Stress and thermal expansion of boron-doped silicon membranes on silicon substrates

A new analysis is presented to describe the weak linear temperature dependence of the stress observed from 293 to 550 K in B-doped silicon membranes supported by silicon substrates. In contrast to a previous treatment, where consideration was given only to the existence of a differential thermal expansion coefficient △ α, the present treatment also takes into account the temperature dependence of the elastic modulus of the membrane, an effect which cannot be neglected when △α is very small. It is now concluded that boron doping to a nominal level of 1020atoms/cm3increases the expansion coefficient of Si over the range 293–550 K by 1.1X 10-8 K, an increment only one-half as large as that previously reported. In addition, the {100} biaxial elastic modulus of the membrane B is deduced to have a temperature coefficient (1 /Bo) dB /dTof — 3.7 X 10 -5/K. The value of the present analysis in avoiding other misinterpretation of the experimental results is pointed out. © 1991, American Vacuum Society. All rights reserved.