# About the semicondunctor quantum well

• wdlang
In summary: I am not familiar with any specific references, but the temperature dependence of the well depth comes from the temperature dependence of the chemical potentials. There are many papers related to the topic. One example is this paper: "A quantitative description of the temperature dependence of the GaAs-AlGaAs gap energy and its implications for optoelectronic devices".
wdlang
consider the GaAs-AlGaAs semiconductor quantum well

the gap of GaAs is situated inside the AlGaAs gap

however, what is its precise position?

What exactly do you mean by position of the gap?

If you mean the band gap energy of GaAs, it is about 1.42 eV at room temperature, but shows strong temperature dependence (have a look at the Ioffe semiconductor database if you want to know the exact numbers).

If you mean the position of the GaAs layer it is located wherever you grow it and as thick as you grow it.

Cthugha said:
What exactly do you mean by position of the gap?

If you mean the band gap energy of GaAs, it is about 1.42 eV at room temperature, but shows strong temperature dependence (have a look at the Ioffe semiconductor database if you want to know the exact numbers).

If you mean the position of the GaAs layer it is located wherever you grow it and as thick as you grow it.

i mean the relative positions of the two gaps

note that there are two materials and two gaps

I suppose you mean the band gap energies by "position".

That question cannot be answered in a general manner as AlGaAs is short for $$Al_XGa_{1-X}As$$. The properties of AlGaAs depend strongly on the Aluminium content. The band gap at room temperature varies between the band gaps of pure GaAs at x=0 and pure AlAs at x=1, which are 1.42 and 2.16, respectively. Unfortunately the dependence is not linear and not trivial. Also, the nature of the band gap changes when increasing x. For x larger than roughly 0.4 the band gap becomes indirect for example. Both band gaps will of course also vary when the temperature is changed, so that the difference between the band gaps is also a non-trivial function of temperature and the Al-content.

Cthugha said:
I suppose you mean the band gap energies by "position".

That question cannot be answered in a general manner as AlGaAs is short for $$Al_XGa_{1-X}As$$. The properties of AlGaAs depend strongly on the Aluminium content. The band gap at room temperature varies between the band gaps of pure GaAs at x=0 and pure AlAs at x=1, which are 1.42 and 2.16, respectively. Unfortunately the dependence is not linear and not trivial. Also, the nature of the band gap changes when increasing x. For x larger than roughly 0.4 the band gap becomes indirect for example. Both band gaps will of course also vary when the temperature is changed, so that the difference between the band gaps is also a non-trivial function of temperature and the Al-content.

you missed my question

i do not care the specific materials, i do not care the temperature dependence

the question comes from the quantum well

what is the depth of the quantum well for the electron?

The conduction band offset is roughly 330 meV, assuming an x ~ 0.3.

wdlang said:
you missed my question

i do not care the specific materials, i do not care the temperature dependence

the question comes from the quantum well

what is the depth of the quantum well for the electron?

Sigh, ok...you are new to this I assume...the depth of the quantum well is given by the energy gap (or conduction band) differences of the two materials used and therefore the well depth intrinsically depends on temperature and material composition. For square wells it is on the order of 330 meV for x=0.3 as LewisEE pointed out, it is about 150 meV for x around 0.1 to 0.15.

There is no "THE" depth of a quantum well.

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In order to calculate quantum well depths, you have to know the band gaps and the band alignments. The band alignments are rather hard to come by from scratch, put typical values are published. For band alignments, I use the http://prb.aps.org/abstract/PRB/v39/i3/p1871_1" if you know the parameters.

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Cthugha said:
Sigh, ok...you are new to this I assume...the depth of the quantum well is given by the energy gap (or conduction band) differences of the two materials used and therefore the well depth intrinsically depends on temperature and material composition. For square wells it is on the order of 330 meV for x=0.3 as LewisEE pointed out, it is about 150 meV for x around 0.1 to 0.15.

There is no "THE" depth of a quantum well.

but the principle is the chemical potentials are the same?

chrisbaird said:
In order to calculate quantum well depths, you have to know the band gaps and the band alignments. The band alignments are rather hard to come by from scratch, put typical values are published. For band alignments, I use the http://prb.aps.org/abstract/PRB/v39/i3/p1871_1" if you know the parameters.

yes, i am absolutely new to this field

is there any good reference?

i guess the temperature dependence of the well depth comes from the temperature dependence of the chemical potentials. is that right?

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wdlang said:
but the principle is the chemical potentials are the same?

Well, for undoped samples the chemical potential must be continuous across the junction.

wdlang said:
is there any good reference?

There is lot of stuff on several different levels of complexity. One might start from chapter 9 of "Fundamentals of Semiconductors" (2010 edition) by Cardona and Yu and follow the references therein if the treatment is too basic.

wdlang said:
yes, i am absolutely new to this field

is there any good reference?

i guess the temperature dependence of the well depth comes from the temperature dependence of the chemical potentials. is that right?

To start, you can google "varshni bandgap model" or something similar and read the first few websites.

## 1. What is a semiconductor quantum well?

A semiconductor quantum well is a thin layer of a semiconductor material that is sandwiched between two layers of a different semiconductor material. This structure creates a potential well that confines electrons and holes, allowing for quantum effects to occur.

## 2. How do quantum wells work?

Quantum wells work by creating a barrier for electrons and holes to move through. When the electrons and holes are confined within the well, they exhibit quantum properties such as quantized energy levels and tunneling. This makes quantum wells useful for various applications such as lasers and transistors.

## 3. What are the advantages of using semiconductor quantum wells?

One of the main advantages of using semiconductor quantum wells is their controllable bandgap. By adjusting the thickness of the well layer, the bandgap can be tuned to specific energy levels, making them useful for optoelectronic devices. They also have high carrier mobility and can operate at room temperature.

## 4. What are some common materials used for semiconductor quantum wells?

Some common materials used for semiconductor quantum wells include gallium arsenide (GaAs), gallium nitride (GaN), and indium phosphide (InP). These materials have suitable bandgaps for optoelectronic applications and can be combined to create heterostructures with desired properties.

## 5. What are some applications of semiconductor quantum wells?

Semiconductor quantum wells have a wide range of applications, including optoelectronics, quantum computing, and sensing. They are commonly used in laser diodes, LEDs, and solar cells. They also play a crucial role in the development of quantum dot devices and quantum cascade lasers.

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