Determination of optical constants near the fundamental absorption edge in semiconductors

Abstract

The photoconductivity of semiconductors was considered under the following general conditions: the surface recombination velocity was not equal to zero, the space charge near the surface is taken into account, the value of absorption coefficient was not limited. Solving both the continuity and Poisson equations for an illuminated thick specimen, we obtained a solution which suggests a new combined measurement in order to determine various optical constants. The absorption coefficient and the diffusion length of electrons in CZ grown n-type Si (N _a = 10¹²-10¹³ cm^?3) were measured at room temperature, using the new technique.     

Indirect exciton transitions in the two-photon absorption in semiconductors

The theory of indirect two-photon exciton transitions is developed from third-order time-dependent perturbation theory. The problem is treated by introducing three different band models; a four-band, a two-band and an intermediate (three-band) model. Selection rules and numerical estimates show that the three-band model is the most favourable for this type of process. An application for the case of GaP is performed.     

Emission near the absorption edge in a degenerate GaAs crystal

The stimulated and spontaneous emission functions have been calculated for the band-to-tail and tail-to-tail transitions respectively in n-type photolumineseence, and p-type photoluminescence and electrolu-minescence. The peak in the photon energy as a function of doping for degenerate GaAs at 77 K in the present theory is in good agreement with the experiments of Nathan et al.[1], and of Dapkus et al.[2]. It is also compared to the theory of Adams [3]. It is suggested that the maximum value of the stimulated emission in the n-type photolumineseence is stronger than in p-type photolumineseence for very dense impurities.     

Fine structures of indirect exciton absorption in phosphorus-doped silicon

A new indirect exciton absorption structure has been observed in phosphorus-doped silicon crystals by using a wavelength modulation method. The structure is interpreted in terms of two-electron transitions involving a free exciton and the valley-orbit states of a phosphorus donor, in which the donor is left in the 1s (A₁) singlet state.     

Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors

The two-photon absorption coefficient is calculated from perturbation theory for direct-gap zincblende semiconductors using exact nonparabolic energies and matrix elements. The enhancement due to exciton effects is included. The results are compared to experiment and to other theories including the tunneling or Keldysh theory.     

Analysis of derivative spectrum of indirect exciton absorption in silicon

It is shown that an analysis of the wavelength modulated absorption spectrum enables us to estimate the transition matrix elements in indirect absorption. The transition matrix elements in silicon are determined to be $\text{0.110}\text{h}\text{?}\text{A}\text{?}$ for indirect absorption with the TO phonon, $\text{0.0367}\text{h}\text{?}\text{A}\text{?}$ for the LO phonon and 0.0178 $\text{h}\text{?}\text{A}\text{?}$ for the TA phonon.     

Temperature dependance of the fundamental absorption edge in CdTe

Optical measurements made on CdTe put in light an extrinsic transition previously used to determine the interband edge of this compound. The donor level involved has a depth of 30 meV inside the bandgap at 77°K and of 60meV at 300°K. The value obtained for its temperature coefficient, suggests an association of this level with the L minimum of the conduction band.Also, determined is the true optical bandgap of CdTe between many conflicting results. One obtains: E_g = 1.529 meV with a temperature coefficient of ?3.10^?4eV/°K.     

Modulation of fundamental absorption by free carrier heating in degenerate n-PbTe

An increase of the fundamental interband absorption due to applied electric fields up to 150 V cm^?1 has been found in highly doped n-PbTe at 80 K. The results can be explained by an electron temperature model. An energy relaxation time of 1.8 × 10^?12 sec is obtained from the electron temperature vs field strenght relation.     

Shallow acceptors in ionic semiconductors with a degenerate band

The energy spectrum of an impurity-phonon system in semiconductors with a degenerate valence band ₈ edge is calculated. The matrix Hamiltonian of the problem is represented as a sum of two matrices containing operators of the s and d type respectively. Neglecting the latter matrix, the partition function of the system is represented as a path integral, which is calculated with the help of the variational principle based on the introduction of a trial quadratic Lagrangian. The matrix with operators of the d-type is taken into account as a perturbation. The results are compared with experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–53, January, 1991.     

LO-phonon instability due to indirect interband absorption of a laser field in semiconductors

We investigate here the possibility of excitation and amplification of longitudinal optical (LO) lattice vibrations by electrons due to interband absorption of a laser field in semiconductors. We show that under certain conditions the phonon excitation rate may become greater than the rate of relaxation and the LO-phonon system may reach instability.     

Transverse electroreflectance of GaSe at the fundamental absorption edge

The transverse electroreflectance of GaSe has been measured near the fundamental edge at 4.2 K. The observed structures have been interpreted in terms of the Franz-Keldysh oscillations, the exciton ground state, the first excited state of exciton, and the phonon replica of the exciton ground state.     

Back reflection effect at the fundamental edge of semiconductors in modulated reflectivity measurements

Reflectivity and modulated reflectivity spectra are simulated at the fundamental edge of semiconductors when the back surface of the crystal is taken into account. It is demonstrated that this could give rise to important additional structures, frequently observed but only qualitatively interpreted in most cases. Some expected shapes are presented, arising from direct or indirect absorption with exciton formation. Even if back reflection effects are undesirable in reflectivity experiments, some interesting information could easily be extracted from the spectra, especially for the indirect exciton case.     

Anisotropy in the absorption spectrum of GaTe at the fundamental edge

The wavelength-modulated absorption coefficient of GaTe is measured at the fundamental edge at room temperature. The light is directed perpendicular to the cleavage plane, and its polarization is rotated in the plane itself. The optical constants are seen to vary appreciably for different polarizations, both in intensity and in the energy of the main peak at the absorption edge. A model is proposed to account for the experimental data.     

Magnetic-field-induced nonparabolicity of exciton dispersion in semiconductors with a nondegenerate valence band

The nonparabolicity of exciton dispersion due to the mixing of the ground and excited states of an exciton in an external magnetic field perpendicular to the direction of its motion is considered. A model describing this effect is proposed and the nonparabolicity for an exciton in a CdTe crystal is calculated. The magnetic-field induced exciton nonparabolicity is compared with the effect caused by the nonparabolicity of the electron energy dispersion in the conduction band.     

Direct phonon-assisted transitions near the fundamental absorption edge in CuInSe2

Summary The absorption spectrum near the fundamental absorption edge of an-type CuInSe₂ single crystal grown by the Bridgman method has been studied at 100 and 300 K. An absorption edge corresponding to the direct-band-gap transition is observed at about 1 eV. An additional absorption is observed at lower energies ((0.93÷0.95) eV) and is attributed to direct transitions assisted by long-wave-length optical phonons.

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Riassunto Lo spettro di assorbimento vicino al bordo di assorbimento fondamentale di un cristallo singolo di tipon di CuInSe₂, cresciuto col metodo di Bridgman, è stato studiato a 100 e 300 K. Si osserva un bordo di assorbimento in corrispondenza della transizione del gap di banda diretta a circa 1 eV. Un ulteriore assorbimento è osservato a energie inferiori ((0.93÷0.95) eV) ed è attribuito a transizioni dirette alla presenza di fononi ottici a grande lunghezza d'onda.

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Резюме При 100 К и 300 К исследуется спектр поглощения вблизи основного края поглощения монокристалла CuInSe₂ n-типа, выращенного по методу Ъридгмана, Вблизи 1 эВ обнаружен край поглощения, соответствующий прямому переходу. Дополнительное поглощение наблюдается при меньших энергиях ((0.93÷0.95) эВ) и приписывается прямым переходом, связанным с длинноволновыми оптическими фононами.

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Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Hall mobility of degenerate semiconductors

The dependence ofHall mobility of carriers on impurity content has been theoretically investigated for degenerate semiconductors, taking scattering by lattice vibrations as well as ionized impurities into account. The scattering due to optical modes of lattice vibrations has been neglected, for the sake of simplicity of calculations. This omission is not serious at temperatures, when the impurity scattering is important.     

Thermoreflectance study of direct and indirect excitons near the fundamental edge of GaSe

Thermoreflectance spectra have been obtained on GaSe single crystals between 50 and 300 K and a theoretical model is developed to fit the experimental curves. The main feature of the spectra is due to the disappearance of the back reflection of the sample caused by the small absorption below the direct exciton. The direct excitonic structure is observed at higher energy.