Semiconductor device simulation: the hydrodynamic model - Potentials, IEEE

incorporate hundreds of millions of semiconductor devices (transistors, diodes, optical devices, etc.). To predict the performance of the VLSI circuits, the current-voltage (I-V) characteristics of the semiconductor device are required. Semiconductor device simulation codes provide a way of predicting I-V curves as device parameters are varied, without having to fabricate the device first. (These parameters include semiconductor material, size, doping and geometry.) Thus, many different designs for devices and circuits can be explored efficiently using computer simulations. Promising designs then can be selected for actual fabrication and testing. Many devices including MOSFETs (metal oxide semiconductor field effect transistors) and MESFETs (metal semiconductor field effect transistors) can be modeled using a semiclassical approach. That is, the charge transport of electrons and/or holes is described by the classical Boltzmann equation, or a classical hydrodynamic model with effective masses for electrons and holes input from quantum theory. The charge transport equations are then coupled to Poisson's equation for the electrostatic potential. A Monte-Carlo (particle based) approach to solving the Boltzmann equation is presented by Goodnick, Saraniti, Vasileska and Aboud starting on page 12. Quantum semiconductor devices like resonant tunneling diodes and transistors, HEMTs (high electron mobility transistors), and superlattice devices are increasingly being used in VLSI chips. These devices rely on quantum tunneling of charge carriers through potential barriers for their operation. Advanced microelectronic applications include multiple-state logic and memory devices, and high frequency oscillators and sensors. In addition, the increasing miniaturization enhances “unwanted” quantum effects in standard MESFETs and MOSFETs (for instance, current leakage in the MOSFETs due to quantum tunneling through the oxide insulator between the gate and the channel). Both types of quantum effects must be simulated in order to design robust ultra-small semiconductor devices. A fundamental approach to modeling quantum transport of electrons and holes in semiconductor devices is the Wigner-Boltzmann equation, the quantum generalization of the Boltzmann equation. The Wigner-Boltzmann equation differs from its classical counterpart principally in that particle transport couples to the potential energy in a non-local way; i.e., the values of the electrostatic potential energy integrated over a finite region in space determine the transport at a point in space. Simulating the kinetic equations (the classical Boltzmann equation or the quantum Wigner-Boltzmann equation) is computationally expensive. This is because the distribution function for the electrons or holes is a function of six