An accurate approximation of the generalized einstein relation for degenerate semiconductors

Nilsson, N.G.

doi:10.1002/pssa.2210190159

Cited by 60 publications

(23 citation statements)

References 6 publications

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“…The intravalley diffusion coefficient D, and thus A, can be theoretically estimated from the electron mobil-ity with Einstein's equation 20 k TJ d\nN e \~l D =^-\d{E ¥ /kT)\ ' (6) where ix e is the electron mobility which, for simplicity, is assumed to be isotropic within each valley. With a mobility of 450 cm 2 V -1 sec -1 , taken from Fistul, 21 one finds D = 12.3 cm 2 sec -1 ; this gives by use of Eq.…”

Section: Max-planck-institutfur Festkorperforschung D-7000 Stuttgartmentioning

confidence: 99%

Resonant Raman Scattering by Spin-Density Fluctuations inn-type Germanium

Mestres

Cardona

1985

Phys. Rev. Lett.

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We report the observation of low-frequency Raman scattering by spin-density fluctuations in heavily doped «-type Ge. This scattering resonates at the E\ gaps (-2.2 eV). The resonant enhancement and the absolute values of the scattering efficiencies are estimated and compared with experiment.PACS numbers: 78.30. Gt, 71.25.Tn, 72.80.Cw Light scattering by electronic excitations of free carriers in heavily doped semiconductors has recently received a great deal of attention. 1 " 3 Observations have been reported for bulk samples 4 " 7 and also for nearly two-dimensional structures such as heterojunctions and superlattices. 2,3 In the case of one-component parabolic carrier systems with laser frequencies co L away from electronic resonances, the excitations which contribute to light scattering have longitudinal character. They are thus screened self-consistently by the free-carrier gas. This leads to a quenching of the lowfrequency scattering due to single-particle excitations. Instead, a peak is seen at the plasma frequency of the free carriers, corresponding to scattering by collective excitations (plasmons).Scattering by unscreened excitations can be seen for multicomponent carrier systems. 5 " 7 Of particular importance is the case of the scattering by spin-density fluctuations which occurs for (o L near a resonant gap split by spin-orbit interaction. 8 The density fluctuations of the spin-up and the spin-down components of the electron gas exactly cancel. Since no net charge fluctuation is induced, these excitations are not screened."Single-particle" scattering by spin-density fluctuations (sdf) has been observed for several III-V semiconductors (InSb, 9 GaAs, 4,10 InP 11 ). It appears only for crossed incident and scattered polarizations and is thus easy to separate from the collective chargedensity fluctuations which appear for parallel polarizations. In much of the recent literature on twodimensional systems use is made of this property to separate single-particle from collective excitations. 2,3 This Letter contains the first report of scattering by sdf in a group-IV semiconductor, namely tt-type Ge. This report is not simply an observation of scattering by sdf in a different material. The electrons in «-Ge occupy Fermi ellipsoids centered at the L points, while for InSb, GaSb, and InP the Fermi surfaces are spheres centered at T. Hence in the latter, scattering by sdf resonates at T gaps (E 0 and EQ+ALO) while in w-Ge the resonance occurs at the E\ and E\ +Ai gaps. The properties of the corresponding excitations are different. Also, in «-Ge the mean free path is smaller than in the III-V compounds with minima at T, so much so that k conservation does not seem to play an important role in determining the shape of the scattering by sdf. The observed spectra are fitted with a theoretical expression similar to that recently proposed by Ipatova, Subashiev, and Voitenko for scattering by intervalley density fluctuations in the collision-limited regime. 12,13 The scattering efficiency, measured with respect to ...

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Section: Max-planck-institutfur Festkorperforschung D-7000 Stuttgartmentioning

confidence: 99%

Resonant Raman Scattering by Spin-Density Fluctuations inn-type Germanium

Mestres

Cardona

1985

Phys. Rev. Lett.

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“…Here x = E / kT , x F = E F (Δ N )/ kT , E F (Δ N ) is the carrier density dependent Fermi level, obtained by Nilsson approximation 12 (in which density of states N dos = 2 × 10 19 cm –3 at RT was used), f F = (exp ( x – x F ) – 1) –1 is the Fermi distribution function, and τ i are the appropriate carrier relaxation times.…”

Section: Resultsmentioning

confidence: 99%

Optical monitoring of nonequilibrium carrier diffusion in single crystalline CVD and HPHT diamonds under high optical excitation

Ščajev

Malinauskas

Lubys

et al. 2011

Physica Rapid Research Ltrs

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We report on a novel approach for the contactless, all‐optical study of ambipolar carrier diffusion in single‐crystalline diamond layers. Using interband two‐photon and single photon absorption (at 351 nm and 213 nm), we created a spatially‐modulated free‐carrier light‐induced transient grating and monitored the in‐plane carrier diffusion in a wide range of injected carrier densities (1015cm–3 to 1018cm–3) and temperatures (80 K to 800 K). A drastic decrease of the ambipolar diffusion coefficient from ∼50 cm2/s at low injections to 6–10 cm2/s at high ones was observed at room temperature and even stronger at lower temperatures. The modelling based on bandgap renormalization and electron–hole scattering provided a fit to the injection‐dependent diffusivity. The determined low‐injection ambipolar mobility data for CVD layer were found in a good agreement with electrical time‐of‐flight measurements. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…The new forms are noticeably different from the existing approximations of HðuÞ [11][12][13][14][15][16][17]. For example, [11] used a form…”

Section: Functional Forms To Be Approximatedmentioning

confidence: 94%

“…This change of the growth manner makes its precise and fast computation difficult [5,Section 4]. Refer to the pioneer work of [11] and its followers [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Precise and fast computation of inverse Fermi–Dirac integral of order 1/2 by minimax rational function approximation

Fukushima

2015

Applied Mathematics and Computation

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An accurate approximation of the generalized einstein relation for degenerate semiconductors

Abstract: The diffusivity-mobility ratio of electrons o r holes in semiconductors is usually expressed by the Einstein relation D/JJ = liT/e. Following Spenke (l), Lindholm and Ayers (2) have discussed the diffusivity-mobility ratio for degenerate semiconduc -

Cited by 60 publications

References 6 publications

Resonant Raman Scattering by Spin-Density Fluctuations inn-type Germanium

Resonant Raman Scattering by Spin-Density Fluctuations inn-type Germanium

Optical monitoring of nonequilibrium carrier diffusion in single crystalline CVD and HPHT diamonds under high optical excitation

Precise and fast computation of inverse Fermi–Dirac integral of order 1/2 by minimax rational function approximation

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