# Band offset and strain-induced valence band splitting in semiconductor compounds

My aim is to draw a plot of $GaAs_{1-x}Sb_{x}$/InP (GaAsSb on InP substrate) band offset as a function of As/Sb composition.

The first part is easy if I'm doing this correctly: I found VBO (valence band offset) parameters for GaAs and GaSb, then the bowing parameter for $GaAs_{1-x}Sb_{x}$ VBO and finally the bowing parameter for $GaAs_{1-x}Sb_{x}$ band gap. This is what I got:

However, when I put GaAs or GaSb on InP, strains appear and the valence band is split into heavy hole and light hole subbands. In some articles I found the way to calculate the splitting:

$\Delta E_{HH}=\partial E_H^V + \partial E_S$ $\Delta E_{LH}=\partial E_H^V - \partial E_S$

$\partial E_S=b(1-2\frac{C_{12}}{C_{11}})\epsilon_{||}$ $\partial E_H^V=2 a^V (1-\frac{C_{12}}{C_{11}})\epsilon_{||}$

a, b and Cs are material properties and can be found in this article: http://jap.aip.org/resource/1/japiau/v89/i11/p5815_s1 (Vurgraftman, Meyer, Ram-Mohan)

However, I'm not sure what the $\epsilon_{||}$ is. Is it the direction of growth? Whatever it is, I can't see where I should consider the substrate, as I assume the strain to be substrate-dependent. Is it hidden in the $\epsilon$?

• I deleted Marek's comment now that the solution has been transferred to an answer. (I also fixed the broken image reference in the question) Thanks for following up, alkamid! – David Z Jul 18 '11 at 19:18

$\epsilon=\frac{a_{substrate}-a_{layer}}{a_{substrate}}$