On the Transient Behavior of Semiconductor Rectifiers

The time dependent behavior of semiconductor surface barrier and point contact diodes has been calculated for small variations. (It is assumed here that the surface barrier lies on a semiconducting pellet with uniform cross section. If, on the contrary, the contact area is small compared with the semiconducting surface, like the case considered by Borneman, Schwartz, and Stickler [J. Appl. Phys. 26, 1021–1028 (1955)], then the analysis given for a point contact applies.) It is pointed out that these rectifying barriers have an ac admittance of the form $${\mathrm{Y(j\omega )=G}}_0{\text{(1−Γ)+ΓG}}_0{\text{(1+jωτ)}}^{\frac{1}{2}}{\mathrm{+j\omega C}}_b$$ in which G₀ is the slope of the dc characteristic curve, C_b the barrier capacitance, ω and j the angular frequency and √−1, respectively, and τ the recombination time of minority carriers. The dimensionless constant Γ equals the injection ratio γ with surface barriers, but represents γr₀(L+r₀)⁻¹ with point contacts where r₀ is the effective contact radius, and L the diffusion length of minority carriers. The constant conductance $G_0\text{(1−Γ)}$ is related only to electrons with surface barriers (it is assumed that the semiconductor is n‐type and that the rectifying contact emits holes), but with point contacts it is associated with both electrons and holes. The frequency dependent conductance ${\mathrm{\Gamma G}}_0{\text{(1+jωτ)}}^{\frac{1}{2}}$ is due only to holes in either case. Compared with the conductance ${\mathrm{\Gamma G}}_0{\text{(1+jωτ)}}^{\frac{1}{2}}$ the barrier capacitance C_b ordinarily plays a more dominant role in the frequency dependence of point contacts than with surface barriers, because the value of Γ is r₀(L+r₀)⁻¹ times its value with surface barriers, and normally r₀≪L. The barrier voltage response f(t) to an impulse current has been calculated. Although the expression f(t) is complicated, it may be approximated under representative conditions (depending on bias and nature of the contact) by one of the following functions: e^−t, e^t erfct^½, or {[1–2C(t)] cost+[1–2S(t)] sint} with time t in appropriate units. The functions C(t) and S(t) are the Fresnel integrals defined by the equation $$\mathrm{C(t)-jS(t)=}{\displaystyle {\int }_0^t}\frac{e^{\mathrm{-jx}}\mathrm{dx}}{{\text{(2πx)}}^{\frac{1}{2}}}$$ . A special case of large amplitude behavior, the open circuit voltage decay following the interruption of forward current is also treated. It is found that with surface barriers, the open circuit decay time depends on recombination time of minority carriers, their penetration depth beyond the barrier in the semiconductor, and the injection ratio. With point contacts the decay time depends primarily on the product of the injection ratio and contact radius.