Stress Effects on As Activation in Si
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Stress Effects on As Activation in Si Chihak Ahn1, and Scott T. Dunham1,2 1 Dept. of Physics, University of Washington, Seattle, WA, 98195 2 Dept. of Electrical Engineering, University of Washington, Seattle, WA, 98195 ABSTRACT We studied stress effects on As activation in silicon using density functional theory. Based on lattice expansion coefficient, we calculated the formation energy change due to applied stress and plotted the stress dependence of the AsmV concentration. We found that biaxial stress results in a minimal impact on As activation, which is consistent with experimental observations by Sugii et al. [J. Appl. Phys. 96, 261 (2004)], who found no change in the As activation under tensile stress. INTRODUCTION Stress effects become more important in modern ULSI technology since they can be employed to improve various material properties. Uniaxial stress has been employed in MOSFET devices since the 90 nm node technology step to improve carrier mobility [1]. Properly applied stress can also suppress dopant diffusion [2], enhance activation [3], and reduces the band gap [4]. Therefore, understanding stress effects can provide more room for further MOSFET scaling. As deactivation is governed by AsmVn cluster formation, and clusters with m=1-4 and n=1 are considered as dominant species in deactivation kinetics [5]. Under equilibrium conditions, the concentrations of these clusters are determined by free As and V concentrations and cluster formation energies. The formation energy is a function of the induced strain when stress is applied. The induced strain is the key factor to study stress effects on As activation. The induced strain is generally a rank two tensor, but substitutional dopants produce isotropic lattice distortion, so induced strain due to substitutional dopant becomes scalar defined as ∆ε = (arelaxed − aSi ) / aSi , where arelaxed is the fully relaxed lattice constant with dopant/defect and aSi is equilibrium Si lattice constant. Cargill et al. observed lattice contraction at high active As concentration and attributed it to free electrons at the conduction band edge [6]. However, density functional theory (DFT) predicts that electrons result in lattice expansion (Table 1). To resolve this contradiction, we investigated the detailed local structure around As atoms in Si matrix using DFT, and determined the induced strain. Based on calculated induced strains, stress effects on the active As concentration relative to the total chemical As concentration were predicted. SIMULATION AND RESULT At equilibrium conditions, the change in the concentration of a defect X (As, V or AsmV) due to stress is given by [7]
r
r N X (ε ) ≈ exp(−∆E Xf (ε ) / kT ) , N X (0)
r
(1)
where ∆E Xf (ε ) is the change in the formation energy of X due to stress. In case of the AsmV cluster, it is given by r r r r ∆EAsf m V (ε ) = −Ω0 (∆ε AsmV − m∆ε As )Cε , (2) r
r
where Ω0 is volume of a lattice, ∆ε AsmV ( ∆ε As ) is the induced strain due to AsmV (As), C is the r
elastic stiffness tensor of Si, and ε i
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