In this tutorial we demonstrate how to calculate the internal quantum efficiency of a multi-quantum well structure as the function of the applied forward bias.

nextnano++ is capable of simulating recombination processes such as Shockley-Read-Hall (SRH), Auger and radiative recombination. Only the radiative (direct) recombination process generates photons (spontaneous emission). If it is summed up over the full device, it equals the total number of photons emitted from the device per second, the photocurrent: $I_{\rm photon}$.

$$R_{\rm sp}= c_r (n p- n_{\rm i}^2)$$

$$I_{\rm photon} = \int\limits_{V_0} R_{\rm sp} {\rm d}V$$

If the injected charge carrier current is $I_{charge}$, than the internal quantum efficiency is

$$\eta_{qe} = \frac{I_{photon}}{I_{charge}}$$

recombination_model{
      SRH            = yes       # Shockley-Read-Hall recombination
      Auger          = yes       # Auger recombination
      radiative      = yes       # radiative recombination (direct recombination)
   }

The internal quantum efficiency is automatically calculated when the radiative recombination is switched on

     radiative      = yes       # radiative recombination (direct recombination)

The band structure of the MQW structure can be seen of figure 1 without bias voltage.

An example for the distribution of the recombination processes is plotted in figure 2

The $I-U$ characteristics of the device is plotted in figure 3, where additionally the full photo-current is plotted.

The internal quantum efficiency is plotted in figure 4