Relaxation of a strained quantum well at a cleaved surface

摘要

Scanning probe microscopy of a cleaved semiconductor surface provides a direct measurement of the elastic field of buried, strained structures such as quantum wells or dots, but allowance must be made for relaxation at the surface. We have calculated this relaxation analytically for the exposed edge of a strained quantum well within classical elastic theory for a linear, isotropic, homogeneous medium. The surface bulges outward if the quantum well has a larger natural lattice constant and the dilation changes sign near the surface, which may enhance recombination. Results are given for a well of constant composition or an arbitrary variation along the growth direction and compared with cross-sectional scanning tunneling microscopy of InGaAs quantum wells in GaAs. Consistent values for the composition of the wells were obtained from counting In atoms, x-ray diffraction, and photoluminescence. The lattice constant on the surface and the normal relaxation were compared with the calculation. Qualitative agreement is good but the theory gives only about 80 of the observed displacement. Some of this difference can be explained by the larger size of indium atoms compared with gallium, and the different surface reconstruction and buckling behavior of InAs and GaAs (110) surfaces upon cleavage.