Name:
No.:
Score:
’08 1학기 물리전자 중간 고사
- 주의 사항 - 풀이 과정은 알아보기 쉽게 표현할 것.
풀이 과정이 명확하지 않은 경우에는 “0”점 처리됨.
- 답에는 단위를 꼭 표시할 것.
- 휴대폰 및 계산기 사용 금지.
- 답안지 외 연습장 사용 금지.
- 총 11 문항이니 빼먹지 말고 풀 것.
.
Score:
1. Choose one that is not a unit cell of 2-dimensional lattice structure shown below. ( 5 points )
①
②
③
④
2. Draw a (1 1 1) plane in the coordinates shown below. ( 5 points )
z
a
a
a
y
x
3. Fill in the three blanks in the table below. ( 10 points )
(
(
)
(
)
)
Score:
4. Fill in the blanks below. ( 10 points )
ni 


Ei  

NC NV
EC  EV
2
e
 EG / 2 kT
 mp * 
 3

  kT ln 
 4
 mn * 

p  NV exp 

EV  E F
kT
DN
 N 


  ni exp 



Ei  EF
kT



kT
q
5. Describe the position of the Fermi level in the bandgap when the temperature is 10K, 300K, and
600K for the donor-doped Si with ND=1015/cm3 . Refer to the figure below if needed. ( 10 points )
10K: 위의 그림에서 n/ND ≈ 0 이므로 donor-level (ED)의 state가 대부분 전자로 채워져 있음을 알 수 있다.
따라서 Fermi level (EF)는 ED 위에 있다. 또한 n/ND ≈ 0 인 사실로부터 EF는 EC 아래에 있음을 알 수
있다. 즉, ED < EF < EC
300K: n ≈ ND 이므로 ED의 state는 대부분 비어서 EF < ED 이고, 동시에 n ≈ ND >> ni 이므로 EF > Ei 임을
알 수 있다. 정확히 표현하면, EF = Ei + kTln(ND/ni) ≈ Ei + 0.3eV 이다.
600K: n ≈ ni 이므로 EF ≈ Ei 이다.
Score:
6. Determine the equilibrium electron and hole concentrations inside a uniformly doped sample of Si
under the following conditions: T = 300K, NA = 1016 cm-3, ND ≪ NA ( 5 points )
7. In a nondegenerate silicon sample maintained under equilibrium condition near room temperature, it
is known that ni = 1010 cm-3, n = 2p, and NA = 0, Determine n and ND. ( 5 points )
Equilibrium 상태에서 np = ni2 이고, 문제에서 n = 2p로 주어졌으므로, 아래의 식을 얻을 수 있다.
n  2
ni 2
n
위 식을 풀면, n  2  ni  1.4 1010 cm3
한편, charge neutrality가 만족되어야 하므로,
 n  p  N A   N D   0   2ni 
 ND 
2
ni  7  109 cm 3
2
2
ni  N D  0
2
Score:
8. Consider the following energy band diagram. Take the semiconductor represented to be Si
maintained at 300K with Ei – EF = EG/4 at x = ±L and EF – Ei = EG/4 at x = 0.
① Sketch the electrostatic potential (V) inside the semiconductor as a function of x. ( 5 points )
② Roughly sketch log(n) and log(p) versus x inside the sample. ( 5 points )
③ Indicate the direction of electron diffusion current and drift current at x = ±L/2. ( 5 points )
log(p)
E 

log  ni exp G 
4
kT 

log(p)
log ni
log(n)
log(n)
 EG 

log  ni exp

4kT 

③
x = -L/2
x = +L/2
JN.Diff
→
←
JN.Drift
←
→
Score:
9. A Si sample is maintained under equilibrium conditions at room temperature and a certain region
from x=0 to x=L has the nonuniform donor doping such that
ax
n( x)  N D ( x)  ni exp 

 b 
where a=1.8μm, b=0.1μm, and L=0.8μm.

0 xL
① Draw the energy band diagram for the 0 ≤ x ≤ L region specifically showing Ec, EF, Ei, and Ev
on your diagram. ( 5 points )
② Make a sketch of the electric field (E) inside the region as a function of x, and compute the
value of E at x = L/2. ( 5 points )
Score:
10. A semi-infinite n-type silicon bar (see figure below) is illuminated with light which generates
GL electron-hole pairs per cm3-sec uniformly throughout the volume of the semiconductor.
Simultaneously, carriers are extracted at x = 0 making Δpn = 0 at x = 0. Assuming a steady
state condition has been established and Δpn ≪ n0 for all x, determine Δpn(x) by using the
minority carrier diffusion equation. (n0 is the electron concentration under equilibrium. Δpn
is the deviation of hole concentration from the equilibrium value under arbitrary condition.)
( 10 points )
Score:
11. The energy band diagram of a semiconductor sample maintained at 300K is shown in the figure
below. Answer the questions based on the energy band diagram.
Ec
EG/4
EF
Ei
Ev
0
L/4
L/2
3L/4
L
① Does equilibrium condition prevail? How do you know? ( 5 points )
Fermi level (EF)가 수평이므로 평형상태이다.
② Sketch the electric field (E) inside the semiconductor as a function of x. ( 5 points )
③ Roughly sketch log(n) versus x. ( 5 points )