A Si sample with 10^15 / cm^3 donors is uniformly optically excited at room temperature such tha

step 1 This is the problem number 2. The problem stated that a P -type semiconductor has an accepted de

A Si sample with 10^15 / cm^3 donors is uniformly optically...

Key Concepts

Quasi-Fermi Levels

In non-equilibrium semiconductor physics, distinct quasi-Fermi levels for electrons and holes are defined to account for the separate distributions of these carriers under external excitation. The splitting between these levels reflects the degree of carrier injection and non-equilibrium conditions, and it is essential for analyzing recombination dynamics, carrier distributions, and device behavior under illumination.

Excess Carrier Generation

Excess carrier generation refers to the process by which additional electron-hole pairs are created in a semiconductor due to stimuli such as optical excitation. This increase in carrier concentration, beyond the equilibrium level set by doping, is critical in understanding changes in conductivity and other optoelectronic properties in materials subjected to external injection.

Carrier Lifetime

Carrier lifetime is the average duration a charge carrier exists before recombination. It is a key parameter in determining the steady-state concentration of photo-generated carriers, as it sets the balance between generation and recombination rates. This concept is crucial for evaluating the performance of photoconductive devices and understanding semiconductor dynamics under continuous excitation.

Photoconductivity

Photoconductivity is the phenomenon where a semiconductor’s conductivity increases upon exposure to light due to the generation of additional free carriers. The change in conductivity depends on the mobilities of these carriers and their increased concentration from optical excitation. This concept is vital in the design and analysis of devices like photodetectors and solar cells, where enhanced electrical conduction is a desired outcome.

Doping in Semiconductors

Doping involves the intentional introduction of impurities into a semiconductor to modify its electrical properties, particularly the equilibrium carrier concentration. Under optical excitation, the presence of dopants sets the baseline carrier levels, and the interplay between dopant-induced carriers and photo-generated carriers determines the overall electrical response of the material.

Transcript

00:01 This is the problem number 2.

00:04 The problem stated that a p -type semiconductor has an accepted density of 10 power 18 per centimeter cube if the e .v is 0 .2ev and effective mass of the electrons and the holes are equal to the rest mass of the electron.

00:23 And the first part so that the intrancing conduction in the crystal is negligible at room temperature.

00:31 So here the receptor density is given for p type semiconductor that is p or that is na is given that is 10 power 18 for a centimeter cube and e d minus ev is given which is 0 .2 ev and the effective mass of the electrons and the holes are equal and it is equal to the rest mass of the electron which is 9 .1 into 10 power minus 31 kg and this difference is nothing suppose this is the bottom of the conduction band and this is the top of the valence band and here there is a donor level ed and this difference is is given which is 0 .2 now we have to show that the conduction in this type of the semi -contenture is negligible at room temperature the first part of the question so that the intrinsic conduction in the crystal is negligible at room temperature for this we have to find out first the n i the intrinsic calculation the intrinsic density at room temperature at room temperature the value of the kt is 0 .0259 a and we will use here h bar is equal to 6 .58 into 10 power minus 16 e .v second and the effective mass already used now we have the formula for intrinsic density that is n i n c and the a b n b square root exponential minus a g by k t we know the value this k t and we have to find out this effective density of state that is nc and the nv nc is nothing it is two and this is m e effectively on the electron k t divided by 2 pi h bar square where h bar is the h upon 2 pi and h is the plank constant m power 3 by 2 and here if you substitute the value of the m star that means it is 2 m into k t by 2 pi x b bai h bar square and 3 by 2 then the value is that 0 .016 per centimeter cube and because here k t is constant 2 pi as bar constant that m e is equal to m h bar hence m h is equal to since m s star is equal to m h star is equal to m hence and c that is n b n n c r equal and the value is 0 .0016 per centimeter cube now let's find n i and i is nothing it is 0 .0016 exponential minus e g by 2 k t because the value of this e g is around 4 k t so if we substitute this value, the value of this, let's assume first if eg is equal to 1 .12ev, then this value is minus eg by 2kt is around 4 into 10 power minus 10...

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