Efficient thermoelectric energy conversion on quasi-localized electron states in diameter modulated nanowires
© Zianni; licensee Springer. 2011
- Received: 9 December 2010
- Accepted: 4 April 2011
- Published: 4 April 2011
It is known that the thermoelectric efficiency of nanowires increases when their diameter decreases. Recently, we proposed that increase of the thermoelectric efficiency could be achieved by modulating the diameter of the nanowires. We showed that the electron thermoelectric properties depend strongly on the geometry of the diameter modulation. Moreover, it has been shown by another group that the phonon conductivity decreases in nanowires when they are modulated by dots. Here, the thermoelectric efficiency of diameter modulated nanowires is estimated, in the ballistic regime, by taking into account the electron and phonon transmission properties. It is demonstrated that quasi-localized states can be formed that are prosperous for efficient thermoelectric energy conversion.
- Transmission Coefficient
- Electron Thermal Conductance
- Transmission Resonance
- Diameter Modulation
- Phonon Thermal Conductance
A measure of the thermoelectric efficiency of a material is the dimensionless figure of merit ZT ≡ S 2 σT/κ, where σ is the conductivity, S is the thermopower, κ is the thermal conductivity and T is the absolute temperature. In nanostructures, quantum confinement of electrons and phonons favours their thermoelectric transport properties, resulting in increased thermoelectric efficiency . Nanowires and arrays of nanodots are currently attracting much research interest. It has been theoretically shown that nanodots can have very high thermoelectric efficiencies due to their discrete energy spectrum [2–4]. Quantum confinement causes enhancement of ZT in nanowires. Considerably high values of the figure of merit have been found in very thin wires [5–8]. Despite the noticeable progress in the fabrication of wires with high aspect ratios, the poor mechanical properties of very thin wires is a drawback for developing devices based on them.
Recently, we proposed that increase of the thermoelectric efficiency could be achieved by modulating the diameter of the nanowires . We showed that the electron thermoelectric properties depend strongly on the geometry of the diameter modulation. In this Letter, we focus on the electron propagation states that we reported to have high values of thermoelectric figure of merit when phonon conduction was neglected. The thermoelectric efficiency of these states is estimated, here, by taking into account the electron and phonon transmission properties. In what follows, it is shown that efficient thermoelectric energy conversion can be achieved on electron quasi-localized states in diameter modulated nanowires.
The coefficient α is a measure of the effect of phonon conduction on the thermoelectric efficiency. When phonon conduction is non-negligible, the coefficient α is smaller than 1 and ZT is smaller than ZT 0.
where Ε res and Γ are the energy and the broadening of the resonance respectively.
At the narrow band below the transmission band threshold of the constriction, NB (Figure 2), ZT 0 has considerably smaller values than at R due to higher electron thermal conductance at NB than at R (Figure 5). The power factor, S 2 GT, is considerably higher at NB than at R (Figure 4). At NB, a significant increase of ZT 0 is found with increasing temperature due to: (i) increase of S 2 GT and (ii) decrease of κ e due to heat leakage through propagation band states at higher energies.
It is well known that phonon conduction decreases in nanostructures due to phonon scattering on boundaries and interfaces. In heterostructures, optical and acoustic phonons have been shown to occupy quasi-bound states within narrow bands separated by gaps [12, 13]. It has been shown [14, 15] that in an ideal quantum wire the total acoustic phonon transmission probability exhibits perfect transmission steps. A perfect quantum thermal plateau exists, and at T = 0, its value approaches a universal value, . Quantum wires attached with inhomogeneities such as abrupt junctions and stub structures have already been reported [16–19]. In wires modulated by dots, the phonon transmission spectra have shown to display complex peak-dip structures. The thermal conductance plateau is destroyed and the thermal conductance decreases due to phonon scattering. It has been found [17–19] that the phonon thermal conductance can be adjusted by the attached scattering and it can become smaller than κ 0. We have found that the electron thermal conductance can also be smaller than κ 0. The ratio of the two contributions to the thermal conductance, κ ph/κ e, determines the value of coefficient α, i.e. the decrease of ZT relative to ZT 0.
At NB, ZT decreases relative to ZT 0 but it has values close to and above 1 (Figure 7). This is because: (i) the power factor S 2 GT is not very small (Figure 4) in this case, and (ii) the ratio of κ ph/κ e can be of the order of 1. In the data shown in Figure 7, it has been considered that κ ph is always reduced due to the diameter modulation [17–19]. Hence, ZT of the modulated wire is found higher than that of a uniform thin wire with diameter equal to that of the thin constrictions (Figure 1). It is thereby indicated that increase of the thermoelectric efficiency of nanowires could be achieved by modulating their diameter instead of making them very thin and mechanically unstable.
In the ballistic regime, the thermoelectric efficiency of diameter modulated nanowires is directly related to the energy dependence of the transmission coefficient. For both electrons and phonons, T(E) is sensitive to the geometry of the modulated nanowires [9, 17–19]. Geometry optimization of the diameter modulation could result in optimal electron thermoelectric properties and minimum phonon conduction. This task is very challenging because several geometry lengths are involved. For instance, the formation of quasi-localized states depends on the width and the length of the constrictions relative to the dimensions of the modulating units, by the number of modulating units, by disorder in arrays of non-identical modulation units. The recent progress in the fabrication of nanowires using well-controlled techniques (both epitaxial and etching) could allow for geometry optimization and development of efficient thermoelectric applications based on modulated nanowires.
The thermoelectric efficiency of diameter modulated nanowires has been estimated by taking into account the electron and phonon transmission properties. It has been demonstrated that quasi-localized electron states can be formed that are prosperous for efficient thermoelectric energy conversion. Diameter modulated nanowires provide an architecture suitable for optimization of the transport properties of both electrons and phonons.
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