Faculty Publications - Michael A. Lieberman

Books

• M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, 2nd ed., Wiley Interscience, Hoboken, NJ: Wiley, 2005. [abstract]
• M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, 1st ed., Wiley-Interscience, Hoboken, NJ: John Wiley and Sons, 1994.
• A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed., Applied Mathematical Sciences, Vol. 38, New York, NY: Springer-Verlag, 1992. [abstract]
• A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, 1st ed., Applied Mathematical Sciences, Vol. 38, New York, NY: Springer-Verlag, 1983. [abstract]

Articles in journals or magazines

• E. Kawamura, A. J. Lichtenberg, and M. A. Lieberman, "Secondary electrons in rf and dc/rf capacitive discharges," Plasma Sources Science and Technology, vol. 17, no. 4, pp. 045002-1-11, Nov. 2008.
• T. Mussenbrock, R. P. Brinkmann, M. A. Lieberman, A. J. Lichtenberg, and E. Kawamura, "Enhancement of ohmic and stochastic heating by resonance effects in capacitive radio frequency discharges: A theoretical approach," Physical Review Letters, vol. 101, no. 8, pp. 085004-1-4, Aug. 2008.
• M. A. Lieberman, A. J. Lichtenberg, E. Kawamura, T. Mussenbrock, and R. P. Brinkman, "The effects of nonlinear series resonance on ohmic and stochastic heating in capacitive discharges," Physics of Plasmas, vol. 15, no. 6, pp. 063505-1-7, June 2008.
• Z. Zhou, M. A. Lieberman, S. Kim, S. Ji, M. Deng, and G. Sun, "Low-frequency relaxation oscillations in capacitive discharge processes," Chinese Physics Letters, vol. 25, no. 2, pp. 707-710, Feb. 2008.
• P. Chabert, A. J. Lichtenberg, and M. A. Lieberman, "Theory of a double-layer in an expanding electronegative plasma," Physics of Plasmas, vol. 14, no. 9, pp. 093502-1-11, Sep. 2007.
• E. Kawamura, M. A. Lieberman, A. J. Lichtenberg, and E. A. Hudson, "Capacitive discharges driven by combined dc/rf sources," J. Vacuum Science and Technology A: Vacuum, Surfaces, and Films, vol. 25, no. 5, pp. 1456-1474, Sep. 2007.
• I. Lee, D. B. Graves, and M. A. Lieberman, "Modeling electromagnetic effects in capacitive discharges," Plasma Sources Science and Technology, vol. 17, no. 1, pp. 015018-1-16, Sep. 2007.
• A. C. F. Wu, M. A. Lieberman, and J. P. Verboncoeur, "A method for computing ion energy distributions in multi-frequency capacitive discharges," J. Applied Physics, vol. 101, no. 5, pp. 056105-1-3, March 2007.
• Z. Zhou, M. A. Lieberman, and S. Kim, "Review of relaxation oscillations in plasma processing discharges," Chinese Physics, vol. 16, no. 3, pp. 758-765, March 2007.
• A. Aanesland, M. A. Lieberman, C. Charles, and R. W. Boswell, "Experiments and theory of an upstream ionization instability excited by an accelerated electron beam through a current-free double layer," Physics of Plasmas, vol. 13, no. 12, pp. 122101-1-10, Dec. 2006.
• C. Charles, R. W. Boswell, and M. A. Lieberman, "Xenon ion beam characterization in a helicon double layer thruster," Applied Physics Letters, vol. 89, no. 26, pp. 261503-1-3, Dec. 2006.
• P. Chabert, P. Levif, J. L. Raimbault, J. M. Rax, M. M. Turner, and M. A. Lieberman, "Electron heating in multiple-frequency capacitive discharges," Plasma Physics and Controlled Fusion, vol. 48, no. 12B, pp. B231-B237, Dec. 2006.
• S. Kim, M. A. Lieberman, A. J. Lichtenberg, and J. T. Gudmundsson, "Improved volume-averaged model for steady and pulsed-power electronegative discharges," J. Vacuum Science and Technology A: Vacuum, Surfaces and Films, vol. 24, no. 6, pp. 2025-2040, Nov. 2006.
• S. Kim, Z. Zhou, M. A. Lieberman, and A. J. Lichtenberg, "Relaxation oscillations in a capacitive discharge chamber connected to a peripheral grounded chamber," J. Applied Physics, vol. 100, no. 10, pp. 103302-1-9, Nov. 2006.
• Z. Zhou, M. A. Lieberman, and S. Kim, "Instability parameters of optical oscillation frequency in plasma central discharge and periphery region," Chinese Physics Letters, vol. 23, no. 8, pp. 2251-2254, Aug. 2006.
• A. Aanesland, C. Charles, M. A. Lieberman, and R. W. Boswell, "Upstream ionization instability associated with a current-free double layer," Physical Review Letters, vol. 97, no. 7, pp. 075003-1-4, Aug. 2006.
• M. A. Lieberman, C. Charles, and R. W. Boswell, "A theory for formation of a low pressure, current-free double layer," J. Physics D: Applied Physics, vol. 39, no. 15, pp. 3294-3304, Aug. 2006.
• M. A. Lieberman and C. Charles, "Theory for formation of a low-pressure, current-free double layers," Physical Review Letters, vol. 97, no. 4, pp. 045003-1-4, July 2006.
• P. Chabert, J. L. Raimbault, P. Levif, J. M. Rax, and M. A. Lieberman, "Inductive heating and E to H transitions in high frequency capacitive discharges," Plasma Sources Science and Technology, vol. 15, no. 2, pp. S-130-S136, May 2006.
• M. A. Lieberman, A. J. Lichtenberg, S. Kim, J. T. Gudmundsson, D. L. Keil, and J. Kim, "Plasma ignition in a grounded chamber connected to a capacitive discharge," Plasma Sources Science and Technology, vol. 15, no. 2, pp. 276-287, May 2006.
• E. Kawamura, M. A. Lieberman, and A. J. Lichtenberg, "Stochastic heating in single and dual frequency capacitive discharges," Physics of Plasmas, vol. 13, no. 5, pp. 053506-1-14, May 2006.
• C. G. Goedde, A. J. Lichtenberg, and M. A. Lieberman, "Self-consistent stochastic electron heating in radio frequency discharges," J. Applied Physics, vol. 64, no. 9, pp. 4375-4383, Nov. 1988.
• M. A. Lieberman and A. J. Lichtenberg, "Stochastic and adiabatic behavior of particles accelerated by periodic forces," Physical Review A, vol. 5, no. 4, pp. 1852-1866, April 1972.
• B. G. Logan, A. J. Lichtenberg, M. A. Lieberman, and A. Makhijani, "Multiple-mirror confinement of plasmas," Physical Review Letters, vol. 28, no. 3, pp. 144-147, Jan. 1972.

Articles in conference proceedings

• T. Mussenbrock, D. Ziegler, M. Gebhardt, R. P. Brinkmann, M. A. Lieberman, A. J. Lichtenberg, and E. Kawamura, "Nonlinear resonance effects on electron heating in capacitive discharges," in Proc. 35th IEEE Intl. Conf. on Plasma Science (ICOPS 2008), Piscataway, NJ: IEEE Press, 2008, pp. 1 pg.
• A. C. F. Wu, M. A. Lieberman, and J. P. Verboncoeur, "Ion energy distributions in multifrequency capacitive discharges," in 34th IEEE Intl. Conf. on Plasma Science (ICOPS 2007) Conference Record, Piscataway, NJ: IEEE Press, 2007, pp. 466-466.

Technical Reports

• M. A. Lieberman, A. J. Lichtenberg, S. Kim, and J. T. Gudmunsson, "Ignition Conditions for Peripheral Plasma in a Grounded Chamber Connected to a Dual Frequency Capactive Discharge," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M05/10, March 2005.
• K. Takechi and M. A. Lieberman, "Effect of Ar Addition to an O2 Plasma in a Large Area Plasma Source: O2/Ar Mixture Plasma Modeling and Photoresist Etching," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M01/1, 2001.
• K. Takechi and M. A. Lieberman, "Effect of Ion Energy on Photoresist Etching in an Inductively Coupled Large Area Plasma Source (LAPS)," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M00/58, 2000.
• K. Takechi and M. A. Lieberman, "Kinetics of Photoresist Etching in a Large Area Plasma Source (LAPS)," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M00/40, 2000.
• K. Takechi and M. A. Lieberman, "An Oxygen Discharge Model for a Large Area Plasma Source (LAPS)," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M00/33, 2000.
• K. Takechi and M. A. Lieberman, "Operation of a Large Area Plasma Source (LAPS) with Oxygen Gas," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M00/15, 2000.
• E. Kawamura, V. Vahedi, M. A. Lieberman, and C. K. Birdsall, "Ion Energy Distributions in RF Sheaths; Review, Analysis and Simulation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M98/62, 1998.
• Y. Wu and M. A. Lieberman, "A Traveling Wave Driven, Inductively Coupled Large Area Plasma Source," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M97/68, 1997.
• M. A. Lieberman and V. Godyak, "From Fermi Acceleration to Collisionless Discharge Heating," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M97/65, 1997.
• Y. Lee, M. A. Lieberman, A. J. Lichtenberg, F. Bose, H. Baltes, and R. Patrick, "Global Model for High Pressure Electronegative Radio-Frequency Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M96/23, 1996.
• G. Gregori and M. A. Lieberman, "RF Plasma Potential and Surface Temperature Measurements in an Inductively Coupled Plasma Source," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M96/14, 1996.
• J. Gudmundsson and M. A. Lieberman, "A Simple Transformer Model Applied to a Planar Inductive Plasma Discharge," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M96/3, 1996.
• P. Khoury, M. A. Lieberman, and A. J. Lichtenberg, "Measurement of Synchronization in Noisy and Chaotic Dynamical Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/103, 1995.
• I. Kouznetsov, A. J. Lichtenberg, and M. A. Lieberman, "Modeling Electronegative Discharges at Low Pressure," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/97, 1995.
• M. A. Lieberman and S. Ashida, "Global Models of Pulse-Power Modulated High Density, Low Pressure Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/83, 1995.
• V. Gopinath and M. A. Lieberman, "Simulation and Analysis of a Large Area Plasma Source," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/65, 1995.
• Y. Wu and M. A. Lieberman, "Experimental Modeling of a Traveling-Wave- Excited Inductively Driven Coil for a Large Area Plasma Source for Flat Panel Processing," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/60, 1995.
• E. Kawamura, V. Vahedi, M. A. Lieberman, and C. K. Birdsall, "Review of Ion Energy Distributions in Capacitively Coupled RF Plasma Reactors," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/49, 1995.
• C. Lee, D. Graves, and M. A. Lieberman, "Role of Etch Products in Polysilicon Etching in a High Density Chlorine Discharge," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M95/9, 1995.
• P. Wainman, M. A. Lieberman, A. J. Lichtenberg, R. Stewart, and C. Lee, "Characterization at Different Aspect Ratios (Radius/Length) of a Radio Frequency Inductively Coupled Plasma Source," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M94/56, 1994.
• S. Ashida, M. A. Lieberman, and C. Lee, "Spatially Averaged (Global) Model of the Time Modulated High Density Argon Plasmas," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M94/50, 1994.
• C. Lee and M. A. Lieberman, "Global Model of Ar, O_2, Cl_2, and Ar/O_2 High Density Plasma Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M94/49, 1994.
• J. De Luca, A. J. Lichtenberg, and M. A. Lieberman, "Time Scale to Ergodicity in the FPU System," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M93/92, 1993. [abstract]
• A. J. Lichtenberg, V. Vahedi, M. A. Lieberman, and T. Rognlien, "Modeling Electronegative Plasma Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M93/74, 1993. [abstract]
• C. Lee, D. Graves, M. A. Lieberman, and D. Hess, "Global Model of Plasma Chemistry in a High Density Oxygen Discharge," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M93/54, 1993. [abstract]
• B. Wood, A. J. Lichtenberg, and M. A. Lieberman, "Arnold Diffusion in Many Dimensions," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M93/13, 1993. [abstract]
• M. A. Lieberman and R. Gottscho, "Design of High Density Plasma Sources for Materials Processing," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M93/3, 1993. [abstract]
• V. Vahedi, C. K. Birdsall, M. A. Lieberman, G. DiPeso, and T. Rognlien, "Verification of Frequency Scaling Laws for Capacitive RF Discharges Using Two- Dimensional Simulations," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/146, 1992.
• V. Vahedi, R. Stewart, and M. A. Lieberman, "Analytic Model of the Ion Angular Distribution in a Collisional Sheath," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/114, 1992.
• C. Lee, D. Hess, and M. A. Lieberman, "Plasma and Gas Phase Kinetics of High Density SF_6 Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/95, 1992.
• M. de Sousa Vieira, A. J. Lichtenberg, and M. A. Lieberman, "On Synchronization of Regular and Chaotic Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/72, 1992.
• A. Sato and M. A. Lieberman, "RF Discharge Impedance Measurements and Comparison to a Discharge Model," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/34, 1992.
• B. Lynch, S. Das, M. A. Lieberman, and D. Hess, "Electron Cyclotron Resonance Etching of Silylated Photoresist," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/25, 1992.
• M. de Sousa Vieira, A. J. Lichtenberg, and M. A. Lieberman, "Self-Synchronization of Many Coupled Oscillators," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/20, 1992.
• M. de Sousa Vieira, P. Khoury, A. J. Lichtenberg, M. A. Lieberman, W. Wonchoba, J. Gullicksen, J. Huang, R. Sherman, and M. Steinberg, "Numerical and Experimental Studies of Self-Synchronization and Synchronized Chaos," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M92/5, 1992. [abstract]
• N. W. Cheung, M. A. Lieberman, C. Pico, R. Stewart, J. Tao, M. Kiang, C. Yu, V. Vahedi, B. Troyanovsky, W. En, E. Jones, and J. Benasso, "Plasma Immersion Ion Implantation (PIII) for Integrated Circuit Manufacturing: Fourth Quarterly Progress Report," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/116, 1991.
• M. Williamson, A. J. Lichtenberg, and M. A. Lieberman, "Self-Consistent Electron Cyclotron Resonance Absorption in a Plasma with Varying Parameters," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/114, 1991.
• C. Lee, D. Hess, and M. A. Lieberman, "Plasma Etching of CVD Tungsten Using ECR Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/92, 1991.
• J. Gullicksen, M. de Sousa Vieira, M. A. Lieberman, R. Sherman, A. J. Lichtenberg, J. Huang, W. Wonchoba, M. Steinberg, and P. Khoury, "Secure Communications by Synchronization to a Chaotic Signal," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/89, 1991.
• M. A. Lieberman, N. W. Cheung, C. Pico, R. Stewart, J. Tao, M. Kiang, C. Yu, V. Vahedi, B. Troyanovsky, W. En, E. Jones, and J. Benasso, "Plasma Immersion Ion Implantation (PIII) for Integrated Circuit Manufacturing: Third Quarterly Progress Report," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/86, 1991.
• A. Sato and M. A. Lieberman, "A Two-Coupled-Sheath Model for the Conduction of Current Through Asymmetric Parallel Plate RF Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/81, 1991.
• C. Goedde, A. J. Lichtenberg, and M. A. Lieberman, "Chaos and the Approach to Equilibrium in the Discrete Sine-Gordon Equation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/76, 1991.
• M. A. Lieberman, "Plasma Immersion Ion Implantation (PIII) for Integrated Circuit Manufacturing: Second Quarterly Progress Report," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/63, 1991.
• M. A. Lieberman and N. W. Cheung, "Plasma Immersion Ion Implantation (PIII) for Integrated Circuit Manufacturing," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/26, 1991.
• R. Stewart and M. A. Lieberman, "Model of Plasma Immersion Ion Implantation for Voltage Pulses with Finite Rise- and Fall-Times," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/14, 1991.
• M. de Sousa Vieira, A. J. Lichtenberg, and M. A. Lieberman, "Nonlinear Dynamics of Self-Synchronizing Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/6, 1991.
• D. Carl, D. Hess, M. A. Lieberman, T. Nguyen, and R. Gronsky, "Effects of DC Bias on the Kinetics and Electrical Properties of Silicon Dioxide Grown in an Electron Cyclotron Resonance Plasma," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M91/5, 1991.
• R. Stewart, X. Qian, D. Carl, B. Lake, J. Benasso, R. Lynch, C. Pico, M. A. Lieberman, and N. W. Cheung, "Characterization of the Processing Plasma in an Engineering Prototype Reactor for Plasma Immersion Ion Implantation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/100, 1990.
• X. Qian, N. W. Cheung, and M. A. Lieberman, "Plasma Immersion Ion Implantation for VLSI Fabrication," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/84, 1990.
• B. Wood, M. A. Lieberman, and A. J. Lichtenberg, "Sheath Motion in a Capacitively Coupled Radio Frequency Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/83, 1990.
• D. Carl, M. Williamson, M. A. Lieberman, and A. J. Lichtenberg, "Axial RF Electric Field Intensity and Ion Density During Low to High Mode Transition in Argon Electron Cyclotron Resonance Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/81, 1990.
• V. Vahedi, M. A. Lieberman, M. Alves, J. Verboncoeur, and C. K. Birdsall, "A One Dimensional Collisional Model for Plasma Immersion Ion Implantation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/60, 1990.
• M. A. Lieberman, A. J. Lichtenberg, and S. Savas, "Model of Magnetically Enhanced Capacitive RF Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/58, 1990.
• M. Alves, M. A. Lieberman, V. Vahedi, and C. K. Birdsall, "Sheath Voltage Ratio for Asymmetric RF Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/56, 1990.
• A. Sato and M. A. Lieberman, "Electron Beam Probe Measurements of Electric Fields in RF Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/49, 1990.
• B. Wood, A. J. Lichtenberg, and M. A. Lieberman, "Arnold Diffusion in Weakly Coupled Standard Maps," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/42, 1990. [abstract]
• D. Carl, D. Hess, and M. A. Lieberman, "Kinetics of Photoresist Etching in an Electron Cyclotron Resonance Plasma," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/25, 1990. [abstract]
• H. Wong, X. Qian, D. Carl, N. W. Cheung, M. A. Lieberman, I. Brown, and K. Yu, "Plasma Immersion Ion Implantation for Impurity Gettering in Silicon Plasma Immersion Ion Implantation and Dose Loss in Impurity Gettering Experiment," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/23, 1990. [abstract]
• M. A. Lieberman, A. J. Lichtenberg, and D. Flamm, "Theory of a Helical Resonator Plasma Source," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M90/10, 1990. [abstract]
• M. A. Lieberman and S. Savas, "Bias Voltage in Finite Length, Cylindrical and Coaxial RF Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/121, 1989.
• D. Carl, D. Hess, and M. A. Lieberman, "Oxidation of Silicon in an ECR Oxygen Plasma: Kinetics, Physico-Chemical and Electrical Properties," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/98, 1989.
• C. Goedde, A. J. Lichtenberg, and M. A. Lieberman, "Parametric Instabilities in the Discrete Sine-Gordon Equation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/79, 1989.
• G. Bernstein and M. A. Lieberman, "Secure Random Number Generation Using Chaotic Circuits," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/38, 1989.
• M. A. Lieberman, "Model of Plasma Immersion Ion Implantation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M89/30, 1989.
• G. Misium, A. J. Lichtenberg, and M. A. Lieberman, "Macroscopic Modelling of R.F. Plasma Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/86, 1988.
• R. Moroney, A. J. Lichtenberg, and M. A. Lieberman, "Cavity Perturbation Measurement of Plasma Density in Complex Geometry R.F. Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/81, 1988.
• M. A. Lieberman, "Spherical Shell Model of an Asymmetric R.F. Discharge," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/65, 1988.
• M. A. Lieberman, "Dynamics of a Collisional Capacitive R.F. Sheath," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/62, 1988.
• R. Ratowsky and M. A. Lieberman, "Rays and Waves in a Periodically Perturbed Parallel Plate Waveguide," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/59, 1988.
• C. Goedde, A. J. Lichtenberg, and M. A. Lieberman, "Self-Consistent Stochastic Electron Heating in Radio Frequency Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/29, 1988.
• L. Gu and M. A. Lieberman, "Axial Distribution of Optical Emission in a Planar Magnetron," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/6, 1988.
• A. J. Lichtenberg and M. A. Lieberman, "Diffusion in Two Dimensional Mappings," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/5, 1988.
• G. Bernstein and M. A. Lieberman, "A Method for Obtaining a Canonical Hamiltonian for Nonlinear LC Circuits," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M88/2, 1988.
• M. A. Lieberman, "Analytical Solution for Capacitive R.F. Sheath," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/71, 1987.
• A. Wendt, M. A. Lieberman, and H. Meuth, "Radial Current Distribution at a Planar Magnetron Cathode," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/66, 1987.
• M. A. Lieberman, "Basic RF Discharge Model," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/65, 1987.
• G. Bernstein, M. A. Lieberman, and A. J. Lichtenberg, "Nonlinear Dynamics of a Digital Phase Locked Loop," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/59, 1987.
• A. J. Lichtenberg, M. A. Lieberman, and R. Cohen, "Transient Electrostatic Potentials Driven by Short-Pulse Electron Cyclotron Heating," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/17, 1987.
• H. Ramachandran, A. J. Lichtenberg, M. A. Lieberman, and A. Sen, "Collisional Treatment of the Trapped Particle Mode in Multi-Region Mirror Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/16, 1987.
• B. Archer, H. Meuth, and M. A. Lieberman, "Electron Beam Time-of-Flight Potential Diagnostic," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M87/4, 1987.
• B. Kang, M. A. Lieberman, and A. Sen, "Axial Feedback Stabilization of Flute Modes for Mirror Machines," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/101, 1986.
• A. J. Lichtenberg, M. A. Lieberman, and N. Murray, "The Effect of Quasi-Accelerator Modes on Diffusion," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/100, 1986.
• N. Murray and M. A. Lieberman, "Stochasticity and Resonances in the Two Beam Accelerator," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/76, 1986.
• C. Chang, H. Meuth, M. A. Lieberman, and A. J. Lichtenberg, "Observation of a Potential Barrier Created by Electron Cyclotron Resonance Heating in a Multiple Mirror Plasma," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/68, 1986.
• R. Close, B. Kang, A. J. Lichtenberg, M. A. Lieberman, and H. Meuth, "Experimental Observation of Wall Stabilization of Axisymmetric Mirrors at High Beta," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M86/7, 1986.
• M. A. Lieberman, "Many-Dimensional Hamiltonian Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/74, 1985.
• K. Tsang and M. A. Lieberman, "Transient Chaotic Distributions in Dissipative Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/56, 1985.
• J. Fernandez, C. Chang, A. J. Lichtenberg, M. A. Lieberman, and H. Meuth, "Observation of a Curvature Driven, Trapped Particle Mode Created by a Potential Barrier," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/41, 1985.
• C. Chang and M. A. Lieberman, "Synchronous Electron Beam Diagnostic for Plasma Etching Discharges," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/38, 1985.
• B. Archer and M. A. Lieberman, "Time-of-Flight He+ Beam Potential Diagnostic in Tandem Mirror," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/34, 1985.
• M. A. Lieberman and K. Tsang, "Transient Chaos in Dissipatively Perturbed Near-Integrable Hamiltonian Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M85/26, 1985.
• B. Archer, H. Meuth, and M. A. Lieberman, "Swept-Frequency, 8mm Microwave Interferomete for MXX," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/104, 1984.
• N. Murray, M. A. Lieberman, and A. J. Lichtenberg, "Corrections to Quasilinear Diffusion in Area Preserving Maps," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/102, 1984.
• M. A. Lieberman and C. Chang, "Electron Beam Time-of-Flight Measurements of Plasma Potential in Tandem Mirrors," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/92, 1984.
• B. Kang, M. A. Lieberman, and A. Sen, "Axial Feedback Stabilization of Flute Modes for Mirror Machines," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/61, 1984.
• K. Doniger, M. A. Lieberman, and A. J. Lichtenberg, "A Theoretical Study of ICRF Effects on Multiple Mirror Confinement," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/19, 1984.
• K. Tsang and M. A. Lieberman, "Invariant Distribution on Strange Attractors in Highly Dissipative Systems," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M84/13, 1984.
• J. Howard, A. J. Lichtenberg, M. A. Lieberman, and R. Cohen, "Collisionless Diffusion in Two-Frequency Electron Cyclotron Resonance Heating," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M83/65, 1983.
• J. Fernandez, A. J. Lichtenberg, M. A. Lieberman, and N. Benjamin, "Potential Barrier Decoupling of Stable and Unstable Regions of Average Minimum B Magnetic Mirrors," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M83/22, 1983.
• K. Tsang and M. A. Lieberman, "Analytical Calculation of Invariant Distributions on Strange Attractors," EECS Department, University of California, Berkeley, Tech. Rep. UCB/ERL M83/19, 1983.

Patents

• G. M. Bernstein and M. A. Lieberman, "Method and apparatus for generating secure random numbers using chaos," U.S. Patent 5,007,087. April 1991.