# 1D - UV LED: Quantitative evaluation of the effectiveness of EBL¶

*Section author: Naoki Mitsui*

We investigate how the electron blocking layer (EBL) improves the characteristics of UV LEDs using nextnano++. Current-Poisson equation and semi-classical calculation of optical properties (classical{}) in nextnano++ enables us to quantitatively analyze the effect of this strucutre.

We refer to the structure used to obtain Fig. 28 in the following paper:

- H. Hirayama
*Quaternary InAlGaN-based high-efficiency ultraviolet light-emitting diodes*,Journal of Applied Physics 97, 091101 (2005)

**Sample input file**

1D_DUV_LED_HirayamaJAP2005_EBL_nnp.in

**Table of contents**

## Structure¶

The simulation region consists of the following structure:

n-Al

_{0.18}Ga_{0.82}N layer3-layer MQW based on InAlGaN

Al

_{x}Ga_{1-x}N EBL (Al content = 0.18, 0.24, 0.28)p-Al

_{0.18}Ga_{0.82}N layer

Each layer has the following thickness and doping concentration:

Material |
Thickness |
Doping |

n-Al |
100 nm |
8 \(\times\) 10 |

In |
well: 2.5 nm, barrier: 15 nm |
0 [cm |

Al |
10 nm |
0 [cm |

p-Al |
100 nm |
2 \(\times\) 10 |

Al content x=0.18 in the EBL is used for the structure without EBL, while x=0.24 and 0.28 are for the structure with EBL in different barrier height.

Donor and acceptor ionization energies are defined as 0.030 eV and 0.158 eV where Si and Mg are in mind, respectively.

## Scheme¶

We can specify which simulation or equations would be solved on run{} section in your input file.

In 1D_DUV_LED_HirayamaJAP2005_EBL_nnp.in it is described as

```
run{
strain{}
current_poisson{}
}
```

Then nextnano++ solves the current equation and Poisson equation self-consistently after solving strain equation.

After the Current-Poisson equation is converged, optoelectronic characteristics are calculated according to the specification in the section classical{}.

For further details, please see General scheme of the optical device analysis.

## Results¶

### Current-voltage characteristics¶

Here we show the current-voltage characteristics for the total current density \(I_{\text{total}}\) measured at p-contact and photocurrent density \(I_{\text{photo}}\), which is defined as (2.3.3.28). \(I_{\text{photo}}\) represents the amount of electrical current consumed by the radiative recombination in the total current \(I_{\text{total}}\). Please note that the scales of the y-axis in these graphs are different in 10 times.

We can observe that the smaller \(I_{\text{total}}\) is , the higher the EBL barrier is. On the other hand, at the applied bias of 4.0V, the bigger \(I_{\text{photo}}\) is, the higher the EBL barrier is. We can say that the larger proportion of the total current consists of the photocurrent in the higher EBL structure, which results in the larger IQE.

### Bandedges¶

The following figures show the bandedge profiles and the quasi-Fermi levels for the higher EBL (top) and no EBL (bottom) structure where the total current densities are almost the same around 1.70 \(\times\) 10^{5} A/cm^{2}.
The applied bias is 4.00 V for the left graph and is 3.90 V for the right graph.

### Current Density¶

The following figure show the current density profiles for the higher EBL (top, x=0.28), lower EBL (middle, x=0.24), and no EBL (bottom, x=0.18) structure where the total current densities are almost the same around 1.70 \(\times\) 10^{5} A/cm^{2}.

We can see that the amount of electron current and hole current becomes closer as the EBL height is increased, while the electron current is dominant without EBL. It can be also confirmed that the current overflow is suppressed by the EBL.

#### Charge carrier densities¶

The figures showed below are the electron and hole densities around the MQW region for the structure with higher EBL and without EBL (left, x=0.28 and right, x=0.18) for almost the same current density around 1.70 \(\times\) 10^{5} A/cm^{2}.
The introduction of EBL at 167 nm-177 nm reduces the electron densitiy in the p-AlGaN region.

#### Power of light emission¶

Here we show the relationship between optical power defined in (2.3.3.33) and current density of p-contact for each structure.

### Internal quantum efficiency¶

In nextnano++, the **internal quantum efficiency** is calculated as

where \(I_\text{photo}\) is the photo-urrent consumed by the radiative recombination and \(I_\text{total}\) is the current injected in total.

This quantity shows the improvement by the introduction of higher EBL as follows:

nextnano++ also outputs the **volume quantum efficiency** \(\eta_\text{VQE}\), also known as **radiative efficiency**, which represents the proportion of the radiative recombination rate to the total recombination rate.
This quantity is calculated as

and also shows the improvement by the introduction of EBL:

The IQE can be decomposed like (2.5.3.8) into this volume QE and the **injection efficiency** \(\eta_\text{IE}\), which represents the proportion of the current consumed by the total recombination (radiative + nonradiative) to the total injected current.

Thus using the results of \(\eta_\text{IQE}\) and \(\eta_\text{VQE}\) above, we can also get this \(\eta_\text{IE}\) :

From the above results, we can see that the improvement of IQE due to the introduction of EBL comes from the imrovement of mainly IE rather than volume QE.

## What can we do further?¶

The effect of EBL on the optoelectronic characteristics has been estimated quantitatively using the semiclassical calculation in nextnano++.

We can also optimize the Al content of EBL or the thickness by sweeping the corresponding parameters, for example. Our open source python package nextnanopy is a strong tool for this purpose.

The graphs shown in this tutorial are also generated by a python script using nextnanopy.

*Please help us to improve our tutorial. Should you have any questions or comments, please send to support [at] nextnano.com.*