1. TeraHertz three-dimensional plasma resonances in
InGaAs diodes: a hydrodynamic study
P. Ziadé1,2 , C. Palermo1 , H. Marinchio1 , T. Laurent1 ,
G. Sabatini1 , P. Nouvel1 , Z. Kallassy2 , L. Varani1
TeraLab Montpellier
1Institut d’Electronique du Sud
UMR CNRS–UM2 5214
Université Montpellier 2, France
2 Laboratoire de Physique Appliquée
Université Libanaise, Faculté des Sciences 2
Campus Fanar, Jdeideh, Lebanon
EuMW/EuMIC (Paris) — September 28, 2010

2. Outline
1 Introduction
Context
Motivation
2 Numerical protocol
3 Results and Analysis
Reference sample
Influence of the doping profile
Influence of the geometry
4 Conclusion & Perspectives
1 / 19

3. Outline
1 Introduction
Context
Motivation
2 Numerical protocol
3 Results and Analysis
Reference sample
Influence of the doping profile
Influence of the geometry
4 Conclusion & Perspectives

4. Wanted!
 

 Medical Imaging 

Security applications
 
Domains need spectroscopic means:
 Non-destructive control
 

etc...
 
• non-ionizing radiations
• with underskin and/or underclothes penetration power → λ
• sensitive to various materials: metallic, non-metallic and
organic → f
TeraHertz range:
Good candidate!
2 / 19

5. However!
300 GHz
30 THz
3 THz
1 THz
Visible IR MW
Te r a H e r t z
0.1 μm
1 μm
10 μm
100 μm
300 μm
1 mm
10 mm
• 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

6. Motivation
Some specifications/keywords:
low cost
integrable
room temperature
spatial & spectral resolution
emitter continuous
terahertz
reliable detector
tuneable integration time
et caetera...
4 / 19

7. The plasmonic point of view
Lsd
Lw Lw • Optical beating excitation
Lc Lg Lc
Contact Gate
Vg
Cap layer Schottky
Spacer Delta doping G VT
Channel Id
S D
Buffer
Substrate R
Vd
Plasma waves peak frequency (GHz)
0.65 experiments
0.55 simulations
Gated 2D-plasma: k depending 0.45
Mode 3
e 2 nd 0.35
ω2D = ·k 0.25
κκ0 m∗
0.15 Mode 1
s 0.05
1100 1300 1500 1700 1900 2100
• InGaAs HEMT: Effective gate length (nm)
• Boundary conditions:
k ∝ 1/L • Shown numerically and
• Small m∗ (∼ 10−2 m0 ) experimentally
5 / 19

8. 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 e 2n
ω3D =
dependance) m∗
=⇒ • Compromise
• In0.53 Ga0.47 As:
• ≈ 1 THz for n = 1016 cm−3
• ≈ 10 THz for n = 1018 cm−3
6 / 19

9. 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 study
Influence on E of the doping profile and the geometry?
7 / 19

10. Outline
1 Introduction
Context
Motivation
2 Numerical protocol
3 Results and Analysis
Reference sample
Influence of the doping profile
Influence of the geometry
4 Conclusion & Perspectives

11. Optical beating
Purpose:
THz optical beating
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 excitation
8 / 19

12. 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

13. The numerical strategy
• n(x, t), v (x, t), (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) = G0 δ(t) & Fourier transform → all the THz range at one
sight
10 / 19

14. Outline
1 Introduction
Context
Motivation
2 Numerical protocol
3 Results and Analysis
Reference sample
Influence of the doping profile
Influence of the geometry
4 Conclusion & Perspectives

15. Reference sample: (i) numerical results
Steady-state: Optical excitation:
10
V = 0.5 V & G0 = 1026 cm−3 s−1
Current density (10 A.m )
−2
8 1 n+ region
fR(n+) = 3.6 THz
n region
8
Normalized Amplitude
6 0.8
f3D(n) = 1.1 THz f3D(n+) ≈ fR(n+)
4 0.6
0.4
2 fR(n) = 3 THz
0.2
0
0 0.5 1 1.5 2 2.5 3
0
Voltage (V) 0.001 0.01 0.1 1 10 100
Frequency (THz)
• n+ − n − n+ diode
• Length: 500–500–500 nm • Higher amplitude in n+ -region
• n = 1016 cm−3 ; n+ /n = 10 • f3D (n+ ) fR (n+ )
• I − V : non-ohmic after 0.5 V • Why does fR (n) = f3D (n)?
11 / 19

16. 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

17. Influence of the doping profile: (i) n+ /n = const.
30
fR(n +) n+/n=10
• n+ /n = 10
25 fR(n)
Frequency (THz)
+
f3D(n )
20
f3D(n)
• Frequencies n+ -zones
15 • fR (n ) = f3D (n+ )
+
10 • No coupling
5 • Doping: influence of n+
0
1016 1017 1018 • Frequencies n-zone
−3
n (cm ) • f3D (n) < fR (n) < f3D (n+ )
+ • doping: influence of n & n+
10−25 n −region
n−region
Amplitude (arb. units)
• Resonance “close to”
10
−26 n-mode
• Reasonable coupling
10−27
n+/n=10 • Amplitudes
10−28
• Increase in both region
1016 1017 1018 types
−3
n (cm ) • Amp(n+ ) > Amp(n)
13 / 19

18. Influence of the doping profile: (ii) n = const.
25
n+=1016 cm-3
20
• n = 1016 cm−3 ; n+ /n > 10
Frequency (THz)
15
10
• Frequencies n+ -zones idem
• fR (n ) = f3D (n+ )
+
5
• doping: influence of n+
0
0 50 100 150 200 250 300
+
• Frequencies n-zone
n /n
• f3D (n) < fR (n) < f3D (n+ )
−25 • coupling present
10 +
n −region
n−region • Resonance “closer from” n+
Amplitude (arb. units)
10
−26 mode : stronger coupling
• Amplitudes: idem
10−27
n+=1016 cm-3
• Increase with doping density
• Amplitudes : Stronger
10−28 mode for higher doping
0 50 100 150 200 250 300
+
n /n
14 / 19

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

20. Influence of the device geometry: (i) results
L(n)
L(n+) L(n+)
variation
variation variation
6 −26
Frequency (n) 6 10
−26
5 Frequency (n+) 10
Amplitude (arb. units)
Amplitude (n) 5 fixed n zone
Amplitude (arb. units)
Frequency (THz)
4 Amplitude (n+)
Frequency (THz)
10
−27 4
3 10−27
fixed n zone
+ 3
2 −28
10 2
1
1
0 10−29 10−28
0 1000 2000 3000 4000 0
Internal region length (nm) 0 1000 2000 3000
External region length (nm)
• When L(n) increases:
• fR (n+ ) stays constant • When L(n+ ) increases
• fR (n) decreases to f3D (n) • Weak effect on frequencies
• Strong effect on n • Only amplitudes
resonance • No considerable effect
16 / 19

21. 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

22. Outline
1 Introduction
Context
Motivation
2 Numerical protocol
3 Results and Analysis
Reference sample
Influence of the doping profile
Influence of the geometry
4 Conclusion & Perspectives

23. 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

24. 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

25. TeraHertz three-dimensional plasma resonances in
InGaAs diodes: a hydrodynamic study
P. Ziadé1,2 , C. Palermo1 , H. Marinchio1 , T. Laurent1 ,
G. Sabatini1 , P. Nouvel1 , Z. Kallassy2 , L. Varani1
TeraLab Montpellier
1Institut d’Electronique du Sud
UMR CNRS–UM2 5214
Université Montpellier 2, France
2 Laboratoire de Physique Appliquée
Université Libanaise, Faculté des Sciences 2
Campus Fanar, Jdeideh, Lebanon
EuMW/EuMIC (Paris) — September 28, 2010