This paper presents simple but accurate closed form equations for Band Gap Narrowing (BGN) for n and p type, Si, Ge, GaAs and GexSi1−x alloys and strained layers The equations are derived by identifying the four components of BGN: exchange energy shift of the majority band edge, correlation energy shift of the minority band edge and impurity interaction shifts of the two band edges In the simple parabolic band approximation, the BGN is determined by the effective masses of the carriers and the relative permittivity of the semiconductor For real semiconductors, known corrections due to anisotropy of the bands, due to multi-valleys in a band and due to interactions between sub-bands are used The values of BGN for n Si, n Ge and n and p GaAs calculated using this simple formulation agree closely with the theoretical values calculated by other authors using advanced but complex many body methods and the Random Phase Approximation for screening effects For p Si and p Ge ours appear to be the first calculations taking all interactions into account Experimental values of BGN for all semiconductors except for p Ge for which no data could be found, are also in very good agreement with our theory The Fermi level for n and p Si and p GaAs is determined using the published luminescence data In heavily doped p type semiconductors, the values are found to be considerably smaller than those calculated using the known values of the effective density of states The values of apparent BGN for n and p Si and p GaAs calculated using experimentally determined Fermi levels are in remarkably good agreement with the experimental values derived from device measurements All results are presented in a form which lends itself to numerical computer simulation studies

A simple expression for band gap narrowing (BGN) in heavily doped Si, Ge, GaAs and GexSi1−x strained layers

Application of zinc-blende-related chalcogenide absorbers such as CdTe and Cu(In,Ga)Se2 (CIGSe) has enabled remarkable advancement in laboratory- and commercial-scale thin-film photovoltaic performance; however concerns remain regarding the toxicity (CdTe) and scarcity (CIGSe/CdTe) of the constituent elements. Recently, kesterite-based Cu2ZnSn(S,Se)4 (CZTSSe) materials have emerged as attractive non-toxic and earth-abundant absorber candidates. Despite the similarities between CZTSSe and CIGSe/CdTe, the record power conversion efficiency of CZTSSe solar cells (12.6%) remains significantly lower than that of CIGSe (22.6%) and CdTe (22.1%) devices, with the performance gap primarily being attributed to cationic disordering and associated band tailing. To capture the promise of kesterite-like materials as prospective “drop-in” earth-abundant replacements for closely-related CIGSe, current research has focused on several key directions to control disorder, including: (i) examination of the interaction between processing conditions and atomic site disorder, (ii) isoelectronic cation substitution to introduce ionic size mismatch, and (iii) structural diversification beyond the zinc-blende-type coordination environment. In this review, recent efforts targeting accurate identification and engineering of anti-site disorder in kesterite-based CZTSSe are considered. Lessons learned from CZTSSe are applied to other complex chalcogenide semiconductors, in an effort to develop promising pathways to avoid anti-site disordering and associated band tailing in future high-performance earth-abundant photovoltaic technologies.

Defect Engineering in Multinary Earth-Abundant Chalcogenide Photovoltaic Materials

An outline of infrared localized vibrational mode absorption spectroscopy relevant to silicon impurities in GaAs is presented. Absorption lines from SiGa donors, SiAs acceptors, SiGa-SiAs pairs, SiGa-VGa (Ga vacancy) pairs and a complex Si-X (involving SiAs and VGa) have been identified as well as lines from SiGa-CuGa, SiGa-H, SiAs H and SiGa-BAs pairs. These observations are related to the electrical properties of n-type Bridgman, liquid-encapsulated Czochralski and molecular beam epitaxial (MBE) (001) GaAs, and to p-type liquid phase epitaxial and MBE (111)A layers. The discussion relates to dynamic site switching, effects due to counter-doping with shallow acceptors, the solubility of silicon, and DX behaviour observed in homogeneously doped material and proposed for delta -doped MBE (001) layers. The major problem is to understand the processes that limit the maximum carrier concentration that can be achieved in n-type crystals.

http://iopscience.iop.org/article/10.1088/0268-1242/9/10/001/pdf

The lattice locations of silicon impurities in GaAs: effects due to stoichiometry, the Fermi energy, the solubility limit and DX behaviour

Band gap narrowing (BGN) is one of the crucial heavy-doping effects to be considered for bipolar devices. Using a physically-based approach (E.F. Schubert, Doping in III-V Semiconductors, Cambridge University Press, 1993), we suggest a new BGN model which considers the semiconductor material and the dopant species for arbitrary finite temperatures. This unified treatment is especially useful for accurate device simulation. A comparison with experimental data and other existing models is presented and study of BGN in III-V group semiconductors is performed. Finally, as a particular example we investigated with our two-dimensional device simulator MINIMOS-NT (Simlinger et al., Simulation of submicron double-heterojunction high electron mobility transistors with MINIMOS-NT, IEEE Trans. Electron. Devices, Vol. 44, 1997, pp. 700‐707), the electrical behavior of a graded composition Si:SiGe HBT using a hydrodynamic transport model. © 1999 Elsevier Science S.A. All rights reserved.

/pdf/study-of-dopant-dependent-band-gap-narrowing-in-compound-1cwc0ngnac.pdf

Study of dopant-dependent band gap narrowing in compound semiconductor devices

Degenerately doped (>1019 cm−3) n-type InxGa1−xAs (x∼0.67) and InPyAs1−y (y∼0.65) possess a number of intriguing electrical and optical properties relevant to electro-optic devices and thermophotovoltaic devices in particular. Due to the low electron effective mass of these materials (m*<0.2) and the demonstrated ability to incorporate n-type dopants into the high 1019 cm−3 range, both the Moss–Burstein band gap shift and plasma reflection characteristics are particularly dramatic. For InGaAs films with a nominal undoped band gap of 0.6 eV and N=5×1019 cm−3, the fundamental absorption edge increased to 1.27 eV. InPAs films exhibit a shorter plasma wavelength (λp∼5 μm) in comparison to InGaAs films (λp∼6 μm) with similar doping concentrations. The behavior of the plasma wavelength and the fundamental absorption edge are investigated in terms of conduction band nonparabolicity and Γ-L valley separation using detailed band structure measurements and calculations.

Moss-burstein and plasma reflection characteristics of heavily doped n-type inxga1-xas and inpyas1-y

The optical properties of extremely heavily doped n‐GaAs are examined. Metastable electron concentrations up to 3.2×1019 cm−3 were produced by pulsed‐laser annealing of Si‐implanted GaAs. These very heavily doped layers give plasmon Raman shifts up to 1700 cm−1 and photoluminescence bandwidths of greater than 410 meV. The low‐energy edge of the photoluminescence indicates a band‐edge narrowing proportional to ∼n1/3 and equal to ∼200 meV at the highest electron concentration.

Huade Yao

Papers

Plasmons, photoluminescence, and band‐gap narrowing in very heavily doped n‐GaAs