Description of Current Project ============================== Modern communication technologies demand increasingly faster devices to process high bandwidth data streams. A variety of semiconductor quantum devices, relying on thin layers and abrupt interfaces, are being intensively studied for operation in digital logic circuits operating at terahertz frequencies. Successful integration of these devices into high-speed circuits demands that the discrete device characteristics (current vs. voltage behavior) be controlled within very narrow tolerances. Achievement of this goal requires precise control of layer thicknesses, composition and interface roughness. Such control will not be achieved without the development ane use of sophisticated process models and control methodologies. The goal of the NSF-DARPA funded "Virtual Integrated Prototyping for Epitaxial Growth" program, centered at UCLA and the Hughes Research Laboratories (HRL), is to take the first steps toward achieving this level of control. Materials system ---------------- This program targets a specific material system with a specific goal: controlling the growth rate and morphology of thin films (4-12 monolayers) of aluminum antimonide (AlSb) deposited on indium arsenide (InAs) by molecular beam epitaxy (MBE). We have chosen this material system because of its important application in resonant tunneling devices (RTDs), an example of a quantum device for high speed circuit applications. Controlling nanoscale morphology of barrier layers in quantum devices--for example, the AlSb layer in this prototypical system--is crucial to the reproducibility of these devices. AlSb/InAs is also an excellent prototypical system from a modeling standpoint because it includes many of the features that are present in the growth of any multilayer semiconductor device material, e.g. multiple atomic and molecular species (As_2, Sb_2) and strain that while small, still affects the growth morphology. Modeling and simulation ----------------------- A primary objective of this program is to develop and validate sophisticated process models for thin film deposition techniques, with an emphasis on morphology at the nanometer length scale. Our approach is to develop a hierarchy of models that includes atomistic, continuum and process models validated by experiments. The hierarchy of models is required because an empirical approach is not robust enough to be applicable to a wide range of growth conditions. The hierarchy includes: o Ab initio calculation of activation energies for the key kinetic processes (deposition and surface diffusion, for use in a kinetic Monte Carlo simulation. o Kinetic models, simulated using kinetic Monte Carlo techniques, that include the key kinetic processes (which receive ab initio treatment) to parameterize and calibrate the continuum model. o Continuum equations that provide a suitable basis for developing control models. o Process control models for eventual use in a real-time controller. Control sensor -------------- We will initially use reflection high-energy electron diffraction (RHEED) as our growth sensor for control. This choice is motivated by the following factors: o RHEED oscillation signals contain information about surface morphology in their transient and decay signatures. o The relationship between RHEED oscillations and island step densities has been well established, and hence there is a correspondence between the output of the RHEED sensor and the output of the atomistic model. Team members ------------ A well-integrated team of mathematicians, materials physicists (theoretical and experimental) and control theory specialists is a prerequisite for this program; none of the models described above can be developed in isolation of each other or without experimental input. Our team members and their pertinent areas of expertise are summarized below. Anderson (UCLA) Numerical methods for control and ab initio methods Caflisch (UCLA) Continuum mechanics and Monte Carlo methods Engquist (UCLA) PDEs and numerics Gossard (UCSB) Semiconductor growth and diagnostics Gyure (HRL) Theory and numerics for materials physics Kaxiras (Harvard) Ab initio calculations for semiconductors Meyer (Colorado) Control theory and applications Osher (UCLA) PDEs, numerics and the level set method Vvedensky (Imperial) Theory and numerics for materials physics Weinberg (UCSB) Surface science and microscopy Zinck (HRL) Sensors and semiconductor growth The role of mathematics ----------------------- The development of the atomistic, continuum and process models depends crucially on advances in applied and computational mathematics. There is no existing set of models for thin film growth as fully integrated as the hierarchy proposed here, and the challenges are numerous. Innovative computational methods will improve the efficiency of both ab initio calculations and kinetic Monte Carlo simulations, allowing much more realistic computation as required for our applications. Analysis of the continuum limit for the kinetic Monte Carlo model will transfer information on morphology and material structure from the atomistic to the continuum level. This coarse-graining is one of the most fundamental problems in the mathematics of materials science. Our continuum model describes epitaxial growth through the motion of free boundaries. New methods are required to incorporate free boundary motion into a control model. Industry participation ---------------------- Hughes Research Laboratories is a leader in the development of III-V high speed electronics and is committed to the development of quantum device technology for use in high bandwidth, ultrahigh speed wireless communication applications. The process models developed in this program will play a key role in defining the manufacturing requirements for this important emerging technology.