FANO FACTOR CAN BE A comparative analysis of sequential and coherent model for shot-noise suppression in resonant tunneling diodes MOTIVATION: Since its realization, the double barrier resonant diode (DBRD) proved to be an electron device of broad physical interest because of its peculiar non Ohmic current voltage (I-V) characteristic [1,2]. Even the shot noise characteristics are of relevant interest due to the fact that suppressed as well as enhanced shot noise with respect to its full Poissonian value has been observed [3].The microscopic interpretation of these features is found to admit a coherent [1] or a sequential tunneling [2] approach. The intriguing feature of these two approaches is that from the existing literature it emerges that both of them are capable to explain the I-V experiments as well as most of the shot noise characteristics [3.4]. Therefore, to our knowledge there is no way to distinguish between these two transport regimes and the natural question whether the tunneling transport is coherent or sequential remains an unsolved one. GOAL: Here we answer the above question by announcing that a giant suppression of shot noise occurring before the peak value of the current with a Fano factor below 0.5 is a signature of coherent transport in DBRDs STRUCTURE SEQUENTIAL TUNNELING NOISE CONCLUSIONS We have investigated coherent tunneling in DBRDs that includes both Pauli principle and long range Coulomb interaction. In agreement with existing results, we have found that at 4.2 K shot noise is suppressed mostly because of Pauli correlation. Moreover, the suppression exhibits a Fano factor of 0.5 in a wide region of applied voltages, with a minimum below 0.5 at the current peak in agreement with experiments. Interestingly, we have found that shot noise can be suppressed well below the value of 0.5 also because of Coulomb interaction. This giant suppression is here confirmed by existing experiments at 4.2 K [5]. Therefore, shot noise suppression below one-half of the full Poissonian value is proven to be a signature of coherent tunneling against sequential tunneling in double barrier resonant diodes. We finally want to stress that the main reason of the difference between these approaches stems from the fact that the sequential tunneling is based on a master equation [4] for treating fluctuations of carrier numbers inside the quantum well while coherent tunneling uses the quantum partition noise [3,6]. The master equation describes implicitly a sequential mechanism for a carrier entering/exiting from the well and, as a consequence, its intrinsic limit coincides with that of two independent resistors (or vacuum diodes) connected in series and each of them exhibiting full shot noise. This system yields a maximum suppression of shot noise down to the value of 0.5. By contrast, partition noise, can be fully suppressed down to zero in the presence of a fully transparent barrier like in the case of vacuum diodes. ACKNOWLEDGMENTS: Partial support from the Italian Ministry of Foreign Affairs through the Volta Landau Center (the fellowship of V.Ya.A.), the cofin03 and the SPOT-NOSED project IST of the EC is gratefully acknowledged. BIBLIOGRAPHY 1. L.L. Chang, L. Esaki and R. Tsui, Appl. Phys. Lett., 24, 593 (1974). 2. S. Luryi, Appl. Phys. Lett., 47, 490 (1985). 3. Y.M. Blanter and M. Buettiker, Phys. Rep. 336, (2000). 4. G. Iannaccone, M. Macucci, and B. Pellegrini, Phys. Rev. B 55, 4539 (1997). 5. E.R. Brown, IEEE Trans. on Electron Dev. 39, 2686 (1992). 6. V. Ya Aleshkin and L. Reggiani, N.V. Alkeev, V.E. Lyubchenko, C.N. Ironside, J.M.L. Figueiredo and C.R. Stanley, cond-matter/ v3 11 Dec COHERENT TUNNELING NOISE RESULTS Abstract: Shot noise suppression in double barrier resonant tunneling diodes with a Fano factor well below the value of 0.5 is theoretically predicted. This giant suppression is found to be a signature of coherent transport regime. These predictions are validated by experimental data. Band diagram of the symmetric double barrier structure considered here under an applied voltage V. The bottom of the conduction band in the emitter in the well and in the collector coincides at V=0. CONCLUSION: the current voltage characteristic remains the same but the noise is different when going from the sequential to the coherent model. In particular the coherent model exhibits a Fano Factor value below the value of 0.5 SYMBOL DEFINITION Lino Reggiani (1) Vladimir Ya. Aleshkin (2) (1) INFM National Nanostructure Laboratory, Dipartimento di Ingegneria dell' Innovazione, Lecce University, Italy. (2) Institute for Physics of Microstructures, Nizhny Novgorod, Russia. SEQUENTIAL AND COHERENT TRANSPORT FANO FACTOR CAN BE LOWER THAN 0.5 (GIANT SUPPRESSION) Dependence of current and Fano factor on applied voltage in a symmetric DBRD at 4.2 K in the presence of Coulomb correlations for a carrier concentration in the contacts n=5 x cm -3 (a) and (b) refer to the sequential and coherent tunneling approaches, respectively. Dependence of current and Fano factor on applied voltage in a symmetric DBRD at 4.2 K in the presence of Coulomb correlations for a carrier concentration in the contacts n=5 x cm -3 (a) and (b) refer to the sequential and coherent tunneling approaches, respectively. Dependence of current (a) and Fano factor (b) on applied voltage in a symmetric DBRD at zero temperature in the absence of Coulomb correlations. For convenience dimensionless current and voltages are used. Here I 0 = qm  2 /4(2   h 3 ) and x = 2/(qu-  r ) . Curves labelled as 1, 2, 3 correspond to values of the dimensionless electrochemical potentials: f=1, 15, oo (f=2F L /  ) respectively. FANO FACOR CANNOT DROP BELOW 0.5 (SOFT SUPPRESSION) CONCLUSION: In the absence of Coulomb correlations the Fano factor exhibits a minimum value near the current peak from down to zero

Lecce: 1 – Shot noise in double barrier resonant tunneling (L. Reggiani) 2 – Resistance noise in random resitor network (C. Pennetta)

A comparative analysis of sequential and coherent model for shot-noise suppression in resonant tunneling diodes Lino Reggiani Vladimir Ya. Aleshkin