Milestone primo anno

1. Milestone primo anno • M1.1 Sviluppo di un codice per la simulazione del trasporto e del rumore shot in strutture mesoscopiche, in presenza di droganti distribuiti casualmente, con l’utilizzo di potenziali di confinamento realistici • M1.2 Messa a punto di un sistema di misura a bassissimo rumore operante a temperature criogeniche, sfruttando tecniche di correlazione e il metodo dell’impedenza sostitutiva… • M1.3 Misure di rumore shot su dispositivi a doppia barriera a effetto tunnel risonante, con particolare attenzione alle condizioni di funzionamento con correnti estremamente basse, che possono essere investigate per la prima volta con il sistema di misura

2. Situazione del personale • E’ stata bandita, con un certo ritardo per motivi burocratici, la borsa connessa con il progetto: l’assegnazione della stessa dovrebbe essere fatta lunedi’ prossimo • Nel frattempo una persona ha cominciato a lavorare sul progetto in aprile, su fondi residui CNR • Anche l’attivita’ di un tesista (laurea specialistica) e di un dottorando si inquadrano all’interno del progetto • In parte vi rientra anche quella di un’assegnista di ricerca (al 15% circa)

3. The 1/3 suppression has been experimentally demonstrated for metallic diffusive wires: M. Henny et al., PRB 59, 2871 (1999) Only one experiment exists on diffusive semiconductor nanostructures, and its results are not conclusive: F. Liefrink et al., Phys. Rev. B 49, 14066 (1994) Motivation for the present study Poly metal We have developed a numerical model of conductance and noise in a quantum wire, to understand whether the diffusive regime can actually be achieved Some adjustable parameters have been tuned based on measurements performed on a test structure Drain L

4. General approach • Development of a 3D Schrödinger-Poisson solver to provide the confinement potential • Inclusion of the effects of discrete dopants • Development of a 2D transport simulator suitable for the investigation of conductance and noise • Fabrication of a suitable sample quantum wire • Measurement of sample conductance vs. gate voltage • Calibration of the simulator based on experimental data • Calculation of noise and of the expected Fano factor • Measurement of shot noise in the sample quantum wire

5. Device structure

6. Potential calculation • Poisson equation • The electron density n(f) in the quantum region is obtained from the solution of the Schrödinger equation with density functional theory • p(f), ND+(f), NA-(f) and of n(f) out of the quantum region are given by the corresponding semiclassical expressions • Discretization with the box integration method • Newton-Raphson technique with predictor-corrector iteration scheme

7. 3D Poisson-Schrödinger solver • 1st step: Non linear Poisson equation in 3D • The strong confinement in the x direction, perpendicular to the heterointerface, allows us to decouple the Schrödinger equation into • a 1D equation in the x direction, • a 2D equation in the y-z plane. The density of states in the y-z plane is well approximated by the semiclassical expression. • The boundary condition at the semiconductor-air interface is treated assuming a uniform density of surface states Ds, which behave as donors or acceptors depending on their position (below or above) relative to an effective work function F* (set to 4.85 eV). The electric field is assumed to vanish in the air.

8. Discrete donors • We use a semi-analytical technique to include the effect of discrete donors (otherwise the discretization grid would be prohibitively large) Screening is included following Stern and Howard, PRB 163, 816 (1967) a) b) c) d)

9. Confinement potential Longitudinal cross-section Computed potential

10. Conductance and noise calculation • The transmission matrix is computed with a recursive Green’s function technique

11. Averaging details • The expression for the Fano factor must be modified if the temperature is different from zero • Averaging must be weighted with the derivative of the Fermi function instead of performing it over an ensemble of devices, as it has been often done in the literature

12. Conductance comparison • Parameters have been adjusted to match the conductance curves • Ns=1.13 x 1012 cm-2; Ds=0.5 x 1014 m-2 eV-1

13. Noise results This is consistent with a results for a soft-obstacle model (Macucci et al., to be published in PRB, 2002)

14. Stretched potential L=1 mm L=3 mm L=5 mm Calculations have been repeated for stretched wires, extending the length of the middle section before adding the contribution from the discrete dopants

15. Conclusions and future work • Good agreement has been obtained between the numerical and the experimental conductance, by adjusting donor concentration and surface defect concentration • Noise results show that, due to the relatively small amplitude of the potential fluctuations, a diffusive regime is not reached or, at least, is not a common occurrence • Stretched wires exhibit a similar noise behavior, demonstrating that failure to reach the diffusive regime is not due to the length of the device being less than the elastic mean free path • A better screening model can be developed from numerical calculations on a single impurity with a very fine mesh • The feasibility of noise measurements to validate the model is being assessed

16. Sistema di misura • Il tubo in acciaio inox che contiene l’intero sistema e’ posto all’interno del dewar in modo che il campione si trovi alcuni millimetri al di sopra del livello del liquido criogenico

17. Aspetti in corso di miglioramento • Il principale problema, nel corso delle misure a bassi valori di corrente, sembra essere rappresentato dalle vibrazioni meccaniche • Sono stati tentati vari tipi di supporti antivibranti, con esiti alterni • Da misure di spostamento relativo appare che grossa parte dei disturbi vengono trasmessi dal pavimento • Si e’ quindi pensato di realizzare un supporto di tipo pneumatico, basato su componenti di un tavolo antivibrante gia’ disponibile

18. Tavolo antivibrante

19. Supporto antivibrante per dewar

20. Status criostato a diluizione • La consegna e’ in ritardo, per il momento sono arrivate solo le foto…

21. Risultati delle misure in corso Sono in corso misure nella regione a basse correnti di diodi resonant tunneling, per cercare di individuare l’effetto della transizione tra l’effetto coulombiano e l’effetto Pauli

22. Nuovi risultati per il rumore in cavita’