Influence of stress-dependent surface generation of interstitials on stacking fault growth and dopant diffusion in silicon - Статья

Аrticle: Influence of stress-dependent surface generation of interstitials on stacking fault growth and dopant diffusion in silicon Loiko Konstantin Valeryevich УДК 531 Влияние зависимой от стресса поверхностной генерации междоузлий на рост дефектов упаковки и диффузию легирующих примесей в кремнии Лойко Константин Валерьевич Ph.D. Freescale Semiconductor, Остин, Техас, США Разработана модель зависимой от стресса поверхностной генерации и рекомбинации точечных дефектов в кремнии. С ее помощью смоделированы такие явления, как рост дефектов упаковки и диффузия легирующих примесей в кремнии Ключевые слова: КРЕМНИЙ, МЕЖДОУЗЛИЯ, ТОЧЕЧНЫЕ ДЕФЕКТЫ, ДЕФЕКТЫ УПАКОВКИ, ДИФФУЗИЯ ЛЕГИРУЮЩИХ ПРИМЕСЕЙ UDC 531 Influence of stress-dependent surface generation of interstitials on stacking fault growth and dopant diffusion in silicon Loiko Konstantin Valeryevich Ph.D. Freescale Semiconductor, Austin, Texas, U.S.A. A model is developed for stress-dependent surface generation and recombination of point defects in silicon. Using the model, such phenomena as stacking fault growth and stress-mediated dopant diffusion in silicon are simulated Keywords: SILICON, INTERSTITIALS, POINT DEFECTS, STACKING FAULTS, DOPANT DIFFUSION Introduction Silicon self-interstitials play an important role in the growth of stacking faults and contribute to dislocation nucleation. The effects of stress on dopant diffusion in silicon are also attributed to the behavior of intrinsic point defects in stress fields [1-5]. Equilibrium concentrations of silicon self-interstitials and vacancies are known to depend on stress as follows [6,7]: , (1) , (2) where and are the equilibrium concentrations of interstitials and vacancies, respectively, in the presence of the stress field, and are the stress-free equilibrium concentrations, is pressure, and are the activation volumes, k is Boltzmanns constant, T is absolute temperature. The terms and describe a reversible work process of the point defect formation under stress. They show a change in the Gibbs free energy of the formation of an interstitial or vacancy due the presence of the stress field [7]. Therefore, the activation volumes in Equations 1 and 2, being the coefficients of pressure in the reversible work process, are indeed thermodynamic formation volumes. These activation volumes have been calculated based on the assumption of sphericity of the interstitial and vacancy with radii of 1.11 A and 2.47 A, respectively [1-3], or using ab initio calculations [4,5,8]. Nevertheless, there is no agreement in literature on the values for these parameters. From Equations 1 and 2, the equilibrium concentration of self-interstitials decreases and the equilibrium concentration of vacancies increases under compressive stress. Tensile stress has an opposite effect on the equilibrium point defect concentrations. Since boron and phosphorus are known to diffuse mainly in pairs with interstitials [9], retardation of the diffusion of these dopants is expected under compressive stress. There is some experimental evidence of such retarded diffusion [3,10]. At the same time, boron diffusion enhancement under compressive stress has been reported as well [11,12]. This discrepancy could possibly be explained by differences in point defect interaction with the free surface [4]. Most models of stress-dependent point defect and dopant diffusion consider only bulk interactions. However, stress-dependent surface generation and recombination of point defects may cause significant changes in their distributions. These processes are not well understood due to a lack of experimental results. In this paper, a model is developed for the stress-induced redistribution of intrinsic point defects in silicon. It incorporates equilibrium conditions different for defects at the surface and in the bulk of silicon, taking into account stress-dependent surface generation and recombination of point defects. Using the model, such phenomena as stacking fault growth and stress-mediated dopant diffusion are simulated. 1. Calculation of Activation Volumes for Interstitials and Vacancies In the derivation of the activation volumes for intrinsic point defects, silicon is considered as an elastic continuum. A Si-interstitial is modeled as a non-compressible ball. The radius of the ball equals to the radius of a silicon atom, Ra = 1.32 A [13]. The ball is inserted into a spherical hole having the radius Ri of an interstitial site. The radius of an interstitial site is the maximum radius of a ball that can be inserted into the interstitial site without deforming it. Two interstitial sites in silicon are considered. First, the octahedral site, such as the one which center has coordinates in a unit cell of the silicon lattice. The coordinates of the six nearest lattice sites are ?, ?, 1; ?, 1, ?; 1, ?, ?. The distance between the center of the octahedral site and these lattice sites is a0/8. Therefore, Ri = a0/8 - Ra ? 0.93 A, where a0 = 5.4307 A is the silicon l