An n type semiconductor is disturbed homogeneously with an excess majority concentration dn at certain time instant t0 how long the material takes to revert to thermal equilibrium state?
In many instants the semiconductor materials in electronic devices are injected by either an excess of majority or minority carriers for short time and then the disturbance is interrupted. This determines the dynamic behavior of the devices and how long does the material take to return to the thermal equilibrium after interrupting the disturbance.In this question we restrict ourselves to the disturbance with excess charges.
That totally depends on the semiconductor, i.e. which material, impurities, interfaces etc. I think the concept of lifetime for minority carriers would apply to excess majority carriers as well. But that I don't positively know for sure.
Thank you Dieter for your contribution. Can you explain more specifically which minority carrier concept can be applied to excess majority carrier an how it could be applied. There is a basic difference between the excess majority and the excess minority carrier behavior. I asked this question to work out the difference between the two. The answer is very useful for semiconductor and electronic devices engineer.
Since it is a fine point, i wanted to transfer it to the activists in this field of science. I learned it from my teacher at the technical university of Berlin Professor Gerlach. Thank you my teacher W. Gerlach.
Thank you
Dear Abedlhalim,
thanks for the useful question.
In semiconductor the excess carriers return to equilibrium with an exponential decay. In particular in silicon the decay time can be easily calculated by the Photoconductance Decay (PCD) technique which is non destructive and require few second to give lifetime measurement.
Dear Gianfranco,Thank you for your answer. Yes the decay of the excess of majority carrier concentration will be exponential but the time constant is not the lifetime. Practically it is much smaller than the lifetime for moderate majority carrier concentration. Now we are a step nearer to the answer. I wait for the remaining steps.
Thank you.
Dear Collegues,
Let me introduce an answer to this question because i donot want to busser you..When majority carrier concentration is disturbed by transiently increasing its concentration above thermal equilibrium concentration . it well revert to thermal equilibrium by a process called the dielectric relaxation process. The injected majority excess charges will repel the other majority chargers and displace consequently an equal charge to the surface of the semiconductor. At the end of this process the interior of the semiconductor will be free of the excess charge and also field free. The injected minority charges will charge the surface. The time constant of this relaxation process is the dielectric relaxation time constant T= epslon/sigma where epslon is the dielectric constant and sigma the conductivity. This time constant is much smaller than the minority carrier life time for moderate and heavy doping concentration.
Assume an n type material with majority carrier concentration at equilibrium concentration no and the excess is dn then an elecric field will be developed in the material such that
dE/dx = q dn/ epslon
and from the continuity equation and the above equation we get
-d(dn)/dt= sigma d(dn)/epsilon dx + dn/ Taun where Taun is the electron lifetime.
According to the above equation, The rate of decay of the excess majority charges with time is accomplished by the dielectric relaxation process represented by the first term in the right hand side and the recombination rate represented by the other term.
The time constant of the dielectric relaxation time according to the equation isT= epslon/sigma as mentioned previously.
Practically, T
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