Since Stratton published his famous paper four decades ago, various transport models have been proposed which account for the average carrier energy or temperature in one way or another. The need for such transport models arose because the traditionally used drift-diffusion model cannot capture nonlocal effects which gained increasing importance in modern miniaturized semiconductor devices. In the derivation of these models from Boltzmann's transport equation, several assumptions have to be made in order to obtain a tractable equation set. Although these assumptions may differ significantly, the resulting final models show various similarities, which has frequently led to confusion. We give a detailed review on this subject, highlighting the differences and similarities between the models, and we shed some light on the critical issues associated with higher order transport models.

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A review of hydrodynamic and energy-transport models for semiconductor device simulation

An improved energy transport model for device simulation is derived from the zeroth and second moments of the Boltzmann transport equation (BTE) and from the presumed functional form of the even part of the carrier distribution in momentum space. Energy-band nonparabolicity and non-Maxwellian distribution effects are included to first order. The model is amenable to an efficient self-consistent discretization taking advantage of the similarity between current and energy flow equations. Numerical results for ballistic diodes and MOSFETs are presented. Typical spurious velocity overshoot spikes, obtained in conventional hydrodynamic (HD) simulations of ballistic diodes, are virtually eliminated. >

An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects

High electric fields, that are characteristic of sub‐micron devices, produce highly energetic electrons, lack of equilibrium between electrons, optical phonons, and acoustic phonons, and high rates of heat generation. A simple coupled thermal and electrical model is developed for sub‐micron silicon semiconductor devices consisting of the hydrodynamic equations for electron transport and energy conservation equations for different phonon modes. An electron Reynolds number is proposed and used to simplify the electron momentum equation. On a case study of the metal‐oxide‐semiconductor field‐effect transistor with 0.24 μm gate length, the calculated transconductance of 0.175 1/Ω m agreed well with measured value of 0.180 1/Ω m at 2 V drain voltage. The maximum electron temperature is found to occur under the drain side of the gate where the electric field is the highest. Comparison with experimental data shows the predictions of optical and acoustic phonon temperature distributions to have the correct trend and the observed asymmetric behavior. Increase in substrate boundary temperature by 100 °C reduces the drain current by 17% and decreases the maximum electron temperature by 8%. The first effect increases device delay and the second effect decreases the possibility of device degradation by charge trapping in the gate oxide.

Concurrent thermal and electrical modeling of sub‐micrometer silicon devices

The behavior of small semiconductor devices is simulated using an advanced Monte Carlo carrier transport model. The model improves upon the state of the art by including the full band structure of the semiconductor, by using scattering rates computed consistently with the band structure, and by accounting for both long- and short-range interactions between carriers. It is sufficiently flexible to describe both unipolar and bipolar device operation, for a variety of semiconductor materials and device structures. Various results obtained with the associated DAMOCLES program for n- and p-channel Si MOSFETs, GaAs MESFETs, and Si bipolar junction transistors are presented.

Monte Carlo analysis of semiconductor devices: the DAMOCLES program

A system of generalized hydrodynamic equations is derived from Boltzmann's transport equation for semiconductors without the assumption of a parabolic band structure. After some simplifications these equations can be arranged in such a way that their structure is similar to that of the well-known conventional ones. For this purpose the quantity carrier temperature is redefined and five relaxation times have to be introduced instead of the two in use so far, in order to take nonparabolicity into account. For all quantities of interest results from Monte Carlo simulation are presented for silicon with an impurity concentration of up to 10/sup 18/ cm/sup -3/ and an electric field of up to 200 kV/cm. They show that two of the five relaxation times are not distinguishable; hence, for silicon at room temperature the number of relaxation times can be reduced to four. Considerable deviations from results derived under the assumption of a parabolic band structure demonstrate the necessity of this generalized hydrodynamic model. The new hydrodynamic model is applied to a n-channel LDD MOSFET with a 0.5- mu m channel length. The results agree well with the results of Monte Carlo device simulation. >

Hydrodynamic equations for semiconductors with nonparabolic band structure

Classical semiconductor equations are based on the thermal equilibrium approximation. Limitations introduced by this approximation for the 2-D numerical modeling of n-channel silicon submicrometer MOS transistors are investigated. It is shown that the classical equations are accurate for predicting drain current for devices with effective channel lengths as small as 0.3 mu m. However, accurate substrate current modeling requires a more detailed level of simulation even for devices with longer channel lengths. The solution of the energy conservation equation is discussed. >

The influence of the thermal equilibrium approximation on the accuracy of classical two-dimensional numerical modeling of silicon submicrometer MOS transistors

W.L. Engl

Papers

The influence of the thermal equilibrium approximation on the accuracy of classical two-dimensional numerical modeling of silicon submicrometer MOS transistors