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Cuevas, "General parameterization of Auger recombination in crystalline silicon," Journal of Applied Physics 91, pp. Hall, "Electron–hole recombination in germanium," Physics Review 87, p. Warta, "Field-effect passivation of the SiO2–Si interface Journal of Applied Physics 86, pp. Schmid, "Auger coefficients for highly doped and highly excited silicon," Applied Physics Letters 31, pp. Altermatt, "Models for numerical device simulations of crystalline silicon solar cells - a review," Journal of Computational Electronics 10 (3) pp.
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5th Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), pp. Daub, "Injection dependence of spontaneous radiative recombination in c-Si: experiment, theoretical analysis, and simulation," Proc. Aberle, "Assessment and parameterisation of Coulomb-enhanced Auger recombination coefficients in lowly injected crystalline silicon," Journal of Applied Physics 82, pp. This separation of quasi-Fermi levels is often referred to as the semiconductor's implied open-circuit voltage. When selecting to plot the separation of quasi-Fermi levels on the x-axis of the figure, the program sweeps the excess carrier concentration, Δ n = Δ p, and plots the results against ( E Fn – E Fp) / kT. An analogous equation is used to determine the hole diffusion length.Īll equations also assume that the semiconductor is in steady state and that the steady state carrier concentrations relate to the equilibrium and excess carrier concentrations by n = n 0 + Δ n and p = p 0 + Δ p. The electron diffusion length is determined from the equation L e = Sqrt( D e⋅ τ), where D e is the diffusivity of electrons. It is assumed that N t << p, n, and that the semiconductor is not degenerate. The Shockley–Read–Hall recombination rate is calculated by the equationĪnd where σ n and σ p are the capture cross sections of electrons and holes, v th e and v th h are the thermal velocities of electrons and holes, N t is the concentration of defect states, and E t is the energy of the defect state. The options for the models are summarised in the table below. Various options are given for determining U rad and U Aug, which all depend on the ionised dopant concentration N D + or N A –, the excess electron Δ n or hole Δ p concentration, and n i eff. The effective lifetime τ eff is calculated in the same way from U tot. Where Δ n m is the excess minority carrier concentration, and where 'a' represents either 'rad', 'Aug' or 'SRH'. The lifetime for each mechanism is then determined by The recombination rate is then calculated for radiative U rad, Auger U Aug, and Shockley–Read–Hall U SRH recombination mechanisms, which sum to give the total recombination rate: The intrinsic Fermi energy E i is defined to be zero. The program first applies the band gap models to determine the effective intrinsic carrier concentration n i eff, the conduction band energy E c, the valence band energy E v, the electron Fermi energy E Fn, and the hole Fermi energy E Fp following the procedure used in the band gap calculator.