This simple tutorial shows a simple simulation studies for absorption of semiconductor devices.

The structure is a simple AlGaAs quantum well which can be seen in the following figure.

<caption>The structure of the simulated device</caption>

The barriers are made from AlGaAs, and the well is GaAs.

The optics feature initialization looks like this:

optics{
        name = "all"
	debuglevel = 2

	interband = $INTERBAND # yes
	intraband = $INTRABAND # no

        polarization{ name="y_plus_iz"  re = [0,1,0] im = [0,0,1] }
	polarization{ name="y_minus_iz" re = [0,1,0] im = [0,0,-1] }
		
 	output_transitions = $TRANSISITONS #yes
		
	occupation_threshold = $MIN_OCCUPATION
	energy_threshold = 1E-8
	transition_threshold = $MIN_TRANSISTION
		
	energy_min = $ENERGY_MIN
	energy_max = $ENERGY_MAX
	energy_resolution = $ENERGY_RESOLUTION
		
	k_integration{
	  num_points = $NUM_INTEGRATION_KPOINTS
	  num_subpoints = $NUM_INTEGRATION_INTKPOINTS
	  
	  symmetry = 1			
			
          relative_size = $RELATIVE_INTEGRATION_KSPACE
	}
}

• interband, intraband Initalizes if intra/interband transitions should be calculated or not.
• polarization describes the polarization direction of the electric field. (When there is an 'i' it means it is circulary polarized)
• output_transitions Calculation of the transition matrix elements (yes/no)
• occupation_threshold, energy_threshold, transition_threshold The minimum value of the energy,

occupation and transition intensity of the transition which should be calculated.

• energy_min, energy_max Boundaries of the calculated energy spectra.
• energy_resolution The energy grid spacing of the calculated points in the energy space.
• k_integration defines the points for integrating in the k space

After it has calculated the strain, it calculates the the bandedges of the structure which can be seen on the figure:

<caption> The bandedges in the sample Conduction band HH, and LH bands SO band </caption>

In the quantum well region it can be seen that the bandedge smaller, and the valence band edge is close to the fermi level. That is the reason, why the valence band is populated, and interband transition could happen.

From the bandedges the program calculates the wavefunctions, in each band which is definied in the line:

num_electrons=$NumE
num_holes=$NumH 

It means how many electron and hole states should be calculated. The wavefunctons are plotted on the following figure:

<caption>The wavefunction probabilities for each band</caption>

For each defined polarization the program calculates the transition matrix elements between the states (integration of the wavefunctions in k space). Then it calculates the absorption coefficient (1/mucm) per one transition (it should consider the population of the states). For example one absorption coefficient can be seen as a function of the energy of the incoming field:

<caption>The absorption coefficient between the 1st and the 11th eigenstate of the system as a function of energy</caption>

The overall absorption coefficient of the system is the sum of the partial absorption coefficients of each transition.

<caption>The overall absorption coefficient as a function of energy</caption>

Its imaginary part of the permittivity (related to the conductivity) could be calculated from the absorption coefficient with the following formula if the absorption is small.

$\alpha= \frac{\omega}{n_r c} \cdot \frac{\epsilon_2}{\epsilon_0}$

The values of the imaginary part of the permittivity function is in the files imepsilon*.dat.

The summary of the transitions have been saved in the “transitions_all.dat” files, together with the intensity, and the rate of the transition.