A Systematic Approach for Multidimensional, Closed-Form Analytic Modeling: Minority Electron Mobilities in Ga(1−x)Al(x)As Heterostructures

A significant, practical challenge, which arises in developing computationally efficient physical models for use in computer simulations of microelectronic and optoelectronic devices (for example, transistors in digital cellular phones and lasers in optical networks, respectively), is to represent vast amounts of numerical data for transport properties in two or more dimensions in terms of closed form analytic expressions. In this paper, we present a general methodology to achieve the above goal for a class of numerical data in a bounded two-dimensional space. We then apply this methodology to obtain a closed-form analytic expression for the minority electron mobilities at 300 K in p-type Ga(1−)(x)Al(x)As as functions of the acceptor density N(A) between 10(16) cm(−3) and 10(20) cm(−3) and the mole fraction of AlAs x between 0.0 and 0.3. This methodology and its associated principles, strategies, regression analyses, and graphics are expected to be applicable to other problems beyond the specific case of minority mobilities addressed in this paper.