1. Time Response of the High-field Electron Distribution Function in GaAs
2. Computer simulation of semiconductor devices
3. For a good survey of Monte Carlo see J. M. Hammersley and D. C. Handscomb, “Monte Carlo Methods,” Wiley, New York, 1965. A more detailed work is Yu. A. Shrieder (ed.), “The Monte Carlo Method.” Pergamon, Oxford, 1966. The Monte Carlo method was introduced into modern physics by Ulam (1946) and von Neumann. See: correspondence between von Neumann and Richtmyer (1974) reproduced in J. von Neumann, “Collected Works” (A. H. Taub, ed.). Vol. 5. pp. 751–764. Macmillan, New York, 1963, and S. M. Ulam and J. von Neumann, Bull. Am. Math. Soc. 53, (1947) 1120. A personal account will be found in Chapter 10 of Ulam's autobiography “Adventures of a Mathematician” (1976). Their immediate concern was with nuclear reactor design, but there soon was work on a wide range of applications. The scope and flavor of this activity is indicated by the papers at a 1949 conference – “Monte Carlo Method.” National Bureau of Standards, Applied Mathematics Series, no. 12(1951), and by the bibliography with abstracts in “Symposium on Monte Carlo Methods” (H. A. Meyer, ed.), Wiley, New York, 1956. An interesting early paper with content related to that of the present work is M. L. Goldberger, Phys. Rev. 74, (1948) 1269. Pioneer papers on electron transport in solids were Lüthi and Wyder39, and T. Kurosawa, J. Phys. Soc. Jpn. Supple. 21, (1966) 424. An earlier use of Monte Carlo in physics, in which results of the kinetic theory of gases were tested by simulating the molecular motions, was Lord Kelvin, Phil, Mag. (6th ser.) 2, 1(1901).
4. In an early discussion of the subject, von Neumann17 remarks: we could build a physical instrument to feed random digits directly into a high-speed computing machine. The real objection to this procedure is the practical need for checking computations. If we suspect that a calculation is wrong, almost any reasonable check involves repeating something done before. At that point the introduction of new random numbers would be intolerable.” The sequence of values of a physical variable produced in a particular computer “run” depends on the initial value of the seed integer in The pseudorandom number generator5; but the estimator values given by the computation are useful results to the extent that they are independent of the initial seed integer.:
5. The pseudorandom number generator that was used in the unpublished calculations describedhere, and in Refs. 25, 26, 31, and 45, is an implementation of the Lehmer method for IBM 360 machines. See: D. W. Hutchinson, Commun. ACM 9, 432(1966);