

Introduction  Manual
 Publication
A Short Introduction to EMCUR
By
Xing Zhou and Thomas Y. Hsiang
Department of Electrical Engineering
University of Rochester
Rochester, New York 14627
July 1990
INTRODUCTION
The Monte Carlo (MC) technique, as is used in carrier transport calculations in semiconductors, is a general tool for device modeling and simulation. Like any numerical simulator, the art of simulation is to simplify the design process, to determine ultimate performance limits for a given technology, and to provide physical insights into the device/phenomena under investigation. One of the major advantages of the MC method over other conventional analytic/numerical techniques is its greater ability to handle realistic band and scattering details without assuming a priori the distribution functions. Hence, it is especially useful in modeling submicron devices in which hotcarrier effects as well as time and spacedependent phenomena are dominant.
EMCUR (Ensemble Monte Carlo at the University of Rochester) is a generalpurpose software package for simulating IIIV compound devices with variable band parameters. This version (1R3K) of the program is a onedimensional (1D in r space) simulator which is suitable for simulating nonsteadystate transport processes in bulk materials, bipolartype devices, relaxation of photogenerated carriers, etc. Emphasis in the implementation have been placed on user flexibility and variety of available data.
This memo briefly outlines the major features available
in EMCUR. For more detailed information on the physical models and numerical
algorithms used as well as how to use the program, the reader is referred
to the references listed at the end of this memo.
MAJOR FEATURES
General
Band and Material Models
 Band parameters: (temperaturedependent) band gaps, effective masses, nonparabolic parameters, and userspecified conductionband offset in each valley;
 Material parameters: high and lowfrequency dielectric constants, crystal density, velocity of sound, deformation potentials, and phonon energies.
(Note: All of the above parameters can be overridden by usersupplied parameters.)
Scattering Mechanisms
 Intravalley phonon scattering;
 Polar optical phonon scattering, with or without (selfconsistent) screening;
 Acoustic phonon scattering with deformationpotential interaction;
Simulation Variables
Initial Conditions
 HemiMaxwellian distribution, i.e., one with only positive velocity component along a given direction (cold or hot, with or without drift);
 Velocityweighted Maxwellian distribution (cold or hot, with or without drift);
 Gaussian (in energy) distribution (with userspecified excitation energy and the width of the laser pulse);
 "deltafunction" (in momentum and energy) distribution (Px=Py=0; Pz=Po, where Po corresponds to some userspecified injection energy with a finite width).
(Note: Initial valley occupancy for the ensemble can be randomly assigned according to the userspecified initial valley occupancy probability.)
 Uniform distribution;
 Exponentially decaying function distribution (with userspecified penetration depth and injection level);
 Arbitrary userdefined distribution.
 Rectangular pulse (with userspecified pulse width);
 Gaussian pulse (with userspecified standard deviation);
 Inverse hyperbolic cosine function (with userspecified FWHM width).
(Note: The program can handle variable ensemble size to model the injection of a laser pulse.)
Boundary Conditions
 Periodic boundary condition (for simulating infinite bulk materials);
 Tunneling boundary condition (for simulating heterostructure hotelectron diodes/transistors).
 Fixed voltage at one boundary and fixed field at the other boundary (with userspecified boundary voltage and field).
(Note: A userdefined arbitrary depletion charge inside the device can also be specified.)
Histograms and Estimators
 Average velocity and energy versus distance distributions;
 Potential, field, electron/netcharge concentration profiles inside the device as calculated by the Poisson solver;
 Scattering pattern (i.e., number of scatterings due to each mechanism) as a function of distance;
 Inverse screening lengths versus distance as calculated using the selfconsistent screening model;
 Total scattering rate in each valley as a function of energy, which is updated at each timestep when the selfconsistent screening model and/or electronelectron scattering are enabled.
 Mean of ensemble displacement as well as mean of velocity and energy distributions;
 Average scattering angles (ionized impurity, optical phonon, and acoustic phonon scatterings);
 Average mean free times and mean free paths;
 Scattering rates due to each mechanism;
 Current densities (including emission and tunneling currents if tunneling boundary condition is specified);
 Boundary voltages (potential across the device) as calculated by the Poisson solver;
 Maximum total scattering rates which are used for the piecewise constant GAMMA approach;
 Trajectory of the state of the first electron in the ensemble (valley index, position, velocity, and energy).
Program Outputs
FOR MORE INFORMATION
This memo only presents an outline of the major
features of the EMCUR program. For detailed information on the physical
models, numerical algorithms, and device models used in EMCUR, the reader
is referred to Ref. [1], EMCURAn Ensemble Monte Carlo Program for IIIV
Compound Semiconductor Device Modeling and Simulation, as well as Ref.
[2], EMCUR User's Manual, on how to use the program and examples of typical
outputs produced by EMCUR. Some earlier documentations about EMCUR and
some simulation results are listed in Refs. [3][8]. Recent applications
to the study of photogenerated carrier transport in GaAs surface spacecharge
fields and hotcarrier relaxation and scattering processes in bulk GaAs
can be found in Refs. [9] and [10], respectively.
REFERENCES
[1] X. Zhou and T. Y. Hsiang, "EMCURAn Ensemble Monte Carlo Program for IIIV Compound Semiconductor Device Modeling and Simulation," Research Report No. RR0011189, University of Rochester, November 1989.
[2] X. Zhou and T. Y. Hsiang, "EMCUR User's Manual (Version 1R3K.04)," University of Rochester, October 1989.
[3] X. Zhou, "Band Structure Engineering of IIIV Compound Heterostructures with Monte Carlo Calculations," Ph.D. thesis proposal, University of Rochester, July 1987.
[4] X. Zhou, "Major Features of EMCUR (Version 1R3K.01)," Memo.1, University of Rochester, October 1988.
[5] X. Zhou, "Sample Simulation Results of EMCUR (Version 1R3K.01)," Memo.2, University of Rochester, November 1988.
[6] X. Zhou, R. J. Bowman, and T. Y. Hsiang, "Monte Carlo Simulation of TimeDependent Phenomena in GaAs," Technical Report No. TR0010488, University of Rochester, April 1988.
[7] X. Zhou, R. J. Bowman, and T. Y. Hsiang, "Monte Carlo Simulation of SpaceDependent Phenomena in GaAs," Technical Report No. TR0020588, University of Rochester, May 1988.
[8] X. Zhou and T. Y. Hsiang, "Monte Carlo Study of Photogenerated Carrier Transport in GaAs Surface SpaceCharge Fields," Technical Report No. TR0030289, University of Rochester, February 1989.
[9] X. Zhou, T. Y. Hsiang, and R. J. Dwayne Miller, "Monte Carlo study of photogenerated carrier transport in GaAs surface spacecharge fields," J. Appl. Phys., vol. 66, pp. 30663073, October 1989.
[10] X. Zhou and T. Y. Hsiang, "Monte Carlo determination of femtosecond dynamics of hotcarrier relaxation and scattering processes in bulk GaAs," J. Appl. Phys., vol. 67, pp. 73997403, June 1990.