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Device Simulation of High-Performance Sige Heterojunction Bipolar Transistors

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Device Simulation of High-Performance Sige Heterojunction Bipolar Transistors Device Simulation of High-Performance SiGe Heterojunction Bipolar Transistors vorgelegt von M.Sc. Julian Korn geb. in Heidelberg von der Fakultät IV - Elektrotechnik und Informatik der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften -Dr.rer.nat.- genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr.-Ing. Martin Schneider-Ramelow Gutachter: Prof. Dr. Bernd Tillack Gutachter: Prof. Dr.-Ing. Christoph Jungemann Gutachter: Prof. Dr.-Ing. Wolfgang Heinrich Tag der wissenschaftlichen Aussprache: 27. Februar 2018 Berlin 2018 Abstract Silicon-germanium (SiGe) heterojunction bipolar transistors (HBT) are well suited for high-frequency applications. Their performance has been improved continuously in re- cent years. Today’s SiGe HBT technologies show transit frequencies fT up to 300 GHz and maximum oscillation frequencies up to 500 GHz. Numerical device simulation plays an important role in the development of SiGe HBTs. Possible optimizations of the transistor can be evaluated by simulation, which reduces the number of necessary test wafers. Furthermore, device simulation helps to explore the physical mechanisms that govern the performance of the SiGe HBTs. The benefit of device simulations depends on their predictive power. Limitations in the underlying model of charge transport can lead to false simulation results. Device simulation based on the hydrodynamic transport model is still the workhorse for the optimization and investigation of SiGe HBTs. More rigorous models such as the Boltz- mann transport equation are computationally very expensive, which considerably limits their use. In this thesis, the ability of state-of-the-art hydrodynamic simulation to predict the RF-performance of advanced SiGe HBTs is evaluated. For this purpose, a comprehensive comparison between measured and simulated electrical characteristics is made. SiGe HBTs with a scaled vertical doping profile and a transit frequency above 400 GHz are used in this investigation. The impact of variations of the vertical doping profile on the transit frequency is investigated by simulation and experiment. Possible optimizations of the lateral architecture of the SiGe HBT are explored by means of simulation. i Zusammenfassung Silicium-Germanium (SiGe) Heterobipolartransistoren (HBT) sind für Höchstfrequenz- anwendungen gut geeignet. Ihre Leistungsfähigkeit bei höchsten Frequenzen wurde in den letzten Jahren stetig verbessert. Heutige SiGe HBT Technologien verfügen über Transitfrequenzen fT von bis zu 300 GHz und maximale Oszillationsfrequenzen von bis zu 500 GHz. Numerische Bauelementsimulation nimmt in der Entwicklung von SiGe HBTs eine wichtige Rolle ein. Mögliche Optimierungen des Transistors können vorab mit Hilfe der Simulation getestet werden, was zu einer Reduzierung der Anzahl der benötigten Testwa- fer führt. Zusätzlich trägt die Bauelementsimulation zum Verständnis der physikalischen Mechanismen bei, welche die Leistung des SiGe HBTs bestimmen. Der Nutzen der Bauelementsimulation für die Entwicklung neuer Generationen von SiGe HBTs hängt von deren Vorhersagekraft ab. Unzulänglichkeiten des zugrundeliegen- den Modells des Ladungstransports können zu falschen Simulationsergebnissen führen. Bauelementsimulation, welche auf dem hydrodynamischen Modell des Ladungstrans- ports basiert, ist die meistverwendete Methode zur numerischen Untersuchung und Op- timierung von SiGe HBTs. Exaktere Modelle des Ladungstransports wie die Boltzmann- Transportgleichung erfordern einen sehr hohen Rechenaufwand, welcher ihre Anwendung deutlich einschränkt. In dieser Arbeit wird die Fähigkeit der hydrodynamischen Bauelementsimulation zur Vorhersage der Hochfrequenz-Leistungsfähigkeit moderner SiGe HBTs untersucht. Hier- zu wird ein umfassender Vergleich zwischen simulierten und gemessenen elektrischen Kenngrößen angestellt. Für diesen Vergleich werden SiGe HBTs mit einem skalierten vertikalen Dotierungsprofil verwendet, welche Transitfrequenzen über 400 GHz aufwei- sen. Der Einfluss des vertikalen Dotierungsprofils wird experimentell und simulativ un- tersucht. Mögliche Optimierungen der lateralen Transistorarchitektur werden mit Hilfe der Simulation evaluiert. iii Contents 1. Introduction1 1.1. The SiGe HBT . .2 1.1.1. Figures of Merit . .3 1.1.2. SiGe HBT Performance Factors . .4 1.1.3. Recent Developments . .5 1.2. TCAD for SiGe HBTs . .6 1.3. Thesis Content . .7 2. Device Simulation Framework9 2.1. Semiconductor Equations . .9 2.1.1. Boltzmann Equation . .9 2.1.2. Method of Moments . 10 2.1.3. Hydrodynamic Transport Model . 12 2.1.4. Drift-Diffusion Model . 14 2.1.5. Poisson Equation . 15 2.1.6. Implementation in Device Simulators . 15 2.1.7. Carrier Statistics . 16 2.2. Transport Parameters . 17 2.2.1. Energy Relaxation Time . 17 2.2.2. Mobility . 18 2.2.3. Effective Density of States . 21 2.2.4. Hydrodynamic Model Parameters . 22 2.3. Calibration of the Effective Bandgap in SiGe . 23 2.3.1. Characterization of the Box-Shaped Reference Profiles . 25 2.3.2. Extraction of the Effective Bandgap . 27 2.3.3. Temperature Dependence of the Effective Bandgap . 29 2.4. Summary . 30 3. Comparison of 2D Simulation and Experiment 33 3.1. Experimental Characterization of the Reference Transistors . 34 3.1.1. Electrical Characteristics . 34 3.1.2. Vertical Base Profile . 36 3.2. Setup of the Simulation . 39 3.2.1. Geometry of the 2D Simulation Domain . 39 3.2.2. Doping Profile . 40 3.2.3. Effective Bandgap . 43 3.2.4. Series Resistance . 44 v Contents 3.2.5. Self-Heating . 46 3.3. Calculation of fT and fmax .......................... 48 3.4. Simulation Results . 49 3.4.1. Hydrodynamic Transport Model Parameters . 50 3.4.2. Impact of the Bandgap on the Collector Current Ideality . 51 3.4.3. High Injection and Self-Heating . 55 3.4.4. Transit Frequency . 57 3.4.5. Transit Time Analysis and Comparison with Drift-Diffusion Simu- lation . 58 3.4.6. Impact of the Parasitics . 62 3.5. Summary . 67 4. Impact of Vertical Profile Variations on the Transit Frequency 69 4.1. Simulation of the inner 1D Transistor in Sentaurus Device . 69 4.2. Quasi-Static Transit Time Analysis . 71 4.2.1. Regional Partition of the Transit Time . 73 4.2.2. Small-Signal Equivalent Circuit . 75 4.2.3. Comparison of 1D and 2D Simulation . 77 4.3. Examples of Vertical Profile Variations . 80 4.3.1. Impact of the Base-Emitter Junction Width . 80 4.3.2. Impact of the Selectively Implanted Collector . 83 4.3.3. Impact of the Position of the Heterojunction . 85 4.3.4. Comparison with Profile N3 from Scaling Roadmap . 89 4.4. Sensitivity of the Simulated Transit Frequency to the Vertical Profile . 95 4.5. Summary . 98 5. Impact of Variations of the Lateral Architecture on the RF Performance 99 5.1. Impact of the Width of the Emitter . 100 5.2. Base Link Doping . 102 5.3. Impact of the Collector Window Width . 108 5.4. Impact of the Oxide Thickness . 110 5.5. Analysis of Lateral Scaling of the DOTSEVEN HBT . 113 5.6. Summary . 116 6. Conclusions and Outlook 117 A. Numerical Parameters of the Physical Models 119 A.1. Parameter Values of the Energy Relaxation Time Model . 119 A.2. Parameter Values of the Mobility Model . 119 A.3. Parameter Values of the Effective DOS Model . 122 B. Depth Profiling Techniques 123 B.1. X-ray diffractometry (XRD) . 123 B.2. Secondary Ion Mass Spectroscopy (SIMS) . 124 vi Contents B.3. Energy-Dispersive X-Ray Spectroscopy in a TEM . 124 Bibliography 127 List of Figures 137 List of Tables 141 List of Abbreviations and Symbols 143 Abbreviations . 143 Symbols . 144 List of Publications 145 Publications . 145 Co-authored Publications . 145 vii 1. Introduction Silicon-germanium (SiGe) heterojunction bipolar transistors (HBT) are well suited for radio-frequency (RF) applications. They provide high cut-off frequencies, can handle high power densities and have a high current drive capability and low noise. The per- formance of SiGe HBTs has been improved continuously in recent years. Today, SiGe HBTs are widely used in applications in the mm-wave range, which have traditionally been the domain of III-V compound semiconductors [1, 2]. Modern SiGe HBT technolo- gies such as IHPs SG13G2 reach frequencies of several hundred GHz [3]. Major drivers for this development are applications like broadband communication, automotive radar or millimeter-wave sensing and imaging [4, 5, 6, 7]. Numerical device simulation plays an important role during the development of new technology generations. Variations and optimizations of the device can be evaluated by simulation which helps to reduce the number of test wafers. For example, simulation can be used to predict the impact of optimized doping profiles, device geometries and material compositions on the electrical characteristics of the transistor. The benefit of such simulations depends on their predictive power. Limitations of the physical models which describe the carrier transport can lead to false simulation results. For this reason, a lot of effort has been put into the improvement of the simulation tools. The validity of conventional device simulation methods based on the drift-diffusion and the hydro- dynamic transport models has been extended continuously by including sophisticated models for transport parameters like the mobility [8, 9, 10]. Moreover, advanced simu- lation methods, based on the solution of the Boltzmann transport equation have been developed and applied to SiGe HBTs [11]. The main objective of this work is to evaluate how accurate such simulation methods can predict the performance of modern SiGe HBTs. This
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