SSD ASSIGNMENT - 1
Total Marks: 60
1. Academic dishonesty policies of IIIT Delhi apply. Please have a look at the following before
proceeding:
https://www.iiitd.ac.in/sites/default/files/docs/education/AcademicDishonesty.pdf
2. Checks will be in place to detect copying/plagiarism/cheating
3. Answers should be hand-written on A4 size paper, scanned and submitted in Google
classroom (no printout submission allowed).
Ques1. (CO1) According to classical physics, the average energy of an electron in an electron gas at
thermal equilibrium is 3kT/2. Determine, for T =300 K, the average electron energy (in eV), average
electron momentum, and the de Broglie wavelength. [3 Marks]
Ques2. (CO1) Figure 1 shows the parabolic E versus k relationship in the valence band for a hole
in two particular semiconductor materials. Determine the effective mass (in units of the free
electron mass) of the two holes .[6 Marks]
Figure 1
Ques3. (CO1)(a) Determine the total number (#/cm3 ) of energy states in silicon between Ec and
Ec + 2kT at (i) T =300 K and (ii) T =400 K.
Assume For Silicon , mn*=1.08 m0 Given m0=9.11*10-31 kg.[6 Marks]
Ques4. (CO1)The Fermi energy for copper at T=300 K is 7.0 eV. The electrons in copper follow the
Fermi–Dirac distribution function.
(a) Find the probability of an energy level at 7.15 eV being occupied by an electron. (b) Repeat
part (a) for T =1000 K. (Assume that EF is a constant.) (c) Repeat part (a) for E =6.85 eV and T =300
K. (d) Determine the probability of the energy state at E= EF being occupied at T = 300 K and at T
=1000 K. [4 Marks]
Ques5. (CO1)Silicon at T =300 K is doped with arsenic atoms such that the concentration of
electrons is n0 =7*1015 cm-3 . (a) Find Ec – EF (b) Determine EF – Ev. (c) Calculate p0. (d) Which carrier
is the minority carrier? (e) Find EF – EFi.Take suitable value of effective density of states.
[5 Marks]
Ques6. (CO1) (a) Consider a germanium semiconductor at T =300 K. Calculate the thermal
equilibrium electron and hole concentrations for (i) Nd = 2*1015 cm-3, Na = 0 cm-3, and (ii) Na = 1016
cm-3 , Nd = 7*1015 cm-3 .Given For Ge ni = 2.4*1013 cm-3 [4 Marks]
Ques7. (CO1) A silicon semiconductor material at T = 300 K is doped with arsenic atoms to a
concentration of 2*1015 cm-3 and with boron atoms to a concentration of 1.2*1015 cm-3 . (a) Is the
material n type or p type? (b) Determine n0 and p0. (c) Additional boron atoms are to be added such
that the hole concentration is 4*1015 cm-3 . What concentration of boron atoms must be added and
what is the new value of n0? [4 Marks]
Ques8.(CO1) (a) Determine the position of the Fermi energy level with respect to the intrinsic Fermi
level in silicon at T =300 K that is doped with boron atoms at a concentration of Na =2*1016 cm-3 . (b)
Repeat part (a) if the silicon is doped with phosphorus atoms at a concentration of Nd =2*1016 cm-3.
(c) Calculate n0 and p0 in parts (a) and (b). [3 Marks]
Ques9.(CO1)A semiconductor material has electron and hole mobilities µn and µp, respectively. When
the conductivity is considered as a function of the hole concentration p0, (a) show that the minimum
value of conductivity, 𝞼min, can be written as
𝞼min = 2𝞼i ( µn µp)1/2 / (µn +µp)
where 𝞼i is the intrinsic conductivity, and (b) show that the corresponding hole concentration is
p0 = ni ( µn / µp)1/2. [5 Marks]
Ques10. (CO1) Consider a sample of silicon at T =300 K. Assume that the electron concentration
varies linearly with distance, as shown in Figure 2. The diffusion current density is found to be
Jn =0.19 A/ cm2 . If the electron diffusion coefficient is Dn = 25 cm2 /s, determine the electron
concentration at x =0. [3 Marks]
Figure 2
Ques11.(CO1) The electron concentration in silicon at T =300 K is given by
n(x) = 1016 exp (- x/ 18) cm-3
where x is measured in 𝛍m and is limited to 0 ≤ x ≤ 25 𝛍m. The electron diffusion coefficient is
Dn = 25 cm2 /s and the electron mobility is µn = 960 cm2 /V-s. The total electron current density
through the semiconductor is constant and equal to Jn = -40 A/cm2 . The electron current has
both diffusion and drift current components. Determine the electric field as a function of x which
must exist in the semiconductor. [3 Marks]
Ques12. (CO1) In a GaAs material at T =300 K, the doping concentrations are Nd =8*1015 cm-3 and
Na =2*1015 cm-3 . The thermal equilibrium recombination rate is R0 =4*1014 cm-3s-1 . (a) What is the
minority carrier lifetime? (b) A uniform generation rate for excess carriers results in an excess carrier
recombination rate of R‘=2*1021 cm-3s-1 . What is the steady-state excess carrier concentration? (c)
What is the excess carrier lifetime?[3 Marks]
Ques13. (CO1)A semiconductor is uniformly doped with 1017 cm-3 acceptor atoms and has the
following properties:Dn = 27 cm2 /s, Dp = 12 cm2 /s, τno =5* 10-7 s, and τpo = 10-7s .An external source
has been turned on for t< 0 producing a uniform concentration of excess carriers at a generation
rate of
g’ = 1021 cm-3s-1 . The source turns off at time t= 0 and back on at time t =2 * 10-6 s. (a)
Derive the expressions for the excess carrier concentration as a function of time for 0 ≤ t ≤ ∞. (b)
Determine the value of excess carrier concentration at (i) t= 0, (ii) t =2 * 10-6 s, and (iii) t = ∞.
[8 Marks]
Ques14. (CO1) An n-type silicon semiconductor, doped at Nd =4*1016 cm-3 , is steadily illuminated
such that g’ = 2 * 1021 cm-3s-1 . Assume τpo =5* 10-7 s, and τno = 10-6s . (a) Determine the
thermal-equilibrium value of EF – EFi. (b) Calculate the quasiFermi levels for electrons and holes with
respect to EFi. (c) What is the difference (in eV) between EFn and EF ?[3 Marks]