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# 5-2 拉摩定理和外光電流

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## 5-1 pN接面光二極體的原理

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p+ SiO2 Electrode

ρnet

–eNa eNd

x

x E(x)

R

Emax

e h+

Iph

hυ > Eg

W E

n

Depletion region (a)

(b)

(c) Antireflection coating

Vr

(a) A schematic diagram of a reverse biased pn junction photodiode. (b) Net space charge across the diode in the depletion region. N and N are the donor and acceptor

Electrode Vout

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## 5-2 拉摩定理和外光電流

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e

h

e e

h h

### = v

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229

e h+

iph(t)

Semiconductor

(a)

V

x (b)

(a) An EHP is photogenerated at x = l. The electron and the hole drift in opposite

directions with drift velocities vh and ve. (b) The electron arrives at time te = (L − l)/ve and the hole arrives at time th = l/vh. (c) As the electron and hole drift, each generates an external photocurrent shown as ie(t) and ih(t). (d) The total photocurrent is the sum of hole and electron photocurrents each lasting a duration th and te respectively.

E

l L − l

t

ve vh

vh

0 l L

t e

h+

th

te

t 0

th te

iph(t)

i(t) t

0

th te

evh/L + eve/L evh/L

ie(t) ih(t)

(c) (d) Charge = e

evh/L eve/L

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

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## 5-3 吸收係數和光二極體材料

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0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8

Wavelength (µm)

In0.53Ga0.47As Ge

Si

In0.7Ga0.3As0.64P0.36

InP GaAs

a-Si:H

2 1 3

5 4 0.9 0.8 0.7

1×103 1×104 1×105 1×106 1×107 1×108

Photon energy (eV)

Absorption coefficient (α) vs. wavelength (λ) for various semiconductors (Data selectively collected and combined from various sources.)

α (m-1)

1.0

Figure 5.3

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E

CB

VB

–k k

Direct Bandgap Eg

Photon Ec

Ev

(a) GaAs (Direct bandgap)

E

–k k

(b) Si (Indirect bandgap)

VB

CB

Ec Ev

Indirect Bandgap, E

g

Photon

Phonon

(a) Photon absorption in a direct bandgap semiconductor. (b) Photon absorption in an indirect bandgap semiconductor (VB, valence band; CB, conduction band)

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

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## 5-4 量子效率和響應率

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241

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o

ph

o ph

### R 光電流

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243

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Responsivity (R) vs. wavelength (λ) for an ideal photodiode with QE = 100% (η = 1) and for a typica commercial Si photodiode.

0 200 400 600 800 1000 1200 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Wavelength (nm)

Si Photodiode

λg Responsivity (A/W)

Ideal Photodiode QE = 100% (η = 1)

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

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## 5-5 pin光二極體

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p+

i-Si n+ SiO2

Electrode

ρnet

-eNa eNd

x

x E(x)

R Eo

E

e- h+

Iph > Eg

W (a)

(b)

(c)

(d)

Vr

The schematic structure of an idealized pin photodiode (b) The net Vout

Electrode

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dep

o

r

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249

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251

2

3

4

5

7

6

5

4

-1

-1

### )

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

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253

hυ > Eg

p+ i-Si

e E

h+

Drift Diffusion

### The photogenerated electron has to diffuse to the depletion region where it is swept into the i-layer and drifted across.

Vr

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

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## 5-6 累崩光二極體 (APD)

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š p+ SiO2

Electrode

ρn et

x

x E(x)

R

E hυ > Eg

p

Ip h

e h+

Absorption region Avalanche region

(a)

(b)

(c)

(a) A schematic illustration of the structure of an avalanche photodiode (APD) biased for avalanche gain. (b) The net space charge density across the photodiode. (c) The field across the diode and the identification of absorption and multiplication regions.

Electrode

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

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257 h+

E

n+ p š

e

Avalanche region

e

h+

Ec Ev

(a) (b)

E

### conduction electron with crystal vibrations transfers the electron's kinetic energy to a valence electron and thereby excites it to the conduction band.

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

(b) 一個具有晶格振動的高能傳導電子的撞擊，並將電子動能轉移 給價電子而將它激發到傳導帶。

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SiO2 Guard ring

Electrode Antireflection coating

n n+ n

p+ š p

Substrate Electrode n+

p+ š

p

Substrate Electrode

Avalanche breakdown

(a) (b)

(a) A Si APD structure without a guard ring. (b) A schematic illustration of the structure of a more practical Si APD

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

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## 5-7 累質接面光二極體

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E

N n

Electrode

x E(x)

R

hυ

Ip h

Absorption region Avalanche

region

InP InGaAs

h+ e E InP

P+ n+

Simplified schematic diagram of a separate absorption and multiplication (SAM) APD using a heterostructure based on InGaAs-InP. P and N refer to p and n -type wider-bandgap semiconductor.

Vr

Vout

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

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InP

InGaAs h+

e E

Ec

Ev Ec

Ev

InP

InGaAs Ev Ev InGaAsP grading layer

h+

∆Ev

(a) Energy band diagra SAM heterojunction A there is a valence band ∆Ev from InGaAs to InP tha hole entry into the InP

(b) An interposing grad (InGaAsP) with an inte bandgap breaks ∆Ev and mak easier for the hole to pa layer

(a)

(b)

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P+ךְnP Substrate

P+ךְnP (2-3 µm) Buffer epitaxial layer NךְnP (2-3 µm) Multiplication layer.

Photon

nךְn 0 . 5 3Ga0 . 4 7As (5-10µm) Absorption lay

Electrode

Simplified schematic diagram of a more practical mesa-etched SAGM layered APD.

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

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hυ

h+ e

n+ Ec

Ev

10?0 nm

p+

E

Eg 1

Eg 2

∆Ec

Energy band diagram of a staircase superlattice APD (a) No bias. (b) With an applied bias.

(a) (b)

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

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## 5-8 光電晶體

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n hυ

Base Collector

h+ e Emitter

n+ p

E e

SCL SCL Iph

VBE VBC

VCC

The principle of operation of the photodiode. SCL is the space charge layer or the depletion region. The primary photocurrent acts as a base current and gives rise to a large

photocurrent in the emitter-collector circuit.

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

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## 5-9 光電導檢測器和光電導增益

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Light

w d

A

V Iphoto

A semiconductor slab of length A, width w and depth d is illuminated with light of wavelength λ.

n = no + ∆n p = po + ∆p

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

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273 Iph

Photoconductor e

h+

Iph Iph Iph Iph

A photoconductor with ohmic contacts (contacts not limiting carrier entry) can exhibit gain. As the slow hole drifts through the photoconductors, many fast electrons enter and drift through the photoconductor because, at any instant, the photoconductor must be neutral. Electrons drift faster which means as one leaves, another must enter.

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

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

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## 5-10 光檢測器中的雜訊

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Vou Current

Time Id

Vr

In pn junction and pin devices the main source of noise is shot noise due to the dark current and photocurrent.

n p

Po

Dark

Illuminated Id + Ip h

Id + Ip h + in

R A

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

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### Responsivity(A/W)

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

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0 0.1 0.2 0.3 0.4 0.5 0.6

200 400 600 800 1000 1200 Wavelength(nm)

A B

The responsivity of two commercial Si pin photodiodes

Responsivity(A/W)

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

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### Responsivity(A/W)

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

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x

R E

e h+

iph hυ > Eg

W

Vr

An infinitesimally short light pulse is absorbed throughou depletion layer and creates an EHP concentration that dec exponentially

Photogenerated electron concentration exp(αx) at time t = 0

A B

vde

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Using this formalism we derive an exact differential equation for the partition function of two-dimensional gravity as a function of the string coupling constant that governs the

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This kind of algorithm has also been a powerful tool for solving many other optimization problems, including symmetric cone complementarity problems [15, 16, 20–22], symmetric

[r]

In order to investigate the bone conduction phenomena of hearing, the finite element model of mastoid, temporal bone and skull of the patient is created.. The 3D geometric model