Asghar Asgari, N. Tahmasebizad2D2D2D-Electron density & CB Profile 2-Electron density & CB Profile...

AlGaN/GaN based electroabsorption modulator AlGaN/GaN based electroabsorption modulator operating at fiberoperating at fiber--optics telecommunication wavelengthsoptics telecommunication wavelengths

Asghar AsgariAsghar Asgari, N. , N. TahmasebizadTahmasebizad

Photonics GroupPhotonics Group, , Research Institute for Applied PhysicsResearch Institute for Applied PhysicsUniversity of Tabriz, Tabriz, IRANUniversity of Tabriz, Tabriz, IRAN

[email protected]

8th International Conference onNumerical Simulation of Optoelectronic Devices (NUSOD '08)1 - 5 September 2008, University of Nottingham, United Kingdom

INTRODUCTIONMODELING AND DISCUSTIONS

Subband energy and MQW profileThe effects of electric field

Summary

OutlineOutlineOutline

Applications for AlGaN/GaNApplications for AlGaN/GaNApplications for AlGaN/GaN

IntroductionIntroductionIntroduction

Figure 3 - Four Wavelength Regions of Optical Fiber

Why nitride intersubband devices?Why nitride intersubband devices?Why nitride intersubband devices?

Wavelength tunabilitySpeed:High power-handling:Excellent optical properties and material hardnessAdded functionalities and improved system performances

2D-Electron density & CB Profile 12D2D--Electron density & CB Profile 1Electron density & CB Profile 1

[ ]02

( )( )( ) ( ) ( ) ( )S b F CxxN x e x E x E x

e d eε εσ ⎛ ⎞+

= − Φ + −Δ⎜ ⎟⎝ ⎠

( ) 0.5 9.5x xε = − + (1.3 0.84)be x eVΦ = +

0.7 ( ) (0)C g gE E x E⎡ ⎤Δ = −⎣ ⎦

( ) ( ) (1 ) ( ) (1 ) 1

6.13 (1 ) 3.42 (1 ) 1

g g gE x xE AlN x E GaN x x eV

x eV x eV x x eV

= + − − − ×

= × + − × − − ×

( )( )( )*

2 ln 1 exp /bS i f i b

i i

m K TN ns E E K Tπ

= = + −∑ ∑h


Poisson Eq.Poisson Poisson EqEq..

( )( ) ( )d zd z en zdz dzε Φ⎡ ⎤ = −⎢ ⎥⎣ ⎦

* * *( ) ( ) ( ) ( ) ( ) ( ) ( )d a free free i i ii

n z N z N z n z p z ns z z⎛ ⎞= − − + − Ψ Ψ⎜ ⎟⎝ ⎠

∑

* *( ) / ( ) /

1 1,1 2 1 4f d b a f bd d a aE E K T E E K TN N N N

e e− −⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟+ +⎝ ⎠ ⎝ ⎠ 0aN =

17 31 10dN cm −= ×

1/ 2( )f

free Cb

E zn N FK T

⎛ ⎞−Φ= ⎜ ⎟

⎝ ⎠

,,0int_ berfacetorisemiconducMetalz

insubstratregionneutralzdzd

Φ=Φ=Φ

==

*

1 ( ) ( ) ( )2 ( ) i i i

d d V z z E zdz m z dz

⎡ ⎤⎛ ⎞−+ Ψ = Ψ⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

h

( ) ( ) ( ) ( ) ( )h xc imV z e z V z V z V z=− Φ + + +

[ ]( ) 1 ( )h CV z G z E= − Δ

Schrödinger Eq. 1SchrSchröödinger dinger EqEq. 1. 1

[ ]{ }

( ) , 0 ,

3 (2 / ) cos ( ) / 2, ,

2( )

1, ,

1 ( ) , 0,

h t h t

h t t h th t h t

t

h t

z z z z z a

z z a a z z az a z z a

zG z

z z a

G z z

π π

+ < < −⎧⎪⎪⎪ + − + −⎪ − < < +⎪= ⎨⎪⎪ > +⎪⎪⎪ − − <⎩

1 *2( ) 1 0.773 ln(1 )xc yS

V z x x Rrπ α− ⎛ ⎞⎡ ⎤=− + × + ×⎜ ⎟⎣ ⎦ ⎝ ⎠

( )( )

( )( )

2

0

2

0

, int16

( )

, int16

GaN AlGaN

GaN GaN AlGaN

im

GaN AlGaN

AlGaN GaN AlGaN

ez erface

z

V z

ez erface

z

ε επε ε ε ε

ε επε ε ε ε

⎧ ⎡ ⎤−⎣ ⎦ >⎪ ⎡ ⎤+⎣ ⎦⎪⎪= ⎨⎪⎡ ⎤−⎪⎣ ⎦ <⎪ ⎡ ⎤+⎣ ⎦⎩

)]([)}({)( 0 znnznVzV xcxcxc =≡≡ μ

31

3*31

)(34)(,21)(,)94(

−

⎥⎦⎤

⎢⎣⎡=≡=≡= znazrrrzxx SS

S ππα .)(

)(42

20*

ezmz

ahεεπ

=

Schrödinger Eq. 2SchrSchröödinger dinger EqEq. 2. 2

Initial Ns

Getting Ф

Poisson Eq.

Schrödinger Eq.

Electron Gasand Fermi Eqs.Wave Functions & Ei

Ef, Ns

Image Potential

Converged Ef

Poisson Eq.

Barrier Potential

Exchange & Cor.

( )∑∑==

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −

+==5

12

5

1exp1ln

m b

mfb

mms Tk

EETmkNNhπ

( )

⎥⎥⎦

⎤⎟⎟⎠

⎞⎜⎜⎝

⎛+++

⎢⎣

⎡Δ−+Φ−⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

AlGaN

GaNGaN

GaN

AlGaNAlGaN

CFGaNb

AlGaN

AlGaN

AlGaNGaN

GaNAlGaNS

ddN

dNdN

EEeede

xd

dN

22

)(1

22

11

20

εε

εεσεε

[ ],)()()()(2

0 xExEeedx

exN cfbs Δ−+Φ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

εεσ


0 12 24 36 48 60-1

0

1

2

-4

-2

1

3

5

7

Wav

e fu

nctio

n (1

04 x m

-1/2)

EC (e

V)

X (nm)


12222

2int ])()

2)[(

2())(()(cos)( −−+

ΓΓ×−

∂∂

= ohhh ωω

ππθωα snsm

Bemn NN

TkmF

zFc

Absorption CoefficientAbsorption CoefficientAbsorption Coefficient

erB mnTLCkec

oωε

2

int =h

ocmcn EE −

=ϖ

AlN AlGaN GaN AlN

D4 D3 D2 D1


10 20 30 40 50 60 70

-456.4

-456.2

-456.0

-455.8

-455.6

-455.4

-455.2

-455.0

-454.8

D1,D4= 60(A)D2=20X=0.3F E

XT*

106 (V

/M)

D3(A)

The electric field vs. D3The electric field vs. D3The electric field vs. D3

10 15 20 25 30 35 40-460

-455

-450

-445

-440

D1,D4= 60(A)D3= 20(A)X=0.3

F EX

T*10

6 (V/M

)

D2 (A)


25 30 35 40 45 50-888

-886

-884

-882

-880

D2,D3= 22 (A)X=0.3

F EX

T*10

6 (V/M

)

D1 ,D4 (A)

The electric field vs. D1&D4The electric field vs. D1&D4The electric field vs. D1&D4

10 15 20 25 30 35 40-460

-455

-450

-445

-440

-435

-430

-425

-420

D1,D4 = 60 (A)D3 = 20 (A)X=0.7

F EX

T *10

6 (V/M

)

D2 (A)


10 20 30 40 50

-455.4

-455.2

-455.0

-454.8

-454.6

-454.4

-454.2

-454.0

-453.8

D1,D4 = 60(A)D2 = 20 (A)X=0.7

F EX

T*10

6 (V/M

)

D3 (A)


Absorption CoefficientAbsorption CoefficientAbsorption Coefficient

-569-577-583-595-610-615-621-630-644F×106

0..90.80.60.60.50.40.30.20.1X

The electric field vs. Al molarThe electric field vs. Al molarThe electric field vs. Al molar

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

-450

-440

-430

-420

-410

D1&D4=60(A)D2=10&D3=20(A)

F EXT

*106 (V

/M)

x (AL mole fraction)

The electric field vs. xThe electric field vs. xThe electric field vs. x

Fext ↓ D3 ↑Fext ↑ D2 ↑Fext ↓ D1 & D4 ↑Fext ↓ x ↑

SummarySummarySummary

Any Question?Any Question?Any Question?

Asghar Asgari, N. Tahmasebizad2D2D2D-Electron density & CB Profile 2-Electron density & CB Profile...

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