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