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UNIVERSITY OF CINCINNATI _____________ , 20 _____ I,______________________________________________, hereby submit this as part of the requirements for the degree of: ________________________________________________ in: ________________________________________________ It is entitled: ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ Approved by: ________________________ ________________________ ________________________ ________________________ ________________________ ANALYSIS OF HIGH-FREQUENCY CHARACTERISTICS OF PLANAR COLD CATHODES A thesis submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE (M.S.) in the Department of Electrical and Computer Engineering and Computer Science of the College of Engineering 2003 by Rajesh Krishnan B.E. (Electronics & Instrumentation) Annamalai University Tamilnadu, India, 2000 Committee Chair: Dr Marc Cahay Abstract The possibility of surface emitting cathode, which operates at room temperature, is attractive due to its compactness and reduced weight. Such cathodes, known as cold cathodes, can be used in a variety of electronic devices, including microwave vacuum transistors and tubes, pressure sensors, thin film displays, high temperature and radiation tolerant sensors, among others. Recently, M.Cahay and collaborators have proposed a new cold cathode emitter concept, making use of rare-earth sulphides to reach negative electron affinity at the surface. In this thesis, we investigate two unchartered areas in the physical operation of these cathodes which entails a development of a small signal equivalent circuit of the cathode and the effects of noise (mostly due to shot noise of the injecting contact) on the anode current fluctuations. We find that the efficient direct modulation of the anode current with a small AC signal across the CdS layer is possible. For an InP/CdS/Las cold cathode, the degree of electron beam prebunching is dependent on the cathode to anode spacing but is found to be tunable up to frequency well within the K-band for cathode to anode spacing of a few microns. We also have used an Ensemble Monte-Carlo code to study effects of shot noise, in the anode current, in planar Metal/CdS/LaS cold cathodes. We have identified device parameters and biasing conditions for which regime of shot noise suppression but also shot noise enhancement in the anode current fluctuations can be observed for the same cathode. Acknowledgements First and foremost, I would like to thank my advisor Dr.Marc Cahay for his excellent guidance throughout the course of my thesis. This thesis would not be possible without his help, support and guidance. I would also like to thank the committee members, Dr.Roenker and Dr.Boolchand for taking the time and effort to serve on my thesis defense committee. I would also like to thank the Air Force Research Laboratory, Wright Patterson Air Force Base, Dayton, Ohio for their support. I convey my heartfelt gratitude to my parents and my brothers, Suresh and Ramesh, for their love and encouragement. A special word of mention also goes to Uma, Harini and Vidya. A special word of gratitude goes to Shekhar, Ashita, Bijon, Mita, Karthick and Shobana for their sincere love and solid belief in me. A special word of thanks to Aravind, who was a constant source of encouragement. Thanks to all my friends Narain, Mukesh, Chandan, Raj, Texas Mohan, Pradeep, and all my undergrad friends who have helped me in many ways. I also would like to thank my roomies Prashanth, Thodur and Dom for their constant support. I also would like to thank my lab mates Yamini, Jugul, KP, Kalyan, Venkat and Philip. I have tried to include everyone, but unfortunately it is not possible to name all my friends in a single page. Last but not the least; I thank God for showering His blessings upon me. Contents 1 Introduction and Signi¯cance of the Problem 1 1.1 Background: . 1 1.2 Paradigm Shifts . 5 1.3 Previous Analysis of Metal and InP/CdS/LaS Cold Cathodes . 14 1.3.1 Self-Heating E®ects . 14 1.3.2 Current Crowding E®ects . 16 1.3.3 Space-Charge E®ects . 16 1.4 Outline of Thesis . 19 2 AC Current Crowding E®ects in Planar Cold Cathodes 26 2.1 Introduction . 26 2.2 Small AC Signal Equivalent Circuit . 29 2.3 Results . 33 2.4 Conclusions . 42 i 3 Sub-Poissonian and Super-Poissonian Shot Noise 44 3.1 Introduction . 44 3.2 The Ensemble Monte-Carlo Approach . 48 3.3 The E®ects of Shot Noise . 52 3.4 Numerical Examples . 55 3.5 Shot Noise Power Spectrum . 57 3.6 Conclusions . 72 4 Conclusions and Future Work 78 4.1 Conclusions and Future Work . 78 4.2 Suggestions for future work . 80 4.3 List of Journal Publications, Conference Proceedings Papers and Conference Presentations . 81 A Appendix 85 A.1 Ramo's Current Expression . 85 ii List of Figures 1.1 NEA achieved through band bending at the surface of a semiconductor (p- type doped). When the surface of the semiconductor is covered with a low work function material (Á), the vacuum level outside the semiconductor can end up below the minimum of the conduction band in the bulk. This leads to an e®ective negative electron a±nity, i.e., Âeff < 0. 4 1.2 Schematic representation of a Solid-State Field-Controlled Electron Emitter (SSE). [13,14] . 6 1.3 Experimental Current Density J vs applied ¯eld Fapp characteristics of a SSE. [13,14] . 7 1.4 Schematic conduction band diagram of InGaN=GaN ¯eld emitter. Electrons travel ballistically across the InGaN layer and, thus, e®ectively tunnel from the maximum of the GaN conduction band at the GaN=InGaN interface. [15] 10 1.5 Bottom: I-V characteristics of InGaN=GaN (left) and GaN (right) ¯eld emit- ter array. [15] . 11 iii 1.6 Top: cross-section of the cold cathode proposed in refs [2, 1] between two emitter ¯ngers. The substrate can easy be a metal or a heavily doped n- type InP substrate. Trapping of electrons by the LaS semimetallic thin ¯lm leads to a lateral current flow and current crowding in the structure. Bottom: illustration of the partial reflection of the two-dimensional electron gas in the LaS thin ¯lm upon entering the three-dimensional contact regions where the external bias is applied to Au contacts made to the thick LaS regions. The emission window has a length L in the y direction. 15 1.7 Illustration of the chopping action of the electrostatic potential energy pro¯le in front of the LaS thin ¯lm as a result of the space-charge e®ects in the cathode to anode region. The energy distribution h(E) of the current injected into vacuum is shown under the approximation of ballistic transport(solid line) and for the case of inelastic scattering in the CdS layer(dashed line). In the current self-quenching regime, the potential energy pro¯le can oscillate rapidly in front of the cathode(shown by vertical arrows) and the average current collected at the anode is much smaller than the injected current. 18 2.1 Cross-section of a InP/CdS/LaS cold cathode with two emitter ¯ngers on either side of the emission window. The total base current is the sum of Ib the base current due to the shadowing action of the Au contacts and the current 0 Ib due to trapping of electrons in the LaS layer and lateral motion of carriers along the semimetallic thin ¯lm. 27 iv 2.2 Small AC signal equivalent circuit of the cold cathode shown in Fig.1 including a load resistance RL . 32 2.3 Plot of the anode current and base current as a function of the applied bias across the CdS layer for the InP/CdS/LaS cold cathode with the parameters listed in Tables 2.1 and 2.2. 34 2.4 Plot of the transconductance gm and the inverse of the resistance r¼ as a function of the applied bias across the CdS layer for the InP/CdS/LaS cold cathode with the parameters listed in Tables 2.1 and 2.2. 36 2.5 Plot of bias dependence of the parameter z characterizing the e®ects of DC current crowding in the InP=CdS=LaS cold cathode with the parameters listed in Table 2.1. DC current crowding e®ects are negligible as long as the parameter z stays below 0.3 [1]. 38 2.6 Plot of the bias dependence of the temperature in the intrinsic portion of the cold cathode. The back of the InP substrate is assumed to be at room temperature (300K). The cold cathode parameters are listed in Tables 2.1 and 2.2. 40 2.7 Plot of the voltage VL across the load resistance (RL = 1k­) for the InP/CdS/LaS cold cathode with the parameters listed in Tables 2.1 and 2.2 for two di®erent values of the cathode to anode spacing. The full and dashed curves correspond to an anode to cathode spacing equal to 1 ¹m and 5 ¹m, respectively. 41 v 3.1 Top: cross-section of the cold cathode proposed in refs [3, 2] between two emitter ¯ngers. The substrate can easy be a metal or a heavily doped n- type InP substrate. Trapping of electrons by the LaS semimetallic thin ¯lm leads to a lateral current flow and current crowding in the structure. Bottom: illustration of the partial reflection of the two-dimensional electron gas in the LaS thin ¯lm upon entering the three-dimensional contact regions where the external bias is applied to Au contacts made to the thick LaS regions. The emission window has a length L in the y direction.

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