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.     

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.     

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.     

Phonon-assisted auger recombination in degenerate semiconductors

Phonon-assisted Auger recombination is studied in strongly degenerate semiconductors since normal Auger recombination is negligible in this case. The results are discussed in connection with an electron-hole-plasma. There are some indications that phonon-assisted Auger recombination is an important process in this case.     

Two-photon transitions to exciton states in semiconductors

We consider the gauge invariance of the two-photon transition rate from the crystal ground state to exciton states in semiconductors in the framework of the Wannier model. We show that the non-locality correction in the velocity gauge is essential to preserve the gauge invariance. As a numerical example, we calculate in the length and in the velocity gauge the transition rates for the two-photon direct creation of 2p excitons in a two-band semiconductor.     

Exciton molecules and exciton liquids in semiconductors

Excitons in many-valley semiconductors form molecules consisting of four and more excitons. The degeneracy factor g of the conduction band in germanium is 8, and in silicon g=12. As in acceptors, the hole ground state in excitons is fourfold degenerate. The same is valid for exciton molecules, because they are quantum objects with spherical symmetry. The exciton binding energy in molecules is close to that in exciton-liquid droplets. Experimental evidence is considered for the existence, besides biexcitons, of stable exciton molecules consisting of three and four, and, possibly, 11 and 12 excitons. Molecules containing from five to ten excitons are apparently unstable. Fiz. Tverd. Tela (St. Petersburg) 40, 929–931 (May 1998)     

Perturbation calculation of degenerate hydrogenic exciton levels

Summary In the perturbation calculation of second order for degenerate hydrogenic exciton bound levels the sums over intermediate states are performed analytically with use of the reduced Coulomb Green's function.

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Résumé Dans le calcul perturbative des états liés d'un exciton hydrogéno?de dégenéré la sommation sur les états intermédiaires est effectuée d'une fa?on analytique en utilisant la résolvante coulombienne réduite.

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Riassunto Nei calcoli perturbativi del second'ordine per livelli legati di un eccitone idrogenico degenere si effettua analiticamente la somma rispetto agli stati intermedi usando la funzione di Green ridotta di Coulomb.

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Резюме Используя приведенную кулоновскую функцию Грина, во втором порядке теории возмущений для вырожденных водородных экситонных связанных уровней аналитически вычисляются суммы по промежуточным состояниям.

     

Temperature dependence of the fundamental absorption edge in CuGaSe2

The temperature dependence of the fundamental absorption edge in CuGaSe₂ single crystals was determined in the temperature range from 15 to 300 K. Above about 120 K the gap energy changes linearly with temperature with dE_g/dT = ? (2.1 ± 0.1) eV K^?1. The downshift in dE_g/dT of the I–III–VI₂ compounds compared to their II–VI analogs is discussed accounting for the p-d hybridization of the uppermost valence band.