Abstract
This paper presents two non‐parabolic hydrodynamic model formulations suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship, (ℏk)2/2m = W(1+αW). The second formulation makes use of a power law, (ℏk)2/2m = xWy, for the dispersion relation. The non‐parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation is limited. The power law formulation produces closed form coefficients similar to those under the parabolic band approximation but the carrier concentration can deviate. An extended power law dispersion relation is proposed to account for band structure effects, (ℏk)2/2m = xW1+yW. This dispersion relation closely matches the calculated band structure over a wide energy range and may lead to closed form coefficients for the hydrodynamic model.
Highlights
Current hydrodynamic models consist of a set of conservation equations derived by taking moments of the Boltzmann transport equation
Non-parabolic hydrodynamic models have been reported for homogeneous material systems [1,2,3,4] using the Kane dispersion relationship [5]
Instead of using a classical Kane dispersion law relating the energy and momentum, the band was fit over a specified energy range using two adjustable parameters
Summary
Current hydrodynamic models consist of a set of conservation equations derived by taking moments of the Boltzmann transport equation. Instead of using a classical Kane dispersion law relating the energy and momentum, the band was fit over a specified energy range using two adjustable parameters. The approximations and assumptions implied by assuming the power law formulation were absent It was shown in [7] that the power law dispersion relation leads to a more simplistic and compact formulation than the classical Kane expression. If the power law is fit over the energy range 1.5 < W < 3.0 eV as suggested in [6] the deviation in carrier concentration from the parabolic case and the Kane formulation is greater than 80% at most reduced energy values. To accurately account for the carrier concentration the dispersion relation must match at lower energies and to simulate high energy effects it must match the band structure at higher energies
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