Topological and chemical disorder in group-IV amorphous semiconductors (original) (raw)
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Multiple-order Raman scattering in crystalline and amorphous silicon
Physical Review B, 1993
Raman-scattering measurements have been performed on c-Si and a-Si over a wide range of frequencies, including Stokes and anti-Stokes sides, and up to fourth order. All the features are accounted for by using the same physical parameters in both phases. In particular, it is shown that multiple-order scattering processes are not negligible, but rather of the same order of magnitude as first-order processes. In amorphous materials, light-scattering excess, spurious background, Boson-peak or hot-luminescence processes, which have been recently put forward, turn out to be mainly caused by high-order Ramanscattering processes. I. INTRODUCTION The simplest way to describe the structure of an amorphous material like a-Si consists of considering that short-range coordination is preserved whereas the extended atomic network is random. ' In other words, this means that the local coordination is tetrahedral (sp hybridization) as in crystalline Si (c-Si); the values of the first-nearest-neighbor distance, coordination number, or binding energy remaining more or less the same in the amorphous and crystalline phases. A1so, the covalent nature of the bonds means that short-range interactions play a preeminent role. Hence it is not surprising that the energy spectra of the density of electronic or vibrational states are similar in amorphous Si (a-Si) and c-Si. For example, the semiconducting properties are preserved in a-Si, and the density of vibrational states (DVS) refiects a smoothed version of the crystalline DVS. As a matter of fact, the greatest differences are induced by the presence of dangling bonds. In practice, however, this can be circumvented by sample hydrogenation of the amorphous material, since hydrogen is a good terminator for insaturated bonds. From the theoretical point of view, it has often been shown that the main features of the density of states can be accounted for by a molecular description (tightbinding or valence-force-field models). The effect of the topological disorder mainly consists of a broadening of these features. This work concerns coupling between the corresponding excitations (electron-phonon interaction). Raman spectra in c-Si and a-Si are compared over a wide spectral range, namely in the anti-Stokes and Stokes parts, and up to the fourth order. It is demonstrated that the secondand higher-order effects are not negligible and that the overall scattering efficiency is similar in both materials. The paper is organized as follows. Following this brief introduction, Raman data are first presented and discussed in Sec. II for c-Si, and the variation of the total scattering efficiency versus the scattering order is addressed. Then in Sec. III, Raman results are given and reviewed for hydrogenated a-Si. Finally, in Sec. IV, the accuracy of the proposed model is assessed and the validity of most of the previous scattering analysis on highly disordered materials is questioned. II. RAMAN SCATTERING IN c-Si Prior to analyzing the Raman effect in a-Si, the impact on c-Si must be reconsidered. Indeed, although often researched, this issue contains some areas, often overlooked, which turn out to be particularly important for achieving a precise interpretation of the Raman effect in disordered materials. A. Experimental results
Influence of structural disorder on Raman scattering in amorphous porous silicon
The Raman scattering spectra of amorphous porous silicon are investigated. It is found that the so-called boson peak in the acoustical part of the Raman spectra is more sensitive to the degree of structural disorder than the optical mode, which is normally used to determine the latter. This can be explained by the fact that the coupling coefficient of light to acoustical phonons has an additional factor in comparison with that of optical phonons: the square of inverse correlation length of vibrational excitations. This means that the Raman scattering intensity on acoustical phonons has an additional dependence on the degree of disorder in comparison with the scattering on optical phonons. S0163-18299813119-3 The intensity of Raman scattering is sensitive to the degree of the structural disorder in solids, so this method can be used to measure relative fractions of the amorphous and the crystalline phases. However, there are problems in accurate estimation of such a fraction using experimental Raman spectra. For example, typically the ratio of the amorphous to the crystalline phase in thin silicon films is determined as a ratio of the integral area of a broad amorphouslike peak to a narrow crystalline peak of the transverse optical TO phonon. 1,2 We would like to point out that such a method is not quite accurate, since annealing of amorphous silicon mi-croparticles and films differently influences the Raman spectra in the optical region. For example, in Ref. 3 it was shown that there were no sufficient changes of Raman spectra during annealing of small silicon particles at 800 °C. The spectra have demonstrated only a single amorphouslike TO peak while the films according to the Raman spectra have become totally crystalline. In addition, the Raman scattering on the optical phonon of microparticles (10 nm has always a very large contribution of the amorphous phase, while the high resolution electron microscopy indicates a crystalline structure. 4–6 In the present paper we show that the low-frequency Raman scattering on acoustical phonons is more sensitive to the degree of structural disorder than that on optical phonons, so the area of the acoustic peak corresponds more precisely to the amorphous phase volume. In order to have more pronounced changes of the Raman scattering spectra in amorphous solids in increasing the degree of order one needs to have a sample of the size compared to the vibration correlation length. In this case the changes of the amorphous phase can be observed in the spectra more clearly than in large bulk samples since a larger volume quantity of the ordered phase will take part in the light scattering. From this point of view it is convenient to use either amorphous microparticles or microporous materials. We have selected the amorphous porous silicon since it yields intensive visible photoluminescence, 7,8 i.e., crystallin-ity is not a necessary condition for observation of the intensive visible photoluminescence under room temperature. In addition, using the micro-Raman spectroscopy it was found 9 that areas of porous silicon, which produce the visible lumi-nescence, besides the crystalline phase always contain the amorphous phase as well. This means that the porous silicon has always an amorphous component. These observations initiate us to look for more accurate determination of the ratio of the volumes of the amorphous to the crystalline phase in microstructures. The porous silicon layers were formed by anodizing of silicon substrates of p-type with 100 orientation and re-sistivity 0.006 cm in hydrofluoric acid solution 42.4% HF:H 2 O:C 3 H 7 OH in proportion 2:1:2 at current density 100 mA cm 2. This leads to formation of a silicon layer with 70% porosity and 2 m thickness. To obtain an amorphous layer, irradiation by 10 B ions with the energy 100 keV was performed. For such ions the amorphization dose of the porous silicon was 510 15 cm 2 ; this is one order of magnitude less than the same parameter for the ordinary silicon. The Raman spectra were recorded in 90° geometry of scattering using a double monochromator DFS-52 with the spectral slit of 2 cm 1 and the light wavelength 488 nm in doubly parallel polarization when both the incident and the scattered light beams were polarized in the scattering plane. In Fig. 1 the Raman spectrum of the amorphous porous silicon is shown. It consists of the amorphouslike TO peak at 480 cm 1 and the broad peak at 150 cm 1. The latter peak is absent in the Raman spectrum of the crystalline silicon because the translation invariance leads to the selection rules, which forbid the light scattering by phonons in this spectral region. Traditionally such a peak in disordered materials is called the boson peak. 10 In glasses its frequency b is typically equal to 1/5–1/7 of the Debye frequency; its nature is connected to the structure correlations on nanometer scale and the frequency—to the respective correlation length l, b v/l (v is the sound velocity. The boson peak reflects the excess in comparison with the sound waves vibration density of states in the low-frequency region 20–100 cm 1 , which arises due to such structure correlations. In glasses the small value of the boson peak frequency in comparison with that of TA and LA modes is due to a comparatively large value of the structural correlation length. In tetragonal amor
Configurational and electronic properties of amorphous semiconductors
Brazilian Journal of Physics, 1994
The configurational properties of a-Si, aGe and a-Si l-,C, have been studied by Monte Carlo simulation methods. A special attention is given to the selection of the interatomic potential. The calculated networks for the a-Si and aGe systems are found to be nearly the same with only a small scaling factor of difference for the bond distances and nearly the same bond angles. In the case of a-Si l-,C, we find that a11 C sites a.re 4-fold coordinated, whereas the coordination of Si varies between 3 and 6. The increase of x in a-Si l-,C, increases the amount of 5-fold Si sites and decreases the amount of 4-fold Si sites indicanting an increase of the disorder. With the geometrical structures generated by the Monte Carlo simulation a quantum mechanical investigation is made of the electronic structure of a-Si. Using the INDO method for a cluster "supermolecule" composed of 35 Si atoms saturated with hydrogen atoms the density of states of a-Si is simulated. Configuration interaction calculation is also performed to disciiss the optical absorption spectrum of a-Si.
Electrons and phonons in amorphous semiconductors
Semiconductor Science and Technology, 2016
The coupling between lattice vibrations and electrons is one of the central concepts of condensed matter physics. The subject has been deeply studied for crystalline materials, but far less so for amorphous and glassy materials, which are among the most important for applications. In this paper, we explore the electron-lattice coupling using current tools of first-principles computer simulation. We choose three materials to illustrate the phenomena: amorphous silicon (a-Si), amorphous selenium (a-Se) and amorphous gallium nitride (a-GaN). In each case, we show that there is a strong correlation between the localization of electron states and the magnitude of thermallyinduced fluctuations in energy eigenvalues obtained from the density-functional theory (i.e. Kohn-Sham eigenvalues). We provide a heuristic theory to explain these observations. The case of a-GaN, a topologically disordered partly ionic insulator, is distinctive compared to the covalent amorphous examples. Next, we explore the consequences of changing the charge state of a system as a proxy for tracking photo-induced structural changes in the materials. Where transport is concerned, we lend insight into the Meyer-Neldel compensation rule and discuss a thermally averaged Kubo-Greenwood formula as a means to estimate electrical conductivity and especially its temperature dependence. We close by showing how the optical gap of an amorphous semiconductor can be computationally engineered with the judicious use of Hellmann-Feynman forces (associated with a few defect states) using molecular dynamics simulations. These forces can be used to close or open an optical gap, and identify a structure with a prescribed gap. We use the approach with plane-wave density functional methods to identify a low-energy amorphous phase of silicon including several coordination defects, yet with a gap near that of good quality a-Si models.
Quantifying the Short-Range Order in Amorphous Silicon by Raman Scattering
Analytical chemistry, 2018
Quantification of the short-range order in amorphous silicon has been formulized using Raman scattering by taking into account established frameworks for studying the spectral line-shape and size dependent Raman peak shift. A theoretical line-shape function has been proposed for representing the observed Raman scattering spectrum from amorphous-Si-based on modified phonon confinement model framework. While analyzing modified phonon confinement model, the term "confinement size" used in the context of nanocrystalline Si was found analogous to the short-range order distance in a-Si thus enabling one to quantify the same using Raman scattering. Additionally, an empirical formula has been proposed using bond polarizability model for estimating the short-range order making one capable to quantify the distance of short-range order by looking at the Raman peak position alone. Both the proposals have been validated using three different data sets reported by three different resear...
Semiquantitative scattering theory of amorphous materials
Physical Review B, 2008
It is argued that topological disorder in amorphous solids can be described by local strains related to local reference crystals and local rotations. An intuitive localization criterion is formulated from this point of view. The Inverse Participation Ratio and the location of mobility edges in band tails is directly related to the character of the disorder potential in amorphous solid, the coordination number, the transition integral and the nodes of wave functions of the corresponding reference crystal. The dependence of the decay rate of band tails on temperature and static disorder are derived. Ab initio simulations on a-Si and experiments on a-Si:H are compared to these predictions.
Europhysics Letters (EPL), 1999
New Raman and incoherent neutron scattering data at various temperatures and molecular dynamic simulations in amorphous silica, are compared to obtain the Raman coupling coefficient C(ω) and, in particular, its low frequency limit. This study indicates that in the ω → 0 limit C(ω) extrapolates to a non vanishing value, giving important indications on the characteristics of the vibrational modes in disordered materials; in particular our results indicate that even in the limit of very long wavelength the local disorder implies non-regular local atomic displacements.
Molecular Structure of Se-Rich Amorphous Films
Amorphous Chalcogenides, 2012
Structure and its transformation are examined for amorphous Se-rich As x Se 1-x (0 ≤ x ≤ 0.2) alloys by employment of diffraction and non-diffraction structural probes. It is shown that the molecular structure of amorphous Se (a-Se) on the scale of short-range order is close to that of crystalline phase, while medium-range order differs from the structure of most inorganic glasses and may be placed between three-dimensional network glasses and polymeric ones. Further experiments show the existence of successive phases in laser-induced glasscrystalline transition with pronounced threshold behavior. Below the energy density threshold, E th , only small changes in the local structure of the system can be detected. Above E th , the changes were attributed to crystallization transformation. The corresponding Raman spectra reveal transformation of the system from amorphous into the crystalline phase under laser irradiation. In the binary As x Se 1-x glass system, a change of structural regime takes place near the composition x ≈ 0.04. The presence of this topological threshold is established by direct and indirect evidence, such as peculiarities in the composition dependence of the basic parameters for electron diffraction and Raman vibration modes. The peculiarities are caused by the transition from a chain-ringlike structure to preferentially a chain-like structure. Experiments described in this section have shown that Raman technique is a particularly sensitive method to determine the presence of microcrystal's in the glassy matrix. Room-temperature polarized Raman scattering spectra of model glass have been collected. Low-frequency peaks were observed in the spectra. A model is proposed for explanation of their appearance. It is shown clearly that the low-frequency Raman spectra allow determining the conditions at the boundaries, sizes as well as concentration of micro-heterogeneities in non-crystalline materials. It was established earlier that for all amorphous (glassy) materials a low-frequency peak, observed in the corresponding spectral region of Raman scattering and called boson peak, is inherent. This peak is absent in crystals of the same chemical composition and is associated with space correlations on the scale of medium-range order R c ≈ 10 Å. On the contrary, less known is that a boson peak can give important information about the presence of microcrystalline inclusions and heterogeneities in the low-frequency Raman spectra of glasses irrespective to their chemical composition.
Structure and physical properties of paracrystalline atomistic models of amorphous silicon
Journal of Applied Physics, 2001
We have examined the structure and physical properties of paracrystalline molecular dynamics models of amorphous silicon. Simulations from these models show qualitative agreement with the results of recent mesoscale fluctuation electron microscopy experiments on amorphous silicon and germanium. Such agreement is not found in simulations from continuous random network models. The paracrystalline models consist of topologically crystalline grains which are strongly strained and a disordered matrix between them. We present extensive structural and topological characterization of the medium range order present in the paracrystalline models and examine their physical properties, such as the vibrational density of states, Raman spectra, and electron density of states. We show by direct simulation that the ratio of the transverse acoustic mode to transverse optical mode intensities I TA /I TO in the vibrational density of states and the Raman spectrum can provide a measure of medium range order. In general, we conclude that the current paracrystalline models are a good qualitative representation of the paracrystalline structures observed in the experiment and thus provide guidelines toward understanding structure and properties of medium-range-ordered structures of amorphous semiconductors as well as other amorphous materials.