When the electron is trapped in a trap, to be de-trapped and get free in the conduction band it has to overcome an energy barrier Et, which is the energy location of the trap level below the conduction band. For shallow traps Et is small, so the electrons get free at relatively low temperatures. In deep traps some part of the electrons can remain even at room temperature. The emission from the trap is characterized by the thermal emission rate.

It is interesting to note that the capture into the trap is characterized by the so called capture cross section. The latter depends exponentially on another barrier Eb, called capture barrier (i.e. is proportional to exp(-Eb/kT)) characteristic for the given trap.

first of all there is no perfect crystal. When you are talking about materials prepared in labs, we are definitely dealing with imperfect crytaline materials particularily when it is the case of doped materials. Next at room teperature, There are few electrons that are mobile because of thermal agitation and lowering temperature means stablizing the thermal agitation and at the temperatures as you say 7k, i think almost all the electrons will arrested in their correspondin defects. O think it is the reasons of more electron trappin in the defects. Once you start increasing temperature, the electrons will again gain momentum and and will vibrate and corresponding to a threshold thermal energy, they will overcome the barrier and will again be mobile.

Based on my research done in the thesis: Surface Passivation at cryogenic temperatures (page 43-45, Section called Explaining the lifetime values) I found several tendencies. Mind you that the research was done on the QSSPC tool.

\tau_SRH = (\tau_n0 (p_0 + p_1 + \Delta n) + \tau_p0 (n_0 + n_1 + \Delta n))/(p_0 + n_0 + \Delta n) (1)

n_1 = N_C exp (-(E_C - E_t)/kT)) (2)

p_1 = N_V exp (-(E_t - E_V)/(kT)) (3)

Are the relevant formulas. The defect can be divided into deep level or shallow level defects depending on the amount of energy necessary to remove the electron or hole from trap to conduction/valence band.

Based on the equations and the experimental results I received, I made the conclusion that his leads to for deep defects, that n1 and p1 becomes very small and a lifetime time that goes up with decreasing temperature is seen. If shallow defects dominate, the exponential T-dependency in n1 and p1 is the strongest T-dependency, and a decreasing lifetime proportionally follows a decreasing temperature.

So yes, trapping does depend on temperature. But also on whether it is a deep level or shallow level energy defect.

But it should be said (basically negating my point a bit) that few seem to understand the research I have done. It is perhaps to complex for the simple professor.

There are some basic phenomenon regarding trapping of electrons in materials. Materials have two type defects Shallow and deep level which are called trapping centre. I am attaching an article which has explanation of it.

1. Trapping of electron depends on temperature but there is no such condition such as bellow room temperature.

2. Yes at low temperature the trapped electron will be more stable as compare to room temperature due to lowering of energy reduce entropy. Even at milliKelvin you can freeze them.

Thanks all. As far as I understand, if a trap is labelled as shallow it can easily be emptied by increasing temperature above room temperature (let's say up to 250 'C). However, if a fraction of electrons appear to be still there in the same trap, what could be the reason? I guess that can not be labelled as shallow trap now.

In which conditions, a fraction of electrons can be more thermally stable? Is it sensible? If electrons are trapped efficiently at low temperature and evicted slowly after raising the temperature to RT, any reason that a fraction of electrons will still be stable at RT?

When the electron is trapped in a trap, to be de-trapped and get free in the conduction band it has to overcome an energy barrier Et, which is the energy location of the trap level below the conduction band. For shallow traps Et is small, so the electrons get free at relatively low temperatures. In deep traps some part of the electrons can remain even at room temperature. The emission from the trap is characterized by the thermal emission rate.

It is interesting to note that the capture into the trap is characterized by the so called capture cross section. The latter depends exponentially on another barrier Eb, called capture barrier (i.e. is proportional to exp(-Eb/kT)) characteristic for the given trap.

Dear Vesselin,

Thank you for your answer. Could you please elaborate (or send me papers) this sentence 'In deep traps some part of the electrons can remain at room temperature..........the thermal emission rate'?

Could you please also provide me more details on relation between capture cross section, capture barrier and temperature? I did not know this before.

At a first glance I could recommend

Point Defects in Semiconductors I and II by Lanno and Bourgoin, respectively:

https://www.springer.com/gp/book/9783642815768

and

https://www.springer.com/cn/book/9783642818349

also

Deep Centers in Semiconductors, ed. S.T.Pantelides (Gordon and Breach, New York, 1986)

http://www.gbv.de/dms/ilmenau/toc/111658764.PDF

@Raju first of all we must understand two important points

1. Capture cross-section

2. Emission cross-section

Capture cross-section is temperature independent, however emission cross-section is temperature dependent. If temperature is lowered emission decreases and hence electron remain trapped in the defect center.

As for trap emptying, it is not possible to completly empty a trap because with increase in temperature retrapping kicks in as more and more empty traps are created.

The trapping of an electron on an empty level in a material depends on the probability of occupation of this level with electrons. The probability of occupation f(E) is determined by the Fermi- Dirac statistics where:

f(E) = 1/ (1+ exp (E-Ff)/kT) , where Ef is the Fermi level. For the trap level E=Et

It is clear from this equation that as the T increases the probability of occupation increases. If the trap level lies under the fermi level the reverse is true. That is the occupation probability of the trap level increases. The Fermi level itself is determined by the determined by the balance of electrons and holes in the semicondcutor.

For example assume we have n type impurity acting as donor with a level Ed which is shallow with Ec-Ed is in the order of kT, then at room temperature nearly all donors will be ionized and as the temperature decreases the the fraction of the occupied donor sates gets larger. This continues till all donors gets occupied by their electrons at 0K. This phenomenon as Freeze out of the electrons on their parent donors.

Best wishes