Analytic solutions of charge and capacitance in symmetric and asymmetric double-gate MOSFETs

A one-dimensional (1-D) analytic solution is derived for an undoped (or lightly doped) double-gate (DG) MOSFET by incorporating only the mobile charge term in Poisson\´s equation. The solution is applied to both symmetric and asymmetric DG MOSFETs to obtain closed forms of band bending and inversion charge as a function of gate voltage and silicon thickness. It is shown that for the symmetric DG device, "volume inversion" only occurs under subthreshold conditions, with a slightly negative impact on performance. Comparisons under the same off-state conditions show that the on-state inversion charge density of an asymmetric DG with one channel is only slightly less than that of a symmetric DG with two channels, if the silicon film is thin. From the analytic solutions, explicit expressions for the various components of the equivalent capacitance circuit are derived for symmetric and asymmetric DG devices. These help gain an insight into the electrostatic coupling between the back gate and the front channel in the asymmetric case. Finally, the gate work function requirements are quantified for symmetric and asymmetric DG CMOS, based on threshold voltage considerations