I EEE

O N E LECTRON D EVICES, V OL. E D-26, NO. 4 , A PRIL 1979

453

A nalytical Models of Threshold Voltage and

B reakdown Voltage of Short-Channel

MOSFET‘s Derived from

Two-Dimensional

Ana l ysis

TORU TOYABE, MEMBER,

I EEE, A ND

Abstnzct-Analytical models of threshold voltage breakdown and voltage of short-channel MOSFET’s are derived from the combination of analytical consideration and two-dimensional numerical analysis. An approximateanalytical solution forthesurfacepotential is used to derive the threshold voltage, in contrast with the charge conservation approac:hwhich has been usuallytaken.It is shown that the surface potentid depends exponentially on the distance from the drain, and thiscauses thethreshold voltage to decreaseexponentiallywithdecreasing: channel length. The analytical dependence of threshold voltage on device dimensions, doping, and operating conditions is verified by accurate two-dimensional calculations, and the accuracy of the model is attained by slight modification.

The breakdown voltage of a short-channel n-MOSFET is lowered by a posi1:ive feedback effect of excess substrate current.

From

twodimensional analysis of thismechanism,a simpleexpression of the breakdown voltage is derived.

Using: this model, the scaling down ofMOSFET‘sis discussed. The simple models of thresholdandbreakdownvoltage of short-channel

MOSFET’s arehelpfulbothforcircuit-orientedanalysisandprocess diagnosis where statistical use of the model is often needed.

I . I NTRODUCTION

EMAND for larger scale integration of MOS circuits has urged miniaturization of MOSFET’s with the support of the progress of the lithographic technique. When the channel length of MOSFET’s is of the order of 1 pm, the threshold voltage decreases with the decrease in channel length [ 11, and

D

Manuscript received August 11, 1978;revised October 14, 1978.

The authors are with the Central Research Laboratory, Hitachi,