課程名稱︰固態電子學
課程性質︰選修
課程教師︰吳育任 教授
開課學院：電機資訊
開課系所︰電機工程
考試日期（年月日）︰2014/04/16
考試時限（分鐘）：180分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Open book, total 105 points but maximum one can get is 100
1. At T=300K and consider GaAs material, if the Nd = 10^17 (cm^-3) and the
measured electron carrier density n = 10^-5 (cm^-3). What is the hole
0
concentration and acceptor doping density N ? (10 points)
A
2. If the material's electron mobility is 1000 (cm^2/V-s) and the electron
effective mass is 0.2m , (see textbook chapter 5.1.2). (10 points)
0
(1) What is the diffusion coefficient (Dn)?
(2) What is the average electron velocity at Electric field = 100(V/cm)?
3. For GaAs, if the doping density Nd is 10^17 (cm^-3) and fully activated,
what is the temperature required to have n = 2 x 10^17(cm-3)? (10 points)
0
(Be careful about temperature related constant)
4. As shown in Fig. 5.13, consider Si sample. The device is fabricated by
following geometry: d = 5 x 10^-3 (cm). W = 5 x 10^-2 (cm) and L = 0.5cm.
The electrical measurement are Ix = 1.0 (mA), Vx = 1.50 (V), Bz = 0.05
(tesla). The Hall voltage is V = 1.0 (mV). Please determine (15 points)
H
(a) The conductivity type
(b) The majority carrier concentration (in cm^-3)
(c) The mobility (cm^2/V-s)
5. For the 2 quantum well cases with 1 barrier in between, if the barrier
is thin enough that the coupling between the quantum well is possible.
Please roughly plot out the eigen wave function shape of the first 4
lowest eigen functions (10 points, no calculation needed!)
6. In Fig. 5.6, when temperature decreases, the carrier density decreases
at the same time. But the conductivity decreases, then increases and
decreases again, please explain the reasons for this behavior?
(i.e. what is the major factor to affect this?) (10 points)
7. By considering two major factors limiting the mobility mentioned in the
class. For a doped material, the total mobility at T=300K is 800
(cm^2/V-s) and for the same pure material without doping, the total
mobility at 300K is 1200(cm^2/V-s). What is the total mobility for this
material at T=100K? (both doped and undoped?) (15 points)
8. For a material, the E(k) relation can be expressed as, the unit of k is
m^-1 and unit of E is joule which is in MKS unit
E(k) = e [ 2.0(k /10^10) + 4.0(k /10^10)^2 - 0.5(k /10^10)^3 ]
0 x x x
(a) What is the instant electron velocity at k = 10^9 (m^-1) and
x
k = 3 x 10^9 (m^-1) (5 points)
x
(b) What is the effective mass at the same k point (in unit of m ?)
(5 points) x 0
(c) If the material is a "cubic symmetric system" lattice system
( like Si or GaAs), what is the velocity at the same "ky" point?
(5 points)
9. For a semiconductor GaAs quantum well with infinite potential barrier
assumption, if the bulk material bandgap is 1.42eV, and after quantum
confined effect, the effective bandgap becomes 1.48eV. The electron
effective mass is 0.067m , Heavy hole effective mass is 0.45m . light
0 0
hole effective mass is 0.087m , What is the quantum well width in nm?
0
(10 points)