Strain Measurements in Thin Film Structures by Convergent Beam Electron Diffraction

The Convergent Beam Electron Diffraction technique (CBED) has been applied to determine the lattice strain in Si$_{1-x}$Ge$_x$/Si heterostructures and below patterned films on silicon substrates. The well known problem of the stress relaxation which occurs in thinned TEM samples has been overcome, in the case of the heterostructures, by applying the isotropic elasticity theory to the lattice constants measured along different crystallographic directions through the shift of the High Order Laue Zone (HOLZ) lines in the central disk of the CBED patterns. In this way bulk strain values have been obtained, in good agreement with values deduced from independent techniques. In patterned structures, the high spatial resolution of the CBED technique has been applied to determine the distribution of the components of the strain tensor induced into oxidized silicon substrates by Si$_3$N$_4$ stripes. A good agreement with the results obtained using numerical computations has been found