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MM5017: Electronic materials, devices, and fabrication

Assignment 1

1. A pure semiconductor has a band gap of 1.25 eV. The effective massesare  m∗e  = 0.1me   for electrons and  m

∗

h  = 0.5me   for holes, where  me   isthe free electron mass. Find the following at 300K

(a) Concentration of electron and holes

(b) Fermi energy

(c) Electrical conductivity

Take  µe   = 1400 cm2V   −1s−1 and  µh   = 400 cm2V  

 −1s−1.

2. Does doping always cause an increase in conductivity? Show that con-ductivity can be lowered by doping. Calculate this lowest conductiv-ity that can be obtained and the atomic concentration and type of dopant needed to achieve this. Take   µe   = 1350   cm2V   −1s−1 andµh   = 450  cm

2V   −1s−1 and  ni   = 1010 cm−3. Atomic weight of Si = 28

gmol−1 and density is 2.33  gcm−3.

3. A GaAs device is doped with a donor concentration of 3 × 1015 cm−3.

For the device to operate properly, the intrinsic carrier concentrationmust remain less than 5 percent of the total electron concentration.What is the maximum temperature that the device can operate? TakeE g   = 1.43  eV   ,  N c   = 4.7 × 10

17 cm−3 and  N v   = 7× 1018 cm−3 and

independent of temperature.

4. Si atoms, at a concentration of 1010 cm−3 are added to GaAs. Assumethat the Si atoms are fully ionized and that 5 percent replace Ga atomsand 95 percent replace As atoms. Take temperature to be 300 K.

(a) Determine the donor and acceptor concentrations

(b) Calculate the electron and hole concentrations and the positionsof the Fermi level with respect to  E Fi.

(c) How will you answer to (a) and (b) change if 95 percent of Si goto the Ga sites and 5 percent go to the As sites.

Take   ni  of GaAs to be 1.8 × 106 cm−3,  N c   = 4.7 × 1017 cm−3 andN v   = 7× 10

18 cm−3. Band gap at 300 K is 1.43 eV.

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5. The Bohr radius, according to the hydrogenic model, is given by

a0   =  0h

2

πmee2

For a n-type dopant in Si, calculate the effective Bohr radius. Taker   = 11.9 and  m∗e   = 0.20me. Use this to calculate a minimumconcentration at which the dopant energy levels overlap to give a de-generate semiconductor.

6. A Si sample has been doped with 1015 cm−3 P atoms. The donor energylevel for P in Si is 0.045 eV below the conduction band edge energy.

(a) Where is the Fermi level at 0 K?

(b) At what temperature is the donor 1% ionized? Where is the Fermilevel located at this temperature?

(c) At what temperature does the Fermi level lie in the donor level?

(d) Estimate the minimum temperature when the sample behaves asintrinsic.

(e) Sketch schematically  the change in Fermi level with temperature.

Take the density of states at the conduction and the valence band tobe 1019 cm−3 and independent of temperature. The density of statesat the donor level is 5× 1014 cm−3. The band gap of Si is 1.10 eV andis also temperature independent.

7. An n-type Si sample has been doped with 1 × 1017 P atoms cm−3. Thedrift mobilities of holes and electrons in Si at 300 K depend on thetotal concentration of dopants  N dopant  as follows:

µe   = 88 +  1252

1 + 6.984× 10−18N dopantcm2V   −1s−1

µh   = 54.3 +   4071 + 3.745× 10−18N dopant

cm2V   −1s−1

(a) Calculate the room temperature conductivity.

(b) Calculate the necessary acceptor doping that is required to makethis sample  p-type with approximately the same conductivity.

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