Multiscale Modeling of Stress-Mediated Diffusion in Silicon - Volume Tensors
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MULTISCALE MODELING OF STRESS-MEDIATED DIFFUSION IN SILICON { VOLUME TENSORS
W. WINDL , M. S. DAW , N. N. CARLSON , M. LAUDON Digital DNA Laboratories, Motorola, Inc., Austin, TX Dept. of Physics & Astronomy, Clemson University, Clemson, SC Computational Materials Group, Motorola, Inc., Los Alamos, NM Axiowave Networks, Inc., Marlborough, MA 1
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ABSTRACT
In a previous paper, we presented a general theoretical treatment of the e ect of stress on defect di usion in Si (M. S. Daw, W. Windl, N. N. Carlson, M. Laudon, and M. P. Masquelier, to be published in Phys. Rev. B). In this paper, we discuss the calculation of the parameters governing the stress dependence of the di usivity, which are volume quantities, and present the fully anisotropic volume tensor for vacancy formation in Si.
INTRODUCTION
The e ect of stress on dopant di usion in silicon has recently taken on more importance for microelectronics. Shrinking device dimensions and the introduction of exotic materials in modern microelectronics has caused a re-examination of the e ect of stress on di usion. Stress e ects on dopant di usion have been suggested to cause signi cant deviations in the device characteristics for both nMOS and pMOS devices. ; On the experimental side, contradictory results for the qualitative in uence of stress on boron di usion further motivate a fundamental investigation of stress e ects on di usion: Whereas the measurements of Aziz et al. { suggest enhanced di usivity, other work nds retarded di usion under compressive pressure { . Most theoretical work regarding the e ect of stress on di usion assumes a hydrostatic state of stress in the substrate, which is however only a special case. { Stresses caused by dislocations, deposition processes, thermal and geometric e ects all add to a complex stress state under a multi-layered gate stack. Additionally, a stress concentration typically exists at the gate edge caused by the peeling stress peak at the free edge of the gate stack. The resulting stress concentration can; produce stress magnitudes approaching the material strength even at low temperatures. Until recently, the only fundamental treatment of di usion in a general stress eld was given by the work of Dederichs and Schroeder, who derived the e ect of stress on di usivity of vacancies in simple face-centered cubic (fcc) crystals. However, we found their derivation from microscopic lattice hops ;to be only a special case of a more general solution which we derived in a recent paper. The more universal methodology presented in that paper admits for treatment of arbitrarily complex defects in external elds and establishes the generic relationship between detailed atomistic microscopic di usion processes and longrange di usivity, thus enabling a complete rst-principles calculation of di usion, within the limitations of the underlying transition state theory. 12
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EFFECT OF STRESS ON DIFFUSION
When a defect is created, a solid (which we assume to be uniform in the absence of stress) c
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