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Modeling >> Semiconductor Devices >> direct versus indirect semiconductors
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Message started by mkaragou on Jun 16^th, 2006, 3:15am

Title: direct versus indirect semiconductors
Post by mkaragou on Jun 16^th, 2006, 3:15am

Devices for optical detection make use of direct semiconductors for example GaAs which have their maximum of the valence band at the same location as the minimum of the conduction band in k-E space, whereas indirect semiconductors like Si have their conduction band minimum on another k value than the valence band maximum, which results in a need for an additional electron-phonon interaction and hence in a less efficient detection process.

So now my question: What is the physical cause that explains why a semiconductor material has its conduction band minimum and valence band maximum not at the same k value?

Title: Re: direct versus indirect semiconductors
Post by Geoffrey_Coram on Jun 16^th, 2006, 5:12am

As I understand it, the crystal structure determines the energy and momentum of the electron orbitals (states), and there's no particular reason that the highest occupied state and the lowest unoccupied state should have the same momentum. I mean, even if you go back to a single atom and look at the orbitals, they are shaped differently as you go from s to p to d etc.

Title: Re: direct versus indirect semiconductors
Post by mkaragou on Jun 16^th, 2006, 5:36am

If I remember correctly the lattice structure for GaAs and Si is absolutely the same, apart from the fact that for GaAs two different atom types are involved.

So is it just by chance that some semiconductors are direct and some others are indirect?!?!

I am reading for the second time the very well written book from Kevin Brennan "Physics of Semiconductors" CUP that explains the electrical engineer the world of quantum mechanics and band structure formation in the semiconductor lattice, to get the answer of the question stated above, but I was not able to find the answer,yet.

Title: Re: direct versus indirect semiconductors
Post by Geoffrey_Coram on Jun 19^th, 2006, 5:42am

I wouldn't say it was "by chance" but my impression is that the equations are so complicated that one can't really hope to predict direct vs indirect simply by knowing the crystal structure.

Title: Re: direct versus indirect semiconductors
Post by vivkr on Jun 21^st, 2006, 11:10pm

Geoffrey_Coram wrote on Jun 19^th, 2006, 5:42am:

I wouldn't say it was "by chance" but my impression is that the equations are so complicated that one can't really hope to predict direct vs indirect simply by knowing the crystal structure.

Hi Geoffrey,

I am not sure if the E-k plot cannot be found directly through calculations, although it might need a lot more background in this field. How do we actually know about the E-k plots of Si and GaAs in the first place? I think these have probably been calculated, perhaps with the aid of a computer. I would not imagine that these are measured. What do you think?

Regards
Vivek

Title: Re: direct versus indirect semiconductors
Post by mkaragou on Jun 22^nd, 2006, 3:43am

vivkr wrote on Jun 21^st, 2006, 11:10pm:

I am not sure if the E-k plot cannot be found directly through calculations

The E-k plot is found by calculation but my question was if an intuitive approach exists that can explain the physical reason why some semiconductors are direct whereas others are indirect.

Title: Re: direct versus indirect semiconductors
Post by Croaker on Jun 24^th, 2006, 2:20pm

This page is always helpful for...semiconductor stuff. Still, I wouldn't say there is a good physical reason revealed there...

I tend to agree with Geoffrey that with this material, physical and intuitive are sometimes better left behind in favor of equations.

http://britneyspears.ac/physics/indirect/indirect.htm

Title: Re: direct versus indirect semiconductors
Post by mkaragou on Jun 26^th, 2006, 3:53am

Croaker wrote on Jun 24^th, 2006, 2:20pm:

I tend to agree with Geoffrey that with this material, physical and intuitive are sometimes better left behind in favor of equations.

Oh from my point of view, that is a big error that engineers tend to do,because without intuition no invention is possible either.

Title: Re: direct versus indirect semiconductors
Post by Croaker on Jun 26^th, 2006, 6:51am

mkaragou wrote on Jun 26^th, 2006, 3:53am:

Croaker wrote on Jun 24^th, 2006, 2:20pm:

I tend to agree with Geoffrey that with this material, physical and intuitive are sometimes better left behind in favor of equations.

Oh from my point of view, that is a big error that engineers tend to do,because without intuition no invention is possible either.

That's true in general...my point was that quantum physics don't lend themselves quite so much to intuition as say classical Newtonian physics.

Title: Re: direct versus indirect semiconductors
Post by mkaragou on Jun 27^th, 2006, 3:00am

Croaker wrote on Jun 26^th, 2006, 6:51am:

my point was that quantum physics don't lend themselves quite so much to intuition as say classical Newtonian physics.

Yes this might be true, but sometimes there are these bright moments of understanding...

For example I was always asking myself how it comes that there is an energy band gap in the semiconductor.

A person which bases his understanding solely on equations, would answer that if you put the periodic potential
of the lattice ions in the Schroedinger equation, the solution of the Schroedinger equation with the help of bloch functions
is specified by trigonemtric functions that for some k values are not defined. These forbidden k values correspond to forbidden
energy values.

But this answer lacks any kind of intuitive understanding.

Mr. Brennan on the other hand states in his book that when the k vector falls on the edge of the first Brillouin zone,
standing waves arise because of Bragg reflection and therefore only descrete energy levels are possible and
the propagation of the electron wave is impossible.

But to understand this explanation you have to know what the first brillouin zone in the reciprocal lattice is, you have to
know the principle of Bragg reflection and so on...

I am searching for this kind of explanation to understand the direct/indirect semiconductor phenomenon.

I assume that somehow the symmetry of the ion potential in the elementary lattice cell affects the position of the
conduction band minima and valence band maxima.

Title: Re: direct versus indirect semiconductors
Post by Geoffrey_Coram on Jun 27^th, 2006, 6:53am

I'm not quite sure where you think you're going with this. Even if you did have an intuitive understanding of the energy bands, it's not like you can engineer a new kind of atom that would have just the right electron orbitals to produce a particular direct or indirect bandgap. Maybe I'm wrong, but I think people have been playing with semiconductors long enough that they've tried all the combinations of 3/5 and 2/6 compounds -- there aren't really that many, and using an isotope probably doesn't affect the energy bands much at all.

Title: Re: direct versus indirect semiconductors
Post by Croaker on Jun 27^th, 2006, 8:38am

Geoffrey_Coram wrote on Jun 27^th, 2006, 6:53am:

I was thinking about that too...I like to understand devices, but I shy away from the gory details that get physicists excited. Oh well, whatever floats your boat.

Title: Re: direct versus indirect semiconductors
Post by mkaragou on Jun 28^th, 2006, 12:44am

I am sorry if I bore you. There are so many other interesting threads in this forum. So just ignore me, if you are not interested in my question!