As MOS devices are shrunk to near and submicrometer dimensions, short channel, narrow width and small geometry effects cause variations in the threshold voltage. It is critical for circuit and device designers to be able to predict these variations. This paper reviews and compares the various modeling techniques developed to determine the threshold voltage as a function of device geometry. It is hoped this review will provide insights for the development of new models for today's small devices.

Threshold voltage models of short, narrow and small geometry MOSFET's: A review

A closed-form analytical expression is developed to predict the threshold voltage of a narrow-width MOSFET. The analytical expression developed is the first to include the effects of a recessed tapered oxide, the depletion charge under the thick recessed field oxide due to gate contact overlap and field doping encroachment at the channel edges. The theory is compared with experimental results and the agreement is dose.

A model of a narrow-width MOSFET including tapered oxide and doping encroachment

A closed form analytical expression for the threshold voltage of a small geometry MOSFET is developed. The threshold voltage expression is derived from a three dimensional geometrical approximation of the bulk charge. The threshold voltage is expressed as a function of gate oxide thickness, channel doping concentraton, junction-depth, backgate bias and channel length and width. The theory is compared with experimental results and the agreement is close.

An analytical expression for the threshold voltage of a small geometry MOSFET

Three-dimensional device-physics-based analytical models are developed for subthreshold conduction in uniformly doped small geometry (i.e., simultaneously short channel and narrow width) bulk MOSFETs, for various isolation schemes. Inverse-narrow width effects, where the threshold voltage decreases with decreasing channel width, are predicted by the model for trench isolated MOSFETs. For LOGOS isolated MOSFETs, conventional narrow width effects, where the threshold voltage increases due to decreasing channel width, are predicted. The narrow width effects are found to be comparable to the short channel effects in the absence of significant applied drain biases. However, for larger drain biases, the short channel effects outweigh the narrow width effects due to the weaker potential perturbation at the device width edges compared to the drain end. Unlike the threshold voltage, the subthreshold swing of the device is found to increase with reduced device dimensions regardless of the isolation scheme since both conventional and inverse narrow width effects result in weaker control of the surface potential by the gate.

Three-dimensional analytical subthreshold models for bulk MOSFETs

Fringing field action in metal-oxide-semiconductor (MOS) devices is discussed theoretically. Line capacitance coefficients on silicon-on-sapphire (SOS) and bulk configurations are determined from a three-dimensional model. Increase of threshold voltage of narrow-width devices due to fringing is described.

Fringing Field Effect in MOS Devices

A simple closed-form analytical expression of the threshold voltage for a narrow-width MOSFET is developed. The narrow-width model gives a threshold voltage expression as a function of gate oxide thickness, channel doping concentration, backgate bias and channel width. The theory is compared with experimental results and the agreement is close.

L.A. Akers

Papers

Threshold voltage of a narrow-width MOSFET