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This repo has the Sentaurus Device implementation of InGaAs Double gate FET, that simulates ballistic electron quantum transport by using simple drift-diffusion code.

Sentaurus Device is an advanced multidimensional device simulator capable of simulating electrical, thermal, and optical characteristics of silicon-based and compound semiconductor devices. Sentaurus Device is a new-generation device simulator for designing and optimizing current and future semiconductor devices.

https://www.synopsys.com/silicon/tcad/device-simulation/sentaurus-device.html

The derivation of both models stars from the simple first moment of the Boltzmann transport equation (BTE):

Taking the uni dimensional case of the x-direction:

And if we consider the kinetic limit, where the diffusive electron or hole mobility tends to infinite and we could integrate the grounded source to the drain results in an energy balance for the kinectic electrons flowing from the contacts to the channel, as shown in the following figure.

Then the ballistic velocity of the thermionic electrons (the electrons flowing over the energy barrier) can be calculated in the following form, where the injection velocity (vinj) is the drain-source voltage divided by the thermal voltage.

Then the electron ballistic mobility model can be expressed as the following:

The following model was implemented as an object that the simulator interpreted inside the class and mobility constructor of its software architecture. The following results were obtainted.

The last figure shows the current transfer characteristics of the studied devices. The legend, states the Qtx is the atomistic quantum transport simulation to compare our models. The legend ud, is the diffusive mobility with a constant value and the ub is the ballistic mobility.

As seen from the previous figure int the case of a lower drain-source voltage VDS=50mV, there is still a mismatch in the on current. The reason behind this problem, is the Quasi-Fermi Energy, becomes a resistor in the drain contact therefore affecting the driving force of the denominator of the ballistic mobility expression and violating the principle of charge conservation.

Due to this shortcoming, an improved model of electron ballistic mobility that accounts for charge conservation was developed. Thus:

assures that the calculated electron density of at the top of the conduction barrier is the same at a low drain bias source as the electron density inside of the channel. Thus the current, j at the x point where the conduction band energy is the maximum will be the same as the current at the drain contact, ensuring charge conservation across the whole device.

See next figure to visualize this:

Finally, the new ballistic electron speed can be calculated in the following form:

For a more detailed derivation please visit:

https://www.sciencedirect.com/science/article/abs/pii/S0038110118306439