Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation

Abstract

An analytical model of the band gap narrowing (BGN) in silicon was derived from a non-self-consistent finite-temperature full random-phase approximation (RPA) formalism. Exchange-correlation self-energy of the free carriers and correlation energy of the carrier-dopant interaction were treated on an equal basis. The dispersive quasi-particle shift (QPS) in RPA quality was numerically calculated for a broad range of densities and temperatures. The dispersion was found to be smooth enough for the relevant energies to justify the rigid shift approximation in accordance with the non-self-consistent scheme. A pronounced temperature effect of the BGN only exists in the intermediate density range. The contribution of the ionic part of the QPS to the total BGN decreases from 1/3 at low densities to about 1/4 at very high densities. Based on the numerical results, Padé approximations in terms of carrier densities, doping, and temperature with an accuracy of 1 meV were constructed using limiting cases. The analytical expression for the ionic part had to be modified for device application to account for depletion zones. The model shows a reasonable agreement with certain photoluminescence data and good agreement with recently revised electrical measurements, in particular for p-type silicon. The change of BGN profiles in a bipolar transistor under increasing carrier injection is demonstrated.

Recombination processes in passivated boron-implanted black silicon emitters

“…The J 0e extraction is based on the intrinsic lifetime parametrization by Richter et al 37 and on the band gap narrowing model from Schenk. 38 In addition, corrections can be performed employing finite diffusion coefficients, 39 but they become critical only for very low lifetime values. In this work, neglecting Table I.…”

“Zero-charge” SiO2/Al2O3 stacks for the simultaneous passivation of n+ and p+ doped silicon surfaces by atomic layer deposition

“…As input for the simulations, the fundamental surface recombination velocities for electrons and holes were S n0 ¼ 6500 cm/s and S p0 ¼ 65 cm/s, respectively. In the simulations, Fermi-Dirac statistics were used, in combination with the band-gap narrowing model of Schenk [43], the Auger model of Dziewior and Schmid [55], and the Klaassen mobility model [56]. The bulk SRH lifetimes were τ p0 ¼τ n0 ¼ 1 ms.…”

“…For high positive Q net ¼4.9 Â 10 12 cm À 2 , the reduction of J 0n þ saturated at J 0n þ ¼ 50 fA/cm 2 , behavior which is observed more often for such high charge doses [11,40]. Simulations using the free-ware program EDNA [41], using Fermi-Dirac statistics, the Auger parameterization from Richter et al [42] and the band-gap narrowing model of Schenk [43], indicate that the Auger limit of the n þ region is J 0n þ , Auger ¼16 fA/cm 2 . This significant difference ΔJ 0 of 34 fA/cm 2 can indicate the presence of other recombination processes in the n þ doped region, potentially due to SRH recombination via inactive phosphorus precipitates [44,45].…”

Doping-Less Tunnel Field Effect Transistor: Design and Investigation

“…Lombardi mobility model and concentration dependent SRH recombination model are used [36]. We have not considered the charge induced band-gap narrowing (BGN) [37] while simulating the doping-less TFET. This is because our simulation tool does not have an appropriate model for the carrier induced BGN.…”