Gaetano Bellanca, Stefano TrilloUniversity of Ferrara – Department of Engineering
Luca Stabellini , Wei Lu, Alfredo De RossiThales Research & Technology, Palaiseau, France
Thomas Antoni, Mathieu Carras, Alexandre NedelcuAlcatel-Thales III-V Lab, Palaiseau, France
Aim of the PresentationTo show our approach based on the Finite Difference Time Domain (FDTD) technique for the design and the optimization of Quantum Well Infrared Photodetector (QWIP) devices
Presentation OutlineIntroduction
QWIP
Conclusions
FDTD technique
Results
Efficient Technology useful to detect the e.m. radiation in the IR Spectrum Range Possible applications:
Civil (Security, Surveillance)Medical (Brest Cancer Detection)Military
IntroductionThe Infrared Domain: 0.76 μm ÷ 1000 μm
Introduction: Image Formation
Ultra-violet Visible Reflected IR Thermal IR
0.5 μm 3 μm 10 μm
λReflected Light Emitted
Radiation
Self Radiation
Dark EnvironmentThermal Infrared
Lightened environment Visible - Infrared
Reflection of Solar Radiation
IntroductionThe Image Formation
Lightened environment:Detection of the photons emitted by a light source and reflected by the objects
Dark environment:Objects at non-zero temperature emit photons
Using different detectors it is possible to build up different images of the same scenario
( )Kergksergh
smc
mmW
e
chTETkhc
°===
⎥⎦
⎤⎢⎣
⎡
−=
−
−
−
27
27
8
25
2
3810.110625.6
103
1
12,μλ
λλ
Planck’s law
Introduction
Images of the same human head obtained by different detection techniques
Color ImageVisible Band 0.38 μm ÷ 0.76 μm
B&W ImageVisible Band 0.38 μm ÷ 0.76 μm
Solar ReflectionIR Band 1.0 μm ÷ 1.7 μm
Solar Reflection + Thermal EmissionIR Band 3.4 μm ÷ 5.0 μm
Thermal EmissionIR Band 8.5 μm ÷ 9.5 μm
Infrared DetectorsThermal Detectors
Absorption of IR radiation Increase of T in the detectorExternal Signal
Photonic DetectorsAbsorption of IR radiation (f ∝ Eg) Electron Current
Absorbed λ depend on the semiconductor band-gap
Only λ: Eg > Eg0 can be absorbed
Problems in obtaining detectors for long wave (λ ≈ 10 μm ) IR(small Eg materials: Eg ≈ 0.1 eV)
‘Conventional Detection’ (with weak band-gap materials asHgx-Cd1-xTe) is not efficient (exotic materials, not developed!)
‘Effective’ band-gap materials (GaAs/AlGaAs heterostructures) which use InterSubBand transitions created by Quantum Wells in large-band-gap semiconductors
Quantum Well Infrared Detectors
Photonic detectors with weak bandPhotonic detectors with weak band--gap gap (Hgx-Cd1-xTe)(to have detection @ long wave IR)
x concentration adjusted for λ tuningElectrons excited from VB to CB with inter-sub-band transitionsNot very well developed (exotic materials!)
Quantum Well detectors Quantum Well detectors based on GaAs/AlGaAsheterostructures
Developed since 1990Multi Quantum Well Photonic detectors (QWIP)
Multi Quantum Well IR Detectors
The Detection Process: Inter-Sub-Band transitionsInvolves transitions within the same band
Quantum Well needed
Electron (Hole) from thedoped QW ground state in CB (VB) to un unoccupied state in the same band
Eg(WELL)
Eg(BARRIER)
VALENCE BAND (p-DOPED)
CONDUCTION BAND (n-DOPED) E1
E2
H2
H1
ΔEc
ΔEv
Multi Quantum Well IR Detectors
QW structure designed to have carrier escaping from the well and collected as a (photo) current
2. Tunneling
3. Vertical Transport
1. Absorption
Multi Quantum Well IR DetectorsInterSubBand Transitions
Energy levels inside CB or VB arise from the spatial localization introduced in the QW of a low-band-gap material (GaAs) surrounded by a higher-band-gap semiconductor (AlxGa1-xAs)
Optical Absorption: only the optical field along the superlattice direction (made by the well-barrier structure) is absorbedLight (TEM polarized) orthogonally polarized respect to the directionof interestPolarization rotation (TEM TM)is needed!Diffraction gratings are used
Quantum Well IR PhotodetectorThe Structure of a QW IR Photodetector
Substrate: GaAs Collector and Emitter: doped GaAs:SiActive zone: 40 QWs (doped GaAs, barrier: AlGaAs)Grating: GaAs + metallic coat (Au, Ni)
Pixel ContactCommon Contact
Grating
Quantum Well
Substrate
Incident Light
Collector
Emitter
Thermal Imager (IR Camera)
Photodetectors are assembled in MatricesEach Pixel is a QWIP
QWIP Matrix 640 x 512 Pixel
QWIP Grating
Front optics L1,L2
L3 L4 L5Detector Cooler
Power supply Proximity electronics
Matrices are then put in the detector system and installed inside the IR Camera
The FDTD Approach The Finite Difference in the Time Domain (FDTD) approach is used to design and optimize the performance of QWIPs
Why FDTD? Available in our groupFDTD Properties
Microwave Heating ApplicationsOptics
The FDTD Approach The FDTD Properties☺Generality and Versatility☺Dissipative, Dispersive and Non Linear materials can be
‘easily’ included
Temporal evolution of the e.m. fields
Frequency Domain results available by Fourier Transform
Time and Memory consuming
Problems with devices of several λ on each side are impractical on a simple PC
Lack of Computer Memory (RAM) Long CPU time
Use of Parallel Computing
Parallel FDTD Technique
x
z y
Domain Decomposition
4 PEs
3 PEs
2 PEs
Tot = 24 PEs
Boundary Conditions
Outer Boundaries ABC - PML
Each Block belongs to a single PE
Inner BoundariesData Communication
Message Passing Interface (MPI)
Outer Boundaries
Inner Boundaries
FDTD is well suited for Parallel Computation as the solving algorithm mainly involves ‘local data’
FDTD Simulation of QWIPsSimulation Strategy:
Optimization of the Metallic GratingPEC metallic surfaceReal metal (Drude Model)
Lorentz Model for the InterSubBand AbsorptionTFSF Approach for Field Excitation
Incident Light
Pixel Contact Common Contact
Grating
Quantum Well
SubstrateCollector
Emitter
Grating Optimization
Coupling grating fundamental component of a QWIP (only TM waves are absorbed, but the incident light is mainly TEM Polarized)
TEM to TM Polarization RotationIncreasing of the e.m. field in the active region
(Surface Plasmons + Surface Cavity Effect)
Grating optimization is essential for good QWIP performance
L. Stabellini, M. Carras, A. De Rossi and G. Bellanca, “Design and Optimization of High-Q Surface ModeCavities on Patterned Metallic Surfaces”, IEEE JQE, 2008, in press
Drude model used to describe the interaction between the light and the ‘real’ conductor
Implemented in FDTD using the Auxiliary Differential Equation (ADE) technique
Real ConductorpJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
( ) [ ])(ˆ11ˆ 0
2
0
20
0
ωχεωυω
ωεε
ωευ
ε
+=⎥⎦
⎤⎢⎣
⎡−
+=
+−=∂
∂
−×∇=∂∂
j
EJt
J
JHtE
p
ppp
p
rrr
rrr
ωp: Plasma frequencyυ: Collision frequency
Parameters for Goldωp: 2 π 2.175 10 15 rad/sυ: 2 π 6.5 10 12 rad/s
A Lorentz model can be used to describe InterSubBand absorption of a Quantum Well IR Photodetectors (A. Nedelcu, ‘Detection Infrarouge, Imaginerie Infrarouge’ , Thales Internal Report)
Implemented in FDTD using the ADE TechniqueSame model for both Drude and Lorentz media Multi-Pole Lorentz model integrates the two different material representations in a single procedure (Drude material = zero order pole)
Lorentz Model for InterSubBand Absorption
pJHtE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
( )
( ) [ ])(ˆ1ˆ 021
21
210
0
2101
0
ωχεωωυω
ωεεεεεε
ωεεευ
ε
+=−+
−+=
=∂∂−+−=
∂∂
−×∇=∂∂
∞∞
∞
j
JtPPJ
tJ
JHtE
s
pspp
p
rr
rrr
rrr
ω1: Resonant frequencyυ1: Damping frequencyεs: Static relative permittivityε∞: Infinite relative permittivity
The parameters ω1, υ1, ε∞ and Δε = εs - ε∞ can be obtained starting from the Density Matrix formalism and considering the doping parameters and the refractive index of the semiconductors used in the active region
Parameters for the Lorentz Model
pJHtE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
V. Berger, ‘Proprietes des Doubles Puits Quantiques et Utilisation dans des Dispositif Optoelectroniques’, PhD Thesis, Paris VI, 1992)
Parameters for the Doped Quantum Well (GaAs)
10.08
9.98
10.04
λ (μm)10 155
ε r(λ) − (Real Part)
10.02
10.00
λ (μm)10 155
0
-0.2
ε r(λ) − (Imaginary Part)
-0.16
-0.12
-0.08
-0.04
Excitation of a ‘Plane Wave’ propagating in y directionComputation of the field ‘Scattered’ by the QWIPComputation of the field ‘absorbed’ by the semiconductor
Spectral Response of a QWIPpJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
QWIP
Plane Wave Excitation
FDTD TFSF Domain
Domain forScattering Computation
( ) ( ) ( )
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧ ×
=
−=
∫∫
∑=
iSi
iia
dsP
PPP
2
~~Re
*||||
6..10
HEλ
λλλ
( ) ( )( )λλλ
0PPA a=Normalized
Absorbed Flux A
Complete simulated structure for a realistic QWIPSubstrateGaAs:Si CollectorActive Zone: 40 QW (1.6μm)GaAs:Si EmitterGrating (GaAs) + metallic coat
QWIP ParameterspJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
Λ
a
b/2
x
z
b/2w
y
h Emitter
QW Region
Collector
Substrate
Grating
l
p
d.c. = a / (a+b) = a / Λ
Λ = 2.7 μmh = 0.75 μmw = 0.7 μml = 1.6 μmp = 0.7 μm
DiscretizationΔx=Δy=Δz = 75 nm (36 points/Λ) 7Λ x 7Λ QWIP: 277 x 63 x 277 cellsPML Layer: 14 cells, ρ = 1.0 e-6 (8,465,275 overall mesh points)Temporal Time Step: 7.22 e-16 s
FDTD Simulation ParameterspJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
Input / Output ParametersTFSF Excitation: f0 = 35 THz (λ = 8.5 μm); BW = 12THzDFT Computation: frequency range [25÷45] THz (50 samples)Number of Time steps: 30000Total Computation Time: 8600 s (∼ 2.4 h on 6 PEs – PIV 3GHz)
Good performance with an even number of PEsOptimum Number of PEs existsSpeed-Up (Overall Computations): 7.4 with 8 PEs; 8.3 with 10 PEs
FDTD Parallel Performance (I)
Good scaling of ‘pure computations’ (Yee’s Solver: Solv. H, Solv. E)Boundary Conditions don’t scale as good as the Yee’s SolverNo good performance with an odd number of PEs
FDTD Parallel Performance (II)
E Solver more time consuming than H Solver because of J and Pcomputations (Dispersive Materials in the QW region) Good work balance between E and H in Communication, Excitation and Boundary ComputationDFT computationally intensive
8 PEs
Spectral Response of a QWIPpJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
Ey Field Component @ λ=8.28 μm for a 7 x 7 QWIP
0.25
0.05
6.5 12.0λ (μm)
Λ = 2.7 μmh = 0.75 μmw = 0.7 μml = 1.6 μmp = 0.7 μmd.c. = 0.6
λ (μm)
1.0
12.08.0 10.06.0 14.00.0
0.5
Simul.
Meas.
z
x
y
QWIP OptimizationpJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
0Corrugation Depth (μm)
0.18
0.02
1.60.8
7 × 7 structure (20.5 × 20.5 μm)
0.20
0.02
Corrugation Depth (μm)0 1.6
Drude
PEC
( )
λ
λλμ
μ
Δ=∫
m
m
dAA
5.9
5.70
Average Normalized Absorbed Flux A0
Λ = 2.7 μmh = 0÷ 1.6 μmw = 0.7 μml = 1.6 μmp = 0.7 μmd.c. = 0.6
Optimum value for the Corrugation Depth: h=0.75 μm
Λ = 2.7 μmh = 0.75 μmw = 0.7 μml = 1.6 μmp = 0.7 μmd.c. = 0.6
PEC good approximation for the metallic coating (Au)
QWIP Optimization (II)pJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
7 × 7 structure (20.5 × 20.5 μm)
10.0
0.18
0.10
0.02
QWIP Size(μm) 22.5
Grating
No Grating
1,2 .... 7 periods
( )
λ
λλμ
μ
Δ=∫
m
m
dAA
5.9
5.70
Average Normalized Absorbed Flux A0
Metallic grating is fundamental for optimum performance of the QWIP device
Λ = 2.7 μmh = 0.75 μmw = 0.7 μml = 1.6 μmp = 0.7 μmd.c. = 0.6
Ey Field Component @ λ of the maximum absorption
Grating λ=8.28 μm No Grating λ=8.59 μm
QWIP Optimization (III)pJH
tE rrr
−×∇=∂∂
0ε pJHtE rrr
−×∇=∂∂
0ε
7 × 7 structure (20.5 × 20.5 μm)
Reducing the thickness of the emitters w, the distance between the grating and the active zone decreases, thus increasing the Ey field in the QW zoned.c. = 0.5 allows the best performance of the QWIP
06 12λ (μm)
0.4
w = 0.225 μm
w = 0.375 μm
w = 0.525 μm
w = 0.675 μm
w - Thickness of the Emitter
06 12λ (μm)
0.4
d.c. = 0.5
d.c. = 0.6
d.c. = 0.7
d.c. - Duty Cycle
Λ = 2.7 μmh = 0.75 μmw = 0.225 ÷ 0.675 μml = 1.6 μmp = 0.7 μmd.c. = 0.6
Λ = 2.7 μmh = 0.75 μmw = 0.7 μml = 1.6 μmp = 0.7 μmd.c. = 0.5 ÷ 0.7
1D Coupling Grating QWIP
λ (μm)
1.0
8.07.0 7.56.0 10.00.0
0.5
0.25
0.75
6.5 8.5 9.0 9.5
2D QWIPE⊥E||
1D QWIPE ⊥E||
E⊥
E||
1D Coupling Grating used for ‘polarization sensitive’ devices
Only one linear component of the generally elliptically polarized incident light should be detectedDetection of images with low thermal contrast or cluttered scenesCombining signals from pixels of 1D gratings oriented differently, the full characterization of a linear polarization degree in a scene is allowed
Experimental Results
1D Coupling Grating -Results
E⊥E||
λ (μm)
0.25
0.2
0.15
0.10
0.05
07 8 9 1110 12
FDTD Model
7 × 1 structure (20.5 × 20.5 μm)
Λ = 2.7 μmh = 0.75 μmw = 0.7 μml = 1.6 μmp = 0.7 μmd.c. = 0.5 E||E⊥
Ey Field Component @ λ of the maximum absorption (8.68 μm)
1D Coupling Grating -Results
λ (μm)
1.0
8.07.0 7.56.0 10.0
0.0
0.5
0.25
0.75
6.5 8.5 9.0 9.5
1D QWIP Simul.E||
E⊥
1D QWIP Meas.E||
E⊥
10.5
Simulation vs Measurement
Conclusions
FDTD technique used as a design and optimization tool for QWIP devices
Design and Optimization of the Grating SurfaceInvestigations on the influence of the different parameters on the absorption of a QWIP 2D and 1D coupling grating investigated
Good agreement between simulations and measurements