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Equivalent Circuit of Unsymmetrical Inductance Diode Using Linvill Lumped Model

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Equivalent Circuit of Unsymmetrical Inductance Diode Using Linvill Lumped Model Scholars' Mine Masters Theses Student Theses and Dissertations 1965 Equivalent circuit of unsymmetrical inductance diode using Linvill lumped model Donald Lawrence Willyard Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Electrical and Computer Engineering Commons Department: Recommended Citation Willyard, Donald Lawrence, "Equivalent circuit of unsymmetrical inductance diode using Linvill lumped model" (1965). Masters Theses. 5235. https://scholarsmine.mst.edu/masters_theses/5235 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. EQUIV ALBNT CJ.RCUIT OF UNSYMMETRICAL INDUCTANCE DIODE USDJG LINVJLL LUMPED MODEL BY AP'/ r· ol~'- t'\.)J} - / OONALD L~ vJILLYARD J V~ ~~ :;> A THESIS submitted to the faculty of the UNIVERSITY OF MISSOURI AT ROLLA in partial fulfillment of the requirements for the ~gree of 1-W3TER OF SCIENCE IN ELECTRICAL ENGINEERING Rolla, Missouri 1965 Approved By ~/}/)/~~) ~~ ii ABSTRACT Integrated circuit techniques and applications are rapidJ.y changing the electronics industry. A problem common to both state­ of-the-art approaches to integrated circuit fabrication is that of miniaturizing and intGgrating inductors. It is found that, for a certain range of injection current levels, certain unsymmetrically doped junction diodes have an inductive small-signal impedance. This thesis discusses the theor,y of inductance diodes and applies finite difference equations and the Linvill lumped model to the differential equations that describe their carrier nov.r processes. The static I-V characteristic and the sm~11-signal equivalent circuit at high injection densities are derived. The elements (R,L,C) of this equivalent circuit are given in terms of the Linvill parameters. Impedance calculations are made using this equivalent circuit and are in satisfactory agreement Tdth experimental results for diodes in which the bnse length is not too long compared to the diffusion length. iii ACKNOTtii.. EDGEMENrS The at.Tthor wishes to thank Dr. Ralph Carson of the Electrical Engineering staff. His guidance and manY helpful suggestions regarding the thesis proper were appreciated. Thanks go to the Metallurgical Engineering I:epartment for providing the metallurgical stage microscope. The author expresses his sincere appreciation to his wife for typing the original. copy. iv TABLE OF CONTENTS Page LIST OF FIGURES•••••••••••••••••••••••••••••••••••••••••••••••• v LIST OF TABLES••••••••••••••••••••••••••••••••••••••••••••••••• vi LIST OF SYMBOLS•••••••••••••••••••••••••••••••••••••••••••••••• vii CHAPI'ER I. INTRODUCTION ••••••••••••••••••••••••••••••••• 1 A. Microelectronics••••••••••••••••••••••••• 1 B. Statement of the problem••••••••••••••••• 3 c. Significance of the stuqy................ 3 D. Reasons for the investigation............ 4 CHAPI'ER II. REVIEH OF THE LITERATURE••••••••••••••••••••• 5 A. Active network and hybrid approach....... 5 B. Thin-film approach••••••••••••••••••••••• 7 c. Monolithic approach•••••••••••••••••••••• 8 D. Surmnary••••••••••••••••••••••••••·••••••• 10 CHAPI'ER III. INDUCTANCE DIODES•••••••••••••••••••••••••••• 11 A. Theor.r••••••••••••••••••••••••••••••••••• 11 B. Description of inductance diodes......... 13 CHAPI'ER IV. A DISCUSSION OF :HODELS ••••••••••••••••••••••• 17 CHAPI'ER V. FINITE DIFFERE~CE EQUATIONS AND THE LINVILL MODEL•••••••••••••••••••••••••••• 19 CHAPI'ER VI. ANALYSIS OF AN UNS~RICALLY DOPED P-N DIODE•••••••••••••••••••••••••••••••• 27 A. Lumped model••••••••••••••••••••••••••••• 27 B. Small signal equivalent cir~uit.......... 31 CHAPI'ER VII. COMPARISON HITH EXPERD1ENT ••••••••••••••••••• 41 CHAPI'ER VIII. CONCLUSIONS AND RECOMMENDATIONS •••••••••••••• 45 BIBLIOGRAPHY................................................... 47 APPENDIX A•••••••••••••••••••••••••••••••••••••••••••••·••••••~ 50 APPENDIX B•••••••••••••••••••••••••••••••~••••••••••••••••••••• 52 VITA••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 57 v LIST OF FIGURES Fi.gure Page 1. Narrow-base PIR diode·~··••••••••••~••••••••••••••••••••• 14 2. Wide-base PIR diode •• ~•••••••••••••••••••••••••••••·••••• 16 3· PIN diodA•••••••••••••••••••••••••••••••••••••••••••••••• 16 4. Semiconductor b~1k region•••••••••••••••••••••••••••••••• 20 5. Lumped model of semiconductor bulk••••••••••••••••••••••• 25 6. Unsymmetrically doped junction diode••••••••••••••••••••• 27 7. Model of a p.n junction•••••••••••••••••••••~•••••••••••• 28 8. Lumped model of junction diode••••••••••••••••••••••••••• 30 9. Small-signal equivalent circuit of diode junction........ 36 10. Small-signal equivalent circujx of diode base •••••••••••• 39 11. Equivalent circuit of tmsymmetrical diode•••••••••••••••• 40 12. Impedance magnitude and phase as a function of d-e current for diode #2•••••••••••••••••••••••••••••••• 41 13. Impedance of an unsymmetrically doped diode as a function of d-e current with frequency as a parameter (diode #1)•••••••••••••••••••••••••••••••· 43 14. Impedance of an unsyrnnetricaJ~y doped diode as a function of d-e current with frequency as a parameter (diode #2)•••••••••••••••••••••••••••••••• 44 15. Semiconductor regions of a unijunction transistor~···•••• 51 16. Circuit used to measure diode impedance. • • • • • • • • • • • • • • • • • 51 vi LIST OF TABLES Table Page 1. Impedance magnitude and phase as a function of d-e current (diode #2)••••••••••••••••••••••••••••• 52 2. Measured impedance of diode #1 as a function of d-e c1~rent and frequency•••••••••••••••••••••••••• 53 Measured im:r::edance of diode #2 as a fl.Ulction of d-e current and frequency•••••••••••••••••••••••••• 4. Calculated im~dance of diode #=1 as a fu."1ction of d-e current and frequency•••••••••••••••••••••••••• 55 5. Calculated impedance of diode #2 as a function of d-e current and frequency•••••••••••••••••••••••••• 56 v:ti LIST OF SYMBOLS A ••• diode cross sectional area 0 A ••• angstrom unit c ••• capacitance .... junction capacitance d .... diode base length D ••• effective diffusion constant ••• diffusion constant for electrons ••• diffusion constant for holes e .... magnitude of electronic charge unit ••• electric field intensity h ••• henry (unit of inductance) .... combinance ••• electron diffusance ••• hole diffusance ••• current I ••• intrinsic region ••• electron current ••• hole current ••• electron current density ••• hole current density ••• j\Ulction k ••• Boltzmann's constant L ••• inductor ••• diffusion length for holes .... electron mobilance viii ••• hole mobilance n ••• region o£ semiconductor with excess electrons n ••• mean density of electrons excess density of electrons at noint i ••• 4 ••• electron density in n-region ••• heavily doped n-region N ••• n-type semiconductor N ••• carrier concentration ••• ionized impurity density ••• region o£ semiconductor with excess holes p ••• mean density of holes ••• excess density of holes at point i ••• hole density in n-region ••• heaviLY doped peregion p ••• P-type semiconductor Q ••• quality factor R ••• resistance R ••• infinite recombination velocity center ••• base resistance ••• storance T .... absolute temperature v ••• voltage ••• junction voltage X ••• distance along length of semiconductor bulk ••• impedance 0( • • • short circuit current transfer ratio cr • • • conductivity )l ••• !l'lobU:i.ty of current carriers Jln ••• electron mobility Pp ••• hole mobility Jp .... lifetime or holes w ••• angular frequency bar over symbol indicates complex or phasor quantity CHAPI'ER I INTRODUCTION A. Microelectronics. The term microelectronics means any device-and-circuit technology that allows complete electronic functions to b9 per- formed by a very small module or devi('!e package. Microelectronics encompasses the w:i.d.e spectrum of modern-day electronics advance- ments 1mder the va.ried labels of microminiaturization, molecular electronics. microcircui.ts, thin films, chip and multi-chip circuits, integrated circuits and others. The technology and name that is presently forging ahead as the state-of-the-art is integrated circuits. Although integrated circuits include a family of fabrication techniques, there are only two basically different processes. These generic processes, utilizing entirely different design and fabrication principies, are the silicon monolithic process and the thin film process. The root of the term monolithic may be traced to the Greek: mono--meaning single, and lithos-- meanjng stone. A monolithic circuit is a circuit fabricated from a single stone, or single crystal. The silicon-diffused mono] ithic circuit consists of a number of circuit ele:rnents, both active and passive, dif'fused into a continuous body of single crystal silicon substrate. The term thin film as it applies to integrated circuits is quite ambiguous. The film refers to the coating of dielectric, resistive, conductive, or semiconductive material that is deposited on a passive substrate such as glass or ceramic. Used correctly, thin film defines layer thicknesses in the range from one mono­ o layer (about 5 A) to approximately 1 micron. Any film of larger 2 thickness dimension should be referred to as thick .film. In integrated electronics, it is common to term every deposited l~er a thin film even thot~h it be a mil or more thick. The thin film circuit consists of a number
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