# Calculate Elastic Strain Energy in Solid State Physics

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1. Mar 8, 2015

### pzpzpzp

1. The problem statement, all variables and given/known data
A think film of ErAs(rock salt structure, a=0.574nm) is grown on top of a thick GaAs (Zn-blend structure, a=0.565nm) substrate. The substrate orientation and the film growth direction are both <001>. For very thin films, the ErAs is tetragonally distorted such that its in-plane lattice constants match that of the substrate. This occurs in order to minimize the interfacial energy. Of course, there is also a price paid in terms of elastic strain energy.

Assume that the GaAs substrate is perfectly rigid and that the elastic constants (assume isotropic medium) of ErAs are C11=13*10E11[erg/cm^3] and C12=1.6*10E11[erg/cm^3]. Because there is no shear, the elastic energy density of the film is given by:

2. Relevant equations
U=1/2{C11[εxx^2+εyy^2+εzz^2]+2C12[εxxεyy+εxxεzz+εyyεzz]}

a) what is the elastic strain energy(in eV) per Er atom?

b) What is te value of the in-plane stress?

3. The attempt at a solution

At first, I thought it would be a simple plug-in-and-calculate question, but then I realize that I have no idea how to calculate all the ε's or where and how to find them. Nor do I know the units on those constants. Also, I can't imagine how ErAs "tetragonally distorted" looks like. Would someone help me please?

2. Mar 13, 2015