Bounded Distribution Functions for Applied Physics, Especially Electron Device Simulation at Deep-Cryogenic Temperatures

TL;DR

This paper introduces bounded distribution functions that address numerical underflow and overflow issues in modeling at deep-cryogenic temperatures, enabling more stable simulations without increased computational cost.

Contribution

It proposes new bounded distribution functions that are numerically safe and identical to standard distributions at the physical level for deep-cryogenic temperature modeling.

Findings

Bounded functions prevent numerical underflow/overflow in simulations.

They enable stable modeling at deep-cryogenic temperatures using standard double precision.

Applicable to various branches of applied physics with similar numerical challenges.

Abstract

Numerical underflow and overflow are major hurdles for rolling-out the modeling and simulation infrastructure for temperatures below about 50 K. Extending the numeric precision is computationally intensive and thus best avoided. The root cause of these numerical challenges lies in the Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions. To tackle their extreme values, bounded distribution functions are proposed which are numerically safe in a given precision, yet identical to the standard distributions at the physical level. These functions can help to develop electron device models and TCAD software handling deep-cryogenic temperatures in the default double precision, to keep pace with the rapid experimental progress. More broadly, they can apply to other branches of applied physics with similar numerical challenges as well.