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