Re: What is a Solid State Emmiter?

bjw@xxxxxxxxxxxxxxxxx wrote:
On Jun 22, 7:08 pm, jim beam <spamvor...@xxxxxxxxxxxxxxx> wrote:
b...@xxxxxxxxxxxxxxxxx wrote:
On Jun 20, 9:03 pm, jim beam <spamvor...@xxxxxxxxxxxxxxx> wrote:
Peter Cole wrote:
jim beam wrote:
b...@xxxxxxxxxxxxxxxxx wrote:
what's the transition threshold between photons and phonons?
The way you've phrased this, your question does not make
any sense. Photons are light and phonons are mechanical
motions in a solid. The difference, for semiconductor
transitions, is that photons carry negligible momentum
and phonons have some momentum. So for an electron to
make a transition from one state to another state that
differs in momentum, it has to produce a phonon rather
than a photon. There's not a value of energy gap above
which transitions produce photons instead of phonons or
something like that.
Phonons aren't physical particles. They are a way of
representing the modes of vibration of a solid.
thanks ben. this is indeed what i'm getting at. i've never seen
momentum change described in any analysis of semiconductor electron
energy theory. conduction, yes. excitation state transition, no.
maybe i need to read more, but i'd welcome your enlightenment. peter
seems to think i'm not asking a serious question.

One of my usual references for the quantum mechanics
of electrons in solids is Ashcroft and Mermin's "Solid
State Physics," but it's at my office. Anyway there
seem to be enough materials on the web.

The conduction band in a semiconductor gives the
energy range that electrons in some particular
set of quantum states are allowed to have. However,
electrons (unlike photons) have mass and so an
electron state with some energy may also have a significant
momentum. (Photons have momentum but it's insignificant
at these scales.)
The details of what momentum (p) an electron with
energy (E) has are pretty complex and depend on the
crystalline structure of the material.

http://people.deas.harvard.edu/~jones/ap216/lectures/ls_2/ls2_u7/sse_tut_1/solid1.html

Look at Figures 1.6.1 and 1.6.5 which give a schematic
idea of how the band gap arises in a crystal lattice.
These plot energy versus wavevector k; k is 1/wavelength
of the electron state (represented as a wave) and is here
equivalent to momentum, p = hbar*k. (hbar is Planck's
constant/2pi.)

In the plots on that page such as Figure 1.6.6, the band
structure is such that the energy is symmetric about k=0,
so an electron in some band will settle to the lowest
energy in that band at k=0 and have zero momentum.
However, in real semiconductors this is often not true
and the conduction band energy minimum is at non-zero
momentum. See the figure at

http://en.wikipedia.org/wiki/Indirect_bandgap

and panels (b) and (c) of Figure 4.6.1 at

http://ece-www.colorado.edu/~bart/book/book/chapter4/ch4_6.htm#fig4_6_1
(I gave this link earlier in the thread.)

Momentum is conserved. As section 4.6.1 of that page
discusses, in an indirect band gap material, in order
for an electron to drop from the conduction band to the
valence band it has to lose both energy and momentum.
Photons don't have enough momentum so the reaction
has to produce a phonon (a sound wave oscillation of the
crystal). The phonon can also carry off energy. In order
for any energy to go into light, a two-step process
has to occur involving electron, phonon, and photon.
Although these can occur, they are much less likely,
and so the vast majority of the time an electron will
drop out of the conduction band without producing light.

To make an LED or photodiode, visible or infrared, one
has to overcome this by using a semiconductor material
that has a direct band gap. And if that seems like
a pain in the butt, imagine designing electronic detectors
that work in the thermal infrared!

Ben



interesting stuff. thanks ben - i'll be reading more on that!
.

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