, the instability of the preferred α-Sn phase with its transition to β-Sn at 13.2°C, and the occurring in-plane strain of GeSn on Ge amplify this effect. While not only hindering the incorporation of Sn, the segregation also leads to a high number of lattice defects, and, due to the increasing surface concentration of Sn, to β-Sn clusters and the subsequent epitaxial breakdown. All this together underlines the necessity to perform the epitaxy of SiGeSn at ultra-low substrate temperatures in the range of ${\mathit{T}}_{\mathit{S}}\approx 160°\mathrm{C}$.

However, in this temperature regime, not only the substrate heater itself has an influence on the actual substrate temperature but also the thermal radiation of the molecular beam sources. In fact, their influence is, in this regime, the more dominant one and restricts the controllability of the substrate temperature on the base of thermocouple measurement. Therefore, an alternative method for the measurement of the actual substrate surface temperature is needed.

In this context, the mid-infrared (MIR) pyrometry in the wavelength range of $8\mathrm{\mu m}\le \lambda \le 14\mathrm{\mu m}$ has proven itself as a suitable solution. Possible realizations include mid-infrared cameras as well as single detector pyrometers. The left part of Figure 12 shows a mid-infrared picture of an epitaxial GeSn surface. Besides that, the graph in the right part displays the comparison of the substrate temperature measured once with the thermocouple and the mid-infrared pyrometer in the moment of the growth beginning of an exemplary GeSn layer, more precisely, the opening of the Ge and Sn shutters. For this growth process, the heating power was set to $P_{\text{Heat}}=0\mathrm{W}$ to achieve the desired ultra-low substrate temperature.

Figure 12.

Left: MIR-picture of a Si substrate during a GeSn growth process. Right: Characteristics of the substrate temperature according to the calibrated thermocouple (blue) and the MIR pyrometer (red) at the beginning of a GeSn growth process.

Particularly remarkable is the observable increase of the substrate temperature by $\mathrm{\Delta }T=30\mathrm{K}$, which can only be explained by the thermal radiation of the molecular sources. Considering the required substrate temperature of $T_S\cong 160°\mathrm{C}$, this increase underlines the huge impact of the source radiation on the actual substrate surface temperature.

4. Optimization of the molecular beam epitaxy of SiGeSn

4.1 Influence of the molecular flux distribution on SiGeSn epitaxy

As already mentioned in Section 2.2, the electrical and mechanical properties of SiGeSn strongly depend on its composition. Furthermore, the desired condition for lattice-matched growth of SiGeSn on Ge requires a constant ratio of Si to Sn according to Eq. (9). All this underlines the necessity for an as homogeneous as possible distribution of the involved molecular fluxes of Si, Ge, and Sn. However, as already described in Section 3.1.1, the flux $F_S$ impinging on the substrate follows a cosine distribution of the irradiation angle. Therefore, the installation position and angle of a molecular beam source strongly influence the homogeneity of the epitaxial layer. Since only one source can be placed directly central under the substrate, the sources must be arranged in a circular and tilted manner under the substrate, which leads to an even worse distribution. This results, in turn, in the necessity of substrate rotation during growth to achieve at least circular homogeneity of the epitaxial layers. Altogether, the result is a radial-dependent change in the alloy composition, as seen in the exemplary flux distribution on a 4″ substrate, as shown in the left part of Figure 13.

Figure 13.

Left: Relative flux deviation of Si, Ge, and Sn for an exemplary MBE system on a 4″ substrate. Right: Residual strain distribution of a SiGeSn layer with the lattice-matching fulfilled in the center of the substrate.

As can be seen, the exemplary MBE system shows a divergence of the Si and the Sn flux. Particularly for SiGeSn, this means that the condition for lattice-matching is, in the best case, only fulfilled at one radius. The resulting SiGeSn film is, therefore, not completely strain-relaxed but only strain-reduced. The distribution of the residual strain ${\epsilon }_{\Vert ,\text{SiGeSn}}$ of an exemplary SiGeSn layer with the lattice-matching fulfilled in the substrate center is shown in the right part of Figure 13.

4.2 Influence of the growth temperature on the segregation of Sn

It was already previously mentioned that the admixture of Sn to group IV compounds complicates their epitaxy. The main reason for this is the segregation of Sn, which is, as already explained in Section 2.4, strongly dependent on the growth temperature. It was already reported that Sn segregation seems to be intensified when in-plane strain of the grown film comes into play, as it is the case for Sn-rich GeSn (SiGeSn with $c_{\mathrm{Si}}=0;c_{\mathrm{Sn}}>8\%)$ [17].

However, by the admixture of Si to GeSn, thus the epitaxy of SiGeSn, it has been shown that lattice-matched film growth on Ge can be achieved by fulfilling the condition in Eq. (9). Since the in-plane strain is then almost zero, the segregation of Sn is therefore expected to be much lower as for the epitaxy of Sn-rich GeSn. Therefore, higher substrate temperatures should be possible for the epitaxy of lattice-matched SiGeSn films, which would, in turn, lead to improved crystal quality.

The result of an intensive study to find the optimal growth temperature of lattice-matched, intrinsic SiGeSn is shown in the graph in Figure 14. For this study, the growth temperature was measured and controlled using a MIR pyrometer.

Figure 14.

Overview of the optimal growth temperature of lattice-matched SiGeSn. Green: Regions with satisfactory crystal quality, red: Regions which showed epitaxial breakdown. Orange: Regions with indications for polycrystallinity.

As it can be seen in the XRD spectrum on the left side, the growth of lattice-matched SiGeSn turns to polycrystallinity at too low growth temperatures ($T_S=160°\mathrm{C}$) and too high Sn concentrations ($c_{\mathrm{Sn}}\ge 12.5\%$) due to the reduced surface mobility of the adatoms (see Section 2.1).

In contrast to that, too high growth temperatures ($T_S\ge 250°\mathrm{C}$) not only increases the surface mobility of the adatoms but also strongly intensifies the Sn segregation. Consequently, the incorporation of Sn is reduced so much that the epitaxy process is disturbed, which results in alloy decomposition. Therefore, the XRD spectrum on the right side shows not only a reflection of the SiGeSn film but also of a SiGe film, which does not contain any Sn. In this context, it is often spoken about as an epitaxial breakdown.

The compromise between these extremes can be found at growth temperatures in the range of $T_S=200°\mathrm{C}$ and moderate Sn concentrations ($c_{\mathrm{Sn}}\le 10\%$). Here, the surface mobility of the adatoms is high enough to enable monocrystalline growth. At the same time, the Sn segregation is well limited, so that the epitaxy process is neither disturbed nor broken down. However, if the Sn concentration exceeds $c_{\mathrm{Sn}}>10\%$, the amount of impinging Sn atoms is so high that Sn precipitates can form even at a growth temperature of $T_S=200°\mathrm{C}$. Therefore, other approaches are necessary to achieve a good crystallinity of these Sn-rich SiGeSn compounds. A possible solution would be a reduction of the total growth rate, which would in turn reduce the amount of impinging Sn atoms. Furthermore, the precise control of Sn precipitation is being considered [33].

In contrast to that, low Sn compounds can be grown even at high growth temperatures ($T_S\ge 250°\mathrm{C}$) with a satisfactory quality. Therefore, it can be concluded that the absolute amount of impinging Sn atoms seems to have a substantial influence on the resulting crystal quality at a given growth temperature.

4.3 MBE of SiGeSn device structures for electronics and photonics

The previous section reported the optimal growth temperature as the most important growth parameter, for lattice-matched, intrinsic SiGeSn. However, in most cases, not only intrinsic semiconductor regions have to be grown. In order to enable an electronic device functionality, intrinsic regions often alternate with p- or n-type doped regions. Since such regions have substantially different electrical and optical properties, the emissivity $\epsilon$ of the total layer stack, an important parameter for pyrometry, changes drastically with each material transition. Therefore, the measurement signal that changes in this way can no longer be used for control without any doubt because the actual growth temperature is no longer represented properly.

In order to prove this hypothesis, the growth process of a Ge pin diode serves as an example to investigate. Here, the growth temperature was once measured with a thermocouple and also with the MIR pyrometer. The resulting growth temperature characteristics are shown in Figure 15.

Figure 15.

Growth temperature characteristics of a Ge pin diode measured with a thermocouple (dashed) as well as with a MIR pyrometer (solid).

As it can be seen, the growth temperature, according to the thermocouple signal, remains constant at $T_S=330°\mathrm{C}$ throughout the growth of the p-type doped Ge bottom layer and the intrinsic Ge region. In order to reduce the segregation of Sb (see Section 2.4) during the growth of the n-type doped Ge top layer, the growth temperature was lowered to $T_S=250°\mathrm{C}$. Here, the signal of the thermocouple follows perfectly the desired value. However, at the beginning of the intrinsic region, thus at the interface between p-type doped and intrinsic Ge, the signal of the MIR pyrometer starts to increase strongly. Although the signal then follows the drop of the setpoint, the characteristics show a completely different behavior in the n-type doped region. This can only be explained by a drastic change in the emissivity ε due to each newly introduced interface in the epitaxy layer stack. Consequently, other measurement methods have to be introduced for the growth of device structures, which do not depend that much on the optical properties of the epitaxial layer stack. Another solution for this problem would be an in situ measurement of the emissivity ε, which is, in contrast, quite difficult to realize in the MIR wavelength range of $8\mathrm{\mu }\mathrm{m}\le \lambda \le 14\mathrm{\mu }\mathrm{m}$.

However, the MIR pyrometer is, as explained in Section 3.3, still the most suitable method for the measurement of the actual substrate surface temperature at ultra-low growth temperatures.

5. Conclusion

This chapter has presented the fundamentals to understand the physics behind the MBE of group IV compounds. For this, important effects like adsorption, desorption, and the formation of a nucleus have been discussed in detail. Since the epitaxy of group IV compounds automatically includes heteroepitaxy, its basic growth modes, the requirements of monocrystalline growth, and other principles and effects of heteroepitaxy were presented.

Furthermore, this chapter gives a detailed insight into the main components of a group IV compound MBE system, including selection rules for the right molecular beam source suitable for the material to evaporate. Besides that, essential methods for in situ monitoring of the growth temperature as well as the optical properties of the epitaxial layers, specifically reflectometry and MIR pyrometry have been presented.

Considering the substantial importance of SiGeSn, especially in the current group IV research, the last part of the chapter covers several technical and physical problems of its MBE. This includes the strongly temperature-dependent segregation of Sn, thus the measurement of the actual surface temperature to suppress it, and the control of the layer composition as well as its homogeneity. In conclusion, MBE is presented as a powerful tool to realize heterostructures and devices containing them based on group IV compounds.

Without a doubt, Ge and SiGeSn have shown to be serious candidates for the wavelength extension of Si photonics from the visual spectrum to the near- and mid-infrared spectrum [31]. Nevertheless, breakthroughs are expected to close the gap with the excellence in material and device performance of group III/V compounds and continuous improvements are necessary to utilize the integration potential of a silicon-based structure. In the following part, we mention some of the activities that promise to have a remarkable input on the ongoing progress.

• Increase of process window for MBE of higher Sn content. Now, the growth temperature is limited to about 200°C, and the postgrowth anneal to below 550°C. Partial ionization of the molecular beam and short-time laser anneal could introduce nonthermal energy contributions that improve ordering without destruction of the single crystallinity. Pavels Onufrijevs [32] reported a direct-indirect band structure formation by Nd:YAG pulsed laser anneal of a low Sn concentration GeSn (4% Sn).

• Stabilizing of the single crystalline diamond lattice by low-dimensional structures (quantum well, quantum wire, quantum dot). Bulk GeSn is only stable up to 1% Sn, but crystalline interfaces stabilize thin epitaxial structures more by up- and down interfaces (wells [35]), all-around interfaces (wires [36]), and island formation (dots).

• Local strain platforms for high strain values. Tensile strain and high Sn content favor the formation of a direct semiconductor GeSn by lowering the energy band gap of the direct conduction sub-band below the indirect bandgap that dominates Ge. The global strain platform (virtual substrate, VS) is not as easily applicable as in the SiGe system because of the limitations in Sn content, whereas in SiGe, the Ge content can be varied up to 100% Ge. Laser concepts in GeSn semiconductors rely mainly on direct bandgap material often supported by local strain produced with micromechanical methods. However, laser functions were demonstrated [37], often with optical drive, low power output, and cooled operation. Although the reasons for the low performance are under discussion, the authors of this chapter believe that the high carrier recombination rate is key to understanding, as explained in the following.

• Reduction of the electronic defect states, which are caused by vacancy supersaturation and residual threading dislocations. Vacancies dominate the point defect equilibrium in Ge and GeSn, whereas interstitials dominate in Si. Misfit dislocations in lattice-mismatched heterostructures are connected to the surface by threading dislocations. High-temperature annealing of the virtual substrate (about 800–850°C) reduces the density of threading dislocations to several 10⁷ cm⁻². Any further reduction needs special concentration profiles and superlattice filters. The electronic effects of vacancies and threading dislocations were investigated with the Hall effect, with capacitance-voltage (C-V) and deep-level transient spectroscopy (DLTS). Unintentional p-type doping [38] of several 10¹⁵ cm⁻³, a mid-gap trap level, and a near valence band level were found. High carrier recombination from band gap levels causes high nonideal dark currents [39, 40], reducing the power of lasers and the detectivity of detectors.

• Internal signal magnification for single photon detection and integration of detector arrays. A proof of concept for single photon detection with a 4 × 4 Ge array on Si based on SPAD (single photon avalanche diode) is encouraging for infrared night vision [41]. Detector concepts based on phototransistors [42] are integration friendly for large-area arrays. The phototransistors may be based on a hetero-bipolar transistor [43] or on a field effect transistor [43].

Acknowledgments

The authors want to thank all current and former colleagues of the Institute of Semiconductor Engineering of the University of Stuttgart.