Effect of Degenerate Semiconductor Band Structure on Current-Voltage Characteristics of Silicon Tunnel Diodes

The three components of the band-to-band tunnel current of silicon Esaki junctions at low temperatures, the phonon-unassisted current $i_0$, the TA phonon-assisted current $i_1$, and the TO phonon-assisted component $i_2$, have been derived from the experimental current-voltage characteristics by an empirical, but extremely self-consistent, technique. The components are in constant ratio to each other for a given donor species but junctions formed using Sb gave relatively lower $i_0$ currents than did junctions formed with P- or As-doped material. The three current components have very similar bias dependence which, empirically, turns out to be accurately described by $V\exp (-{\beta }^{\prime }V)$, where ${\beta }^{\prime }$ is a constant for a given junction. Part of the exponential factor represents the bias dependence of the tunneling probability, the remainder enters into the "effective density of states" function. The true peak voltage is given by $\frac{1}{{\beta }^{\prime }}$. The experimental current-voltage curves are compared with each of Kane's theories; the first is for undistorted band edges while the second takes account of the band edge tails in very impure semiconductors. Good agreement is obtained using the latter theory, both as to the over-all shape of the curves and the actual values of the peak voltages.