About the semicondunctor quantum well

[wdlang]

consider the GaAs-AlGaAs semiconductor quantum well

the gap of GaAs is situated inside the AlGaAs gap

however, what is its precise position?

 

[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 wherever you grow it and as thick as you grow it.

 

[wdlang]

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

 

[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.

 

[wdlang]

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?

 

[LewisEE]

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

 

[Cthugha]

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.

 

[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" if you know the parameters.

 

[wdlang]

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?

 

[wdlang]

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?

 

[Cthugha]

but the principle is the chemical potentials are the same?

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

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.

 

[chrisbaird]

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.