elemental; ge, si 2.2 결정격자 crystal; primitive...

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