A Method for Determining the Screening Length of the Coulombic Scattering in Non-Degenerate and Degenerate Semiconductors M. Rudan and G. Perroni E. De Castro Advanced Research Center on Electronic Systems (ARCES), and Department of Electronics, Computer Science and Systems (DEIS) University of Bologna, Viale Risorgimento 2 40136 Bologna, Italy Tel. +39-051-20-93016, Fax. -93779 E- MAIL mrudan@deis.unibo.it, gperroni@deis.unibo.it Abstract A method for directly measuring the inverse screening length in semiconductors in terms of ionized-impurity concentration and lattice temperature is demonstrated, based on a first-principle calculation of the effect of ionized-impurity scattering. No fitting parameters are involved in the derivation, which covers a wide range of doping concen- trations and intrinsically complies with the Mathiessen rule. A new class of integrals is introduced in the calculation. The results are compared with the standard derivation of the inverse screening length from the perturbative solution of the Poisson equation. 1 Motivation Low-field measurements of carrier mobility, coupled with an analytical calculation of the momentum-relaxation time, provide a method for a direct experimental extraction of the dependence of the inverse screening length q 0 on the ionized-impurity concentration N I and lattice temperature T L . This constitutes the basis for deriving a first-principle model of the effect of ionized-impurity scattering on mobility. The concept of inverse screening length is adopted in a number of microscopic models for determining the effect of ionized-impurity scattering (e.g., Brooks-Herring, Taki- moto, and Third-body exclusion models [1]). Such parameter, in turn, depends on the ionized-impurity concentration and lattice temperature through the charge density. Some important issues that play a role in the effect of ionized-impurity scattering on the carrier mobility must be mentioned. The first issue is the questionable approx- imation of replacing the carrier concentration with the impurity concentration in the standard expressions involving q 0 , which leads to an infinite collision cross-section at zero concentration. A second issue is the dependence of the ionized-impurity scattering on temperature, a third one is the different effectiveness of this type of scattering on the majority and minority carriers, which brings about the necessity of distinct mobility models as shown in [2], and a fourth one is the consistency of the result with the Math- iessen rule, which is often missing in models derived from first principles. Here it is shown that combining the definition of the momentum-relaxation time typ- ical of the hydrodynamic transport equations [3] with the concept of screening length