Absorption In Amorphous Semiconductors Research Articles

A Study of a-Si:H Absorption Edge Using Dunstan’s Model

The optical absorption data of Hydrogenated Amorphous Silicon was analyzed using a Dunstan model of optical absorption in amorphous semiconductors. This model introduces disorder into the band-band absorption through a linear exponential distribution of local energy gaps, and it accounts for both the Urbach and Tauc regions of the optical absorption edge.Compared to other models of similar bases, such as the O’Leary and Guerra models, it is simpler to understand mathematically and has a physical meaning. The optical absorption data of Jackson et al and Maurer et al were successfully interpreted using Dunstan’s model. Useful physical parameters are extracted especially the band to the band energy gap , which is the energy gap in the absence of disorder, that can be interpreted as the mobility gap of the material.

Effects of disorder on two-photon absorption in amorphous semiconductors.

Structural disorder inherent to amorphous materials affords them unique, tailorable properties desirable for diverse applications, but our ability to exploit these phenomena is limited by a lack of understanding of complex structure-property relationships. Here we focus on nonlinear optical absorption and derive a relationship between disorder and the two-photon absorption (2PA) coefficient. We employ an open-aperture Z-scan to measure the 2PA spectra of arsenic (III) sulfide (As2S3) chalcogenide glass films processed with two solvents that impart different levels of structural disorder. We find that the effect of solvent choice on 2PA depends on the energy of the exciting photons and explain this as a consequence of bonding disorder and electron state localization. Our results demonstrate how optical nonlinearities in As2S3 can be enhanced through informed processing and present a fundamental relationship between disorder and 2PA for a generalized amorphous solid.

Distribution of electron density of states in allowed bands and interband absorption in amorphous semiconductors

Different types of electronic transitions and the corresponding spectral characteristics of the absorption coefficient of amorphous semiconductors, where the energy of absorbed photons exceeds the mobility band gap, have been investigated. Partial spectral characteristics of the absorption coefficient and, correspondingly, the distributions of the electron density of the states involved in these optical transitions are obtained for the case where the electron densities of states in the allowed bands and the tails of these bands change with energy according to the power and exponential laws, respectively. The conditions for the occurrence of a peak in the spectral characteristic of the interband absorption coefficient are determined.

Properties of A-(Si,Ge) Materials and Devices grown using Chemical Annealing

ABSTRACTChemical annealing is a powerful technique for controlling H bonding and optical absorption in amorphous semiconductors. We have shown previously that the use of careful chemical annealing by Argon can lower the bandgap of a-Si:H while maintaining electronic properties in both films and devices. In this work, we describe new work on chemical annealing of A-(Si,Ge):H films and devices. The technique consists in growing very thin layers (1-3 nm) of A-(Si,Ge) from mixtures of hydrogen, Silane and Germane, and then subjecting this thin layer to ion bombardment by Ar. The cycle is repeated many times to achieve the desired thickness of the intrinsic layer. The resulting film and device were measured for their composition using energy dispersive spectroscopy (EDS) analysis. We discovered that the composition itself, namely the Ge:Si ratio in the film, could be varied by changing the ion bombardment conditions. Lower energy bombardment led to a higher Ge:Si ratio for the same germane/Silane ratio in the gas phase. By controlling ion bombardment during the Ar annealing cycle, we were able to reduce the H content of the film and achieve good electronic properties. It will be shown that by appropriate control over ion energies, one can obtain films and devices which are of good quality and low bandgap as well.

On the light absorption in amorphous semiconductors

Recent measurements of optical absorption in doped amorphous semiconductors (a-Si : H and a-Ge : H) have revealed that long-range potential fluctuations play a decisive role in the absorption mechanism. The theory of such effects was initially developed for crystalline semiconductors, and it is usually not applied in the appropriate form for the interpretation of experimental data in amorphous materials. We use this theory in the analysis of optical-absorption data for amorphous semiconductors, and show its quantitative agreement with experimental results.

Phenomenological scaling of optical absorption in amorphous semiconductors

The concept of a universal absorption edge spectrum, L(E), is proposed for amorphous semiconductors. It follows from the renormalization group treatment and perturbative calculations that the Urbach regime, L(E) ∝ exp[ E E u ] , is continuously connected to the Tauc regime, L( E) ∝ ( E − E o) n T , with E u and E o being closely correlated, while the gap, E o, should be determined with the Tauc exponent, n T ≅ 3. The plausibility o the theoretical prediction is argued in light of experimental results on hydrogenated amorphous silicon alloys.

Optical absorption in amorphous semiconductors.

We use the joint density-of-states function to study the optical-absorption spectrum of amorphous semiconductors. To determine the overall joint density of states, we average a local joint density of states over spatially correlated Gaussian distributions of conduction-band and valence-band potential fluctuations. Our results span the transition from below to above the energy gap and both analytical and numerical results are obtained. Spatial correlations are found to play a dramatic role in influencing the shape of the optical-absorption spectrum. We apply this formalism to the case of hydrogenated amorphous silicon and several other amorphous semiconductors of interest, and find that our results are consistent with those of experiment.

Optical absorption spectra and energy band gap in praseodymium borophosphate glasses

There has been some emphasis recently on the optical properties of glassy and amorphous semiconductors doped with small amounts of rare earth ions [1–8]. These glasses are potential materials for lasing action. This arises from the fact that the electrons responsible for the spectral and magnetic properties of rare earth ions are 4f electrons, which are very effectively shielded from interaction with external forces by the overlaying 5S and 5P shells. Therefore their energies and the energies of the f–f transitions are not likely to be significantly affected by external fields. Some features of the band structure of glasses can be understood by an analysis of the optical absorption edge. The electronic states of the glasses interact with the incoming radiation and give rise to optical absorption. Doping of V2O5–P2O5 glasses by different rare earth oxides does not show any significant change in optical ‘‘band gap’’ Eopt (it varies from 2.20 eV to 2.37 eV only) [7]. This slight difference in calculated Eopt values for different dopants is a consequence of small differences in the observed position and slope of the absorption edge. A survey of the literature indicates that rare earth oxide glasses have not been studied for their optical band gap and related properties [9–11]. Ahmed et al. [4] studied the optical energy gap of praseodymium phosphate glass. They analysed their data on the basis of modern theoretical models of amorphous solids. There are no other reports on rare earth oxide glasses. Thus it was of some interest to study the nature of the optical energy gap of rare earth doped glasses and to see the effect of composition on the position of the absorption edge and the value of the so-called optical energy gap. The present communication reports such studies on Pr-doped B2O3– P2O5–BaO glasses. Borophosphate glasses of final composition B2O3–P2O5–BaO in the ratio of 40, 45 and 15 mol % were prepared from analytical reagent grades of H3BO3, NH4H2PO4 and BaCo3 in 10 g batches. The praseodymium oxide added to the glass was Pr6O11 (99.99%). The chemicals were obtained from E. Merck (India) Ltd, Glaxo India Ltd and Aldrich Chemical Company, USA, respectively. Batches containing 0.1, 0.3, and 0.5 mol % of Pr in the base glass materials were mixed in an agate pestle mortar for 30 min, and were thermally treated in an alumina crucible up to 1000 8C in steps of 100 8C starting from 300 8C. A hold time of 6 h was given at each temperature step. Homogeneity of the melt was ensured by stirring the melt with an alumina rod from time to time. The melt was quenched by pouring into a rectangular-shaped depression in a copper plate. Glasses contained no crystalline phases as revealed by an X-ray diffractogram of the specimen. The glass samples were polished using cerium oxide power. The absorption spectra were recorded using Perkin Elmer Lambda-4B UV/VIS Spectrophotometer in the wavelength range 200–900 nm. Four sharp absorption peaks at 445.5, 470.5, 482.8 and 591 nm were observed in the visible region. Fig. 1 shows the optical absorption spectra for several compositions of Pr-doped borophosphate glasses. On the basis of a comparison of the present spectra with the work already reported [1–3], the absorption peaks observed at 442.0, 469.6, 481.8 and 587.8 nm may be assigned as arising due to the transitions H4? P2, H4? P1, H4? P0 and H4? D2, respectively. This assignment of peaks similar to the ones existing in the literature for different materials containing Pr ions, is justified if we remember that f–f transitions are only weakly affected by the environment of the praseodymium ion [2, 12, 13]. This also explains the observed sharpness of the peaks. In crystalline materials, the Eopt value is directly obtained from the absorption. However, for amorphous materials in general and oxide glasses in particular, the optical absorption at the fundamental edge may be used to estimate Eopt values using a theory due to Davis and Mott [14]. The absorption in amorphous semiconductors obeys a quadratic relation for the inter-band non-direct transitions:

Models of optical absorption in amorphous semiconductors at the absorption edge — A review and re-evaluation

Davis-Mott and Tauc models of optical absorption at the absorption edge in the high absorption coefficient region (α≥104cm−1) are carefully reviewed with regard to their theoretical foundations, assumptions, mathematical derivations, and results. The full implications of these models are exploited, and it is found that the Davis-Mott model for negligible matrix elements between localised states could account for the cubic power law behaviour ofα with photon energyħω of some amorphous semiconductors such as a-Si. A fractional power law to find the optical band gapEopt, of the form [αħω ∝ (ħω−Eopt)r; 2≤r≤3] based on Davis-Mott model is proposed in which the indexr can be a function of disorder. The Tauc model has further been extended to the case of negligible matrix elements between localised states, in which the same square power law forα vs.ħω with the same meaning of the optical gap as in the original Tauc model has resulted. A consideration of the case of unequal matrix elements for those transitions between localised states and those between extended states is also included. The meaning ofEopt has been re-assessed and it is emphasized that it is an extrapolation of delocalised states to the zero of the density of states rather than a threshold energy for the onset of some kind of optical transitions.

Optical Absorption in Amorphous Semiconductors

This paper is dedicated to recent experimental studies of the optical absorption edge in non-hydrogenated and hydrogenated amorphous tetracoordinated semiconductors. Attention is first paid to the respective contributions of the density of states near the band edges and of the matrix elements, and the derivation of a so-called amorphous "optical gap" is discussed. The sub-band gap absorption, which can now be determined accurately down to quite low levels by sensitive techniques like the photothermal deflection spectroscopy, is then analyzed in terms of disorder and defects. Problems related to hydrogen incorporation, doping, light-induced effects and alloying are considered in the Si case. The specificity of disorder and defects in amorphous III-V compounds is also pointed out.

Determination of Carrier‐Carrier and Carrier‐Phonon Relaxation Times from Ultrafast Photoinduced Absorption in Amorphous Semiconductors

Determination of Carrier‐Carrier and Carrier‐Phonon Relaxation Times from Ultrafast Photoinduced Absorption in Amorphous Semiconductors

Theoretical studies of optical absorption in amorphous semiconductors

The tight-binding model of a disordered two-band semiconductor due to Abe and Toyozawa (1981) is studied. Using three basically different approaches the imaginary part of the dielectric constant is calculated. First, for a short-ranged disorder potential, a mode-coupling theory is formulated which allows one to go beyond the convoluted density-of-states approach. Second, the optical spectra for a Bethe lattice, both with and without disorder, are calculated. This allows the identification of matrix-element effects in terms of the coupling to nearest, next-nearest sites, etc. The mode-coupling theory is then tested against the numerical Bethe-lattice results. Both methods yield a maximum of the matrix elements for transitions just below the gap of the ordered system. However, the absorption tail is essentially given by the convoluted density of states. Third, a long-ranged spatial correlation of site energies due to charged centres is treated by numerically solving for the eigenvalues and eigenvectors of a one-dimensional system. The absorption tail turns out to be exponential. This tail, in contrast to the case of short-ranged disorder potential, is dominated by the matrix elements.

Theoretical Studies of Optical Absorption in Amorphous Semiconductors

Theoretical Studies of Optical Absorption in Amorphous Semiconductors

Optical absorption in amorphous semiconductors

By combining our recent results on the electronic structure for disordered systems, and the constancy of the matrix elements, we show that the Urbach tail arises from states localized by fluctuations on single sites and not from Halperin-Lax tail states.

A new theory of optical absorption in amorphous semiconductors

We propose a new approximation scheme for the dielectric constant of disordered semiconductors. We consider a two band model with short ranged static diagonal disorder and include the electron-phonon interaction. We calculate the dipole-dipole correlation function which determines the electronic susceptibility. The zeroth order approximation to this function yields the susceptibility in terms of the convoluted density of states. Going beyond this approximation, we treat the self-energy of the dipole-dipole correlation function. By decoupling the configurational average and approximately calculating the infinite continued fraction for the self-energy we arrive at an expression for the susceptibility. It can be written as the susceptibility of the ordered system with its frequency argument shifted by a complex frequency dependent relaxation function.

Transient induced absorption in amorphous semiconductors from picoseconds to milliseconds

The Physics and application of transient induced absorption spectroscopy in amorphous materials associated with photoexcited carriers is discussed. We show that in a-Si:H, both picoseconds carriers trapping in gap states and the consecutive miliseconds bimolecular recombination, show the characteristic properties of the dispersive transport. We conclude that in high quality materials, exponential band tails exist from 0.01 eV to at least 0.4 eV from the band edges.

Optical absorption in semiconductors within the framework of the configurational-coordinate model

Abstract A calculation of optical absorption in amorphous semiconductors in a wide spectral region has been made on the basis of a ‘molecular’ approach. The theoretical spectral dependence of the absorption coefficient is in a good agreement with experiment. An expression giving the relationship between the slope of the Urbach tail and the parameters describing the behaviour of the optical absorption coefficient at higher photon energies, has been obtained.

Transient photoconductivity and photo-induced optical absorption in amorphous semiconductors

Abstract Amorphous semiconductors and insulators display the phenomenon of dispersive transport: the average mobility of the carriers decreases with time after pulsed excitation. A simple model explains how multiple trapping (MT) in a continuous distribution of localized states gives rise to dispersion. This model is then used to show what can be learned about the material from a complete study of its dispersive transport when MT is known to be the origin of the dispersion. Transient photo-induced optical absorption (PA) provides a direct test of the presence of the MT mechanism. Transient photocurrent (PC) then provides the spectrum of the localized states when examined in the time regime before recombination begins. Using this density of states, many of the parameters that characterize transport and recombination, both monomolecular (MR) and bimolecular (BR), can be determined. The assumption that thermal excitation from localized states to higher-energy transport states limits both thermalization and r...

Picosecond Relaxation of Optically Induced Absorption in Amorphous Semiconductors

Picosecond relaxation of optically induced absorption in $a$-Si, $a$-Si:H, and ${\mathrm{As}}_{2}{\mathrm{S}}_{3\ensuremath{-}x}{\mathrm{Se}}_{x}$ ($0.25l~xl~0.75$) was studied with a passively mode-locked cw dye laser. In silicon, the results can be described in terms of trapping by defects. The fast recovery of absorption in chalcogenides indicates that recombination of highly localized excitons is the dominant mechanism in the decay of carriers excited at the Urbach edge.

On the theory of exciton absorption in amorphous semiconductors

AbstractAn investigation is made of the exciton effects, including the effect of the deformation of the internal state due to “collisions” with the random barriers in the case when ϱ ∼ L ‐ De, on the absorption coefficients of amorphous solids characterized by a Gaussian random potential. The factor exp [η2(1  αnl) β2] in the density matrix due to the random potential, appearing in this case, is shown to be responsible for an approximately Gaussian shape of the absorption edge.