NonIdeal Effects in MOSFETs Part II Mobility Variations

Non-Ideal Effects in MOSFETs Part II

Mobility Variations v Field on the carriers in the channel is composed of 2 components. v Variation of resulting field along the channel. v Due to scattering (function of resulting field), there is a variation of the mobility in the channel.

Velocity Saturation • The velocity of charge carriers, such as electrons or holes, is proportional to the electric field that drives them, but that is only valid for small fields. • As the field gets stronger, their velocity tends to saturate. That means that above a critical electric field, they tend to stabilize their speed and eventually cannot move faster. • Velocity saturation is specially seen in short-channel MOSFET transistors, because they have higher electric fields.

§ In digital Ics, transistors are typically used with shortest possible gatelength for high-speed operation. § In a very short-channel MOSFET, ID saturates because the carrier velocity is limited to ~ 107 cm/sec.

Velocity Saturation

Velocity saturation influence on I-V characteristics

Velocity saturation influence on transfer characteristics

Velocity saturation-special case

Sub-threshold conduction VGS < VT

Sub-threshold conduction Diffusion currents by electrons in the Fermi-tail, thus will be exponentially dependent on gate voltage

Sub-threshold conduction Weak inversion Small voltage drop across channel ->potential - constant Potential barrier between S&G n+ p junction -> diffusion of carriers with sufficient energy (Fermi-tail ) np-diode potential barrier is decreasing -> current exponential function of VGS- VT

Carriers: graphically At higher energies exponential variation of free carrier density Number of free carrier and position of the Fermi -level are related.

Sub-threshold conduction Diffusion currents by electrons in the Fermi-tail Exponential sub-threshold current

Sub-threshold slope Sub-threshold current

Sub-threshold conduction MOS-bipolar equivalent in weak inversion MOS in weak inversion = Parasitic BJT with “base” controlled via capacitive divider. The S-B-D = npn sandwich with mobile minority carriers in the p-type bulk region. This is equivalent to a BJT, except that the base potential is controlled through a capacitive divider Cox and Cdepl and not directly by carrier injection via the third electrode.

Sub-threshold conduction MOS-bipolar equivalent in weak inversion Consequence for current

Gate leakage current § Increases with gate oxide (Si. O 2) scaling. § High-k gate oxides can be used to lower gate leakage. § Independent of temperature.

Influence of statistical variations in doping atoms in bulk underneath channel When this volume is very small, due to the statistical distribution of the doping atoms, the bulk doping might be different from device to device.

Dopants in a small transistor. 3 D simulation of a 30 nm by 30 nm field-effect transistor domain that contain random discrete dopants in the source, drain, and substrate(bulk). The electrostatic potential is color-mapped from red(1 V) through the rainbow to blue (0 V). Potential fluctuations in the channel associated with the random distribution of dopants results in differing characteristic for each devices. (Top Inset) Schematic diagram of the basic interconnect wiring structure of a field-effect transistor. (Bottom Inset) Circuit diagram symbol for a fieldeffect transistor. CREDIT : A BROWN/UNIVERSITY OF GLASGOW Ref. Roy, Asenov, Where do dopants go? Science magazine.

Conclusion • Different short channel effects contribute to a deviation of the current-voltage characteristic based on the “simple” MOSFET model : DIBL and leakage currents are the main culprits. • Present day devices need more ingenious models. - 2 -D and 3 -D device simulators are commercially available • MEDICI, TAURUS • ATLAS • We need novel device geometries or material systems to deal with these problems.