Question

Describe the term- Minority carrier injection in forward bias.

Answer 1

When a p-n juction is forward biased, minority carriers are injected into the semiconductors on the two sides of the junction. These minority carriers diffuse about an eventually recombine with the majority carriers. The distribution of the minority carriers is described by the diffusion equation. In general, the diffusion equation is,

Here δn is the excess minority electron concentration on the p-side of the junction and δp is the excess minority hole concentration on the n-side of the junction. Dn and Dp are the diffusion constants for electrons and holes and τn and τp are the recombination times. In steady state the minority concentrations do not change and the derivative with respect to time is zero. The diffusion equation can then be rewritten as,

Here Ln² = Dnτn and Lp² = Dpτp are the diffusion lengths for electrons and holes. The general solution of this differential equation is,

If there are metal contacts to the diode at positions -xp and xn (the gray regions in the diagram) then due to the increased recombination there, the minority carrier concentrations at the contacts are the equilibrium concentrations. Thus the excess minority carrier concentrations are zero at those positions: δn(-xp) = 0, δp(xn) = 0. The boundary conditions at the edges of the depletion layers are δn(-Wp) = np0(exp[e(V - Vbi)/kBT] - 1), δp(xn) = pn0(exp[e(V - Vbi)/kBT] - 1).