Subthreshold behavior of uniformly and nonuniformly doped long-channel MOSFET

The subthreshold turnoff behavior of the long-channel MOSFET (metal-oxide-semiconductor field-effect transistor) is characterized by the gate bias swing
S
needed to reduce the subthreshold current one decade. Here a simple formula for S is derived which includes source-to-substrate reverse bias and ion-implanted doping profile effects. For uniformly doped structures it is shown that curves of given
S
can be constructed on an oxide thickness versus doping level plot, making estimates of
S
for any choice of these parameters particularly simple. A separate family of curves is needed for each value of source-to-substrate bias V
S
. Source-to-substrate reverse bias greatly reduces S in devices with large S values, but cannot reduce S to its theoretical minimum value,
S_{\min} = (kT/q)
ln 10, at reasonable values of V
S
. It is found that the effect of nonuniform doping is determined mainly by the dose and centroid of the depleted portion of the excess surface doping, provided buried channels do not occur and provided the implant is not primarily located in the inversion layer itself. Higher doses and deeper implants increase
S
. The maximum value of
S
for a given implant dose and source-to-substrate reverse bias occurs for that range of implantation which places the implant near the depletion edge. Consequently, the use of implants in small MOSFET's to control threshold punchthrough and parasitic capacitances will cause turnoff degradation.