Deep Sub-micron MOSFET Modelling

The theory of MOSFET as a barrier controlled device also brings to light some ultimate limits of a MOS device. Minimum Energy for a switching event It is known that minimum barrier energy required for a switching event in a MOS transistor is given by the formula – The only variable in the equation for minimum energy is temperature. To analyse how the minimum energy required varies with the temperature, a graph of minimum energy against temperature is plotted. Minimum channel length Minimum switching time

Below is an example of a MOSFET with a metal (aluminium) gate. Threshold Voltage on Gate Oxide Thickness An increase in the threshold voltage is seen with increase in oxide thickness. However, the metal gate device seems to have a higher threshold voltage than the polysilicon gate device. The difference is more apparent as the oxide thickness increases. Threshold Voltage on Gate Length Increasing the gate length increases threshold voltage. A metal gate device seems to offer a higher threshold voltage than its polysilicon counterpart. Threshold Voltage on heavy Drain Doping Concentration The choice of material for the gate is in not to the source/drain doping concentrations. In both the devices, the threshold voltage remained constant throughout. However, metal gate device tends to offer a lower threshold voltage. Threshold Voltage dependency on Channel Doping Concentration The channel doping concentration has an effect on the threshold voltage. For both devices, the threshold voltage ...

The earliest technologies of the MOSFET used a metal for the gate (not self-aligned) terminal. The threshold voltage (and consequently the drain to source on-current) is determined by the work function difference between the gate material and channel material (essentially the substrate material). When metal was used as gate material, the large transistor sizes led to large gate voltages (3V to 5V), the threshold voltage (resulting from the work function difference between a metal gate and silicon channel) could still be overcome by the applied gate voltage (|V G - V TH | > 0). As transistor sizes were scaled down, the applied signal voltages were lowered to avoid gate oxide breakdown, hot-electron reduction, power consumption reduction etc. A transistor with a high threshold voltage would become non-operational under these new conditions. Thus, poly-crystalline silicon (polysilicon) became the modern gate material because it is the same chemical composition as the silicon channe...

The output resistance is an important performance metric in a MOSFET. The output resistance is not an inherent property of a MOSFET. Rather, it is a characteristic that is used to justify the effect of channel-length modulation on a MOSFET’s small-signal behaviour. When the MOSFET is operating in the saturation region, the channel is ‘pinched-off’ in the drain end. The drain current is not affected by the drain-to-source voltage in the saturation region. The MOSFET acts like a current source controlled by the overdrive voltage V OV (V OV = V GS – V TH ). This assumption is based on the idea that increasing the drain-to-source voltage does not alter the channel once it has become pinched-off. In practicality, the drain-to-source voltage has a significant effect on the channel - the pinch-off point is moved toward the source, which results in more drain-to-source current as drain-to-source voltage is increased. This necessitates an additional circuit element to account for this ...

Trans-conductance is often regarded as an indicator of performance. It is defined as the ratio of change in output current to the change in the gate voltage at a constant drain voltage. Trans-conductance is given by – Transconductance dependency on gate oxide thickness The trans-conductance dependency on the gate oxide thickness is given by the following equation. For the different values of gate oxide thickness for the MOS reference device which was grown earlier, the trans-conductance was calculated to test how it is affected by different gate oxide thickness.  It is seen that the trans-conductance decreases with increase in gate oxide thickness. The trend seems to follow a linear decrease, the trans-conductance decreases as the gate oxide thickness increases. Transconductance dependency on gate length The dependency o transconductance on the gate length is characterized by the following equation. The equation suggests a inverse relationship. It is seen that the...

The  threshold voltage , commonly abbreviated as V TH , of a MOS FET is the minimum gate-to-source voltage V GS (th)  that is needed to create a conducting path between the source and drain terminals. It is an important scaling factor to maintain power efficiency, and an important device performance metric. Threshold Voltage dependency on gate oxide thickness The dependency is governed by the following equation. The gate oxide was varied from a thickness of 20Å to 313.76Å by varying the diffusion time and temperature. As can be seen, the threshold voltage ‘V TN ’ has an almost linear increase with increase in gate oxide thickness. An increase in oxide thickness also results in an increase in the threshold voltage. This is because as the thickness increases, more voltage is required to create the inversion layer in the substrate, just below the gate oxide. Threshold voltage dependency on gate length The threshold voltage of the MOSFET depends on the gate le...

For a MOSFET, the output characteristics is a set of curves - Output drain current against the drain voltage for various values of gate voltage. Output characteristics The output characteristics obtained are as below. The output characteristics – I D vs V DS was simulated on the reference device for various values of V GS at 0.7V, 1V, 2V and 3V. The output characteristics are obtained by increasing V DS keeping the gate-to-source voltage V GS . It is seen that the maximum current (current in saturation region) increases as the V GS is increased. For a particular  V GS  curve, i nitially, as V DS increases, the current increases rapidly in an exponential manner until the voltage reaches pinch-off value. Thereafter, there is hardly any change in the output current i.e. the current saturates. This is the maximum amount of current from the device. Output characteristics based on square-law theory The following equations are used to compute the output ...