1. 1 Jean-François Millithaler A Monte Carlo investigation of plasmonic noise in nanometric n-In 0.53 Ga 0.47 As channels Italian team : J.-F. Millithaler, L. Reggiani Universita degli studi del Salento French team : J. Pousset, L. Varani, C.Palermo, W. Knap Université Montpellier II Spanish team : J. Mateos, T. Gonzalez, S. Perez, D. Pardo Universidad de Salamanca

2. 2 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

3. 3 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

4. 4 Jean-François Millithaler TeraHertz Radiation Situated between 0.3 and 30 THz, 10 -3 and 10 -5 m Energy between 1 meV et 100 meV Interesting physicals properties absorption by water, oscillations of molecules (organic, inorganic, biological), non-ionising, etc. Strong issue for many domains : Telecommunications, high-resolution spectroscopy, imaging, security, etc. Motivation TeraHertz Applications require low cost, integrated, tunable THz source @room temperature

5. 5 Jean-François Millithaler Potential electronic emitter and detector HEMT (High Electron Mobility Transistor) High frequency instabilities 2D Electron gas (plasma) in the channel Study of THz generation mechanism TeraHertz InfraredMicro-wave Motivation OpticElectronic

6. 6 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

7. 7 Jean-François Millithaler Analytical model Bulk = 3D electron gas 2D electron gas 3D plasma frequency 2D plasma frequency Simulations 3D to 2D ?

8. 8 Jean-François Millithaler Monte Carlo Model Length (L) : 10 -2 to 10 µm Width (W) : 1 to 100 nm Concentration : 10 15 to 10 18 cm -3 Applied Voltage Simulations Study of voltage fluctuations : Monte Carlo Simulator Resolution of Poisson equation

9. 9 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

10. 10 Jean-François Millithaler Bulk characteristics 10 17 cm -3 : v = 2.3 10 5 m/s at E = 4.2 kV/cm 10 18 cm -3 : v = 1.9 10 5 m/s at E = 4.7 kV/cm Results Typical current-voltage characteristic

11. 11 Jean-François Millithaler Monte Carlo vs RLC model L = 0.1 µm W = 100 nm n 3D = 10 17 cm -3Results RLC model : slopes Resonant frequency

12. 12 Jean-François Millithaler Asymptotic decay like f -2 Momemtum frequency f m Fitting with Gaussian function Results 10 15 cm -3 10 17 cm -3 10 18 cm -3

13. 13 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

14. 14 Jean-François Millithaler n 3D =10 16 cm -3, n 3D =10 17 cm -3, n 3D =10 18 cm -3 Frequency vs Length Results 3D (W = 100 nm) 2D (W = 1 nm)

15. 15 Jean-François Millithaler Influence of the width 2D agreement for W=1 & 2 nm 2D for W > 5 nm and 0.1 5 nm and 0.1 < L < 2.0 µm 3D for W > 5 nm and L > 2.0 µm Results W = 100 nm W = 1 nm W = 2 nm W = 5 nm W = 10 nm Increase of the plasma peak when L decreases Peak independent of W n 3D = 10 17 cm -3

16. 16 Jean-François Millithaler 2D-3D Cross-over Same behaviour for different concentrations Cross-over for width around 10 nm Results 3D behaviour 2D behaviour Value of frequency peak vs Width for L = 0.1 ( ) and 1.0 µm ( )

17. 17 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

18. 18 Jean-François Millithaler Resistivity Balistic : independant of length Diffusive : proportional to length Results Good agreement with Butcher equation

19. 19 Jean-François Millithaler Amplitude of the peak Results 10 18 cm -3, W = 1nm Balistic regime conclusion : Independent of W Peak disappears at L = 1 nm

20. 20 Jean-François Millithaler Outline Motivation Simulations : Analytical and Monte Carlo Results General features of bulk Ohmic regime Balistic regime Saturation regime Conclusion and open problems

21. 21 Jean-François Millithaler From plasma to Gunn (1/2) n 3D = 10 17 cm -3 L = 0.5 µm W = 1 nm Results

22. 22 Jean-François Millithaler From plasma to Gunn (2/2) Results n 3D = 10 18 cm -3 L = 0.5 µm W = 1 nm

23. 23 Jean-François Millithaler Conclusion Equilibrium W > 100 nm : 3D Plasma W < 100 nm : cross-over 3D-2D Plasma around 10 nm Ohmic Balistic -> L L < 100 nm Plasma frequency independent of W Plasma peak suppressed at shorter L Saturation -> cross-over Plasma to Gunn frequency

24. 24 Jean-François Millithaler Open points For W = 5 and 10 nm -> 2D and 3D behaviour depending of the length. In the balistic regime, when L < 100 nm, the simulations exhibit a frequency peak which is unexpectedly independent of W, and whose amplitude decreases significantly at lowering the channel length. Electrostatic screening for a 2D electron gas remains in general an unsolved problem.

25. 25 Jean-François Millithaler Thank you for your attention

26. 26 Jean-François Millithaler

27. 27 Jean-François Millithaler

28. 28 Jean-François Millithaler

29. 29 Jean-François Millithaler Main conclusion Independent of W Peak disappear at L = 1 nm

30. 30 Jean-François Millithaler Ohmic regime conclusion Cross-over between 2D and 3D Cross-over for width around 10 nm, independently of the concentration