Atomic Diffusion Processes in Silicon
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ATOMIC DIFFUSION PROCESSES IN SILICON SOKRATES T. PANTELIDES IBM Research Division Thomas J. Watson Research Center Yorktown Heights, NY 10598
ABSTRACT The mechanisms of self-diffusion and dopant impurity diffusion in silicon have been the subject of intense debate since the 1960's. Until the mid-1980's, there was only limited experimental information and virtually no theory. In the last five years, however, first-principles calculations of many key quantities and new experimental data have led to significant progress. This paper traces the major theoretical advances and the key experimental data that have resolved many controversies and have provided a fairly comprehensive picture of diffusion processes. Theory has also recently provided detailed microscopic information about the diffusion of interstitial hydrogen.
INTRODUCTION Questions of atomic diffusion in Si have been quite controversial largely because experimental data are incomplete and theory for the underlying key quantities was, until recently, lacking. In this paper, we will first trace briefly a number of key theoretical developments that happened in recent years. We will then describe the impact of these developments on our understanding of self-diffusion, dopant impurity diffusion and hydrogen diffusion. In each of these cases, we will discuss the historical background and key experimental advances that also contributed to unraveling many puzzles. The prospects for future developments to elucidate remaining questions are assessed as very promising.
THEORETICAL DEVELOPMENTS In order to obtain a complete theoretical description of atomic diffusion processes in a crystal, one must first be capable of calculating the properties of point defects. Until about the end of the 1970's, the theory of point defects was quite primitive. Though a number of formalisms had been developed, actual calculations were limited to simple techniques that entailed drastic approximations whose consequences could not be assessed.' Beginning in 1978, there has been an explosion in theoretical developments for describing point defects in semiconductors. Two seminal papers by Baraff and Schluter 2 and by Bernholc, Lipari and Pantelides 3 reported practical Green's-function approaches that allowed first-principles calculations of the charge density and energy levels of point defects at the same level of sophistication and accuracy as was already possible for perfect bulk crystals and surfaces. The Schroedinger equation for a point defect in an oth-
Mat. Res. Soc. Symp. Proc. Vol. 163. ©1990 Materials Research Society
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erwise perfect crystal was solved self-consistently without free parameters. The Green's-function approach was used widely by many authors over the next several years. 4 In 1984, Car, Kelly, Oshiyama and Pantelides5 implemented a modified Green'sfunction approach and reported total energies, which are key quantities in diffusion questions as formation and migration energies. Independently, Bar-Yam and Joannopoulos 6 showed that a supercell approach, which
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