### Electron ground state energy dependence on alloy composition in a quantum well

In this simple example we demonstrate how the ground state energy of the electron changes in a $Ga_{x}In_{1-x}As/GaAs$ quantum well, when the $Ga$ concentration in the well changes

We need to define a variable $x_alloy$ in the parameters window, and create a parametric sweep for that variable from $0.0$ to $1.0$. We have to use this variable as concetration when we set up the alloy material from $InAs$, $GaAs$ and $GaInAs$

In order to calculate the ground state energy in the function of the alloy concentration, we have to define a line probe for the barrier, and the well materials, and set the expression for the probe to $Calculator_G_up_energy_0_INTERNAL$. This name corresponds to the $Calculator$ named envelope function calculator, which calculates the spin $up$ wave-functions of the electron state at the $G$(gamma) point.

The calculated energy dependence is plotted in Figure 1.

The energy shifted electron wave functions are plotted in Figure 2, which shows that because of the energy gap between the barrier and the well lowers(and the mass also changes) the width of the wave-function gets wider.