Infrared Absorption? There are always some photons around.

Thank u for your answer, however, almost all textbooks avoid to discuss this case although its a matter of intresting !!

Well, any textbook should contain a chapter about light absorption/photoconductivity. But the photoconductivity from the background radiation is not very interesting because its exact magnitude depends on a big number of random parameters and it is very difficult to estimate the numbers theoretically.

Thanks a lot , but what is the role of this background radiation in estimating the temperature of the solid material? How it affect lattice vibration for example?

Well, if you put your sample under the sun it will be heated up while the transparent air around may be cool. Though In laboratory I believe it is safe for the most purposes to assume that the sample is in good equilibrium with an environment. Of course one can speculate about non-equilibrium additions from background radiation but unless one have a phenomenon to explain it is pointless. That is about Occam's razor. Lattice temperature is very inertial parameter.

Anyway it is easy to check experimentally. Cover your device with a black cloth and repeat measurements. :)

Pure silicon at room temeprature will have holes in the valence band and electrons in the conduction band even in dark. The reason is that at nonzero temepratures the Fermi fubction that essentially defines the occupation of bands is not a strict step function, but snoothed by temparature. After you go through the math (that you can find in ant solid state physics textbook), you will find that for an intrinsic semiconductor the number of conduction electrons is porportional to exp(-Eg/2kT). For silicon with Eg = 1.1 eV and kT = 0.026 eV this number is about 10^(-10), resulting in about 10^11 cm^-3 conduction electrons.

Sorry for the typos, still trying to type too fast on a touchscreen...

Thanks, but what about physical point of veiw (not mathmatical) perhaps i know the derivation of these equations, but still we are in need of physical interpretation of how electron-hole pairs will produced without need of 1.1 ev?

Physically it means that at RT there are some (not many) electrons that have enough energy to transition over the 1.1 eV gap. That RT corresponds to 25 meV does not mean that this is the maximum kinetic energy that the electrons can have, it is the average.

Thanks a lot, well we return back to the idea of statistcs, i. E. A number of electrons may have the chance to acquier (1.1ev) and others with no enough energy to leave the valance toward the conduction band is it the case?

Each electron has a chance to aquire big energy, but the bigger energy - the lesser probability. So they have a little chance to jump high and, when they are high, they have a big chance to jump down back. Or, in terms of lifetimes, each electron waits for a long time in valence band, then goes to the conduction band, waits for a short time there and then goes back to the valence band. And again and again. And that continuous jumping of all electrons makes Fermi statistics according to formulas.

thanks alot , what do u mean with Occam's razor?

It is a kind of methodology principle in science. Something like "don't invent complicated ideas when simple ones will do." You can see in wikipedia.

Dear Abdulghefar,

This question is really good question. Assuming pure perfect crystalline silicon at zero Kelvin all valence electrons will be bound to their valence bond and reside in the valence band. No free electron hole pairs exists. By supplying thermal energy to silicon. the silicon lattice atoms begins to vibrate producing phonons that have a range of momentum and energy values. They interchange energy and momentum with the valence electrons. Only electrons at the top of the valence band can be knocked out by phonons from the valence band to the the conduction band. Since the minimum energy required for this process as you said is equal to the energy gap and the average energy of the phonons is kT= 0.026 eV at room temperature, then multiphonon share in this process. Which means it is probable that a valence electron laying at the top of the valence band is hit by multiple phonons having overall energy greater or equal to the energy gap energy. This type of interaction was studied intensively in the literature of the recombination and generation processes via deep laying impurities. The situation is very similar. It is about the mechanism of interaction between electrons and phonons when the electron energy is apprechiabley larger than the average phonon energy.

You can find in the literature of the electron phonon scattering more details about this process.

I hope i shed some light on this not simple topic in semiconductor physics.

Dear Abdulghefar

The situation I thin is very similar to the evaporation from water surface. Even though water molecules require 100 deg.C at atm. presure to escape as vapour, they do that at room temperature in a small way which we call evaporation. This is because even though the Energy of most of the gas molecules is equivalent to the value determined by RT, some small fraction of them will have very high energy equivalent to high temperature and some fraction will have very low energy equivalent to very low temperature. (remember Boltzmann stats). These high energy air molecules can noc out water moelcules from the surface of water. In a similar way even at RT some valence electrons will acquire sufficient energy as discussed by Abdelhalim to jump to the conduction band. I thin this will give you a physical idea of the process. Mathematically it is as explained by Filip Tuomisto that Fermi function is not a 'step' function. Best regards.

thanks for all, specially Dr. Zekry for his informative explination, there are several phenomena in physics that needs explination. hf (Plank constant times frequencey) is energy , KT (Boltizman constant times temperature) is energy too, when discussing lattice heat capacity with Debey's models, for debey's temperature THETA D, we say that: (hf=KT) in order that we can define the highest frequency aquierd by the lattice (which is called Debey's frequency) in 1st BZ . just for such special cases we can equate hf with KT... is it the case??