ShockleyReadHall

Shockley–Read–Hall recombination, often abbreviated SRH recombination, is a trap-assisted nonradiative recombination mechanism in semiconductors. It occurs when charge carriers recombine via defect states within the band gap, known as traps or deep levels. The process is especially important when mid-gap defects are present and can dominate over radiative or Auger pathways under certain conditions.

In the SRH model, defect states with energy E_t between the conduction band E_c and valence band E_v mediate recombination. Electrons or holes are captured by the trap and then recombine with a carrier of the opposite type. Capture rates depend on the trap density N_t, capture cross sections for electrons and holes (sigma_n and sigma_p), and the carriers’ thermal velocity. The trap energy determines occupation probabilities through parameters n1 and p1, linked to the band edges and temperature.

The recombination rate per unit volume is U = (n p − n_i^2) / [tau_p (n + n1) + tau_n (p + p1)], where n and p are electron and hole concentrations, n_i is the intrinsic concentration, and tau_n and tau_p are capture-limited lifetimes given by tau_n = 1 /(sigma_n v_th N_t) and tau_p = 1 /(sigma_p v_th N_t). Here n1 = N_c exp(-(E_c − E_t)/kT) and p1 = N_v exp(-(E_t − E_v)/kT). Temperature and defect properties thus strongly influence U.

SRH recombination is a primary nonradiative pathway in many semiconductors with mid-gap defects, affecting minority-carrier lifetimes, dark currents, and the efficiency of solar cells and LEDs. The model is foundational in defect characterization and device simulations.

Historically, the theory was developed by William Shockley, Martin Read, and John B. Hall in the 1950s and 1960s, giving it the common name Shockley–Read–Hall recombination.