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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
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
2D-Electron density & CB Profile 22D2D--Electron density & CB Profile 2Electron density & CB Profile 2
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
2D-Electron density & CB Profile 32D2D--Electron density & CB Profile 3Electron density & CB Profile 3
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)
2D-Electron density & CB Profile 32D2D--Electron density & CB Profile 3Electron density & CB Profile 3
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
2D-Electron density & CB Profile 32D2D--Electron density & CB Profile 3Electron density & CB Profile 3
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)
The electric field vs. D2The electric field vs. D2The electric field vs. D2
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)
The electric field vs. D2The electric field vs. D2The electric field vs. D2
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)
The electric field vs. D3The electric field vs. D3The electric field vs. D3
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?