Tutorials 2E8 – Semiconductor materials II
1. Calculate the approximate donor binding energy for Ge (r=16, mn*= 0.12m0) ?
2. In which group (column) of the Periodical Table of Elements do Silicon and Germanium
belong?
3. Name a few elemental semiconductor materials and compound semiconductor materials
(at least 2 of each type).
4. What are the main differences between semiconductive, insulative and conductive
materials?
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5. Calculate the electrical conductivity of pure Si at 20ºC and 150ºC. For Si at room
temperature, the energy gap Eg = 1.1 eV, the intrinsic carrier concentration ni =1.5 x 1016 /m3,
the electron mobility μn = 0.135 m2/Vs, and the hole mobility μp = 0.048 m2/Vs.
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6. A Si sample is doped with 1017 Arsenic (As) atoms/cm3. What is the equilibrium hole
concentration p at 300 K? Where is EF relative to Ei? For Si ni = 1.5x1010 cm-3?
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DATA SHEET:
Free electron rest mass mo
Boltzmann’s constant k
9.11xl0-31kg
1.38 x 10-23 J/oK = 8.618x10-5 eV/K
Planck’s constant h
6.63x10-34 J s
Electronic charge q
Intrinsic carrier concentration of Si ni
1.6 x 10-19 C
1.5 x 1010 cm-3
Room temperature value of kT
0.0259 eV
Energy band gap Eg of Si
1.1 eV
Permittivity of vacuum  0
8.85 x 10-14F/cm
Reduced Planck’s constant
  h / 2
Speed of light
3 x 108 m/s
ΔT=1 oC = 1 K = 1.8°F; 1W = 3.41214 BTU/h; 1 ft = 0.3048 m; 1 ft = 12 in
mn* q 4
Eb 
2 K 22
;
K  40 r ;
f ( E F )  1  exp ( E F  E F ) / kT 
1
N c  2(
2mn* kT 3 / 2
)
h2
;
𝜎 = 𝑛𝑖 𝑞(𝜇𝑛 + 𝜇𝑝 );
 t   t  l0
;
;
2m *p kT
h2
1
1  exp ( E  E F ) / kT 

;
n0 
;
  1/ 
)3/ 2
p0  N v exp  ( EF  Ev ) / kT  ; ni  N c N v e  Eg / 2 kT
k
𝜎 = 𝜎0 exp⁡(−
;
q d

A t
t 
;
 f ( E ) N ( E )dE
Ec
n0  ni exp ( EF  Ei ) / kT  ;
;
C  k 0 A / d
1
1


11 2
N v  2(
n0  N c exp  ( Ec  EF ) / kT 
n 0 p0  ni2
f (E) 
𝐸𝑔
2𝐾𝑇
l
 t
l0
p0  ni exp ( Ei  E F ) / kT  ;
); 𝜎𝑛 = 𝑛0 𝑞𝜇𝑛 ; 𝜎𝑝 = 𝑝0 𝑞𝜇𝑝 ;
;
F  I  l  B  Sin ;
R
l
A
;
n c/v;
vl f
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