# About the semicondunctor quantum well

1. Jul 12, 2011

### wdlang

consider the GaAs-AlGaAs semiconductor quantum well

the gap of GaAs is situated inside the AlGaAs gap

however, what is its precise position?

2. Jul 13, 2011

### Cthugha

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 whereever you grow it and as thick as you grow it.

3. Jul 13, 2011

### wdlang

i mean the relative positions of the two gaps

note that there are two materials and two gaps

4. Jul 13, 2011

### Cthugha

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.

5. Jul 13, 2011

### wdlang

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?

6. Jul 13, 2011

### LewisEE

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

7. Jul 13, 2011

### Cthugha

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.

Last edited: Jul 13, 2011
8. Jul 13, 2011

### chrisbaird

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" [Broken] if you know the parameters.

Last edited by a moderator: May 5, 2017
9. Jul 13, 2011

### wdlang

but the principle is the chemical potentials are the same?

10. Jul 13, 2011

### wdlang

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?

Last edited by a moderator: May 5, 2017
11. Jul 14, 2011

### Cthugha

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

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.

12. Jul 14, 2011

### chrisbaird

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