Quantum size effects in a one-dimensional semimetal

We study theoretically the quantum size effects in a one-dimensional semimetal by a Boltzmann transport equation. We derive analytic expressions for the electrical conductivity, Hall coefficient, magnetoresistance, and the thermoelectric power in a nanowire. The transport coefficients of semimetal oscillate as the size of the sample shrinks. Below a certain size the semimetal evolves into a semiconductor. The semimetal-semiconductor transition is discussed quantitatively. The results should make a theoretical ground for better understanding of transport phenomena in low-dimensional semimetals. They can also provide useful information while studying low-dimensional semiconductors in general.Comment: 5 pages in PDF; LaTeX sourc

Thermoelectricity in Nanowires: A Generic Model

By employing a Boltzmann transport equation and using an energy and size dependent relaxation time ($\tau$) approximation (RTA), we evaluate self-consistently the thermoelectric figure-of-merit $ZT$ of a quantum wire with rectangular cross-section. The inferred $ZT$ shows abrupt enhancement in comparison to its counterparts in bulk systems. Still, the estimated $ZT$ for the representative Bi$_2$Te$_3$ nanowires and its dependence on wire parameters deviate considerably from those predicted by the existing RTA models with a constant $\tau$. In addition, we address contribution of the higher energy subbands to the transport phenomena, the effect of chemical potential tuning on $ZT$, and correlation of $ZT$ with quantum size effects (QSEs). The obtained results are of general validity for a wide class of systems and may prove useful in the ongoing development of the modern thermoelectric applications.Comment: 15 pages, 6 figures; Dedicated to the memory of Amirkhan Qezell

Small normal-metal tunnel junctions in electromagnetic environment

The effect of the electromagnetic environment on single junctions and on one- and two-dimensional arrays of junctions has been studied theoretically. The phase-correlation theory [or the P(E) theory], originally developed for the weak tunneling regime, its extension to the regime of strong tunneling, and the quasiclassical Langevin equation model have been investigated in more detail. The path-integral method and the voltage fluctuations model are shortly introduced. Limitations of each model along with its domain of applicability have also been discussed. The main results of the phase-correlation theory in the high temperature limit, i. e. for junctions with the Coulomb gap smaller than the thermal energy kBT, are reviewed. While doing this, emphasis has been put on the Coulomb blockade thermometry (CBT) applications. Results have been earlier obtained for the case of negligible environmental impedance. Here, the effect of the electromagnetic environment is investigated both theoretically and experimentally. This is done first for the single tunnel junctions, then for the one-dimensional (1D) and finally for two-dimensional (2D) arrays of tunnel junctions. It is shown that the effect of the electromagnetic environment is most pronounced for solitary tunnel junctions and, as another important example for two-junction arrays, and becomes negligible by increasing the number of junctions in an array. Furthermore, the strong tunneling corrections to the basic phase-correlation theory improve the agreement between the theory and our measurements in the case of solitary tunnel junctions with resistances much smaller than the quantum resistance RK ≈ 25.8 kΩ. Performing the Monte-Carlo simulations for arrays of tunnel junctions with N ≥ 2, we show that there is a value of external electromagnetic impedance, typically ~ 0.5 kΩ, at which the half-width of the conductance curve around zero bias voltage, V1/2, shows a maximum. This observation is further confirmed by the measured data, although the quantitative agreement is only fair. Introducing a relatively simple theory for the high-conductance 1D arrays, i.e. for arrays in the strong tunneling regime, the measured data for these structures together with their comparison to the theoretical predictions are presented. This is done with an eye on CBT applications. The desired strong tunneling correction to the simple linear relation used in the thermometry, V1/2,0 = 5.439NkBT/e, is given. The effect of non-homogeneity of tunnel junctions on the tunneling in the arrays has been discussed, as well. In the last part, assuming that the tunneling regime is sequential, the P(E) theory has been applied to the topologically simple two-dimensional structures. The results have been compared to the measured data, and it has been shown that, as thermometers, 1D arrays are superior to their 2D counterparts

Tuning the crystallinity of thermoelectric Bi2Te3 nanowire arrays grown by pulsed electrodeposition

International audienceArrays of thermoelectric bismuth telluride (Bi2Te3) nanowires were grown into porous anodic alumina (PAA) membranes prepared by a two-step anodization. Bi2Te3 nanowire arrays were deposited by galvanostatic, potentiostatic and pulsed electrodeposition from aqueous solution at room temperature. Depending on the electrodeposition method and as a consequence of different growth mechanisms, Bi2Te3 nanowires exhibit different types of crystalline microstructure. Bi2Te3 nanowire arrays, especially those grown by pulsed electrodeposition, have a highly oriented crystalline structure and were grown uniformly as compared to those grown by other electrodeposition techniques used. X-ray diffraction (XRD) analyses are indicative of the existence of a preferred growth orientation. High resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) confirm the formation of a preferred orientation and highly crystalline structure of the grown nanowires. The nanowires were further analyzed by scanning electron microscopy (SEM). Energy dispersive x-ray spectrometry (EDX) indicates that the composition of Bi-Te nanowires can be controlled by the electrodeposition method and the relaxation time in the pulsed electrodeposition approach. The samples fabricated by pulsed electrodeposition were electrically characterized within the temperature range 240 K<=T<=470 K. Below T≈440 K, the nanowire arrays exhibited a semiconducting behavior. Depending on the relaxation time in the pulsed electrodeposition, the semiconductor energy gaps were estimated to be 210-290 meV. At higher temperatures, as a consequence of the enhanced carrier-phonon scattering, the measured electrical resistances increased slightly. The Seebeck coefficient was measured for every Bi2Te3 sample at room temperature by a very simple method. All samples showed a positive value (12-33 µV K-1), indicating a p-type semiconductor behavior