James J. Filliben

*Statistical Engineering Division, ITL*

Herbert S. Bennett

*Semiconductor Electronics Division, EEEL*

*The Problem: *
This collaboration focuses on the regression modeling of
electron mobility for p-type gallium aluminum arsenide (GaAlAs)
in the "minority electron" case-that is, for the case where
there are fewer electrons than holes. Quantum mechanical
non-linear integral-differential equations give a self-consistent
description of carrier transport and mobility in
*Ga*_{1-y}*Al*_{y}*As*/*GaAs* heterostructures, where y is the mole
fraction of AlAs. Many hours of NIST Cray CPU time were spent (by Bennett) to
solve these complex equations. The results are usually given via
numerical tables for describing quantitatively how the electron
mobility varies with dopant density and aluminum arsenide mole
fraction, but interpolatory use of such look-up tables in
semiconductor device simulators on engineering workstations is
computationally inefficient-particularly for industry. We are
thus led to the desired output from the data analysis, namely, a
closed-form 2-dimensional analytic function f such that

mobility = f(dopant density, mole fraction).

*Importance: Device Simulators: *
If such a function can be derived, then it will represent a
significant increase in computational efficiency via the
inclusion of more physically correct mobility models in
commercial semiconductor device simulators. The combination of
the existing NIST Cray-generated mobility data and the derived
2-dimensional analytic function will lead to computer simulators
that are at once both more parsimonious (fewer unknown or
variational parameters) and more accurate (improved predictability).

*Application: Cell Phones: *
One example of the importance of more physically correct mobility
models concerns the design of microwave heterojunction bipolar
transistors (HBTs) used in the linear power amplifiers of digital
cell phones. The design challenges/goals are low noise and very
linear/efficient power amplifiers that enable longer talk times
and superior adjacent-channel rejection in the dense channel
packing so commonly encountered for maximal communications system
capacity. Designers of such transistors rely on improved device
simulators to give them physical insights for optimization, to
provide a source of expert knowledge from others, and to save
money/time-to-market by reducing the number of experiments needed
for design verification.

*Collaborative Seminar: *
A new SED seminar series ("The Statistical Engineering
Division Case Studies Series") was initiated to serve
as the forum for presenting this interlaboratory collaboration to
the NIST staff. A joint Bennett/Filliben talk
was presented in December of 1998 to discuss
the systematic 6-step methodology (involving transformations, admissible
non-linear models, separable functions, and melding functions).

Figure 17: This plot shows the data analysis sequence
for the non-linear fitting of p-type electron mobility
as a function of density and mole fraction.