Optical absorption in semiconductors with high impurity concentrations in the presence of an electric field

Lukes, Timothy J.; Somaratna, K.T.S.

doi:10.1088/0022-3719/3/10/006

Cited by 20 publications

(17 citation statements)

References 14 publications

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“…The second derivative line shape of the (E 0 Ј ,E 1 ) structure is surprising since the only mechanism that has been shown to give rise to a d 2 ⑀ b /dE 2 line shape is an electroreflectance effect in heavily doped semiconductors, 11 which is clearly not relevant here. Instead, we interpret this result as a consequence of the near degeneracy of the E 0 Ј and E 1 critical points of Si as follows.…”

Section: Discussionmentioning

confidence: 87%

Evidence of near-surface localization of excited electronic states in crystalline Si

Mantese¹

1997

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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Surface- and interface-related spectra, obtained either directly by techniques such as reflectance-difference (-anisotropy) spectroscopy or indirectly by subtracting pseudodielectric function spectra obtained ellipsometrically on surfaces with different chemical termination, exhibit features related to energy derivatives of the bulk dielectric function. We argue that these spectra provide direct evidence that the excitations involved are localized both in space and time. These data unequivocally indicate that critical point energies obtained from above-band-gap ellipsometric or reflectrometric optical spectra are not necessarily equal to bulk values, and that surface chemical and structural termination is at least one contributing factor. Present surface-optical calculations do not include these effects, which may explain, in part, remaining discrepancies between theory and experiment.

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Section: Discussionmentioning

confidence: 87%

Evidence of near-surface localization of excited electronic states in crystalline Si

Mantese¹

1997

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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“…(23,26). Those results were also compared with other theoretical results, obtained at − = 0, in the small time approximation [21,29,30] and in the full ground-state case and deep-tail approximation [21], which were found to be constant, being not correct, as discussed also in Eq. (26).…”

Section: Introductionmentioning

confidence: 76%

“…Moreover, as noted in Eqs. (B.5, B.6) of the Appendix B, when the small time approximation (STA) is used: Δr ≃ 0 [17,21,22,29,30], W (ν , N) ≃ η . Therefore, Eq.…”

Section: Feynman Path-integral Methodsmentioning

confidence: 99%

“…In the present paper, the degenerate d-Si system is considered, noting that all the optical, electrical, and thermoelectric properties given in the degenerate a-Si system can also be investigated by a same treatment. So, in the degenerate d-Si system, a good knowledge of: (i) energy-band structure parameters such as: the reduced band gap [7][8][9][10][11][12], N [11,12] and effective donor ionization energy [13], (ii) exponential conduction-band tails [14][15][16][17][18][19][20][21][22][23][24][25] and Fermi energy [26][27][28], and finally (iii) optical [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], electrical , and thermoelectric [58,61,68,…”

Section: Introductionmentioning

confidence: 99%

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Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures

Cong¹

2018

AJMP

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In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of , a ≥ 1 being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of / for total electron energy 0, vanished at the conduction-band edge: 0, and for 0 exhibited their exponential tails, going to zero as → 0 and ∞, and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of , p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.

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“…It has been shown that the broadening caused by impurities assumes a Gaussian form [58]. However, different broadening mechanisms give rise to different lineshapes.…”

Section: Description Of the Model And The Fitting Proceduresmentioning

confidence: 99%

Modeling the Optical Constants of Ternary Alloys Using Modified Oscillator Model: Application to AlxGa1?xN

Djurišić

2001

phys. stat. sol. (a)

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The optical constants of hexagonal Al x Ga 1--x N alloys for the perpendicular polarization (E ? c) have been modeled in the energy range up to 10 eV for compositions 0x 1. The model employed for describing the dielectric function is the modified oscillator model. The main difference between the employed model and the conventional oscillator model is the use of an adjustable broadening function instead of the Lorentzian one. One additional adjustable parameter per oscillator determines the type of broadening. The adjustable broadening enables us to model transitions with inhomogeneous broadening (i.e. broadening which is not purely Lorentzian) with a single oscillator, while in the conventional oscillator model superposition of several oscillators would be required. We employ a total of five oscillators, giving 21 parameters for each composition, i.e. 84 parameters for the entire composition range 0x 1. This is significantly less than the number of parameters used in modeling the optical constants of Al x Ga 1--x As using harmonic oscillators, where 144 parameters were employed (F. L. Terry, Jr., J. Appl. Phys. 70, 409 (1991)).

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Optical absorption in semiconductors with high impurity concentrations in the presence of an electric field

Cited by 20 publications

References 14 publications

Evidence of near-surface localization of excited electronic states in crystalline Si

Evidence of near-surface localization of excited electronic states in crystalline Si

Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures

Modeling the Optical Constants of Ternary Alloys Using Modified Oscillator Model: Application to AlxGa1?xN

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