Determination of strain distributions from X-ray Bragg reflexion by silicon single crystals

Abstract

Accurate determination of strain distributions normal to the crystal surface is attempted through best-fitting of intensity profiles recorded with a double-crystal diffractometer and corresponding theoretical curves computed within the frame of the dynamical diffraction theory. The strain distributions are assumed to be one-dimensional and their functional forms are supposed from the sample preparation process. The fits are quite satisfactory for three samples prepared by boron diffusion, phosphorus diffusion and epitaxic growth with germanium doping. For samples containing boron and phosphorus, sheet-resistivity measurements combined with anodic oxidation showed diffusant distributions which were reasonably proportional to the strain distributions assumed above. Ratios of strain to impurity concentration measured here are ca 40% larger than those defined for uniform doping; simple elasticity considerations give an interpretation of this fact and the factor can be expressed in terms of stiffness constants.