Question

1. (a) Draw the band diagram for phosphorous doped silicon, including both the majority and minority carriers as well as any dopant levels. Provide the expression for the minority carrier density in terms of the majority carrier density. Show all your steps and label clearly. (b) Draw the band diagram for boron doped silicon, including both the majority and minority carriers as well as any dopant levels. Provide the expression for the minority carrier density in terms of the majority carrier density. Show all your steps and label clearly.

Answer 1

Doping is done to increase the conductivity of semiconductor. It is the introduction of impurities. When we dope with group z elements (B,AL), then that is called P-type semiconductor. When we dope with group 5 elements (N,Ph) then that is called N-type semiconductor. (a) In case of phosphorus doped silicon, It is an no type semiconductor, Phosphorus acts a donor. dopant - Phosphorus has one extra valence election (with respect to Silicon), So it contributes elections. So, Majority carrier – elections Minority carrier holes * In intrinsic semiconductor, there are earual no of electrons & holes: (Thermally generated) But in N-type, the donor dopants are able to form a donor level in the band gap near the conduction hood, so the donated electrons will reauire a much smaller increase in energy to te excited into conduction band, where the free flowing electrons can increase the conductivity & if we consider that all the electrons. in donor level move to conduction band (100% ionization) then the a majority carrier concentration becomes No (almost) where, No = concentration of Donon dopants. Note We are neglecting the elections thermally gener neraled electrons

because thermally generated elections are very less with respect to No. from mass action law, np = ni ni = intrinsic carrier : np = nir concentration » No. Pa ni + P = 8 minority carrier concentration - 0 1 Band Diagram (Phosphorous doped silicon) » electrons (mojority carriere) ..oooo. C.B (conduction --------- - Donor Energy level 0 0 0 V.B (valence band) holes (minority carriers) Ec Ev N-type Semiconductor lowest energy level of highest » » » c.B V.B Majority carrier Minority carrier density - No density - No

(6) In care of boron doped silicon It is a p type semiconducton. Boron acts as a acceptor. It's valence election number is 3. So, due to vacancy it create hole, which con accept electron. Here , majority carrier → holes Minority earrier elections Here, the the accepton dopants form a acceptor energy level in the band gap near the valence band. So, the electrons from of valence band can easily move to the acceptor energy level , creating & hole in valence band. There holes contribute conductivitý in ptype semiconduc Here, NA = concentration of acceptor dopants a concentration of majority carriers (holes) Band Diagram (Boron dorn doped silicon) elections Acceptor energy level oooooooooooo V.B holes p-type semiconductor (thermally generated holes are neglected) Majority Minority Density = NA Density - Carrier Carrier ni intrinsic carrier concentration, Eg forbidden energy gap.