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.

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.

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


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.

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


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

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


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.

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.