半導體科學與發光二極體eportfolio.lib.ksu.edu.tw/user/t/0/t094000004/repository/微波光電... ·...

118

第三章

半導體科學與發光二極體

119

目錄

3-1 半導體概念與能帶3-2 直接和非直接能隙半導體：E-k圖3-3 pn接面原理3-4 pn接面能帶圖3-5 發光二極體3-6 LED材料3-7 異質接面高強度LEDs3-8 LED特性3-9 光纖通訊用LED

120

3-1 半導體概念與能帶

121

2 s Band

Overlapping energybands

Electrons2 s2 p

3 s3 p

1 s 1sSOLIDATOM

E = 0

Free electronElectron Energy, E

2 p Band3s Band

Vacuumlevel

In a metal the various energy bands overlap to give a single bandof energies that is only partially full of electrons. There are stateswith energies up to the vacuum level where the electron is free.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖3.1 金屬中，不同能帶相重疊以得到特定的單一能帶，此能帶上只填滿部份的電子。當能態高於自由能階時，電子是不受束縛而可自由移動的。

122

Electron energy, E

Conduction Band (CB)Empty of electrons at 0 K.

Valence Band (VB)Full of electrons at 0 K.

Ec

Ev

0

Ec+χ

(b)

Band gap = Eg

(a)

Covalent bond Si ion core (+4e)

(a) A simplified two dimensional view of a region of the Si crystalshowing covalent bonds. (b) The energy band diagram of electrons in theSi crystal at absolute zero of temperature.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖3.2 (a) 描述矽晶體共價鍵的簡化2維區域示意圖。(b)絕對温度零度時，矽晶體的電子能帶圖。

123

e–hole

CB

VB

Ec

Ev

0

Ec+χ

EgFree e–hυ > Eg

Hole h+

Electron energy, E

(a) A photon with an energy greater than Eg can excite an electron from the VB to the CB.(b) Each line between Si-Si atoms is a valence electron in a bond. When a photon breaks aSi-Si bond, a free electron and a hole in the Si-Si bond is created.

hυ

(a) (b)

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖3.3 (a) 光子能量大於 Eg 時會將 VB 中的電子激發至CB。(b) 在 Si-Si 原子間的線，表示共價鍵中的的價電子，當光子將 Si 與 Si 間的鍵結打斷，則在 Si–Si 鍵結中將形成一自由電子和電洞。

125

E

g(E) fE)

EF

nE(E) or pE(E)

E E

Forelectrons

For holes

[1–f(E)]

nE(E)

pE(E)

Area = p

Area = � nE(E)dE = n

Ec

EvEv

Ec

0

Ec+χ

EF

VB

CB

(a) (b) (c) (d)g(E) ∝ (E–Ec)

1/2

(a) Energy band diagram. (b) Density of states (number of states per unit energy perunit volume). (c) Fermi-Dirac probability function (probability of occupancy of astate). (d) The product of g(E) and f(E) is the energy density of electrons in the CB(number of electrons per unit energy per unit volume). The area under nE(E) vs. E isthe electron concentration.


任何材料系統，其改變，代表每個電子的電功輸入或輸出。假設 V 是兩點的位能差，則

(2)

FE∆

eVEF =∆

126

132

e–

(a)

As+

x

As+ As+ As+ As+

EcEd

CB

Ev

~0.05 eV

As atom sites every 106 Si atoms

Distance intocrystal

(b)Electron Energy

(a) The four valence electrons of Asallow it to bond just like Si but the fifthelectron is left orbiting the As site. Theenergy required to release to free fifth-electron into the CB is very small.

(b) Energy band diagram for an n-type Si dopedwith 1 ppm As. There are donor energy levels justbelow Ec around As+ sites.


B–h+

(a)

x

B–

Ev

Ea

B atom sites every 106 Si atoms

Distanceinto crystal

~0.05 eV

B– B– B–

h+

VB

Ec

Electron energy

(b)

(a) Boron doped Si crystal. B has only three valence electrons. When itsubstitutes for a Si atom one of its bonds has an electron missing and therefore ahole. (b) Energy band diagram for a p-type Si doped with 1 ppm B. There areacceptor energy levels just above Ev around B– sites. These acceptor levels acceptelectrons from the VB and therefore create holes in the VB.


圖3.6 (a) Si 晶體中摻雜硼，硼只有三個價電子，當它取代矽原子時，共價鍵中將缺少一個電子，而形成一個電洞。(b) p-型矽摻1ppm硼之能帶圖。在位置周遭有受體能階恰高於Ev，這些受體能階從 VB 接受一個電子，因此在 VB 產生電洞。

−B

134

135

Ec

Ev

EFi

CB

EFp

EFnEc

Ev

Ec

EvVB

(a) (c)(b)

Energy band diagrams for (a) intrinsic (b) n-type and (c) p-typesemiconductors. In all cases, np = ni2. Note that donor and acceptorenergy levels are not shown.


136

CB

g(E)

E

Impuritiesforming a band

(a) (b)

EFp

Ev

EcEFn

Ev

Ec

CB

VB

(a) Degenerate n-type semiconductor. Large number of donors form aband that overlaps the CB. (b) Degenerate p-type semiconductor.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

137

V

n -Type Semiconductor

Ec

EF − eV

A

B

V(x), PE (x)

x

PE (x) = �eV

Energy band diagram of an n-type semiconductor connected to avoltage supply of V volts. The whole energy diagram tilts becausethe electron now has an electrostatic potential energy as well

EElectron Energy

Ec − eV

Ev− eV

V(x)

EF

Ev


圖3.9 n-型半導體外加 V 伏特電壓時的能帶圖，整個能帶圖歪斜是由於電子現在具有像井般靜電位能。

141

3-2 直接和非直接能隙半導體：E-k圖

142

為了找尋晶體中電子的能量，我們必須去解3維週期性位能的薛定格方程，我們首先設想一維晶體，如圖3.10所示，每個原子的電位能相加，以得全部的位能函數V(x)，顯然地即為具有晶體週期為a在x的電位函數，因此，，因此我們的工作是去求解薛定格方程，

(1)

=+=+= )2()()( axVaxVxV

0)]([2 222

=−+ ψxVEmdxψd e

144

r

PE(r)PE of the electron around anisolated atom

When N atoms are arranged to formthe crystal then there is an overlapof individual electron PE functions.

x

V(x)

x = Lx = 0 a 2a 3a

0aa

Surface SurfaceCrystal

PE of the electron, V(x), insidethe crystal is periodic with aperiod a.

The electron potential energy (PE), V(x), inside the crystal is periodic with the sameperiodicity as that of the crystal, a. Far away outside the crystal, by choice, V = 0 (theelectron is free and PE = 0).


圖3.10 電子位能 PE 、 V(x) 在晶體中呈週期性 a ，並具有和晶體相同的週期性，晶體外之遠處，可選擇 V = 0( 電子是自由的及 PE = 0)。

146

Ek

kš /a–š /a

Ec

Ev

ConductionBand (CB)

Ec

Ev

CB

The E-k Diagram The Energy BandDiagram

Empty ψk

Occupied ψkh+

e-

Eg

e-

h+

hυ

VB

hυ

ValenceBand (VB)

The E-k diagram of a direct bandgap semiconductor such as GaAs. The E-kcurve consists of many discrete points with each point corresponding to apossible state, wavefunction ψk(x), that is allowed to exist in the crystal.The points are so close that we normally draw the E-k relationship as acontinuous curve. In the energy range Ev to Ec there are no points (ψk(x)solutions). ?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

147

E

CB

k–k

Direct Bandgap

(a) GaAs

E

CB

VB

Indirect Bandgap, Eg

k–k

kcb

(b) Si

E

k–k

Phonon

(c) Si with a recombination center

Eg

Ec

EvEc

Evkvb VB

CB

ErEc

Ev

Photon

VB

(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs istherefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced fromthe maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination ofan electron and a hole in Si involves a recombination center .


148

3-3 pn接面原理

149

nno

xx = 0

pno

ppo

npo

log(n), log(p)

-eNa

eNd

M

x

E (x)

B-

h+

p n

M

As+

e–

Wp Wn

Neutral n-regionNeutral p-region

Space charge region Vo

V(x)

x

PE(x)

Electron PE(x)

Metallurgical Junction

(a)

(b)

(c)

(e)

(f)

x

–WpWn

(d)

0

eVo

x (g)

–eVo

Hole PE(x)

–Eo

Eo

M

ρnet

M

Wn–Wp

ni

Properties of the pn junction.


圖3.13 pn接面的特性

為了全部電荷維持電中性，左手邊的總電荷，必須等於右手邊，所以

(1) ndpa WNWN =

150

155

Neutral n-regionNeutral p-regionEo – E

Log (carrier concentration)

Holediffusion

Electrondiffusion

np(0)

Minute increase

pn(0)

pnonpo

pponno

V

Excess holes

Excess electrons

x′x

(a)

W

e(Vo–V)eVo

M

x

Wo

Hole PE(x)

(b)

SCL

Forward biased pn junction and the injection of minority carriers (a) Carrierconcentration profiles across the device under forward bias. (b). The holepotential energy with and without an applied bias. W is the width of the SCLwith forward bias?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

159

Jelec

x

n-region

J = Jelec + Jhole

SCL

Minority carrier diffusioncurrent

Majority carrier diffusionand drift current

Total current

Jhole

Wn–Wp

p-region

J

The total currentanywhere in the device isconstant. Just outside thedepletion region it is dueto the diffusion ofminority carriers.


162

C

WnWp

Log (carrier concentration)

np(0)pnonpo

ppo nno

V

x

p-side

SCL

pn(0)

pM

M

nM

n-side

B

HolesElectrons

A D

Forward biased pn junction and the injection ofcarriers and their recombination in the SCL.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖3.16 順向偏壓在 pn 接面和在 SCL 的注入載子和它們的復合情形。

166

nA

I

Shockley equation

Space charge layergeneration.

V

mAReverse I-V characteristics of apn junction (the positive andnegative current axes havedifferent scales)

I = Io[exp(eV/ηkBT) − 1]


圖3.17 pn接面的順向和逆向特性 I-V ( 正和負電流軸，有不同的刻度，因此在原點是不連續的。

167

WoWo

Neutral n-regionNeutral p-region

x

W

HolesElectrons

DiffusionDrift

x

(a)(b)

ThermallygeneratedEHP

pnonpo

Vr

Eo+E

Minority CarrierConcentration

e(Vo+Vr)eVo

W(V = –Vr)

MHole PE(x)

Reverse biased pn junction. (a) Minority carrier profiles and the origin of thereverse current. (b) Hole PE across the junction under reverse bias


假設是因為晶格熱振動而產生電子–電洞對的平均時間，也稱為平均發生時間，對一，每單位體積熱生速率必為，因為它取單位體積下，平均秒去產生 n1 個EHP，而且因為 WA 是空乏區的體積，其中 A 是截面積，EHP的速率或電荷載子產生是，電洞和電子兩者在乏區漂移，同時每一個貢獻相同的電流，所觀察到的電流必為，因此在SCL內，由於熱產生電子–電洞所產生的逆向電流成份可表示成

(16)

gτgτgτ

gin τ/

gτ

giAWn τ/)(

giWne τ/)(

g

ieWnJτ

=gen

168

169

逆向偏壓使乏區寬度 W 變寬，因此增加，總逆向電流密度為擴散和產生成份的加總，亦即

(17)

genJ

revJ

g

ii

ae

e

dh

h eWnnNL

eDNL

eDJτ

+⎟⎟⎠

⎞⎜⎜⎝

⎛+= 2rev

0.002 0.004 0.006 0.0081/Temperature (1/K)

10 -1 6

10 -1 4

10 -1 2

10 -1 0

10 -8

10 -6

10 -4

Reverse diode current (A) at V = −5 V

Ge Photodiode323 K

238 K0.33 eV

0.63 eV

Reverse diode current in a Ge pnjunction as a function of temperature ina ln( Irev ) vs. 1/ T plot. Above 238 K, Irevis controlled by n i2 and below 238 K itis controlled by n i. The vertical axis isa logarithmic scale with actual currentvalues. (From D. Scansen and S.O.Kasap, Cnd. J. Physics. 70 , 1070-1075,1992.)


圖3.19 由對的圖可知鍺 pn 接面的逆向電流為溫度的函數238K。以上被 ni2 控制，而低於238K時，是由控制，垂直軸為自然對數軸，具有一實際電流值。

)ln( revI T/1revI

171

180

3-4 pn接面能帶圖

181

EcEv

Ec

EFp

M

EFn

eVo

p nEo

Evnp

(a)

VI

np

Eo–E

e(Vo–V)

eV

EcEFn

Ev

Ev

Ec

EFp

(b)

(c)

Vr

np

e(Vo+Vr)

EcEFn

Ev

Ev

Ec

EFp

Eo+E (d)

I = Very SmallVr

np

Thermalgeneration Ec

EFnEv

Ec

EFp

Ev

e(Vo+Vr)

Eo+E

Energy band diagrams for a pn junction under (a) open circuit, (b) forwardbias and (c) reverse bias conditions. (d) Thermal generation of electron holepairs in the depletion region results in a small reverse current.

SCL


圖3.20 接面在 (a) 開路 (b) 順向偏壓 (c) 逆向偏壓情況下的能帶圖 (d) 乏區中熱產生電子–電洞對而生成一小逆向電流。

182

3-5 發光二極體

183

hυ - Eg

Eg (b)

V

(a)

p n+

EgeVo

EF

p n+

Electron in CBHole in VB

Ec

Ev

Ec

Ev

EF

eVo

Electron energy

Distance into device

(a) The energy band diagram of a p-n+ (heavily n-type doped) junction without any bias.Built-in potential Vo prevents electrons from diffusing from n+ to p side. (b) The appliedbias reduces Vo and thereby allows electrons to diffuse, be injected, into the p-side.Recombination around the junction and within the diffusion length of the electrons in thep-side leads to photon emission.


184

Light output

Insulator (oxide)p

n+Epitaxial layer

A schematic illustration of typical planar surface emitting LED devices. (a) p-layergrown epitaxially on an n+ substrate. (b) First n+ is epitaxially grown and then p regionis formed by dopant diffusion into the epitaxial layer.

Light output

pEpitaxial layers

(a ) (b )

n+Substrate Substrate

n+

n+

Metal electrode


185

Light output

p

Electrodes

LightPlastic dome

Electrodes

Domedsemiconductor

pn Junction

(a) (b) (c)

n+n+

(a) Some light suffers total internal reflection and cannot escape. (b) Internal reflectionscan be reduced and hence more light can be collected by shaping the semiconductor into adome so that the angles of incidence at the semiconductor-air surface are smaller than thecritical angle. (b) An economic method of allowing more light to escape from the LED isto encapsulate it in a transparent plastic dome.

Substrate


186

3-6 LED材料

187

Ec

Ev

EN

(b) N doped GaP

Eg

(a) GaAs1-yPyy < 0.45

(a) Photon emission in a direct bandgap semiconductor. (b). GaP is anindirect bandgap semiconductor. When doped with nitrogen there is anelectron trap at EN. Direct recombination between a trapped electron at ENand a hole emits a photon. (c) In Al doped SiC, EHP recombination isthrough an acceptor level like Ea.

Ec

EvEa

(c) Al doped SiC


188

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6λ

1.7Infrared

GaAs1-yPyIn1-xGaxAs1-yPy

AlxGa1-xAs

x = 0.43

Indirectbandgap

Free space wavelength coverage by different LED materials from the visible spectrum to theinfrared including wavelengths used in optical communications. Hatched region and dashedlines are indirect Eg materials.

In0.49AlxGa0.51-xP


189

3-7 異質接面高強度LEDs

191

2 eV

2 eVeVo

Holes in VB

Electrons in CB1.4 eV

No bias

Withforwardbias

Ec

EvEc

Ev

EFEF

(a)

(b)

(c)

(d)

pn+ p

∆Ec

GaAs AlGaAsAlGaAs

ppn+

~ 0.2 µm

AlGaAsAlGaAs

(a) A doubleheterostructure diode hastwo junctions which arebetween two differentbandgap semiconductors(GaAs and AlGaAs)

(b) A simplified energyband diagram withexaggerated features. EFmust be uniform.

(c) Forward biasedsimplified energy banddiagram.

(d) Forward biased LED.Schematic illustration ofphotons escapingreabsorption in theAlGaAs layer and beingemitted from the device.


GaAs

圖3.26 (a) 一雙異質結構二極體有兩接面，在兩不同能隙半導體(GaAs和AlGaAs) 間，(b) 誇張的簡化能帶圖，必須是均一的，(c) 順向偏壓下之簡化能帶圖(d)順向偏壓LED，圖示解說光子逃脫離AlGaAs的再吸收層和從這些元件發射出來。

192

3-8 LED特性

193

E

Ec

Ev

Carrier concentrationper unit energy

Electrons in CB

Holes in VBhυ

1

0

Eg

hυ1

hυ2

hυ3

CB

VBλ

Relative intensity

1

0λ

1λ

2λ

3

∆λ∆hυ

Relative intensity

(a) (b) (c) (d)

Eg + kBT

(2.5-3)kBT

1/2kBT

Eg1 2 3

2kBT

(a) Energy band diagram with possible recombination paths. (b) Energy distribution ofelectrons in the CB and holes in the VB. The highest electron concentration is (1/2)kBT aboveEc . (c) The relative light intensity as a function of photon energy based on (b). (d) Relativeintensity as a function of wavelength in the output spectrum based on (b) and (c).


194

V

2

1

(c)

0 20 40I (mA)0

(a)

600 650 7000

0.5

1.0

λ

Relativeintensity

24 nm

∆λ

655nm

(b)

0 20 40I (mA)0

Relative light intensity

(a) A typical output spectrum (relative intensity vs wavelength) from a red GaAsP LED.(b) Typical output light power vs. forward current. (c) Typical I-V characteristics of ared LED. The turn-on voltage is around 1.5V.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

200

3-9 光纖通訊用LED

201

(a) Surface emitting LED (b) Edge emitting LED

Doubleheterostructure

Light

Light


圖3.29 (a)面發射LED，(b)邊緣發射LED

202

ElectrodeSiO2 (insulator)

Electrode

Fiber (multimode)

Epoxy resin

Etched wellDouble heterostructure

Light is coupled from a surface emitting LEDinto a multimode fiber using an index matchingepoxy. The fiber is bonded to the LEDstructure.

(a)

Fiber

A microlens focuses diverging light from a surfaceemitting LED into a multimode optical fiber.

Microlens (Ti2O3:SiO2 glass)

(b)


圖3.30 (a)光由面發射LED耦合進入多模光纖，其中使用折射率匹配的環氧樹脂光纖被黏合於LED結構上，(b)微透鏡將面發射LED的發散光聚焦並導入多模光纖中。

203

Schematic illustration of the the structure of a double heterojunction stripecontact edge emitting LED

InsulationStripe electrode

SubstrateElectrode

Active region (emission region)

p+-InP (Eg = 1.35 eV, Cladding layer)

n+-InP (Eg = 1.35 eV, Cladding/Substrate)

n-InGaAs (Eg = 0.83 eV, Active layer)

Currentpaths

L

60-70 µm

Light beam

p+-InGaAsP (Eg = 1 eV, Confining layer)

n+-InGaAsP (Eg = 1 eV, Confining layer) 12 3200-300 µm

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖3.31 以圖示說明雙異質接面條狀接觸邊緣發射LED結構

204

Multimode fiberLens

(a)

ELED

Active layer

Light from an edge emitting LED is coupled into a fiber typically by using a lens or aGRIN rod lens.

GRIN-rod lens

(b)

Single mode fiberELED


圖3.32 典型地藉由使用透鏡或GRIN棒型透鏡，可將邊緣發射LED的光耦合到光纖中。

206

800 900

–40°C

25°C

85°C

0

1

740

Relative spectral output power

840 880Wavelength (nm)

The output spectrum from AlGaAs LED. Valuesnormalized to peak emission at 25°C.


207

0.20.4

0.60.8

11.21.4

1.61.8

22.2

2.42.6

0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62Lattice constant, a (nm)

GaP

GaAs

InAs

InP

Direct bandgapIndirect bandgap

In0.535Ga0.465AsX

Quaternary alloyswith direct bandgap

In1-xGaxAs

Quaternary alloyswith indirect bandgap

Eg (eV)

Bandgap energy Eg and lattice constant a for various III-V alloys ofGaP, GaAs, InP and InAs. A line represents a ternary alloy formed withcompounds from the end points of the line. Solid lines are for directbandgap alloys whereas dashed lines for indirect bandgap alloys.Regions between lines represent quaternary alloys. The line from X toInP represents quaternary alloys In1-xGaxAs1-yPy made fromIn0.535Ga0.465As and InP which are lattice matched to InP.


209

第三章目錄3-1 半導體概念與能帶3-2 直接和非直接能隙半導體：E-k圖3-3 pn接面原理3-4 pn接面能帶圖3-5 發光二極體3-6 LED材料3-7 異質接面高強度LEDs3-8 LED特性3-9 光纖通訊用LED

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