Condensed Matter Physics

Problem 1: Donors and acceptors in an intrinsic semiconductor (‘5 marks)
Two types of dopants are added to an intrinsic semiconductor Si: (i) Boron and (ii) Arsenic. Which one will be
acting as a donor and wich one – as an acceptor? Justify your answer.
Problem 2: The Fermi level (5 marks)
In a semiconductor at room temperature (300 K) the intrinsic carrier concentration is 1.5 x 10’6m‘3 . It is converted
to an extrinsic semiconductor with donor concentration of ro-‘Om-i Calculate the shift in the Fermi level due to
doping.
Problem 3: An extrinsic semiconductor cf 15 marks)
A piece of Si wafer with the intrinsic carrier concentration 1.5 x 1010 cm’3 is n-doped at a level of 3 x 10’16 cm”.
It is exposed to light that generates 10‘9 electron-hole pairs per second per cm3- The hole lifetime is t}, = 6 us.
i) Find the minority carrier concentration p2 before the light is turned on.
ii) Find the minority carrier concentration p” after the light is turned on.
iii) The Si wafer is exposed to the light for a while and then the light is turned off. Find the time it takes
for the minority carrier concentration to reach the level of 1.1112. Assume exponential drop of the carrier
concentration once the light is off.

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