Mark Lundstrom 1)
09/13/2014 SOLUTIONS: ECE 305 Homework: Week 4 Mark Lundstrom Purdue University Answer the following questions about resistivity at T = 300 K. a) Compute the resistivity of intrinsic Si, Ge, and GaAs. b) Compute the resistivity of n-­‐type Si, Ge, and GaAs doped at N D = 1019 cm -3 . Assume complete ionization of dopants. Solution: 1a) Compute the resistivity of intrinsic Si, Ge, and GaAs. From Fig. 3.5 of SDF for lightly doped material. µ p = 460 cm 2 V-s Si: µ n = 1360 cm 2 V-s Ge: µ n = 4000 cm 2 V-s µ p = 1900 cm 2 V-s GaAs: µ n = 8000 cm 2 V-s µ p = 400 cm 2 V-s From Fig. 2.20 of SDF (for 300 K): Si: ni = 1.00 × 1010 cm -3 Ge: ni = 2.3× 1013 cm -3 ni = 2.25 × 106 cm -3 GaAs: Si: ρ =
(
1
1
=
= 1.0 × 1010 × 1.6 × 10−19 × (1360 + 460 )
nqµ n + pqµ p ni q µ n + µ p
(
ρ (Si) = 3.4 × 105 Ω-cm )
)
−1
Ge: ρ =
1
(
ni q µ n + µ p
ρ ( Ge ) = 46 Ω-cm )
(
= 2.3× 1013 × 1.6 × 10−19 × ( 4000 + 1900 )
)
−1
GaAs: ρ =
(
1
ni q µ n + µ p
)
(
= 2.25 × 106 × 1.6 × 10−19 × (8000 + 400 )
)
−1
ρ ( GaAs ) = 3.3× 108 Ω-cm ECE-­‐305 1 Fall 2014 Mark Lundstrom 09/13/2014 HW4 Solutions (continued): 1b) Compute the resistivity of n-­‐type Si, Ge, and GaAs doped at N D = 1019 cm -3 . Assume complete ionization of dopants. From Fig. 3.5 of SDF for lightly doped material (hole can be ignored). Si: µ n = 110 cm 2 V-s Ge: µ n = 900 cm 2 V-s GaAs: µ n = 3200 cm 2 V-s Si: ρ =
(
1
1
=
= 1.0 × 1019 × 1.6 × 10−19 × 110
nqµ n nqµ n
)
−1
ρ (Si) = 5.7 × 10−3 Ω-cm Ge: ρ =
(
1
1
=
= 1.0 × 1019 × 1.6 × 10−19 × 900
nqµ n nqµ n
)
−1
ρ ( Ge ) = 6.9 × 10−4 Ω-cm Si: ρ =
(
1
1
=
= 1.0 × 1019 × 1.6 × 10−19 × 3200
nqµ n nqµ n
)
−1
ρ ( GaAs ) = 2.0 × 10−4 Ω-cm 2)
Determine the diffusion coefficient for electrons in Si at T = 300 K for the following two conditions. a) Intrinsic Si b) Si doped at N D = 1019 cm -3 Solution: 2a) intrinsic Si From Fig. 3.5 of SDF for lightly doped material. Si: µ n = 1360 cm 2 V-s Dn k BT
kT
=
→ Dn = B µ n µn
q
q
Dn =
k BT
µ = 0.026 × 1360 q n
Dn = 35 cm 2 s ECE-­‐305 2 Fall 2014 Mark Lundstrom 09/13/2014 HW4 Solutions (continued): 2b) Si doped at N D = 1019 cm -3 From Fig. 3.5 of SDF for lightly doped material. Si: µ n = 110 cm 2 V-s Dn =
k BT
µ = 0.026 × 110 q n
Dn = 2.9 cm 2 s 3) For the energy band sketched below, provide sketches of the following: 3a) the carrier densities, n(x), and p(x) vs. position. 3b) the electrostatic potential, ψ ( x ) , vs. position. 3c) the electric field E vs. position. 3d) the space charge density, ρ ( x ) vs. position Solution: 3a) The carrier densities, n(x), and p(x) vs. position 3b) The electrostatic potential, ψ ( x ) , vs. position ECE-­‐305 3 Fall 2014 Mark Lundstrom 09/13/2014 HW4 Solutions (continued): 3c) The electric field E vs. position 3d) The space charge density, ρ ( x ) vs. position. ECE-­‐305 4 Fall 2014 

Übung 2.2

Week 5 Homework Assignment

Counting holes with Fourier transform Tamás Hausel

BONEO PARK 24