TeraHertz three-dimensional plasma resonances in InGaAs diodes: a hydrodynamic study
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Transcript of TeraHertz three-dimensional plasma resonances in InGaAs diodes: a hydrodynamic study
TeraHertz three-dimensional plasma resonances inInGaAs diodes: a hydrodynamic study
P. Ziadé1,2, C. Palermo1 , H. Marinchio1, T. Laurent1,G. Sabatini1, P. Nouvel1, Z. Kallassy2 , L. Varani1
TeraLab Montpellier
1 Institut d’Electronique du SudUMR CNRS–UM2 5214
Université Montpellier 2, France
2 Laboratoire de Physique AppliquéeUniversité Libanaise, Faculté des Sciences 2
Campus Fanar, Jdeideh, Lebanon
EuMW/EuMIC (Paris) — September 28, 2010
Outline
1 IntroductionContextMotivation
2 Numerical protocol
3 Results and AnalysisReference sampleInfluence of the doping profileInfluence of the geometry
4 Conclusion & Perspectives
1 / 19
Outline
1 IntroductionContextMotivation
2 Numerical protocol
3 Results and AnalysisReference sampleInfluence of the doping profileInfluence of the geometry
4 Conclusion & Perspectives
Wanted!
Domains
Medical Imaging
Security applicationsNon-destructive control
etc...
need spectroscopic means:
• non-ionizing radiations• with underskin and/or underclothes penetration power → λ
• sensitive to various materials: metallic, non-metallic andorganic → f
TeraHertz range:Good candidate!
2 / 19
However!
Vi s i b l e I R M W0.
1 μ
m
1 μ
m
10 μ
m
100 μ
m
300 μ
m
1 m
m
30 T
Hz
3 TH
z
1 TH
z
300
GH
z
10 m
m
T e r a H e r t z
• Frontier position: difficulties to make devices• Between Infrared and microwaves• Between electronics and optics → Different technologies• Main strategies: technology transposition
Technology transfer to the industry:TeraHertz range is a gap
3 / 19
MotivationSome specifications/keywords:
low costroom temperature
integrable
emitter
detectorreliabletuneable integration time
continuousterahertz
spatial & spectral resolution
et caetera...
4 / 19
The plasmonic point of view
Contact Gate
Delta doping
SchottkyCap layer
Spacer
Buffer
Channel
Substrate
Lc Lg
Lsd
Lc
LwLw
Gated 2D-plasma: k depending
ω2D =
√e2ndκκ0m∗︸ ︷︷ ︸
s
·k
• InGaAs HEMT:• Boundary conditions:
k ∝ 1/L• Small m∗ (∼ 10−2 m0)
• Optical beating excitation
S D
GId
R
Vg
Vd
VT
0.05
0.15
0.25
0.35
0.45
0.55
0.65
1100 1300 1500 1700 1900 2100
Plas
ma
wav
es p
eak
frequ
ency
(GH
z)
Effective gate length (nm)
Mode 3
Mode 1
experiments
simulations
• Shown numerically andexperimentally
5 / 19
Another possible way
• 2D-gated (HEMT): promising way• Shown to work at room temperature• For emission & detection
• Mode depending on geometry, Tunability/ Small dimensions → power limitations
=⇒
• 3D electron gas, powerfull (bulk)/ Not tunable a priori (no geometry
dependance)• Compromise
• In0.53Ga0.47As:• ≈ 1 THz for n = 1016 cm−3
• ≈ 10 THz for n = 1018 cm−3
ω3D =
√e2nm∗ε
6 / 19
Aim of this work
• How can the 3D-diodes work within the THz range?
• Characterization of the plasma modes of both zones
• 1st order study: excitation by a THz optical beating
Systematic studyInfluence on E of the doping profile and the geometry?
7 / 19
Outline
1 IntroductionContextMotivation
2 Numerical protocol
3 Results and AnalysisReference sampleInfluence of the doping profileInfluence of the geometry
4 Conclusion & Perspectives
Optical beating
THz optical beating
Purpose:Force plasma wave oscillations @ THz
• Optical beating 2× 1.55 µm• with a THz frequency difference• THz glittering infrared spot
Infrared carrier
THz enveloppe
• not a THz propagating field
• InGaAs: 1.55 µm sensitive• spot ⇒ photogeneration pulsed at THz frequency
• Action on free electron density → plasma wave excitation8 / 19
Choice of a numerical model
• Physical approach: Drift-diffusion, Hydrodynamics, Monte Carlo
• Bias: high electric fields → Drift-diffusion• 2 junctions
• Fast materials• Velocity overshoots → Drift-diffusion• Far for equilibrium transport• non-uniform quantities
• Electrons photo-generation → Monte Carlo• Different time scales
Hydrodynamics• 1D modeling (3 equations)• Poisson equation (1 equation)
9 / 19
The numerical strategy
• n(x , t), v(x , t), ε(x , t), E (x , t), are calculated
• Electric field: related to emission ability
infrared pulse
electric field
V
• Here: calculation of the impulse response of E (t)• in the middle of each zone• G (t) = G0δ(t) & Fourier transform → all the THz range at one
sight
10 / 19
Outline
1 IntroductionContextMotivation
2 Numerical protocol
3 Results and AnalysisReference sampleInfluence of the doping profileInfluence of the geometry
4 Conclusion & Perspectives
Reference sample: (i) numerical results
Steady-state:
0
2
4
6
8
10
0 0.5 1 1.5 2 2.5 3
Cur
rent
den
sity
(108 A
.m−2
)
Voltage (V)
• n+ − n − n+ diode• Length: 500–500–500 nm• n = 1016 cm−3 ; n+/n = 10• I − V : non-ohmic after 0.5 V
Optical excitation:V = 0.5 V & G0 = 1026 cm−3s−1
0
0.2
0.4
0.6
0.8
1
0.001 0.01 0.1 1 10 100
Nor
mal
ized
Am
plitu
de
Frequency (THz)
n regionn+ region
fR(n+) = 3.6 THz
fR(n) = 3 THz
f3D
(n) = 1.1 THz f3D
(n+) ≈ fR(n+)
• Higher amplitude in n+-region• f3D(n+) ' fR(n+)
• Why does fR(n) 6= f3D(n)?
11 / 19
Reference sample: (ii) analysis
fR(n+) = f3D(n+) f3D(n) < fR(n) < f3D(n+) fR(n+) = f3D(n+)
• n−zone:• Resonance is redshifted• Coupling between f3D(n) and f3D(n+)• Resonance at an intermediate frequency
• n+−zone:• Resonance at the awaited frequency• No mode coupling
• Explanation: systematic study
12 / 19
Influence of the doping profile: (i) n+/n = const.
0
5
10
15
20
25
30
1016 1017 1018
Freq
uenc
y (T
Hz)
n (cm−3)
fR(n+)fR(n)
f3D(n+)f3D(n)
n+/n=10
10−28
10−27
10−26
10−25
1016 1017 1018
Ampl
itude
(arb
. uni
ts)
n (cm−3)
n+−regionn−region
n+/n=10
• n+/n = 10
• Frequencies 〉〉 n+-zones• fR(n+) = f3D(n+)• No coupling• Doping: influence of n+
• Frequencies 〉〉 n-zone• f3D(n) < fR(n) < f3D(n+)• doping: influence of n & n+
• Resonance “close to”n-mode
• Reasonable coupling
• Amplitudes• Increase in both region
types• Amp(n+) > Amp(n)
13 / 19
Influence of the doping profile: (ii) n = const.
0
5
10
15
20
25
0 50 100 150 200 250 300
Freq
uenc
y (T
Hz)
n+/n
n+=1016 cm-3
10−28
10−27
10−26
10−25
0 50 100 150 200 250 300
Ampl
itude
(arb
. uni
ts)
n+/n
n+−regionn−region
n+=1016 cm-3
• n = 1016 cm−3 ; n+/n > 10
• Frequencies 〉〉 n+-zones idem• fR(n+) = f3D(n+)• doping: influence of n+
• Frequencies 〉〉 n-zone• f3D(n) < fR(n) < f3D(n+)• coupling present• Resonance “closer from” n+
mode : stronger coupling
• Amplitudes: idem• Increase with doping density• Amplitudes : Stronger
mode for higher doping
14 / 19
Influence of the doping profile: (iii) synthesis
• n+−regions:• No coupling• No considerable effect of the doping ratio• fR corresponds to f3D and controled by n+
• Stronger modes for higher concentrations
• n−region:• Mode coupling• Intermediate frequency• Stronger coupling [fR(n)→ f3D(n+)] when n+/n increases
• Interpretation:• Coupling controled by the strongest mode (n+)
Possible application:Design n+ and n to tune fR(n)
15 / 19
Influence of the device geometry: (i) resultsL(n)
variation
0
1
2
3
4
5
6
0 1000 2000 3000 400010−29
10−28
10−27
10−26
Freq
uenc
y (T
Hz)
Ampl
itude
(arb
. uni
ts)
Internal region length (nm)
Frequency (n)Frequency (n+)
Amplitude (n)Amplitude (n+)
fixed n+ zone
• When L(n) increases:• fR(n+) stays ' constant• fR(n) decreases to f3D(n)• Strong effect on n
resonance
variation
L(n+) L(n+)
variation
0
1
2
3
4
5
6
0 1000 2000 3000
10−28
10−27
10−26
Freq
uenc
y (T
Hz)
Ampl
itude
(arb
. uni
ts)
External region length (nm)
fixed n zone
• When L(n+) increases• Weak effect on frequencies• Only amplitudes• No considerable effect
16 / 19
Influence of the device geometry: (ii) analysis
• Frequency coupling concerns only n−region
• n+−region length is not a critical parameter
• n−region length influences the coupling• 3D-plasma mode from contacts: vanishes in the n−active region• L(n) increases: contact effects less important
When L(n) increases:fR(n)→ f3D(n)
17 / 19
Outline
1 IntroductionContextMotivation
2 Numerical protocol
3 Results and AnalysisReference sampleInfluence of the doping profileInfluence of the geometry
4 Conclusion & Perspectives
Conclusion
• Presence of plasma modes• Awaited 3D-plasma mode in the n+−region• Intermediate frequency within the n−region• Coupling controled by n+-zones with strongest mode
• Doping concentration• Mode stronger for higher electron density• Stronger coupling for higher n+/n• Tune fR(n) with n+ and n
• Geometry• Coupling not depending on the n+-region length• Coupling decreases when the n−region length increases• Tune fR(n) with L(n)
18 / 19
Perspectives
• Behaviour when changing V• bias tunability?• Observed on 2D-gated
• Electrical perturbation• Instead of optical beating• Both perturbations (heterodyne detectors as in 2D-gated)
• Other materials• InAs and other rapid materials• GaN, InN and other nitrides
• Experimental measurements
19 / 19
TeraHertz three-dimensional plasma resonances inInGaAs diodes: a hydrodynamic study
P. Ziadé1,2, C. Palermo1 , H. Marinchio1, T. Laurent1,G. Sabatini1, P. Nouvel1, Z. Kallassy2 , L. Varani1
TeraLab Montpellier
1 Institut d’Electronique du SudUMR CNRS–UM2 5214
Université Montpellier 2, France
2 Laboratoire de Physique AppliquéeUniversité Libanaise, Faculté des Sciences 2
Campus Fanar, Jdeideh, Lebanon
EuMW/EuMIC (Paris) — September 28, 2010