Amorphous Tetrahedral Semiconductors Research Articles

Extended-range order in tetrahedral amorphous semiconductors: The case of amorphous silicon

This paper reports the presence of extended-range ordering in the atomic pair-correlation function of amorphous silicon ($a$-Si) using ultra-large atomistic models obtained from Monte Carlo and molecular-dynamics simulations. The extended-range order manifests itself in the form of radial oscillations, on the length scale of 20-40 angstrom, which are examined by directly analyzing the radial distribution of atoms in distant coordination shells and comparing the same with those from a class of partially-ordered networks of Si atoms and disordered configurations of crystalline silicon from an information-theoretic point of view. The study suggests that the extended-range radial oscillations principally originate from the propagation of radial ordering from the first few atomic shells to a distance of up to 40 angstrom. The effect of these oscillations on the first sharp diffraction peak (FSDP) in the structure factor is addressed by obtaining a semi-analytical expression for the static structure factor of $a$-Si, and calculating an estimate of the error of the intensity of the FSDP associated with the truncation of radial information from distant shells. The results indicate that the extended-range oscillations do not have any noticeable effects on the position and intensity of the FSDP, which are primarily determined by the medium-range atomic correlations of up to a length of 20 angstrom in amorphous silicon.

Direct evidence for the behaviour of single and bipolarons in chalcogenide glasses

We report direct evidence for the characteristic behavior of single and bipolarons in chalcogenide glasses by using broad band impedance spectroscopy. The measured ac conductivity, σ(f, T) of Te based glasses exhibit distinct behavior from those reported in amorphous tetrahedral semiconductors depending on the temperature and frequency. At low temperatures, the measured conductivity is exclusively due to the bipolarons between two charged defect centers. On the other hand, at high temperatures we find in addition to bipolaronic contribution, the single polaron hopping between a charged and neutral defect centers. The behavior of both types of charge carrier (single and bipolaron) shows the distinct relaxation characteristics within the measured frequency window. Remarkably, we observe existence of neutral defect centers with large concentration in tellurium-based chalcogenide glass under dark (normal) conditions revealed by the electron spin resonance (ESR) spectroscopy, which is an essential component for the single polaron hopping process. The estimated neutral defect centers from the dc conductivity measurements are in agreement with those derived from the ESR results. Further, we found that the effective correlation energy (Ueff) becomes less negative in glasses which exhibit single polaron hopping than the glasses found to exhibit typical bipolaronic conduction. The present work unequivocally demonstrates the characteristic behavior of single and bipolarons in chalcogenide glasses and its interdependence on thermal history of the glass samples.

Disorder by design: A data-driven approach to amorphous semiconductors without total-energy functionals

X-ray diffraction, Amorphous silicon, Multi-objective optimization, Monte Carlo methods. This paper addresses a difficult inverse problem that involves the reconstruction of a three-dimensional model of tetrahedral amorphous semiconductors via inversion of diffraction data. By posing the material-structure determination as a multiobjective optimization program, it has been shown that the problem can be solved accurately using a few structural constraints, but no total-energy functionals/forces, which describe the local chemistry of amorphous networks. The approach yields highly realistic models of amorphous silicon, with no or only a few coordination defects (≤1%), a narrow bond-angle distribution of width 9–11.5°, and an electronic gap of 0.8–1.4 eV. These data-driven information-based models have been found to produce electronic and vibrational properties of a-Si that match accurately with experimental data and rival that of the Wooten-Winer-Weaire models. The study confirms the effectiveness of a multiobjective optimization approach to the structural determination of complex materials, and resolves a long-standing dispute concerning the uniqueness of a model of tetrahedral amorphous semiconductors obtained via inversion of diffraction data.

Reverse Monte Carlo modeling of amorphous silicon

An implementation of the Reverse Monte Carlo algorithm is presented for the study of amorphous tetrahedral semiconductors. By taking into account a number of constraints that describe the tetrahedral bonding geometry along with the radial distribution function, we construct a model of amorphous silicon using the reverse monte carlo technique. Starting from a completely random configuration, we generate a model of amorphous silicon containing 500 atoms closely reproducing the experimental static structure factor and bond angle distribution and in improved agreement with electronic properties. Comparison is made to existing Reverse Monte Carlo models, and the importance of suitable constraints beside experimental data is stressed.

Realistic models of binary glasses from models of tetrahedral amorphous semiconductors

We present an approach for modeling binary glasses beginning with models of tetrahedral amorphous semiconductors and report models of glassy ${\mathrm{GeSe}}_{2},{\mathrm{SiSe}}_{2},{\mathrm{SiO}}_{2},$ and ${\mathrm{GeSe}}_{4}.$ The topology of our models are analyzed through partial pair correlations and static structure factors. Structural properties, including the first sharp diffraction peak, electronic and vibrational properties are all in agreement with experiment. Our approach is simpler and faster than traditional melt-quench simulations and emphasizes the importance of correct topology of starting structure for successful modeling.

Modelling the structure factors and pair distribution functions of amorphous germanium, silicon and carbon

We present the results of calculations of the static structure factor S( k) and the pair distribution function g( r) of the tetrahedral amorphous semiconductors germanium, silicon and carbon using the structural diffusion model (SDM). The results obtained with the SDM for S( k) and g( r) are of comparable quality with those obtained by the unconstrained Reverse Monte Carlo simulations and existing ab initio molecular dynamics simulations for these systems. We have found that g( r) exhibits a small peak, or shoulder, a weak remnant of the prominent third neighbour peak present in the crystalline phase of these systems. This feature has been experimentally found to be present in recently reported high energy X-ray experiments of amorphous silicon (Phys. Rev. B 60 (1999) 13520), as well as in the previous X-ray diffraction of as-evaporated amorphous germanium (Phys. Rev. B 50 (1994) 539).

Universal distribution of optically excited carriers in tetrahedral amorphous semiconductors

The decay of optically excited electrons and holes in tetrahedrally coordinated amorphous semiconductors is a universal property of these amorphous solids [Phys. Rev. Lett. 84 (2000) 4180]. The experimental measurements employ a seldom-used electron spin resonance (ESR) detection technique that surpasses the sensitivity of previous measurements by several orders of magnitude. This technique employs second harmonic detection (SH-ESR) of the ESR. Measurements have been performed over a wide range of excitation intensities (nW/cm 2 to W/cm 2) on hydrogenated amorphous silicon (a-Si:H) and hydrogenated amorphous germanium (a-Ge:H). Using the SH-ESR technique, the kinetics can be studied down to saturated carrier densities as low as approximately 10 14 cm −3 . In addition to the long-time decay curves, both the saturated densities of carriers after long-time irradiation and the most probable recombination lifetimes for the optically excited carriers in a-Si:H agree well with models for the universal diffusion and recombination of carriers at low temperatures. Similar results are obtained for samples of a-Ge:H with germanium dangling-bond densities ≲10 17 cm −3 . A comparison of the ESR lineshapes for the electrons and holes trapped in the conduction and valence band tails, respectively, with electrons and holes trapped in a divacancy in crystalline silicon shows that the asymmetries and localizations of the wavefunctions are similar in both cases.

Optical properties of fully amorphous silicon

We have determined the complex dielectric function, $\ensuremath{\varepsilon}(E)={\ensuremath{\varepsilon}}_{1}(E)+i{\ensuremath{\varepsilon}}_{2}(E),$ for self-implanted amorphous silicon (a-Si) by spectroscopic ellipsometry (SE) in the 1.5--5.2-eV photon-energy range at room temperature. The measured SE spectra show a single broad peak in ${\ensuremath{\varepsilon}}_{2}(\ensuremath{\sim}26.6)$ at $E\ensuremath{\sim}3.45\mathrm{eV},$ which is typically observed in amorphous tetrahedral semiconductors. The SE $\ensuremath{\varepsilon}(E)$ data, together with the literature data which exhibit the largest peak in ${\ensuremath{\varepsilon}}_{2}(\ensuremath{\sim}30)$ at $E\ensuremath{\sim}3.7\mathrm{eV}$ and have been widely used as a reference of ``dense'' a-Si, are analyzed by means of the Bruggeman effective-medium approximation. The results clearly indicate that the self-implanted a-Si sample is in the fully amorphous state, while the literature data contain microcrystalline component $(\ensuremath{\mu}c\ensuremath{-}\mathrm{Si})$ in its spectra. The volume fraction of $\ensuremath{\mu}c\ensuremath{-}\mathrm{Si}$ is estimated to be about 53%. The optical spectra of $\ensuremath{\mu}c\ensuremath{-}\mathrm{Si}$ are found to be quite different from those of single-crystalline silicon, especially in the vicinity of the sharp critical-point features. The SE $\ensuremath{\varepsilon}(E)$ data of the self-implanted a-Si are successfully parametrized using Jellison-Modine's dispersion expression.

Fluctuation Microscopy Studies of Medium-range Order Structures in Amorphous Tetrahedral Semiconductors

AbstractWe applied fluctuation microscopy technique to study medium-range order in tetrahedral semiconductor materials, such as amorphous silicon, amorphous diamond-like carbon films. It is shown that this technique is very sensitive to local structure changes in the medium range order and promises solutions to open questions that cannot be answered by current techniques. For asdeposited amorphous germanium and silicon, we previously identified a fine-grain para-crystallite structure [1, 2], which will be relaxed into a lower-energy continuous random network structure after thermal annealing. With the same fluctuation microscopy technique, we however found that thermal annealing introduces medium-range order in amorphous diamond-like carbon films. Future studies will be focused on modeling and systematic exploration of annealing effects.

Fluctuation Microscopy: A New Class of Microscopy Techniques for Probing Medium Range Order in Amorphous Materials

Abstract Amorphous materials are devoid of periodic long range order, but at the nearest-neighbor level they possess a high degree of short-range order. In amorphous tetrahedral semiconductors, such as Si and Ge, this short-range order arises because each atom attempts to satisfy four bonds arranged as a regular tetrahedron. It is the rotations about each bond, from the second-nearest-neighbor outwards, that result in the loss of long-range order. It is apparent from modeling of amorphous materials, that there is considerable flexibility as to how rapidly the medium-range-order diminishes. The continuous random network (CRN) is a hypothetical tetrahedral extended structure wherein the atoms possess full four-connected coordination, but have minimal medium-range order. However, real amorphous materials infrequently exhibit true CRN-like topologies. Traditionally, diffraction has been used to study short- and medium-range order in amorphous materials. Assuming kinematical scattering, and that every atom has a similar environment, a radial distribution function (RDF) can be extracted which is sensitive only to the averaged atom pair-correlations out to ∼1 nm.

Paracrystallites found in evaporated amorphous tetrahedral semiconductors

Variable coherence microscopy shows that as-deposited amorphous germanium and silicon contain medium-range order. The ordering can be explained by a fine-grained paracrystallite material in which intergranular stress has been relaxed by deformation. On annealing, the paracrystallite structure transforms towards the lower-energy continuous random network (CRN). We present data on a variety of vacuum-evaporated samples, and on molecular dynamics simulations of candidate structures.

Optical dispersion relations in amorphous semiconductors InSb and GeSe2

The pseudodielectric-function spectra, ε(E)=ε1(E)+iε2(E), of amorphous (a-) InSb and GeSe2 semiconductors in the 1.5–5.5 eV photon-energy range at room temperature were measured by spectroscopic ellipsometry. The samples studied were prepared by radio frequency planar magnetron sputtering (a-InSb), and by the melt-quenching technique (a-GeSe2). The ε2(E) spectra for these semiconductors showed a single broad peak (a-InSb) and a double-peaked structure (a-GeSe2), respectively. The single broad peak found in a-InSb is typically observed in amorphous tetrahedral semiconductors. The double-peaked structure in the ε2(E) spectrum of a-GeSe2 closely resembles the a-Se and a-Te spectra and is described by a simple model consisting of two valence bands and a lower conduction band. The experimental ε2(E) spectra are analyzed using Jellison-Modine model [Appl. Phys. Lett. 69, 371 (1996)], and excellent agreement is achieved between the calculation and experiment over the entire range of photon energies. Dielectric-related optical constants, such as the complex refractive index, absorption coefficient, and normal-incidence reflectivity, of a-GeSe2 have also been presented.

Elastic softness of amorphous tetrahedrally bonded GaSb and(Ge2)0.27(GaSb)0.73semiconductors

We have measured the longitudinal and transverse acoustic wave velocities in bulk pressure-amorphized $a$-GaSb and $a\ensuremath{-}({\mathrm{Ge}}_{2}{)}_{0.27}(\mathrm{GaSb}{)}_{0.73}$ semiconductors and in their polycrystalline analogs. Although the densities of crystalline and amorphous states were practically equal, a significant softening of the bulk (29--35 %) and shear (41--46 %) elastic moduli has been found for amorphous phases. The ultrasonic data for bulk moduli are in good agreement with the previous direct volumetric measurements. Results of the present study combined with critical review of previous works allowed us to find specific features of elastic behavior of amorphous tetrahedral semiconductors (including group IV elements and group III-V compounds), and compare them to other classes of disordered solids.

Topology of Amorphous Tetrahedral Semiconductors on Intermediate Length Scales

Using the recently-proposed ``activation-relaxation technique'' for optimizing complex structures, we develop a structural model appropriate to a-GaAs which is almost free of odd-membered rings, i.e., wrong bonds, and possesses an almost perfect coordination of four. The model is found to be superior to structures obtained from much more computer-intensive tight-binding or quantum molecular-dynamics simulations. For the elemental system a-Si, where wrong bonds do not exist, the cost in elastic energy for removing odd-membered rings is such that the traditional continuous-random network is appropriate. Our study thus provides, for the first time, direct information on the nature of intermediate-range topology in amorphous tetrahedral semiconductors.

Onset of a nonoptimal hopping regime for ac conductivity in amorphous gallium antimonide

A possible explanation has been found for the typical discrepancy between the parameters of localized states as determined from the static and dynamic hopping conductivities in tetrahedral amorphous semiconductors. It is shown for the example of a-GaSb that the Mott hopping length R opt, the correlation length for nonoptimal hops L T , and the ac hopping length R ω are related as R opt <L T <R ω , as a result of which the Mott law holds for the dc conductivity and the Zvyagin regime of nonoptimal hops holds for the ac conductivity σ(ω). The observed value of σ(ω) is two orders of magnitude lower than the conductivity calculated by the Austin-Mott formula for the parameters of localized states found from dc measurements. A model that quantitatively describes the static and dynamic conductivity of a-GaSb with the aid of a single set of parameters characterizing the Miller-Abrahams resistor network is proposed.

Structural and Electronic Properties of a-Gaas: A Tight-Binding–Molecular-Dynamics–Art Simulation

ABSTRACTBy combining tight-binding (TB) molecular dynamics (MD) with the recently-proposed activation-relaxation technique (ART), we have constructed structural models of a-GaAs and a-Si of an unprecedented level of quality: the models are almost perfectly four-fold coordinated and, in the case of a-GaAs, exhibit a remarkably low density of homopolar bonds. In particular, the models are superior to structures obtained using melt-and-quench TB-MD or quantum MD. We find that a-Si is best described by a Polk-type model, while a-GaAs resembles closely the mechanical model proposed by Connell and Temkin, which is free of wrong bonds. In this paper, the structural, electronic, and dynamical properties of a-GaAs based on this approach will be reviewed, and compared to experiment and other structural models. Our study provides much-needed information on the intermediate-range topology of amorphous tetrahedral semiconductors; in particular, we will see that the differences between the Polk and Connell-Temkin models, while real, are difficult to extract from experiment, thus emphasising the need for realistic computer models.

Nonequilibrium Phase Transformations in Diamond and Zincblende Semiconductors under High Pressure

AbstractThe problem of nonequilibrium phase transformations is reviewed for compression of diamond, zincblende, and amorphous tetrahedral semiconductors and for decompression of their high‐pressure phases. The importance of lattice or network dynamical properties for the nature of nonequilibrium transformations is shown. Using low‐temperature quenching of high‐pressure phases, we obtained new Crystalline phases for Ge and Ge‐Gash solid solutions, which have X‐ray patterns very similar to corresponding data for rhombohedral R8 silicon. We established that a number of anomalous features, like elastic softness, pressure‐induced geometrical distortion, and strong bulk modulus softening (δB/δP &gt; 0), distinguish the pressure behavior of the amorphous tetrahedral network in a‐GaSb from its crystalline counterpart.

Boson peak in the Raman spectra of amorphous gallium arsenide: Generalization to amorphous tetrahedral semiconductors.

We report on the observation of the boson peak in amorphous (a) GaAs formed by high-energy ion bombardment of the crystalline lattice. The experimental data are analyzed according to the theory of inelastic light scattering from fractons. The correlation length \ensuremath{\xi} and the spectral dimension d\ifmmode \tilde{}\else \~{}\fi{} of the fractal are determined. In comparison to a-Si:H the crossover frequency from the phonon to the fracton scattering regime, ${\mathrm{\ensuremath{\omega}}}_{\mathrm{co}1}$, is lower and scales according to mass law, confirming the vibrational character of the boson peak. The origin of the fractals in tetrahedral amorphous semiconductors is discussed in terms of strained nanometer blobs of host atoms whose overcoordination is relaxed through bond percolation. The intensity increase of the boson peak relative to the amorphous component during the process of amorphization of GaAs, and the increase in the carbon content in a-Si:H, shows a composite structure that consists of a strained fractal region in the relaxed network. Some experimentally observed anomalies such as low values of the sound velocity in tetrahedral amorphous semiconductors, and transformation of the vibrational spectrum by quenching in ${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$ are qualitatively explained by the fractal model. On the basis of maximum positions of the boson peak and the first sharp diffraction peak observed in the structure factor of inelastic x-ray or neutron scattering of amorphous semiconductors, the correlation lengths of medium-range order (MRO) are determined and compared for different tetrahedral and vitreous amorphous semiconductors. The observed three to four times shorter value of MRO in tetrahedral relative to vitreous amorphous semiconductors is used to explain a number of differences between their properties.

Magnetic Susceptibility of Tetrahedrally Bonded Amorphous Semiconductors

A special theoretical formulation on the magnetic susceptibility of tetrahedral amorphous semiconductors is proposed. This formulation is based upon a Wannier representation involving two terms: a diamagnetic term and a paramagnetic contribution. In addition, electron-spin resonance referred to amorphous silicon is considered.

High pressure solid state amorphization of Si, Ge and solid solutions Si:GaAs, Ge:GaSb

Abstract The bulk amorphous tetrahedral semiconductors (Si, Ge. Si0.89(GaAs)0.11, Ge1−x(GaSb)x (0.12<X<I)) were obtained using solid state amorphization. The disordering process occurs at the decompression of high pressure phases Si II, Gell at low temperatures and of solid solutions Sill: GaAs, GeII: GaSb at room temperature. The structure and stability of the obtained phases were investigated