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A comparative analysis of sequential and coherent model for
shot-noise suppression in resonant tunneling diodes
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.
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.
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
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 1016 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 1017 cm-3 (a) and (b) refer to
the sequential and coherent tunneling approaches, respectively.
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
CONCLUSIONS
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.
SEQUENTIAL AND COHERENT TRANSPORT
SEQUENTIAL TUNNELING NOISE
FANO FACOR CANNOT DROP BELOW 0.5 (SOFT SUPPRESSION)
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 I0 = qm G2
/4(2p2 h3) and x = 2/(qu-er) G. Curves labelled as 1, 2, 3
correspond to values of the dimensionless electrochemical
potentials: f=1, 15, oo (f=2FL /G) respectively.
CONCLUSION: In the absence of Coulomb
correlations the Fano factor exhibits a minimum value
near the current peak from 0.381 down to zero
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.
COHERENT TUNNELING NOISE
SYMBOL DEFINITION
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-2001-38899 of the EC is gratefully acknowledged.
FANO FACTOR CAN BE
BIBLIOGRAPHY
FANO FACTOR CAN BE LOWER THAN 0.5 (GIANT SUPPRESSION)
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/0304077v3 11 Dec.
2003.
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