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University Microfilms, Inc., Ann Arbor, Michigan APPLICATION of the SHOCKLEY-READ RECOMBINATION

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University Microfilms, Inc., Ann Arbor, Michigan APPLICATION of the SHOCKLEY-READ RECOMBINATION This dissertation has been 64—6944 microfilmed exactly as received PANG, Tet Chong, 1929- APPLICATION OF THE SHOCKLEY-READ RECOMBINATION STATISTICS TO THE STUDY OF THE P*NN+ DIODE. The Ohio State University, Ph.D., 1963 Engineering, electrical University Microfilms, Inc., Ann Arbor, Michigan APPLICATION OF THE SHOCKLEY-READ RECOMBINATION STATISTICS TO THE STUDY OF THE P+NN+ DIODE DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Ftiilosophy in the Graduate School of The Ohio State lhiversity By Tet Chong Pang, B.S., M.Sc. The Ohio State lhiversity 1963 Approved by Adviser Department of Electrical Engineering PLEASE NOTE: Figures are not original copy. Pages tend to "curl". Filmed in the best possible way. UNIVERSITY MICROFILMS, INC. ACKNOWLEDGMENTS This research was started when the author was a student of Professor E. Milton Boone to whom he is ever grateful for his overall guidance and understanding over the years. He is deeply indebted to Professor Marlin 0. Thurston for his encouragement and many elucidating discussions. It is a pleasure to acknowledge the assistance in computer programming given by the staff of the Numerical Computation Laboratory, The Ohio State Lhiversity, in particular, Professor Theodore W. Hildebrandt. CONTENTS Page ACKNOWLEDGMENTS..................................... ii LIST OF ILLUSTRATIONS................................ v Chapter I INTRODUCTION ............................... 1 II RECOMBINATION OF ELECTRONS AND HOLES ........... 3 III SHOCKLEY-READ RECOMBINATION STATISTICS ......... 6 IV DETERMINATION OF CARRIER DENSITIES ............ 12 V CONDUCTIVITY MODULATION AND NEGATIVE RESISTANCE .............................. 17 Conductivity modulation ................... 17 Negative resistance ...................... 17 Lifetime variation with carrier density .... 18 VI ANALYTICAL APPROACH TO THE SOLUTION OF TRANSPORT EQUATION ...................... 24 VII NUMERICAL APPROACH TO THE SOLUTION OF TRANSPORT E Q U A T I O N ...................... 28 Runge-Kutta-Gill m e t h o d ................... 28 Simpson's three-point formula ............. 30 Computer-graphical m e t h o d ................. 31 VIII DERIVATION OF THE BOUNDARY VALUES .............. 33 IX DETERMINATION OF THE APPLIED POTENTIAL ......... 38 X DISCUSSION ................................. 45 XI CONCLUSION ................................. 60 OONTTJJTS (continued) Appendix Page I AN APPROACH TO NUMERICAL SOLUTION OF DIOEE EQUATIONS WIIH SPACE C H A R G E ............ 62 II INTEGRATION OF THE APPROXIMATE EQUATION ................................. 65 III COMPUTER PROGRAM AND EXAMPLE ................ 67 BIBLIOGRAPHY ....................................... 73 AUTOBIOGRAPHY....................................... 75 iv LIST OF ILLUSTRATIONS Figure Page 1. Electronic Transition Scheme ................... 6 2. Energy Diagram Showing Various Energy Levels in the Band Gap ...................... 7 3. Excess Electron Density Versus Excess Hole Density . ........................... 14 4. Derivative of Electron Density with Respect to Hole Density as a Function of Excess Hole Density ...................... 16 5. Effective Lifetime for Holes as a Function of Excess Carrier Density ............ 22 6 . Effective Lifetime for Holes as a Function of Excess Carrier Density . ........ 23 7. Five Possible Carrier Distribution in the N-region of a Diode under Forward B i a s .............................. 34 8 . A Planar N+NP+ Diode Structure ................. 37 9. Potential Diagram of a Forward Biased P-N Junction Diode .................. 40 10. Potential Diagram of a P^NN4 D i o d e .............. 43 11. Modified Carrier Distribution and Its G r a d i e n t .............................. 46 12. Calculated V-I Curve of a P+NN+ Diode under Forward Bias (Sp=3xl0~^**t no=7xl010) .... 49 13a. Calculated Applied Voltage Components and V-I Curve (Sp=3xl0-14, n=7xlOil) .......... 51 13b. Calculated Voltage Drop in the Base and Total Applied Voltage ................... 52 v LIST OF ILLUSTRATIONS (continued) Figure Page 14. Calculated V-I Curve (SpSlO”^*4, nQ=7xlO^-^)....... 53 15. Calculated Voltage Components and V-I Curve (Sp=10-15, a = 1 0 ) ................... 54 16. Calculated Voltage Components and V-I Curve (Sp=10-15, a = 2 0 ) ................... 55 17. Figure 14 Redrawn on Linear Scale .............. 57 18. Figure 15 Redrawn on Linear Scale .............. 58 vi CHAPTER I INTRODUCTION The fabrication of semiconductor devices consists largely of the introduction of electronically active imperfections into the crystal­ line semiconductor. Of these imperfections, donor and acceptor im­ purities are added deliberately to control the conductivity, while others such as recombination centers, trapping centers, and scat­ tering centers are unavoidably present also. Sometimes these centers are the result of residual impurities in the crystal or of defects introduced during the crystal growing process. They may also be cre­ ated as a result of the device fabrication process or by bombardment with high energy particles such as beta particles, alpha particles, or fast neutrons. In general, increase in the number of active centers (other than donors or acceptors) in a semiconductor device tends to increase the effective resistance of the device through deterioration or change of one or more of the physical parameters as lifetime, mobility and free carrier density. The manifestation can take many forms such as higher voltage drop, lower anplification and higher leaking current. Centers that behave as traps nay affect the rise time, the decay time and the switching time of some devices. The presence of such active centers in a device is not all of negative value; they are sometimes purposely incorporated in the 2 semiconductor naterial to i m p r o v e the performance of devices such as switching diodes. Hie negative resistance characteristic of certain diodes is found to be due to active canters. The fabrication of par­ ticle detectors and radiation dosimeters is based on the fact that damage in semi conductor materials due to particle borrbardment are electronically active and are almost permanent. The object of this work is to investigate theoretically the effect of electronically active centers on the current-voltage characteristic of a wide base P+NN4 silicon diode. The Shockley-Read monovalent flaw model of the electronic transition process at the active center is applied in the analysis. Instead of a constant lifetime, the S-R re­ combination rate as a function of injection and capture cross sections is used* This adds considerable complexity to the analytical solution. Because of the nonlinear nature of the differential equation involved, numerical solution seems to be the only method if the full significance of the active centers is to be revealed. For this purpose the Runge- Kutta iterative numerical integration is chosen for its simplicity and its adaptability to computer calculation. The current-voltage characteristics of an assumed planar structure have been calculated far several combinations of the flaw density, the net donor density, and the capture cross section for holes and for electrons. Diodes with a low equilibrium carrier density in the N- region have been found to exhibit negative resistance characteristics. Other irregularities that have been observed experimentally can be ex­ plained satisfactorily by the Shockley-Read recombination mechanism. CHAPTER II RECOMBINATION OF ELECTRONS AND HOLES In a semiconductor, electronic transitions take plaoe continuously. Electrons nay be thermally excited from the valence band into the con­ duction band, or into localized levels in the band gap; they may also be excited from localized levels into the conduction band. To main­ tain balance, the inverse process of de-excitation takes plaoe at the same time. In thermal equilibrium, the rate of each process and its inverse are equal and balance in detail. To avoid confusion, a few words of explanation are given here of some of the terms used in connection with flaws and recombination. The term * recombination1' suggests the oombining of two charged par­ ticles, an electron and a hole, When recombination takes place, the charges of the two particles cancel each other. On the other hand, capture suggests immobilization of a free carrier; the recombination process may take place at the same time, but this need not be. If the center is neutral to begin with, after oapturing an electron it would be negatively charged. Now if this same center captured a hole, this hole would recoirbine with the previously captured electron. A capture without reoonbination releases potential energy equal to the energy difference of the initial and the final state of the carrier, while a reoonbination involves the potential energy of the electron- hole pair. 3 1+ The terns "flaw," "center," "states," and "level" refer to the same thing in one plaoe or another, although each term has a somewhat different connotation. Loosely, a flaw denotes a disruption of the crystal lattice either by impurity atoms in interstitial or substi­ tutional states, dislocations or other defects. A center denotes a location at which electronic activities can take plaoe. The term "state" originates from the quantum theory of matter, while the term "level" has significance in connection with the energy level of a state. Returning to the main discussion, in the band-to-band de-excita- tion process, the potential energy of the electron-hole pair released in the process trust
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