Under forward-bias conditions, the space-charge recombination current can be calculated from the Shockleyâ€“Readâ€“Hall (SRH) model via a mid-gap recombination center. The recombination rate derived from the SRH model is given by
where Ï„0 = 1/NtÏƒ vÂ is the effective carrier lifetime.
(a) Find the conditions of maximum recombination rate from (1).
(b) If the recombination current in the junction space-charge region can be derived from
where Ur is given by (1), and xn and xp are the depletion layer widths in the n and p regions, respectively, show that the recombination current density can be expressed by
where Wâ€™ is the portion of the depletion region in which the recombination current is dominant, which is valid for qVa > 3kBT .