elemental; ge, si 2.2 결정격자 crystal; primitive...
TRANSCRIPT
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
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.
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
* 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
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
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
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 =
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
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
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
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
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
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
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
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
* 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.
* Haynes-Shockley Experiment
Chapter 6 pn Junction
6.1 Structure and energy-band diagram
p-type Semiconductor
n-type semiconductor
majority and minority carrier
space charge region
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
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
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]
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
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.
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
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
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
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
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
image charge
objective2; To calculate the Schottky barrier lowering and
the position of the maximum barrier height
homojunction; same semiconductor junction
same energy gap Eg
heterojunction; two different semiconductor junction
optic device GaAs-AlGaAs,
high frequency device
Triangular potential well → solve by quantum mechanics
Schrodinger equation