Global TCAD Solutions

Cutting-Edge TCAD
09.09.2014

SISPAD 2014: Accurate Modeling of Low-Field Mobilities

On the Validity of Momentum Relaxation Time in Low-Dimensional Carrier Gases


A poster session by our colleague sheds some light on a popular but not always correct approximation, and provides a physically sound, yet efficient algorithm:

Momentum Relaxation Time – and its Weaknesses

The momentum relaxation time (MRT) is widely used to simplify low-field mobility calculations including anisotropic scattering processes. Although not always fully justified, it has been very practical in simulating transport in bulk and in low-dimensional carrier gases alike. We review the assumptions behind the MRT, quantify the error introduced by its usage for low-dimensional carrier gases, and point out its weakness in accounting for inter-subband interaction, occurring specifically at low inversion densities.

The figure on top shows the electron mobility calculated using MRT for n-type MOS channels at different substrate orientations (transport direction is ⟨110⟩, the indices 2-4 refer to the expressions shown the table):

MRT 4 and 5 deviate from f1 at low inversion densities but are a good approximation at high densities.
MRT 2 overestimates mobility by a factor of ten (not shown) while MRT 3 diverges.

Caveats and a more Thorough Alternative

We conclude that the MRT can provide remarkably accurate results regarding its simplifications, although one needs to be careful about the choice of the weighting factor Θn,n′;k,k′. The normalized, group velocity-based expression in Eq. (9) gives the most accurate and stable results. However, systematic errors still occur in multi-subband systems and accuracy is orientation-dependent. Simultaneously, we developed a computationally efficient method to directly compute the carrier distribution response and, from it, the exact channel mobility, thus avoiding the MRT and its problems while remaining competitive in terms of computational effort.

Availability

GTS customers can benefit from this model, as it is included in current  VSP (Vienna Schrödinger-Poisson) versions.

References

SISPAD 2014, Yokohama, Japan
Session P1, Z. Stanojevic et al.

Authors: Z. Stanojevic, O. Baumgartner, M. Karner, La. Filipovic, C. Kernstock, and H. Kosina (Vienna University of Technology / GTS)