Thermal Bulk Emission and Generation Statistics and Associated Phenomena in Metal-Insulator-Semiconductor Devices under Non-Steady-State Conditions

The non-steady-state statistics is derived for traps in the depletion layer of semiconductors. These results are applied to traps in the depletion region of metal-oxide-semiconductor systems, to obtain the emission current vs temperature ($I_e-T$) characteristic associated with the emission of electrons (in the case of $n$-type semiconductors) from traps in the upper half of the band gap. It is shown that the $I_e-T$ characteristic is a direct image of the trap distribution in the upper half of the band gap. The generation current vs temperature ($I_g-T$) characteristic associated with the electron-hole generation process that occurs subequent to the emission process is also derived using the statistics. The $I_g-T$ characteristic is shown to contain a single pronounced maximum from which the so-called carrier lifetime may be determined. Furthermore, if the leading edge of the peak is plotted in the form ${log}_e$ $I_g$ vs $T^{-1\mathrm{}}$ the resulting characteristic is a straight line, the slope of which provides the activation energy of the generation process. It is predicted that the donor density of the semiconductor and its activation energy can be obtained by applying the technique at low temperatures. The extension of this technique to reverse-biased $p-n$ junctions, Schottky-barrier diodes, and highly defect semiconductors is discussed.