The exact low-frequency capacitance-voltage characteristics of metal-oxide-semiconductor (MOS) and semiconductor-insulator-semiconductor (SIS) structures

Accurate low-frequency MOS (metal-oxide-semiconductor) and SIS (semiconductor-insulator-semiconductor) C-V curves are found by solving Poisson´s equation in the bulk semiconductor using regions of analytic solution joined by numerical solutions of specified accuracy. The technique uses the full Fermi function for the electron, hole, and impurity bands; thus valid results can now be obtained for partially ionized impurity bands, and situations in which the valence or conduction bands are bent through the Fermi level. The calculation can be carried out for any temperature and allows for band structure in the valence and conduction bands. Surface states are incorporated at the interface and the usual low-frequency capacitance curves are obtained for the MOS device. As expected, the C-V curves in the SIS case are more complex. The n-i-n (n-type semiconductor, insulator, n-type semiconductor) device shows two depletion minima separated by a center maxima whose size is sensitive to surface-state charge. In the p-i-n device, the depletion minima can be seen separately only if the impurity concentrations of the semiconductors differ by a factor of five or more. In that case, a deep narrow minimum due to the lightly doped semiconductor can be seen superimposed on one end of a broad shallow minimum due to the heavily doped semiconductor. This work predicts an interesting high-frequency response for the n-i-n structure, namely a bell-shaped C-V curve. This type of C-V response has not been observed to date in two-terminal passive devices, and may lead to SIS applications as a new type of parametric capacitor.