Hunk Iruc f'kam
[email protected] HWM
I
.u
j
T (0105
2
AQSdmt +hm an amm has CL radius r and rnc un- cc :e cubxc w3+ln a Farawa-
I
7 rind WC number 05 an mm: per unit can, +ne dismnu bdween two neat-«f
g neighbovng atom: and ne pQLUnS PraLHon Fbv a £31,; 1in
Fermi Function
2
N D N A N D N A
2
n
ni
2
2
1/ 2
2
N A N D N A N D
2
p
ni
2
2
J p|drift q p Vdp
J n|drift q n Vdn
J p|drift q p p E
J n|drift q n n E
dp
Jp | diff q Dp
dx
1 dEc 1 dEi 1 dEv
q dx q dx q dx
dV
E field
dx
Dp
p
p
t
p
P
n
q = 1.6 x 10-19 coul.
k = 8.63 x 10-5 eV/T
KT= 26meV (T = 300K)
Parameters for Silicon that you may wish to use on this test:
At room temperature:
EG = 1.12eV
ni = 1010/cm3
n = 1350 cm2/V-sec
2
cm /V-sec
n = 4 x 10-5 sec
sec
At 500K:
n = 400 cm2/V-sec
TES
Parameters to use for the problems:
KT(300K) = 26meV
K = 8.617 x 10-5 eV/K
q= 1.6x10-19 C
Silicon:
Eg = 1.12eV
Si(T = 300K):
ni (T = 300K)= 1010 /cm3
Si(T = 300K):
p = 480 cm2/V-sec
Si(T = 300K):
Dp = 10 cm2/sec
-6
p = n = 6x10 sec
(excess minority carrie
B. OLSON
ECE 330
Midterm1 - SOLUTIONS
1)
TEST A (Yellow) Ei-EF = .31eV p = 1.51x1015 n = 6.6x104
TEST B (Salmon) Ei-EF =.185eV p = 1.23x1013 n = 8.13x106
2)
TEST A l/A = 2 T = 500K
q ni ( n up )
l
R
A
Na 1012 , ni 3 1014
Na Nd Na
Is Na ni ? NO!
We may no
Parameters to use for the problems:
KT(300K) = 26meV
K = 8.617 x 10-5 eV/K
q= 1.6x10-19 C
Silicon:
Eg = 1.12eV
ni (T = 300K)= 1010 /cm3
s(Silicon) = Ks o = (11.8)(8.85x10-14 F/cm)
MIDTERM 1A
93 TOTAL points
1)
(3pts) Determine the average kinetic energy o
Parameters to use for the problems:
Silicon:
Eg = 1.12eV
Si(T = 300K):
ni (T = 300K)= 1010/cm3
s(Silicon) = Ks o = (11.8)(8.85x10-14 F/cm)
ox(SiO2) = Kox o = (3.9)(8.85x10-14 F/cm)
TEST A
1) Below is a band diagram of a Silicon based MOS Capacitor at room
Parameters to use for the problems:
KT(300K) = 26meV
K = 8.617 x 10-5 eV/K
q= 1.6x10-19 C
Silicon:
Eg = 1.12eV
Si(T = 300K):
ni (T = 300K)= 1010 /cm3
s(Silicon) = Ks o = (11.8)(8.85x10-14 F/cm)
MIDTERM 1A
73 TOTAL Points
1)
(4pts) Name two sources of scat
1)
A sample of Silicon at 350 K is doped such that Nd = 1015 cm-3and Na = 1012 cm-3.
Assume that at this temperature: ni = 3 x 1011 cm-3, n = p = 3x10-6sec, Ln = .0089cm
Lp=.005cm
Determine the resistivity. You may assume that one number is much bigger th
q = 1.6 x 10-19 coul.
K = 8.62 x 10-5 eV/T
K=1.38 x 10-23 J/T
KT= 26meV (T = 300K)
Parameters for Silicon that you may wish to use on
this test:
At room temperature(300K):
EG = 1.12eV
ni = 1010/cm3
n = 1350 cm2/V-sec
2
cm /V-sec
Dn = 25cm2/sec
10cm2/sec
n
Parameters to use for the problems:
KT(300K) = 26meV
K = 8.617 x 10-5 eV/K
q= 1.6x10-19 C
Silicon:
Eg = 1.12eV
Si(T = 300K):
ni (T = 300K)= 1010 /cm3
s(Silicon) = Ks o = (11.8)(8.85x10-14 F/cm)
MIDTERM 1A
1) (2pts) Which is true (circle one)
a) Mobility d
B. OLSON
ECE 330
Homework 3
1. Note You are also responsible for the examples that were done in class. The band diagram
shown represents a sample that is 6.5m long. For this diagram answer the questions below. You may
assume that E1 = .32 1019 Joules and
B. OLSON
ECE 330
Homework 2 - SOLUTIONS
1. Since n n p p we can assume that:
=
=
1
1
=
q(n n + p p)
q n n
1
= 4 cm
1.6 1019 1350 n
n
= ND = 1.15 1015 cm3
2. (a) Since the material is intrinsic n = p = ni
=
=
1
1
=
q(n n + p p)
q(n + p )ni
1
= 42.3 cm
19
B. OLSON
ECE 330
Homework 1
Parameters to use:
q = 1.6 1019 coulombs
K = 8.617 105 eV /K
1. Determine KT at 400K. Express your answer in eV and in Joules.
2. Develop an expression for the total number of available STATES per unit volume in the conduction
B. OLSON
ECE 330
Homework 1 - SOLUTIONS
1. First we determine KT in eV:
KT (eV ) = 400K 8.617 105 eV /K = 34 103 eV.
Then we determine it in Joules:
KT (J) = KT (eV ) 1.6 1019 = 5.51 1021 J.
2.
m 2mn (E Ec)
gc (E) = n
2 h3
p
2
Number of states/cm
=
=
=
Z
B. OLSON
ECE 330
Homework 3 - SOLUTIONS
dEF
dx
dEi
dx =
1. (a) yes, because:
(b) Note where
= 0.
0 there is no drift current
1
(c) Note where
dEi
dx
= 0 there is no carrier gradient and no diffusion current
(d) Electrostatic Potential (Voltage) as a funct
B. OLSON
ECE 330
Homework 4
Unless told otherwise, use thefollowing parameters:
KT (T = 300K) = 26meV , K = 8.617 105 eV /K, q = 1.6 1019 coul
1. A sample of material has a diffusion coefficient of 15cm2 /sec. Determine the mobility at T=500K.
2. At t = 1
Introduction to Semiconductors
Atoms Contain
e-
nucleus
Electrons
e-
Valence Electrons:
The number of
electrons in the
outermost shell
Nucleus
Protons
Neutrons
Semiconductors: an introduction
Classification of Materials in terms of electrical resistivity:
B. OLSON
ECE 330
Homework 1 - SOLUTIONS
1. First we determine KT in eV:
KT (eV ) = 400K 8.617 105 eV /K = 34 103 eV.
Then we determine it in Joules:
KT (J) = KT (eV ) 1.6 1019 = 5.51 1021 J.
2.
m 2mn (E Ec)
gc (E) = n
2 h3
p
2
Number of states/cm
=
=
=
Z
ECE 330
Introduction to Semiconductor Devices
Jenny Zhen Yu
[email protected]
Department of Electrical and Computer Engineering
California State Polytechnic University, Pomona
Spring 2017
Crystal Structures
Periodic Table
Abundances of the Elements
the first
x
Physical constants .
t
Constant Symbol . Magnitude E
i
Avogadros number N. 6.023 X 1013 molecnlesfrnol E
Boltzmann's constant I: 1.38 X lOl": EEK =. 8.62 X 105 eWK
Electronic charge 6] 1.6 X 10': C E . E
Electronvolt eV 1.6 X 1059 J E
Freemelectmn mas
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 3
Due Thursday, 20 April
1. (a) Under equilibrium conditions and T > 0 K, what is the probability of an electron state
being occupied if it is located at the Fermi level?
(b) If EF
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 2
Due Tuesday, 18 April
1. A light source contains a 10-W mercury-vapor lamp. Assuming that 0.1 percent of the
electric energy is converted to the ultraviolet emission line of 253.
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 8
Due Thursday, 25 May
1. Given a planar p+ -n Si step junction diode with an n-side doping of ND=1015/cm3 VBR=320
V and T=300 K, determine
(a) The depletion width at the breakdown
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 6
Due Thursday, 11 May
1. Calculate the electron and hole concentration under steady-state illumination in an n-type
silicon with GL=1016 cm-3s-1, Nd=1015 cm-3, and n=p=10 s.
2. De
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 7
Due Thursday, 18 May
1. A Si p-n junction is doped with ND=5x1015 cm-3 and NA=2x1016 cm-3. Calculate the built-in
potential Vbi, xp, xn and the total depletion width W.
2. A sili
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 5
Due Thursday, 4th May
Midterm exam Error correction.
330-homework-sp17.tex
Spring 2017
Z. Yu
1
ECE 330: Introduction to Semiconductor Devices
Homework Assignment 9
Due Thursday, 1 June
1. A p+-n silicon diode is used as a varactor. The doping concentrations on the two sides of
the junction are Nd=1015, Na=1019, respectively. Assuming the bu