When using drift diffusion model to investigate the charge extraction from a slab of semiconductor, if you do not include a recombination term into your calculations, does this set the charge carrier lifetime to infinity? Or is there another mechanism that limit it and set it to some finite value? I'm particularly interested in how COMSOL handle it in their semiconductor module, but any general information on how this is handled is welcome.
Thank you.
Recombination should not be considered zero otherwise generation will be infinite. In thermal eequilibrium, generation rate and recombination rate becomes equal. If we generate extra charge carriers by some external means, recombination also increases and a new equilrium is set up. Carrier lifetime can not be infinite whether it be majority carrier lifetime or minority carrier lifetime.
Recombination rate can never be zero in a semiconductor; that concept is meaningless. Minority carriers all the time recombine; simultaneously they are generated.
In thermal equilibrium, the recombination rate equals the generation rate; consequently, there is no net recombination or generation.
In non-equilibrium, i.e. when an external force is applied, either excess carriers are generated or the carrier density is lower than the equilibrium density. For example, in a pn junction diode, for forward bias, there will be net recombination, as the minority carrier recombination rate will exceed its generation rate; the reverse is true for reverse bias, and there will be net minority carrier generation. The driving force for minority carrier generation/recombination is the quantity (pn - niE2).
Recombination/generation is a relaxation process and helps the semiconductor to return to equilibrium, if the equilibrium is disturbed.
As long as the external force is present, the semiconductor can simply be not in equilibrium (contrary to comment by Dr. A. Kumar).
In addition to what Prof Kar has said, net generation/recombination rate is ~ (p.n - n_i^2)/t_l where t_l is the carrier lifetime. If you make the lifetime arbitrarily large, the rate becomes very small. For real systems, it is best to find out the right t_l and use that in calculations. If the dimensions of the system are much smaller than a diffusion length, you could assume t_l to be infinitely large and ignore net generation/recombination.
Yes I agree with Geetak. That is how the diode in a ideal situation is analyzed by making the G=R=0. The effect of these assumptions are as follows
if Recombination is made zero this directly reflects the current density profile inside the device. This can be explained using the continuity equation dn/dt =dJn/dx+G-R. In steady state dn/dt=0, with Zero recombination and Generation, it forces the current density to be spatially constant in side the device. This is what happens in side the depletion region of a PN diode where the recombination is negligible. Moreover when you set recombination equal to zero it won't consider the carrier lifetime effect at all.
COMSOL solves the Poisson's, Transport and the Continuity equations where none of the equations are directly related to the carrier life time. Only continuity equation is related to the carrier life time with the recombination term, which is a material parameter given by the user. So COMOSL will not consider any value for the lifetime.
This is a different situation, where carriers will drift instead of diffusing (which depends on the carrier life time), which is governed by the drift length.
- Badges
- Science topic