  We theoretically analyse band-to-band tunneling (BTBT) in highly-mismatched,
narrow-gap dilute nitride and bismide alloys, and quantify the impact of the N-
or Bi-induced perturbation of the band structure -- due to band-anticrossing
(BAC) with localised impurity states -- on the electric field-dependent BTBT
generation rate. For this class of semiconductors the assumptions underpinning
the widely-employed Kane model of direct BTBT break down, due to the strong
band edge nonparabolicity resulting from BAC interactions. Via numerical
calculations based on the Wentzel-Kramers-Brillouin approximation we
demonstrate that BAC leads, at fixed band gap, to reduced (increased) BTBT
current at low (high) applied electric fields compared to that in a
conventional InAs$_{1-x}$Sb$_{x}$ alloy. Our analysis reveals that BTBT in
InN$_{x}$As$_{1-x}$ and InAs$_{1-x}$Bi$_{x}$ is governed by a field-dependent
competition between the impact of N (Bi) incorporation on (i) the dispersion of
the complex band linking the valence and conduction bands, which dominates at
low field strengths, and (ii) the conduction (valence) band edge density of
states, which dominates at high field strengths. The implications of our
results for applications in avalanche photodiodes and tunneling field-effect
transistors are discussed.
