elemental; ge, si 2.2 결정격자 crystal; primitive...
TRANSCRIPT
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Chapter1. crystal structure
1.1 반도체 재료
elemental; Ge, Si
화합물 반도체; GaAs, Gap, InP, ZnS
2.2 결정격자
crystal; primitive cell이 주기 으로 배열
(a) single crystal
(b) amorphous solid
(c) polycrystaline solid
primitive cell; minimum volume cell
1.3 lattice type
14 lattice types in 3 Dimension
S.C, b.c.c f.c.c
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1.5 Index system for crystal system
crystal면의 치와 방향을 기술하는 것은 다음규정에 의해 결정된
다.
(ㄱ) 면과의 교차 을 기본벡터(x, y, z)의 정수배로 나타낸다.
(ㄴ) 이 숫자들의 역수를 취하고 이들을 최소의 정수 h k l의
set로 표 한다.
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1.6 다이아몬드 격자구조
diamond structure may be viewed as two fcc structures displaced
from each other by one-quarter of a body diagonal
1.7 반도체 결정성장
과제; 1. 결정의 완 화
2. carrier불순물의 균일한 doping
3. 불순물 제어
4. 결정의 형화
* Czochralski방법
직경제어---인상속도가 1차
2차 으로 가열온도
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* floating-zone방법(부유 역 용융법)
고주 유도가열에 의해 용융 를 형성하여 그것을 단결정의 길이
방향으로 이동하는 방법으로 단결정 성장
* Epitaxy
Epi----> upon, taxis-----> ordered
기 웨이퍼 에 방향성을 가진 단결정을 기르는 기술
격자구조와 격자상수가 같으면 epitaxial층을 형성하기 용이함
(a)CVD; chemical vapor deposition
(b)LPE; Liquid phase epitaxy
(c)MBE; molecular beam epitaxy
온공정 doping control 용이
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1.8 고체의 결합력
(a) ionic bond; NaCl, CsCl
bond resulting from the electrostatic interaction of
oppositely charged ions, nearly filled shell
(b) covalent bond; 공유결합, atom이 자를 공유하여 이상기체화
Ge, Si, C는 채워진 상태에 비해서 4개의 자가 부족
(c) metallic bond; 외각의 자유 자들과 양이온 심체의 상호작용
(d) Van Der Walls bond (among molecules)
(interaction between dipole moment and induced dipole
moment) attractive
(e) Hydrogen bond highly polar H2O
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Chapter2. Introduction to the Quantum Theory of Solids
1920년 원자규모에서 일어나는 상을 규명하는데 고 역학으로는
설명되지 않고 양자역학의 개념을 도입하여 성공 으로 해석
(a) photoelectric effect( 효과)
Em = hν - W Em; 자에 지(kinetic E)
W; work function(eV)
(b) wave-particle duality
De Broglie P = h/λ, λ = h/P, mv = h/λ
Davission-Germer experiment
(c) uncertainty principle
자의 치와 속도의 동시측정은 불확실하다. (h크기 이상으로)
ΔP ΔX ≥ h , △E △t ≥ h
2.1 Schrodinger wave equation
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2.1.1 The infinite potential well
wave function Ψ(x) = C sin(nπx/a) where n = 1, 2, 3,...
total energy E = h2n2/8ma2 where n = 1, 2, 3,...
2.1.2 step potential function
Reflected probability density function
R =
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2.2 Periodic table
Pauli exclusion principle; no two electrons in an atom
can exist in the same quantum state.
orbital quantum # l = 0, 1, 2,----- n-1
n; total quantum #
magnetic quantum # m = 0, ±1, ±2,-----±l
spin state s = ±h/4π
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2.3 Energy band
Bragg condition
Laue diffraction
energyε versus wave vector κ
(a) for a free electron
(b) for a single crystal
Energy gap Eg is of decisive significance in determining a
solid is an insulator or a conductor.
conduction band
valance band
energy gap
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2.5 Electrical conduction
drift current J = NqVd (A/cm2)
effective mass m* = (d2E/dk24π2h2)-1
concept of hole
Metal, Insulators, and Semiconductors
2.6 Statistical Mechanics
The density of quantum states per unit volume of crystal
g(E) = {4π(2m)3/2E1/2}/h3
The density of allowed energy state in the conduction band
gc(E) = {4π(2mn)3/2(E-Ec)1/2}/h3
The density of allowed energy state in the conduction band
gv(E) = {4π(2mp)3/2(Ev-E)1/2}/h3
Fermi-Dirac probability function
fF(E) = [ 1 + exp((E - Ef)/kT))]
그림 2.32
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Chapter 3 The Semiconductor in Equilibrium
3.1 charge carriers
the thermal- equilibrium concentration
of electrons no and po
no = ∫gc(E)fF(E) dE = Nc exp[-(Ec - Ef)/kT]
po = ∫gv(E)[1 - fF(E)] dE = Nv exp[-(Ef - Ev)/kT]
ni2 = NcNv exp[-(Ec - Ev)/kT] = NcNv exp[-Eg/kT]
2 Emidgap = (Ec + Ev)
Efi = Emidgap + 0.75 kT ln(m*p/m*n)
Ionization energy and Ⅲ-Ⅴ semiconductor
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3.3 Extrinsic Semiconductor
no = ni exp[(Ef - Efi)/kT]
po = ni exp[-(Ef - Efi)/kT]
ni = Nc exp[-(Ec - Efi)/kT]
nopo = NcNv exp[-Eg/kT] = ni2
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3.4 Position of Fermi Energy Level
Ec -Ef = kT ln(Nc/no)
Ef - Ev = kT ln(Nv/po)
Ec - Ef = kT ln(Nc/Nd)
objective; To determine the required donor impurity concentration
to obtain a specified Fermi energy
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Chapter.4 Carrier Transport
4.1 Drift charge movement due to an electric field
current density J = n e vd
= n e μ E
vd; drift velocity μ; mobility E; electric field
vd = μE, μ= vd/E = Eζ/m*
ζ; mean collision time
resistivityρ = (conductivity σ)-1
V = I R R = ρL/A
Objective; To determine the doping concentration and majority
carrier mobility, given the conductivity of n-type semiconductor
4.2 Diffusion
Jn = eDnΔn Dn; electron diffusion coefficient
total current density
J = enμnE + epμpE + eDnΔn - eDpΔp
그림 4.11
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Graded impurity distribution
Ex = -(kT/eNd(x))dNd(x)/dx
Objective; To determine the induced electric field
in a semiconductor in thermal equilibrium,
given a lineal variation in doping concentration
Einstein relation
kT/e = Dn/μn = Dp/μp
Table 4.2
The Hall effect
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* continuity equations
δn/δt = - (δFn-/δx) + gn - n/ζn
time -dependent diffusion equation
mbipolar transport equation
objective; (1) To determine the time behavior of excess carriers as
a semiconductor returns to thermal equilibrium.
objective; (2) To determine the steady-state spatial dependence of
the excess carrier concentration.
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* Haynes-Shockley Experiment
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Chapter 6 pn Junction
6.1 Structure and energy-band diagram
p-type Semiconductor
n-type semiconductor
majority and minority carrier
space charge region
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built-in potential
Poisson's equation
d2Φ/dx2 = -ρ(x)/ε, E(x) = -dΦ/dx
Space charge width
W = { (2εV/e)[(Na + Nd)/NaNd]}1/2
그림6.6
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6.2 Junction capacitance and one-sided junction
C = ε/W, C = dQ/dV
objective 1; To calculate the junction capacitance
of a pn junction
objective 2; To determine the impurity doping
concentrations in a p+n junction given
the parameters from Fig6.11
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Chapter 7 Diode
7.1 Current-voltage relationship
np = npo exp(eVa/kT), npo = ni2/Na
pn = pno exp(eVa/kT), pno = ni2/Nd
minority carrier distribution
x>xn, δpn(x) = pn(x) - pno, d2δpn/dx
2 - δpn/Lp2 = 0
x<xp, δnp(x) = np(x) - npo, d2δnp/dx
2 - δnp/Ln2 = 0
diode current equation
I = Is[exp(eV/kT) - 1]
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objective; To calculate the electric field required to
produce a given majority carrier drift current.
7.2 small-signal model of the pn junction
그림7.13
conductance gd = dId/dV]v=vQ
resistance rd = (gd)-1 = Vt/IQ
capacitance Cd = (1/2Vt)(Ipoζpo + Inoζno)
transition cap.; 이 역의 dipole에 의한 합 정 용량
diffusion cap.; 이 역 부근의 minority carrier에 의한 정 용량
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objective1; To calculate the small-signal admittance
of a pn junction diode
7.3 Junction breakdown voltage(p+n junction)
Emax = eNdXn/e, Xn ~ [2eVr/eNd]1/2,
VB = eEc2/2eNb
objective2; To design an ideal one-sided n+p junction
diode to meet a breakdown voltage specification.
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7.4 Charge storage and diode transients
storage time ts
ts ~ ζpo ln[1 + IF/IR]
ζpo ; minority carrier lifetime
IF ; forward-bias current
IR ; reverse-bias current
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7.5 pn junction solar cell (태양 지)
발 (luminescence)
1. photoluminescence, 2. 음극선 발 (TV, OSC.) 3. 계발
photolum.
a. 빛의 흡수로 valance band의 자가 conduction band로 여기
b. 격자에 에 지를 주고 conduction band 표면부근으로 이동
c. 재결합(E-H pair)------ 자 방출
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open circuit voltage Voc = Vt ln(1 + Isc/Is)
Vt; kT/e , Isc; short circuit current
power delivered to the load P = IV
conversion efficiency η= ImVm/Pin
변환효율 GaAs; 25%, Si; 17%, amorphous Si; 8~10%
maximum area in the solar cell I-V charac.
참조; 그림 7.31 ~ 7.33
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p-n junction 합제작
* 성장형 합; 결정성장 과정 에 불순물을 용융제에 첨가.
Epitaxial growth
* 합 형 합; 1950 ~ 60년
Ge 시료 에 In; 160oC에서 용융용해체를 형성
In에 Ge를 공 , seed결정
* 확산형 합; diffusion
시료표면의 합부 깊이는 diffusion시간과
온도에 의해 제어
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Chapter8 Metal-Semiconductor contact
정류 합
ohmic 합
work-function(photoelectric effect)
objective1; To calculate the theoretical barrier height,
built-in potential barrier, and maximum electric field in a
metal-semiconductor diode for zero applied bias
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image charge
objective2; To calculate the Schottky barrier lowering and
the position of the maximum barrier height
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homojunction; same semiconductor junction
same energy gap Eg
heterojunction; two different semiconductor junction
optic device GaAs-AlGaAs,
high frequency device
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Triangular potential well → solve by quantum mechanics
Schrodinger equation