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3.3.4 Non-Linear Modeling of Electron Mobilities in p-type Compound Semiconductors
James J. Filliben
Herbert S. Bennett 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 Ga1-yAlyAs/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.
Date created: 7/20/2001 |