The determination of impurity concentrations and activation energies from Hall measurement data.

摘要

An algorithm was developed to perform least squares fitting of Hall measurement data in order to determine the underlying impurity concentrations and activation energies causing the observed carrier concentrations. The algorithm is different than other methods currently used because it models the Fermi energy as function of temperature only. The Fermi energy model allows the algorithm to not make any assumptions about the doping levels of the semiconductor being studied, so the algorithm is completely general for both degenerate and non-degenerate semiconductors.;The least squares fitting takes place in three steps. First, a functional approximation for the Fermi energy is calculated which depends only on temperature. The second step is to generate an initial estimate using the calculated Fermi energy. The third step for the algorithm is an iterative process. The impurity concentrations and activation energies are updated using a group coordinate descent. That is, in alternate steps, the activation energies are held fixed while the concentration values are updated, then the impurity concentrations are held fixed while the activation energy values are updated. The update process continues as long as the new values result in a better fit to the Hall data than the current values.;The algorithm was implemented as a 7,000 line extensible, self-contained, stand-alone application written in ISO standard C. Therefore, the C source code is fully portable. The implementation did not make use of any preexisting code or mathematical libraries in order to keep the application free of any license or use restrictions.