Theoretical Solid-State Physics for Semiconductors
Contact: Herbert S. Bennett
CONTENTS
- Goals
- What are Semiconductor Device Simulators and the Physical Models Therein?
- Why are Semiconductor Device Simulators and Robust Physical Models Important?
- What is the Computational Methodology?
- Applications of NIST Enhanced Physical Models
- Impact
- Links
- Collaborators
- Credits
ROM SOLID-STATE PHYSICS SUCH AS THIS:
TO POSSIBLY HIGHER PERFORMANCE AND RUN TIMES FOR SOLID-STATE ELECTRONICS DEVICES SUCH AS HAND-HELD VIDEOPHONES
Image Adapted from Videomaker, December 1999, page 13, and used by permission from the Editor of Videomaker Magazine.
- Apply quantum mechanical concepts from solid-state physics to develop robust physical models for use in understanding and simulating the electronic, optical, and magnetic behavior of elemental and compound semiconductors.
- Provide semiconductor manufacturers with such models to improve design strategies and device performance and reliability.
WHAT ARE SEMICONDUCTOR DEVICE SIMULATORS AND THE PHYSICAL MODELS THEREIN?
Modeling and simulation in the semiconductor industry are very diverse. This project emphasizes those physical models used in device simulators for elemental and compound semiconductors devices such as field effect and bipolar transistors, light emitting diodes, and solid-state lasers. Such devices are the hardware building blocks for most information technologies.
Device simulators require:
- Input parameters for physical models of carrier mobilities, lifetimes, and concentrations, band structure changes, changes in the carrier densities of states, and other effects due to many-body interactions.
- Numerical, self-consistent solutions of non-linear, coupled integro-differential equations in three dimensions.
- Visualization of massive amounts of data from the computer simulations either by using graphics and/or by deriving multi-dimensional, closed-form analytic expressions to represent the numerical results. The use of closed-form analytic expressions makes it much easier to transfer the NIST results to industry for use in commercial and sometimes proprietary software.
WHY ARE SEMICONDUCTOR DEVICE SIMULATORS AND ROBUST PHYSICAL MODELS IMPORTANT?
The following trends in the semiconductor industry are occurring concurrently with rapid changes in the applications of semiconductors. The competitiveness among many semiconductor manufacturers is shifting from an emphasis on technology and fabrication to a much greater emphasis on product design, architecture, algorithm, and software; i.e., shifting from technology oriented R&D to product-oriented R&D in which computers, modeling, and simulation become increasingly crucial for marketplace success. Other trends include:
- Increased costs for R&D and production facilities, which are becoming too great for any one company or country to accept.
- Shorter process technology life cycles.
- Emphasis on faster characterization of manufacturing processes, assisted by modeling and simulation
Computer simulations, often called technology for computer assisted design (TCAD) offer many advantages such as:
- Evaluating "what-if" scenarios rapidly
- Providing problem diagnostics
- Providing full-field, in-depth understanding
- Providing insight into extremely complex problems/phenomena/product sets
- Decreasing design cycle time (savings on hardware build lead-time, gain insight for next product/process)
- Shortening time to market
Computer simulations are particularly useful in meeting the demands imposed by the major industry trends identified in technology roadmaps from ITRS (International Technology Roadmap for Semiconductors), NEMI (National Electronics Manufacturing Initiative), and OIDA (Optoelectronics Industry Development Association); namely - lower product cycle time, increasing product complexity at both the component and system level, "doing it right the first time," and rapid volume ramp-ups.
Some TCAD prerequisites are:
- Modeling and simulation require enormous technical depth and expertise not only in simulation techniques and tools but also in the fields of physics and chemistry.
- Laboratory infrastructure and experimental expertise are essential for both model verification and input parameter evaluations in order to have truly effective and predictive simulations.
- Software and tool vendors need to be closely tied to development activities in the research and development laboratories.
These prerequisites may have considerable business, cost, confidentiality, and logistical implications, and must be carefully evaluated.
WHAT IS THE COMPUTATIONAL METHODOLOGY?
This project depends on fundamentally understanding condensed matter physics. Such physics is expressed theoretically in terms of combinations of Poisson's and Schroedinger's (quantum mechanics) equations, the charge neutrality equation, and the semiconductor transport equations. These coupled, non-linear equations in 3-dimensions are solved self-consistently by discretizing the equations and then diagonalizing the resultant very large, dense, and complex matrices.
NIST has developed a unique theory that is capable of treating both sides of the Mott transition. The Mott transition is the transition from primarily insulating behavior to semiconducting behavior as the dopant density increases. The solutions to coupled equations in this NIST theory are bifurcated and thereby this one theory accounts for both bound-like and continuum-like states in the vicinity of the Mott transition. The Mott transition region is of technological significance for mobile, hand-held transceivers and cellular phones with digital video capabilities.
Some other examples from the semiconductor industry that require high-end computing follow. The names appearing in brackets are associated with the key coupled equations that have to be solved self-consistently, if possible:
- Calculating the electronic structure and transport properties for microelectronic devices that treat all of the conduction and valence sub-bands.
[Schroedinger, Poissson and Shockley] - Interpreting scanning capacitance microscopy measurements for 3-dimensional doping profiles in fully scaled field effect transistors with resolutions of 1 nm to 2 nm.
[Schroedinger, Poissson and Shockley] - Understanding the buckling effect in nano-structures; that is, observing a few atoms out of place and determining whether it is due to the interaction of the probe tip with the surface or whether it is a property of the surface.
[Schroedinger, Poissson and Shockley] - Simulating the optical and electronic behavior of vertical cavity surface emitting lasers (VCSEL) without and especially with quantum dots in the VCSEL quantum well.
[Maxwell, Schroedinger, Poissson and Shockley] - Calculating electronic energy levels of photonic molecules.
[Maxwell, Schroedinger, Poissson and Shockley] - Predicting the RF behavior of semiconductor microwave devices.
[Maxwell, Schroedinger, Poissson and Shockley]
APPLICATIONS OF NIST ENHANCE PHYSICAL MODELS
Technology roadmaps from consensus-based planning efforts, such as those from the ITRS, NEMI, and OIDA, stress the need for predictive physical models that describe carrier transport in compound semiconductors. As a response to this need, Herbert Bennett calculated from quantum mechanical principles the electron and hole mobilities for the ternary compound semiconductors AlGaAs. The results from such calculations lead to better designs and increase productivity in the electronics industry because it is much cheaper to do mobility calculations than to do experiments on large numbers of samples with several values of doping concentrations and composition.
Some suppliers and users of software for simulating semiconductor processes and performance of microelectronic and optoelectronic devices inserted Bennett's mobility models into their simulation tools. Companies, universities, and government agencies use such software throughout the world to simulate and understand better the electrical and optical behavior of lasers, light emitting diodes, transistors, and power amplifiers for the next generation of cell phones that can also receive and transmit digital video. The response has been very positive. In addition, others are considering using some of the underlying elements in Bennett's calculations, such as scattering rates and perturbed carrier densities of states, in Monte Carlo based simulators.
Other research groups have used Bennett's physical models. Prof. Jerry Woodall, Yale University and 2002 National Medal of Technology Laureate, used Bennett's expressions for effective intrinsic carrier concentrations to design and understand more completely the performance of heterojunction bipolar transistors (HBTs) such as those are used in advanced optoelectronic systems. Prof. Mark Lundstrom, Purdue University and 2002 IEEE Daniel E. Noble Awardee, used these expressions to suggest better ways to make more efficient solar cells.
The impact of this work suggested more physically correct strategies based on quantum mechanics for the design of heterojunction bipolar transistors used in linear power amplifiers of cellular phones and other transceivers - very common IT appliances and in other bipolar devices such as solar cells.
Visualization of Dielectric Response Function in Compound Semiconductors
Slides from a recent IEEE EDS Distinguished Lecturer talk
Silvaco International, Inc.
Siborg Inc
Yale University
Stanford University
Purdue University
University of California - San Diego
The vast majority of the deliverables from this project depended in part on having access to ITL's centralized-computing staff for consultations in developing software and to centrally-supported computers accessible over the NIST internal network. In fact, without the support from ITL staff such as Alan Heckert, James Filliben, William George, Howard Hung, Denis Lehane, William Mitchell, James Sims, and Judith Devaney, the impact and timeliness of the deliverables would have been much less. We thank them and other ITL staff too numerous to mention.
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