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1
Jean-François Millithaler
A Monte Carlo investigation of plasmonic noise innanometric n-In0.53Ga0.47As channels
Italian team :Italian team : J.-F. MillithalerJ.-F. Millithaler, L. Reggiani, L. ReggianiUniversita degli studi del SalentoUniversita degli studi del Salento
French team :French team : J. Pousset, L. Varani, C.Palermo, W. Knap J. Pousset, L. Varani, C.Palermo, W. KnapUniversité Montpellier IIUniversité Montpellier II
Spanish team :Spanish team : J. Mateos, T. Gonzalez, S. Perez, D. Pardo J. Mateos, T. Gonzalez, S. Perez, D. PardoUniversidad de SalamancaUniversidad de Salamanca
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte CarloSimulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte CarloSimulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
TeraHertz RadiationTeraHertz Radiation
Situated between 0.3 and 30 THz, 10Situated between 0.3 and 30 THz, 10-3-3 and 10 and 10-5-5 m mEnergy between 1 meV et 100 meVEnergy between 1 meV et 100 meVInteresting physicals propertiesInteresting physicals properties
absorption by water, oscillations of molecules (organic, inorganic, absorption by water, oscillations of molecules (organic, inorganic, biological), non-ionising, etc.biological), non-ionising, etc.
Strong issue for many domainsStrong issue for many domains : :Telecommunications, high-resolution spectroscopy, imaging, Telecommunications, high-resolution spectroscopy, imaging, security, etc.security, etc.
MotivationMotivation
TeraHertzTeraHertz
Applications require low cost, integrated, tunable THz source @room Applications require low cost, integrated, tunable THz source @room temperaturetemperature
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Jean-François Millithaler
Potential electronic emitter and detectorPotential electronic emitter and detector
HEMT HEMT (High Electron Mobility Transistor)(High Electron Mobility Transistor)
High frequency instabilitiesHigh frequency instabilities
2D Electron gas (plasma) in the 2D Electron gas (plasma) in the channelchannel
Study of THz generation mechanismStudy of THz generation mechanism
TeraHertzTeraHertzInfraredInfrared Micro-waveMicro-wave
MotivationMotivation
OpticOptic ElectronicElectronic
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte Carlo Simulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
Analytical modelAnalytical model
Bulk = 3D electron gasBulk = 3D electron gas
2D electron gas2D electron gas
3D plasma frequency3D plasma frequency
2D plasma frequency2D plasma frequency
SimulationsSimulations
3D to 2D ?3D to 2D ?
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Jean-François Millithaler
Monte Carlo ModelMonte Carlo Model
Length (Length (LL) : 10) : 10-2-2 to 10 µm to 10 µm
Width (Width (WW) : 1 to 100 nm) : 1 to 100 nm
Concentration : 10Concentration : 101515 to 10 to 101818 cmcm-3-3
Applied VoltageApplied Voltage
SimulationsSimulations
Study of voltage fluctuations :Study of voltage fluctuations :
Monte Carlo SimulatorMonte Carlo Simulator
Resolution of Poisson Resolution of Poisson equationequation
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte CarloSimulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
Bulk characteristicsBulk characteristics
10101717 cm cm-3-3 : v = 2.3 10 : v = 2.3 1055 m/s at E = m/s at E = 4.2 kV/cm4.2 kV/cm
10101818 cm cm-3-3 : v = 1.9 10 : v = 1.9 1055 m/s at E = m/s at E = 4.7 kV/cm4.7 kV/cm
ResultsResults
Typical current-voltage Typical current-voltage characteristiccharacteristic
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Jean-François Millithaler
Monte Carlo vs RLC modelMonte Carlo vs RLC model
L = 0.1 µmL = 0.1 µm
W = 100 nmW = 100 nm
nn3D3D = 10 = 101717 cm cm-3-3
ResultsResults
RLC model :RLC model :
slopesslopes
Resonant frequencyResonant frequency
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Jean-François Millithaler
Asymptotic decay like fAsymptotic decay like f-2-2
Momemtum frequency fMomemtum frequency fmm
Fitting with Gaussian Fitting with Gaussian functionfunction
ResultsResults
101015 15 cmcm-3-3 101017 17 cmcm-3-3
101018 18 cmcm-3-3
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte CarloSimulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
nn3D3D=10=101616 cm cm-3-3, , nn3D3D=10=101717 cm cm-3-3, , nn3D3D=10=101818 cm cm-3-3
Frequency vs LengthFrequency vs Length
ResultsResults
3D (W = 100 nm)3D (W = 100 nm) 2D (W = 1 nm)2D (W = 1 nm)
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Jean-François Millithaler
Influence of the widthInfluence of the width
2D agreement for W=1 & 2 nm2D agreement for W=1 & 2 nm
2D for W > 5 nm and 0.1 < L < 2.0 µm2D for W > 5 nm and 0.1 < L < 2.0 µm
3D for W > 5 nm and L > 2.0 µm3D for W > 5 nm and L > 2.0 µm
ResultsResults
W = 100 W = 100 nmnm
W = 1 nmW = 1 nm
W = 2 nmW = 2 nm
W = 5 nmW = 5 nm
W = 10 nmW = 10 nm
Increase of the plasma peak when Increase of the plasma peak when
L decreasesL decreases
Peak independent of WPeak independent of W
nn3D3D = 10 = 101717 cm cm-3-3
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Jean-François Millithaler
2D-3D Cross-over2D-3D Cross-over
Same behaviour for different concentrationsSame behaviour for different concentrations
Cross-over for width around 10 nmCross-over for width around 10 nm
ResultsResults
3D behaviour3D behaviour
2D 2D behaviourbehaviour
Value of frequency peak vs Width for L = 0.1 ( ) and 1.0 µm ( )Value of frequency peak vs Width for L = 0.1 ( ) and 1.0 µm ( )
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte CarloSimulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
ResistivityResistivity
Balistic : independant of Balistic : independant of lengthlength
Diffusive : proportional to Diffusive : proportional to lengthlength
ResultsResults
Good agreement with Butcher equationGood agreement with Butcher equation
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Jean-François Millithaler
Amplitude of the peakAmplitude of the peak
ResultsResults
10101818 cm cm-3-3, W = 1nm, W = 1nm
Balistic regime conclusion :Balistic regime conclusion :
Independent of WIndependent of W
Peak disappears at L = 1 nmPeak disappears at L = 1 nm
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Jean-François Millithaler
OutlineOutline
MotivationMotivation
Simulations : Analytical and Monte CarloSimulations : Analytical and Monte Carlo
ResultsResultsGeneral features of bulkGeneral features of bulk
Ohmic regimeOhmic regime
Balistic regimeBalistic regime
Saturation regimeSaturation regime
Conclusion and open problemsConclusion and open problems
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Jean-François Millithaler
From plasma to Gunn (1/2)From plasma to Gunn (1/2)
nn3D3D = 10 = 101717 cm cm-3-3 L = 0.5 µm W = 1 nm L = 0.5 µm W = 1 nm
ResultsResults
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Jean-François Millithaler
From plasma to Gunn (2/2)From plasma to Gunn (2/2)
ResultsResults
nn3D3D = 10 = 101818 cm cm-3-3 L = 0.5 µm W = 1 nm L = 0.5 µm W = 1 nm
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Jean-François Millithaler
ConclusionConclusion
EquilibriumEquilibrium
W > 100 nm : 3D PlasmaW > 100 nm : 3D Plasma
W < 100 nm : cross-over 3D-2D Plasma around 10 nmW < 100 nm : cross-over 3D-2D Plasma around 10 nm
Ohmic Ohmic
Balistic -> L < 100 nm Balistic -> L < 100 nm
Plasma frequency independent of WPlasma frequency independent of W
Plasma peak suppressed at shorter LPlasma peak suppressed at shorter L
Saturation Saturation
-> cross-over Plasma to Gunn frequency-> cross-over Plasma to Gunn frequency
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Jean-François Millithaler
Open pointsOpen points
For W = 5 and 10 nm -> 2D and 3D behaviour For W = 5 and 10 nm -> 2D and 3D behaviour depending of the length.depending of the length.
In the balistic regime, when L < 100 nm, the In the balistic regime, when L < 100 nm, the simulations exhibit a frequency peak which is simulations exhibit a frequency peak which is unexpectedly independent of W, and whose amplitude unexpectedly independent of W, and whose amplitude decreases significantly at lowering the channel length.decreases significantly at lowering the channel length.
Electrostatic screening for a 2D electron gas remains Electrostatic screening for a 2D electron gas remains in general an unsolved problem.in general an unsolved problem.
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Jean-François Millithaler
Thank you for your attentionThank you for your attention
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Jean-François Millithaler
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Jean-François Millithaler
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Jean-François Millithaler
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Jean-François Millithaler
Main conclusionMain conclusion
Independent of WIndependent of W
Peak disappear at L = 1 nmPeak disappear at L = 1 nm
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Jean-François Millithaler
Ohmic regime conclusionOhmic regime conclusion
Cross-over between 2D and 3DCross-over between 2D and 3D
Cross-over for width around 10 nm, independently of Cross-over for width around 10 nm, independently of the concentrationthe concentration