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Localization effects in the tunnel barriers of phosphorus-doped silicon quantum dots
12. F. H. L. Koppens, C. Buizert, K. J. Tielrooij, I. T. Vink, K. C. Nowack, T. Meunier, L. P. Kouwenhoven, and L. M. K. Vandersypen, Nature 442, 766 (2006).
16. Tunneling rates are generally defined for single tunneling events from the Fermi energy of the source lead to a well defined energy level in the dot. The value of this rate can be measured directly by the use of single shot measurement techniques. However, in the case of standard DC measurements where the integration time is much larger than the tunneling time, many tunneling events happen. In doped material, the disorder lifts the level degeneracy and the measured tunneling rate across the barrier is modified by including a factor γ ∼ N2 where N is the number of active dopants on each side of the barrier. By taking into account a depletion region of ∼ 15 nm at the Si-SiO2 interface and an effective SOI thickness of 20 nm after oxidation, we find N ∼ 392 atoms and γ ∼ 6.17 × 105, if spin degeneracy is taken into account.
20. The power of the heat transfer is ∝Tep+2 − T0p+2 where p is related to the temperature dependence of electron-phonon scattering time τ−1 ∝ Tp. In a metal, p = 3 and, if the electronic system is decoupled from the phonon bath, it is expected that p = 0. In silicon, scattering by acoustic phonons is the dominant process at low temperature and p = 3/2. In the cotunneling regime, the power of the Joule effect is ∼VSD4, leading to a bias dependent electron temperature Te ∼ VSD8/7 at high source drain biases.
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We have observed a negative differential conductance with singular gate and source-drain bias dependences in a phosphorus-doped siliconquantum dot. Its origin is discussed within the framework of weak localization. By measuring the current-voltage characteristics at different temperatures as well as simulating the tunneling rates dependences on energy, we demonstrate that the presence of shallow energy defects together with an enhancement of localization satisfactory explain our observations. Effects observed in magnetic fields are also discussed.
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