# nextnano.QCL - Software for Quantum Cascade Lasers

### nextnano.QCL

Summary and introduction

Software documentation

Examples

### nextnano.MSB

Summary and introduction

### nextnano++

Software documentation

Examples

### nextnano³

Software documentation

### nextnanomat

Software documentation

### nextnano GmbH

nnp:optics:internal_quantum_efficiency

# Emission: Internal Quantum Efficiency

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

### Physics Model

nextnano++ is capable of simulating recombination processes such as Shockley-Read-Hall (SRH), Auger and radiative recombination. Only the radiative (direct) recombination process (spontaneous emission) generates photons. If radiative recombination $R_{\rm sp}(x)$ 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 $I_{\rm charge}$, then the internal quantum efficiency $\eta_{\rm qe}$ is

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

### Input file structure

#### Drift Diffusion

recombination_model{
SRH            = yes       # Shockley-Read-Hall recombination
Auger          = yes       # Auger recombination
}


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

     radiative      = yes       # radiative recombination (direct recombination)


## Results

### Bandstructure

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

### Recombination

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

### Current-Voltage Characteristics

The $I-V$ characteristics of the device is plotted in figure 3. This figure also includes the full photo current.

### Quantum Efficiency

The internal quantum efficiency is plotted in figure 4