The band gaps for small Si nanoclusters
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 191 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 261 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\n'}],latestNews:[{slug:"intechopen-partners-with-ehs-for-digital-advertising-representation-20210416",title:"IntechOpen Partners with EHS for Digital Advertising Representation"},{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"}]},book:{item:{type:"book",id:"3293",leadTitle:null,fullTitle:"Recent Advances in Autism Spectrum Disorders - Volume I",title:"Recent Advances in Autism Spectrum Disorders",subtitle:"Volume I",reviewType:"peer-reviewed",abstract:'The pace of research on Autism Spectrum Disorders (ASD) can only be described as extraordinary as this volume shows. 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Nanocrystals",doi:"10.5772/22015",slug:"silicon-nanocrystals",body:'\n\t\tSilicon has many advantages over other semiconductor materials: low cost, nontoxicity, practically unlimited availability, and decades of experience in purification, growth and device fabrication. It is used for almost all modern electronic devices. However, the indirect energy gap in bulk crystalline Si makes it unable to emit light efficiently and thus unsuitable for optoelectronic applications. For example, lasers, photodetectors are not constructed from silicon. On the other hand, although silicon is widely used for solar cell fabrication, the efficiency can not exceed the Schockley and Queisser limit in single band gap device, because of its inability to absorb photons with energy less than the band gap and thermalisation of photon energy exceeding the band gap. One approach for tackling this disadvantage is to use tandem cells, which can implement the increasing of the number of band gaps (Conibeer et al., 2006; Cho et al., 2008). Moreover, the band gap in silicon is too small to interact effectively with the visible spectrum. If the gap could be adjusted, silicon would be used for either electronic or optical application. In 1990, it was firstly observed experimentally by Canham (Canham, 1990), that photoluminescence (PL) occurs in the visible range at room temperature in porous silicon (PS). Since then the silicon clusters or silicon quantum dots (Si-QDs) or silicon nanocrystals (Si-NCs) have attracted much of research interest, and many of theoretical models, computations, and experimental results on band structures, PL and other electronic properties have been reported during the last decades (Öğüt et al., 1997; Fang & Ruden, 1997; Wolkin et al., 1999; Wilcoxon et al., 1999; Soni et al., 1999; Vasiliev et al., 2001; Garoufalis & Zdetsis, 2001; Carrier et al., 2002; Nishida, 2004; Biteen et al., 2004; Tanner et al., 2006). The results from these reports show that in low-dimension silicon structures, such as silicon nanocrystals or silicon quantum dots, electronic and optical properties can be quite different from those of silicon bulk counterpart, for instance, free-standing Si-NCs show strong luminescence, the color of which depends on the size of the Si-NCs, and the gap and energy increase when their size is reduced. Therefore, the energy gap can be tuned as a function of the size of quantum dots.
\n\t\t\tWe are especially interested in the theoretical study on the band gap and the optical spectrum with respect to the size of the Si-NCs or Si-QDs and surface terminations and reconstructions.
\n\t\t\tThe effective mass approximation (EMA) is used by Chu-Wei Jiang and M. Green to calculate the conduction band structure of a three-dimensional silicon quantum dot superlattice with the dots embedded in a matrix of silicon dioxide, silicon nitride, or silicon carbide( Jiang & Green, 2006), and later the EMA is only of partial use in determining the absolute confined energy levels for small Si-NCs, because it has been found a decreasingly accurate prediction of the confined energy level by the EMA as the Si-QDs size decreases( Conibeer et al., 2008).
\n\t\t\tTime dependent density functional theory (TDDFT) has been performed by Aristides D. Zdetsis and C. S. Garoufalis over the last ten years (Garoufalis & Zdetsis, 2001; Zdetsis & Garoufalis, 2005). In their calculations the Si dangling bonds on the surface of the Si-NCs are passivated by hydrogen and oxygen. In the DFT method, they have used the hybrid nonlocal exchange correlation functional of Becke and Lee, Yang and Parr, which includes partially exact Hartree–Fock exchange (B3LYP). Their results are in excellent agreement with accurate recent and earlier experimental data. It is found that the diameter of the smallest oxygen-free nanocrystal that could emit PL in the visible region of the spectrum is around 22 Å, whereas the largest diameter falls in the range of 84– 85 Å. The high level and the resulting high accuracy of their calculations have led to the resolution of existing experimental and theoretical discrepancies. Their results also clarify unambiguously and confirm earlier predictions about the role of oxygen on the gap size. More recently, they report accurate high level calculations of the optical gap and absorption spectrum of ultra small Si-NCs of 1nm, with hydrogen and oxygen passivation (with and without surface reconstruction) (Garoufalis & Zdetsis, 2009). They show that some of the details of the absorption and emission properties of the 1 nm Si nanoparticles can be efficiently described in the framework of TDDFT/B3LYP, by considering the effect of surface reconstruction and the geometry relaxation of the excited state. Additionally, they have examined the effect of oxygen contamination on the optical properties of 1nm nanoparticles and its possible contribution to their experimentally observed absorption and emission properties.
\n\t\t\tBy performing the same method, TDDFT, the optical absorption of small Si-NCs embedded in silicon dioxide is studied systematically by Koponen (Koponen et al., 2009). They have found that the oxide-embedded Si-NCs exhibit absorption spectra that differ significantly from the spectra of the hydrogen-passivated Si-NCs. In particular, the minimum absorption energy is found to decrease when the Si-NCs are exposed to dioxide coating. The absorption energy of the oxide-embedded Si-NCs remains approximately constant for core sizes down to 17 atoms, whereas the absorption energy of the hydrogen-passivated Si-NCs increases with decreasing crystal size. They suggest a different mechanism for producing the lowest-energy excitations in these two cases.
\n\t\t\tWang, et al, generate and optimize geometries and electronic structures of hydrogenated silicon nanoclusters, which include the
The optical absorption spectra of SinHm nanoclusters up to 250 atoms are computed using a linear response theory within the time-dependent local density approximation (TDLDA) (Vasiliev et al., 2001). The TDLDA formalism allows the electronic screening and correlation effects, which determine exciton binding energies, to be naturally incorporated within an ab initio framework. They find the calculated excitation energies and optical absorption gaps to be in good agreement with experiment in the limit of both small and large clusters. The TDLDA absorption spectra exhibit substantial blueshifts with respect to the spectra obtained within the time-independent local density approximation.
\n\t\tTypically, the size of Si-QDs is less than ten nanometers which is close to the exciton Bohr radius of bulk silicon. Owing to the extreme small dimensions, silicon quantum dots exhibit strong quantum confinement which causes the band gaps to widen, the electronic states to become discrete, and the oscillator strength of the smallest electronic transitions to increase. Generally, at ideal conditions, we consider that the interior of the dot has the structure of crystalline silicon while the surface of the dot is passivated with specific atoms depending on the surrounding environment of the dot, such as hydrogen, oxygen and so on.
\n\t\t\tDirect physical evidence of the crystallinity of Si-QDs has been obtained from high resolution TEM, see Fig. 1a and b (Conibeer et al., 2006). Crystal planes are apparent in many of the darker areas in these HRTEM images. The darker areas are denser material in a less dense matrix, which are attributed to Si-NCs in a SiO2 matrix.
\n\t\t\t\tCross-sectional TEM (a) HRTEM (b) images of Si QDs in oxide. (a) Shows the layered structure and (b) shows individual nanocrystals in which crystal planes can be seen
Scientists also have studied about the nanostructures of Si QDs in other dielectrics such as silicon nitride and silicon carbide, see Fig. 2a and b (Conibeer et al., 2006, 2008). Results from HRTEM images are very promising, showing crystalline nanocrystals in the nitride matrix and carbide matrix.
\n\t\t\t\tFrom the introduction stated above, we can see that it is reasonable to suppose that the interior of the dot has the structure of crystalline silicon while the surface of the dot is passivated with specific atoms at ideal conditions.
\n\t\t\t\tHRTEM images of Si-QDs in (a) silicon nitride and (b) silicon carbide
Lots of experimental researches have been made on the electronic and optical properties of Si-QDs. However, several factors contribute to making the interpretation of measurements a difficult task. For instance, samples show a strong dispersion in the QD size that is difficult to be determined. In addition, Si-NCs synthesized by different techniques often show different properties in size, shape and the interface structure (Guerra et al., 2009). For the reasons stated above, the majority of experimental work give diverse results. Therefore, theoretical model calculations for some ideal structures have been considered very necessary to investigate the properties of Si-QDs. Generally, passivated-surface silicon nanoclusters are the ideal theoretical structure for us to study Si-QDs. In this section, we will introduce several ideal structures of Si-QDs in theoretical simulation.
\n\t\t\t\tHydrogen is often used as the passivating agent for the silicon nanocluster surface in most of the theoretical calculations and computations. It is generally accepted that hydrogen-passivated silicon nanocluster (SinHm cluster) is the simplest structure to represent Si-QDs in a vacuum environment and can reproduce most of the experimental results in despite of neglecting some interface effects.
\n\t\t\t\t\tIn Fig. 3, some idealized hydrogen-passivated quantum dots of silicon are illustrated. The interior of the dot consists of silicon atoms in the diamond structure; the surface of the dot is hydrogen-passivated. We can see that hydrogen atoms remove all dangling bonds on the surface.
\n\t\t\t\tSi-QDs are believed to be the luminescence centres in PS. Experimental measurements on PS samples have indicated that a large PL redshift is observed as soon as the freshly etched samples (oxygen-free PS) are transferred from Ar to a pure oxygen atmosphere or to air; however, no redshift at all is detected when the samples are kept in pure hydrogen atmosphere or in vacuum (Wolkin et al., 1999). Therefore, it is obviously that the chemistry of oxygen at the surface has played an important role when PS is exposed to air and has to be considered in theoretical models for this problem.
\n\t\t\t\t\tStructures of SinHm clusters represented in terms of ball-and-stick models. Yellow balls denote Si atoms and the white balls denote surface H atoms
There are totally four possible oxygen passivations on the surface of Si-QDs: (i) double-bonded, (ii) backbonded, (iii) bridge-bonded and (iiii) inserted oxygen configurations. The ball and stick representations of these oxygen passivation configurations are illustrated in Fig. 4. Compared with corresponding hydrogen-passivated silicon clusters, oxidized clusters are built up by substituting H or Si atoms on the surface with oxygen. From (b) to (e), they are double-bonded, backbonded, bridge-bonded and inserted oxygen configurations, respectively. It should be noted that the backbonded oxygen configuration is different in geometry from the bridge-bonded oxygen configuration, in that the former can preserve hydrogen coverage on a Si nanocrystal and retain the number of Si atoms when it is oxidized, while in the latter, one oxygen atom replaces a surface SiH2 dihydride on the initial dot causing a decrease of the number of H and Si atoms. In another word, for the backbonded oxygen configuration, the oxygen atom is situated between the nearest-neighbor Si atoms while in the bridge-bonded oxygen configuration it is situated between the second nearest-neighbor Si atoms, referring Fig. 4(c) and (d).
\n\t\t\t\t\tBall and stick representations of four possible oxygen passivation configurations, the yellow balls represent Si atoms, red balls represent O atoms, and the white balls, H atoms: (a) initial hydrogen-passivated silicon cluster, (b) double-bonded oxygen passivation configuration (c) backbonded (d) bridge-bonded (e) inserted oxygen configuration
Actually there may exist other oxygen-contamination on the surface of Si-QDs when oxidized. Zdetsis and Garoufalis (Zdetsis & Garoufalis, 2005) proposed a structure that can maintain the Td symmetry of the nanocrystals, considering only double-bonded oxygen configuration, see Fig. 5.
\n\t\t\t\t\tStructure of oxidized nanocrystals with Td symmetry: The blue spheres are Si atoms, the red spheres are O atoms, and the white spheres are H atoms
Si-QDs are often embedded in a dielectric matrix based on the fabrication of Si-QDs. Therefore, it is necessary to build an appropriate structure to simulate Si-QDs in such kind of environment.
\n\t\t\t\t\tStructures of Si-QDs embedded in an ionic environment, SiO2, Si3N4, SiC matrix and a co-valent environment (left to right; top to bottom): SiH4, Si5(CH3)12, Si10(NH2)16, Si14(OH)20, Si18F24, Si26H32, Si35(CH3)36; Si53(NH2)48, Si84(OH)64, Si165F100\n\t\t\t\t\t\t\t
\n\t\t\t\t\t\tKönig et al (König et al., 2009) have used F, OH, NH2, CH3 and H groups as the passivating agent for the Si clusters surface to simulate Si-QDs embedded in an ionic environment, SiO2, Si3N4, SiC matrix and a co-valent environment, respectively, see Fig. 6. Apparently, these structures are simply built by replacing all the hydrogen atoms on the surface of hydrogen-passivated Si clusters with F, OH, NH2 and CH3 groups, respectively.
\n\t\t\t\t\tHowever, there are many more complex structures when Si-QDs embedded in a SiO2 matrix. For instance, Koponen et al (Koponen et al., 2009) put forward some structures in which Si clusters are embedded in one or two neutral SiO2 shells and the outermost layer of the cluster is hydrogen passivated in order to get rid of dangling bonds and to better mimic the effect of bulk silicon oxide. One of these structures is presented in Fig. 7(a). In addition, Guerra et al (Guerra et al., 2009) obtained a crystalline embedded structure from a β-cristobalite (BC) matrix by removing all the oxygen atoms included in a cut-off sphere, whose radius determines the size of the Si-QDs. The final optimized structure of the Si32 in β-cristobalite matrix is illustrated in Fig. 7(b).
\n\t\t\t\t\ta) A stick and ball representation of Si17@Si24O36H60 (Si clusters embedded in one neutral SiO2 shell), (b) The final optimized structure of the Si32 in β-cristobalite matrix
From the introduction stated above, we can clearly see that different structures should be used for simulating Si-QDs in different environment. Besides the structures presented above, there are many other structures used to simulate Si-QDs, we’ll not elaborate here. It is crucial to choose an appropriate structure for a certain problem, otherwise the results may be inaccuracy and make no sense.
\n\t\t\t\tLocal-density approximations (LDA) are a class of approximations to the exchange correlation energy functional in DFT that depends solely upon the value of the electronic density at each point in space (and not, for example, derivatives of the density or the Kohn-Sham orbits). It was used to study on the band gap and PL of Si-QDs in early researches because of its simplicity and low computation cost. However, it is well known that time-independent LDA calculations typically underestimate the experimental photo-absorption gaps of Si-QDs (Vasiliev et al., 2001). TDLDA is then developed by Vasiliev as a natural extension of the ground state density-functional formalism and LDA, designed to include the proper representation of excited states.
\n\t\t\tThe computation software we used is CASTEP module of Material Studio. CASTEP is an ab initio quantum mechanical program employing DFT to simulate the properties of solids, interfaces, and surfaces for a wide range of materials classes such as ceramics, semiconductors, and metals. First principle calculations allow researchers to investigate the nature and origin of the electronic, optical, and structural properties of a system without the need for any experimental input. It allows to choosing local, gradient-corrected, and non-local functionals for approximating exchange and correlation effect, and non-local functional include screened exchange, HF, B3LYP and PBE0. The screened exchange LDA (sX-LDA) is used to calculate the band structures of silicon quantum dots by considering the computational cost and accuracy. The structures with hydrogen and oxygen passivations are partially shown in Fig. 3 and Fig.4, respectively.
\n\t\tResearches of Si-QDs can be divided into two groups: experimental measurements and theoretical simulations. The results of experiments are coincide with that of simulations to some extent, in spite of some discrepancies attributing to the measurement errors in experiments and the idealized structures in simulations. In this section, some results from other researchers are introduced first. Our computational results are then illustrated in the figures.
\n\t\t\tVery Large amounts of works have been done on light emission from Si-QDs because they are believed to be the luminescence centres in PS which had been observed having visible PL and electroluminescence at room temperature. Generally, the properties of Si-QDs are studied by measuring their PL in experiments. As we mentioned above, it is so hard to precisely control the purity and size of the sample that the results of different experiments may be differ from each other to some extent.
\n\t\t\t\tSummary of experimental data on peak PL energy versus Si- QD size
\n\t\t\t\t\tWilcoxon et al (Wilcoxon et al., 1999) had summarized most of the existing experimental results for PL peak energies as a function of the diameter of the Si-QDs, see Fig. 8. We note that there are differences in the dependence on size reported by different authors. As explained by Wilcoxon et al, all PL peaks of SiO2 capped Si-QDs or Si-QDs embedded in glass matrices fall into the shaded region of the diagram while the experimental data for the oxygen-free samples (for the same value of the diameter) fall above this shaded region. So we can clearly see that the interface situation plays a significant role in the luminescence from Si-QDs.
\n\t\t\t\tIn addition, Wolkin et al (Wolkin et al., 1999) obtained a similar conclusion by comparing the PL of PS samples in different atmosphere, see Fig. 9. They first examined the freshly etched samples (oxygen-free PS) with different porosities (equal to different sizes of Si-QDs) and emitting throughout the visible spectrum. Then the oxygen-free PS samples were exposed to air and their PL energies were measured again. We can clearly see from Fig. 9 that after exposure to air, a redshift of the PL is observed, which can be as large as 1 eV for blue luminescent samples that contain QDs smaller than 2 nm. Besides, authors pointed out that a PL redshift was also observed as soon as the oxygen-free PS samples were transferred from Ar to a pure oxygen atmosphere while no redshift at all was detected when the samples were kept in pure hydrogen atmosphere or in vacuum. Moreover, they found that there is an upper limit of the emission energy (2.1 eV) which is independent of size. So the conclusion is that the surface passivation plays an important role, especially the chemistry of oxygen at the surface can cause an evident change on the PL of Si-QDs and an upper limit of energy gap.
\n\t\t\t\tRoom temperature PL spectra from PS samples with different porosities kept under Ar atmosphere (a) and after exposure to air (b)
On the whole, despite some inevitable differences, the experimental results show that for ultra pure Si-QDs as their sizes decrease, there is a considerable blue-shift in the peak PL energy which is due to the increase of band gap. However, if the Si-QD is not pure enough, much more complex results will be obtained due to the influence of impurity contamination and complicate interface situation.
\n\t\t\tAs we have mentioned above, a number of computations based on TDDFT, TDLDA, and other methods have been performed to simulate the properties of Si-QDs with different structures and passivations. In this section, we are going to introduce our calculation results and some theoretical results from other reports.
\n\t\t\t\tZdetsis and Garoufalis calculated the band gaps of hydrogen-passivated Si-QDs using TDDFT, the results are shown in Table 1 (Zdetsis & Garoufalis, 2005). As it can be easily seen in Table 1, with the size of Si-QDs decreases, the band gaps increases.
\n\t\t\t\t\tWe have calculated the energy gaps of silicon QDs of different sizes from 0.6nm to 2nm in diameter by using the CASTEP computation program, which employ the plane-wave peseudopotentials method based on DFT. Some of the structures of Si-QDs we used are shown in Fig. 3. In the computations, screening exchange LDA (sX-LDA)/CA-PZ is used as the type of exchange-correlation potential. As comparison, LDA/CA-PZ is selected as the type of DFT exchange-correlation potential and calculations are performed again. The results are shown in Fig. 10. It can be seen that LDA/CA-PZ suffer from the well-known underestimation of the energy gap while sX-LDA/CA-PZ can obtain a more accurate result which is well consistent with the results from other literatures (Vasiliev et al., 2001; Conibeer et al., 2006).
\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t
5 | \n\t\t\t\t\t\t\t\t17 | \n\t\t\t\t\t\t\t\t6.66 | \n\t\t\t\t\t\t\t
17 | \n\t\t\t\t\t\t\t\t353 | \n\t\t\t\t\t\t\t\t5.03 | \n\t\t\t\t\t\t\t
29 | \n\t\t\t\t\t\t\t\t65 | \n\t\t\t\t\t\t\t\t4.53 | \n\t\t\t\t\t\t\t
35 | \n\t\t\t\t\t\t\t\t71 | \n\t\t\t\t\t\t\t\t4.42 | \n\t\t\t\t\t\t\t
47 | \n\t\t\t\t\t\t\t\t107 | \n\t\t\t\t\t\t\t\t4.04 | \n\t\t\t\t\t\t\t
71 | \n\t\t\t\t\t\t\t\t155 | \n\t\t\t\t\t\t\t\t3.64 | \n\t\t\t\t\t\t\t
99 | \n\t\t\t\t\t\t\t\t199 | \n\t\t\t\t\t\t\t\t3.39 | \n\t\t\t\t\t\t\t
147 | \n\t\t\t\t\t\t\t\t247 | \n\t\t\t\t\t\t\t\t3.19 | \n\t\t\t\t\t\t\t
The band gaps for small Si nanoclusters
Energy gaps of silicon QDs as a function of the QD diameter with H-termination from our work (■) & (●), and from the literatures [(▲) & (◄) from Vasiliev et al; (▼) from Conibeer et al]
Luppi and Ossicini (Luppi & Ossicini, 2005) carried out density-functional theory calculations on oxidized Si-QDs using local density approximation, considering three kinds of oxygen configurations: double-bonded, backbonded and bridge-bonded. The structures’ schematic diagram has been shown in Fig. 4. They pointed out that the multiple presence of silanonelike Si=O bonds can be a reliable model for explaining the PL redshift observed in oxidized PS samples. The same conclusion has been reached by Zdetsis and Garoufalis (Zdetsis & Garoufalis, 2005) using TDDFT. Some of their calculated structures have been shown in Fig. 5.
\n\t\t\t\t\tHowever, a model based on a backbonded oxygen configuration has been proposed by Nishida to explain the observed PL redshift (Nishida, 2006). Nishida carried out self-consistent calculations using the extended Hückel-type non-orthogonal tight-binding method (EHNTB) for three different oxygen configurations (double-bonded, backbonded and inserted). The results are illustrated in Fig. 11. The author pointed out that the energy gaps calculated for Si dots double-bonded to oxygen are gradually decrease from 2.2 eV to about 1.7 eV with increasing dot size and the inserted oxygen configuration does not cause a significant energy-gap redshift even in the smallest Si-QD. At last he found out that the energy gaps calculated for the Si-QDs backbonded to oxygen coincide well with luminescence redshifts observed in PS.
\n\t\t\t\t\tCalculated energy gaps as a function of the diameter (D) of the Si -QDs studied. The dashed line shows the oxidation-induced peak energy (at ∼2.1 eV) in PL spectra observed in PS
Obviously, the two conclusions stated above contradict each other. For this reason, we have performed calculations using the CASTEP computation program for all four kinds of oxygen configurations. The results we obtained based on LDA method are shown in Fig. 12, from which we can safely come to a conclusion that it is the formation of a Si=O double bond which is responsible for the PL redshifts in PS and other three types of oxygen configurations only cause a few decrease in energy gap.
\n\t\t\t\t\tThe discrepancy between the above results may be due to the difference of the oxygen geometries, initial silicon clusters and the models based on different theories. So it is clear that different structures or models may obtain quite different results.
\n\t\t\t\tKönig et al performed a systematic analysis of Si-QDs embedded in different environment by non-periodic spatial space density-functional–Hartree–Fock (DF–HF) computations of Si clusters comprising 1–165 Si atoms corresponding to a spherical QD diameter of dQD=3.4–18.5Å (König et al., 2009). Some of the structures they used have been shown in Fig. 6 and their simulation results are illustrated in Fig. 13. Obviously, it shows that different interface termination causes different energy gaps. However, we can see that the entire trends of different interface terminations are the same. It is that the energy gap increase with the size decreasing.
\n\t\t\t\t\tCalculated energy gaps as a function of the diameter (D) of the Si-QDs
Band gaps as a function of the diameter of Si-QDs with different interface terminations. For clarity, the graph is split into two sub-graphs with different energy scale. The points for the Si10X16 clusters (dQD = 7.3 Å) are shown in both graphs
There are many more complicate calculations simulating Si-QDs in specific environments, we’ll not list them one by one here. From the results above, we know that many factors will influence the properties of Si-QDs, other than the size, the interface termination also have a significant impact, so we should make an comprehensive considerations to study the properties of Si-QDs.
\n\t\t\t\tThe band gap of Si-NCs or Si-QDs is size-dependent, and the energy of PL can be tuned from the near infrared to the ultraviolet by changing the size of nanocrystals. The surface passivation also plays an important role in determining the band gap. The third generation photovoltaic (PV) solar cell using tandem cells, which is based on Si quantum dots nanostructures, is proposed by Martin Green group (Conibeer et al., 2006, 2008). A number of theoretical models, computations results on PL have been reported, and much of research effort on the properties of Si-QDs has been performing currently. Based on CASTEP quantum mechanical program with choice of sX-LDA/CA-PZ, the band gap of Si-QDs with H-passivation and O-passivation is calculated. The results show that band gap increases when the size of quantum dots decreases for both H-passivation and O-passivation structures. The computation method sX-LDA/CA-PZ is comparable with TDLDA in the computational accuracy. Further research on the band gap and PL of Si-QDs by choosing other non-local functional as the exchange correlation is in progress.
\n\t\tThis work is partially supported by National High-Tech Research and Development Program of China under Grant No 2007AA04Z301.
\n\t\tCancer remains the killer disease in the world, and currently it has become a dangerous public health problem in many countries. In all kinds of cancer, the problem arises when cancer cells begin to grow in uncontrolled manner or do not die when they should do so. In addition, breast cancer is a malignant tumor that is considered the most common type of cancer occurs in women and the second type of cancer in general. It has been announced, that more than 2 million new cases have been registered worldwide in 2018 [1]. Awareness of symptoms and the need for screening are very important to reduce the risk of cancer [2].
\nIn medical imaging, it has been shown that early detection and proper treatment of breast cancer reduces the mortality rate by 20–40% [3]. The use of Mammography, represents an effective tool in the early detection of the breast cancer. As a result, many computer-aided diagnostic (CAD) systems have been developed using digital image processing techniques applied to mammography images. These systems are very useful to help radiologists in the early detection of breast cancers and then to classify the breast tumor as malignant or benign [4, 5, 6].
\nIn general, any CAD system can be composed of three different steps: image pre-processing step, features extraction and selection step and finally the classification step. For the breast cancer detection and classification, many works have been presented to improve the efficiency of the CAD systems. In the pre-processing step, the pectoral muscle removal and the region of interest (ROI) extraction rest a big challenge. Numerous segmentation algorithms have been also proposed to suppress the pectoral muscle [7, 8, 9, 10]. However, there is no universal segmentation algorithm that can give acceptable results for all cases.
\nIn the features extraction step, different techniques can be used like, shape and texture features [11, 12], morphological and texture features [13], independent component analysis (ICA) [14], the discrete cosine transform (DCT) [15], the discrete wavelet transform (DWT) [16, 17] and other transforms. In [18], the authors used non-subsampled contourlet transformation together with discrete wavelet transform with gray level co-occurrence matrix for texture features extraction. Salabat Khan et al. used a Gabor filter blank (GBF) optimized by Particle Swarm Optimization (PSO) for the extraction of Gabor characteristics [19]. Mughal B et al. used the backpropagation neural network on the hat transformation with gray level co-occurrence matrix (GLCM) features [20].
\nFor the classification step, the most used classifiers are Artificial Neural Networks (ANN), Support Vector Machine (SVM), Naïve Bayes (NB) and
In this chapter, we propose a new computer-aided diagnostic system to classify breast tumors as malignant or benign. In the pre-processing step, we have proposed a new algorithm to select a limited triangular region that contains the pectoral muscle to be eliminated, and then apply the SRG segmentation algorithm. Features extraction and selection are also very important processes to improve the system performances in classification and pattern recognition methods. By using discrete Fourier transform or discrete cosine transform, we obtain a frequency domain representation of the image that can be considered as a set of features for pattern recognition problems. While the FFT give complex coefficients, the DCT provide real values in the frequency domain. We have used the DCT transform for feature extraction, and we have proposed the selection of the most significant features using the (DPA) algorithm [24]. Finally, we have evaluated the performances of the algorithm using SVM, ANN, NB and KNN classifiers and the MIAS database mammograms [25].
\nThe proposed Computer-aided diagnostic system (CAD) that is used to classify the breast tissue in mammograms as malignant or benign is divided into three basic processing steps as shown in Figure 1.
\nFlow chart of CAD system for breast cancer classification.
This step represents an important one in most CAD systems. The image pre-processing helps strongly in the selection of the region of interest (ROI) that contains the abnormalities. It is performed to remove the unwanted objects, which include artifacts, labels, background noises and to suppress the pectoral muscle (Figure 2). The use of efficient image processing methods is an indispensable step for achieving a high accuracy classification in CAD systems for the diagnosis of breast cancer.
\nThe preprocessing steps of mammogram image: (a) original image, (b) noise removed image, (c) binary image, (d) largest area, (e) image right flipped, (f) parenchyma of the breast.
There are various types of noises affected on mammogram images, such as Salt and pepper noise, Speckle noise, Gaussian noise and Poisson noise. Therefore, it is important to remove the noises to enhance the image quality on the preprocessing step. Traditionally, the median filter is a well-known used filter for this kind of noises, due to its nonlinear behavior, its simplicity and capability to preserve edges [26]. The median filter replaces each pixel value by the median of all the neighboring pixels values in a window. In this chapter, we used a (3x3) median filter to reduce noise in the mammogram images.
\nIn order to remove all unwanted objects in the selected image and separate the breast profile, we follow the next four steps:
Step (1) Thresholding of the mammogram image by 0.0706 normalized value.
Step (2) Mark all regions in the thresholded image (i.e., Artifacts, labels, …).
Step (3) Calculate the area of each region, and select the largest one.
Step (4) The result of the step (3) is then used as a mask of the original grayscale mammography image.
In the mammogram preprocessing, the identification and extraction of the pectoral muscle is one of the major challenges in Medio lateral Oblique (MLO) view. It could be noticed here, that this step is important to improve the diagnostic accuracy of the CAD system. The difficulty in removing the pectoral muscle is due to the following reasons [27]:
Homogeneous area situated in the top left/right corner contains the brightest pixels in the image.
The pectoral muscle boundary shape is concave, convex or a mixture of both of them.
The density of the pectoral muscle area appears at approximately with similar density as the dense tissues.
Varying position, size, shape and texture from image to image.
In this chapter, we present a new algorithm for pectoral muscle suppression, this operation is based on the Localization of the triangular region that contains the Pectoral Muscle, where the Seeded Region Growing (SRG) algorithm is invoked in this operation.
\n\n | \n|
Step (1) | \n\n | \n
Step (2) | \n\n | \n
Step (3) | \n\n | \n
Step (4) | \n\n | \n
Step (5) | \n\n | \n
Step (6) | \n\n | \n
Step (7) | \n\n | \n
The region of interest (ROI) | \n
Seeded Region Growing (SRG) is a useful image segmentation technique for medical images that is initially proposed by R. Adams et
The advantage of applying the (SRG) method into the localized triangular ABC region (Figure 3) is to remove only the pectoral muscle, without completely suppressing the triangular region as in some other methods. Figures 3
Localization of the ABC triangle in the left upper quadrant.
Pectoral muscle segmentation steps: (a) mammogram top left quadrant, (b) triangular mask, (c) masked top left quadrant, (d) suppression of the pectoral muscle, (e) cropped top left quadrant without pectoral muscle.
Identification of the region of interest (ROI). (a) Cropped image, and (b) Selected region of Interest (ROI).
The Seed point is selected automatically by considering the results obtained from step (4) of algorithm 1.
\n\nFigure 5(a) shows the cropped image, where Figure 5(b) shows the selected region of interest (ROI). All obtained (ROI) images are resized in order to get the same dimension.
\nFeatures extraction plays an essential role, and a challenging step in the accurate classification and diagnostic rate of mammograms. In this chapter, we have used features extracted from the image in the frequency domain representation. The most used transform to this domain is the discrete Fourier transform with its fast algorithm (FFT) [29]. In classification problems, for example, Fourier descriptors have been used for pattern recognition [30, 31]. Another interesting transform is the discrete cosine transform (DCT) which decomposes the image on a set of cosine functions. It provides a real representation of the image contrary to the FFT, which give complex coefficients.
\nThe frequency domain features are very used in the classification and pattern recognition field. However, the hard task is the selection of the transformed coefficients, while these coefficients do not have the same aptitude to discriminate between the different classes. However, the use of the standard approaches to select these coefficients are not always efficient in selecting the most discriminative coefficients. In this chapter, we present a novel features extraction technique that is composed of two phases. In the first one, the discrete cosine transforms (DCT) is applied on all the obtained regions of interest (ROI), and then the low frequency coefficients in the upper left corner (ULC) are retained. In the second phase, a combination of the retained frequency coefficients with the discriminative power coefficients algorithm [24] is proposed to calculate the discrimination power matrix, which is given by the ratio between the two variances, the between-class variance and the within-class variance. Where, high classification accuracies are represented by high rate values.
\nThis mathematical tool transforms any signal or image from the spatial domain to frequency domain. It has been widely used in digital signal and image processing, where its major advantages over the FFT reside in giving real coefficients. In addition, it concentrates the information in the low frequency region. Fast implementation can be obtained by using the FFT algorithm [29] which make the use of this transform very simple in real-time applications. It is defined by Eq. (1):
\nwith\n
and \n
After the calculation of the DCT coefficients, we retain only the 512x512 region in the upper left corner (ULC coefficients). In the feature’s selection step, a new most discriminative power analysis (DPA) algorithm has been proposed to select the most significant features that have the high discrimination power (DP) values.
\nThe calculation of the (DP) for each transformed coefficient is shown in the (DCT-DPA) algorithm shown below. Considering an image \n
\n\n
The \n
with \n
The classification is the last step to identify if the breast tumor is benign or malignant. It plays a vital role in the medical image diagnosis field. Therefore, the images need to be classified with maximum accuracy. As a result, some automated classification methods have been proposed. In this part, we presented some of these classifiers including NB, SVM, ANN, and KNN that are used for breast cancer detection. A brief description of these algorithms will be presented as well as their advantages and disadvantages.
\nSVMs are a set of machine learning algorithms that help solve problems associated with classification, regression, and fault detection. They are considered to be among the algorithms that are distinguished by their strong theoretical guarantee and their great flexibility. They are also considered among the easiest algorithms in terms of ease of use even in cases where there is a little knowledge of data extraction.
\nThe SVMs use increases widely in medical imaging field especially for breast cancer diagnosis [32]. The basic principle of SVM in this chapter is to separate and classify images into two categories malignant and benign using a hyperplane decision boundary, ensuring a maximum distance between different data sets and the boundary separating them. For linearly separable data, the hyperplane decision boundary is given by [33]:
\nwhere
SVM generally gives good accuracy with less memory use.
It works very well in cases where the separation margin between data sets is clear.
It can also solve any complex problem by specifying different kernel function.
The main disadvantages of the SVM algorithm are the difficulty of choosing the appropriate kernel function and the long training time for large datasets.
\nThe artificial neural networks are feed-forward networks that can be trained to classify inputs according to target classes. Generally, a neural network is composed of three layers: an input layer, a hidden layer and an output layer [34]. Usually, only the input and output signals of the network are already known [17]. The process of training an artificial neural network before setting it up represents a serious operation and affects directly the final obtained results. This operation depends on some constraints like the initial parameters setting, the use weights, bias and finally the used algorithm learning rate. To adjust the weights of the ANN, one can use some learning methods like the back-propagation or an optimization algorithm. In this work, the input layer is based on the number of the features selected, the hidden layer contains 10 neurons, and finally the out layer.
\nNaive Bayes is becoming increasingly popular in many areas, it has shown excellent performances for classification tasks. It is a simple probabilistic classifier based on Bayes\' theorem, which is based on conditional probabilities [35]. A Naive Bayes classifier assigns a new observation to the most probable class, assuming the features are conditionally independent for a given the class value. It is easy and fast to predict the class of the test data set, but their biggest disadvantage is its requirement to an independent predictor [15].
\n\n
where
To validate the proposed system, experiments were performed on the digital mammography images from the Mammographic Image Analysis Society (MIAS) database [25]. The MIAS database is a standard and publicly available database of digital mammogram images. Each mammogram is 1024 × 1024 pixels of size with a resolution of 200 microns. MIAS contains 322 mammograms for right and left breast of 161 patients in the mediolateral oblique (MLO) view, 61 mammograms were diagnosed as benign, 54 as malignant and 207 normal. The performance of the proposed method has been tested based on algorithms’ accuracy, sensitivity and specificity using the following expressions:
\nWhere:
\n\n\n
\n\n
\n\n
\n\n
In this test, we have calculated the \n
\nTable 1 shows a comparison of the measured performances of the SVM, ANN, NB and KNN classifiers. It is observed that the classification accuracy can reach 100% for the (ANN) classifier, is 98.8, 96.7%, 87.3% for SVM, NB and KNN respectively. We have evaluated the classification performances of the proposed algorithm according to the number of the used features in the classification.
\nClassifiers | \nSensitivity (%) | \nSpecificity (%) | \nAccuracy (%) | \n
---|---|---|---|
KNN | \n91.05 | \n82.67 | \n87.3 | \n
NB | \n97.9 | \n97.3 | \n96.7 | \n
SVM | \n99.5 | \n98.1 | \n98.8 | \n
ANN | \n
Classification performance using ANN, SVM, NB and KNN classifiers.
Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes, KNN, K-nearest neighbors.
The SVM, ANN, NB and KNN classifiers are used to classify input images into benign or malignant. The sensitivity, accuracy and specificity are shown in Table 2. According to the results in Table 2, we can see that small number of features (100 features in this case) can achieve best performances in the case of 512x512 ULC size. In addition, we have studied the effect of the ULC size on the obtained results. The accuracy curve of the classification accuracy versus the ULC size is shown in Figure 6. The number of used features is 100 features.
\n\n | ANN | \nSVM | \nNB | \nKNN | \n|
---|---|---|---|---|---|
ULC size | \nN. of Features | \nAccuracy (%) | \n|||
128x128 | \n60 | \n95.6 | \n86.76 | \n90.6 | \n77.9 | \n
80 | \n96.5 | \n90.3 | \n92.3 | \n78.5 | \n|
100 | \n98.2 | \n94.7 | \n92.6 | \n79.7 | \n|
256x256 | \n60 | \n98.2 | \n91.2 | \n93.2 | \n75.0 | \n
80 | \n97.3 | \n91.7 | \n95.3 | \n75.8 | \n|
100 | \n98.2 | \n93.8 | \n93.8 | \n76.1 | \n|
512x512 | \n60 | \n98.2 | \n92.1 | \n93.8 | \n77.0 | \n
80 | \n99.1 | \n97.3 | \n97.3 | \n79.1 | \n|
100 | \n|||||
1024x1024 | \n60 | \n98.2 | \n92.6 | \n93.1 | \n82.6 | \n
80 | \n96.5 | \n88.5 | \n93.2 | \n83.5 | \n|
100 | \n97.3 | \n91.7 | \n94.1 | \n85.6 | \n
Classification accuracy with various sizes of ULC and different numbers of features.
Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes, KNN, K-nearest neighbors.
Classification accuracy performances vs. the ULC sizes with 100 features.
\nFigure 7 represents the variation of the classification accuracy according to different features’ number with a fixed ULC size of 512x512. Figure 8 demonstrates the classification performance of ANN using the confusion matrix for training, test and validation data.
\nClassification performances vs. the number of features. (ULC size of 512x512).
Confusion matrix for training, test and validation data.
To show the efficiency of the presented technique, Table 3 shows a comparison between the results of the proposed algorithm with previous results, which are reported in the literature. We can see that the proposed CAD system gives better accuracy results compared to those obtained using the other methods.
\nAuthors | \nYear | \nDatabase | \nClassifier | \nClasses | \nAccuracy (%) | \n
---|---|---|---|---|---|
Lima [12] | \n2016 | \nMIAS | \nSVM | \n2 | \n94.1 | \n
Singh [37] | \n2017 | \nMIAS | \nRF | \n2 | \n97.3 | \n
Elmoufidi [38] | \n2017 | \nMIAS | \nSVM | \n2 | \n94.4 | \n
Mughal [20] | \n2018 | \nMIAS | \nNNB | \n2 2 | \n98.5 95 | \n
Benzebouchi [22] | \n2019 | \nMIAS | \nSVM | \n2 | \n94.0 | \n
Benhassine [15] | \n2019 | \nMIAS | \nANN SVM NB | \n2 | \n100 94.1 92.6 | \n
El-Sokary [39] | \n2019 | \nMIAS | \nSVM | \n2 3 | \n92.5 90.0 | \n
Benhassine [17] | \n2020 | \nMIAS | \nANN SVM RF NB | \n2 | \n99.1 99.4 98.2 97.7 | \n
Taifi [18] | \n2020 | \nMIAS | \nSVM | \n2 | \n94.1 | \n
\n | \n | \n | KNN | \n2 | \n88.8 | \n
Luqman [40] | \n2020 | \nMIAS CBIS-DDSM | \nDeep Lab Mask-RCNN | \n2 | \n95.0 98.0 | \n
Proposed method | \n2020 | \nMIAS | \nANN SVM NB KNN | \n2 | \n100 98.8 97.6 87.3 | \n
Comparison results of the proposed method with existing methods.
Abbreviations: ANN, artificial neural network; SVM, support vector machines; NB, Naive Bayes; RF, random Forest; KNN, k-nearest neighbors; M-RCNN and Dee Lab (two deep learning-based instance segmentation Frameworks); Subset of CBIS-DDSM Curated Breast Imaging of DDSM (Digital Database for Screening Mammography).
We have developed in the present chapter a new CAD system used for mammogram images classification. It consists of three main parts. First, we remove all unnecessary regions or objects from the input image, where we have proposed a mixed approach for pectoral muscle removing which can improve the diagnostic accuracy of the developed CAD system. Then, we have focused in our work on frequency domain features where we have used the discrete cosine transform (DCT). The extracted features are subject to a selection process that choose only the most important features. This step is done using the discriminant power analysis (DPA) algorithm. Finally, some of the most known classifiers in the field are used to make the final decision. The proposed system is evaluated on mammogram images from the MIAS database, where we have shown that a small number of selected features can give good results of the accuracy, sensitivity and specificity. The obtained results prove that the frequency domain features can give high performances especially with the use of the discrimination power analysis, and highlight the importance of DCT transform in recent artificial intelligence applications. The comparison of the obtained results with those obtained using recently proposed techniques shows the superiority of the proposed algorithm against the other methods.
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