7.1 Conclusion
In this thesis, we have studied energy (charge and heat) transport and
conversion in semiconductor nanocrystal solids. This work focuses on the
measurement and the interpretation of temperature-dependent thermopower and
electrical conductivity of PbTe and Ag2Te nanocrystals as well as PbTe nanocrystal
solids doped with Ag2Te nanocrystals. The main results are presented in the following
categories.
1. The slope of the thermopower versus inverse temperature plot obtained from PbTe
nanocrystal solids reveals the Fermi energy level with respect to the transport energy
which is key in estimating the carrier concentration in semiconductors.
2. The y-intercept of the thermopower versus inverse temperature plot obtained from
PbTe nanocrystal solids reflects the sharpness of the electronic density of state
distribution. This reveals the origin of enhanced thermopower in nanostructures with
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3. Temperature-dependent conductivity combined with thermopower measurements
were performed on each of the PbTe and Ag2Te nanocrystal solids to reveal the Fermi
energy level and the energetic disorder affecting the carrier mobility.
4. Temperature-dependent conductivity combined with the thermopower
measurement were performed on PbTe nanocrystal solids mixed with Ag2Te
nanocrystal dopants. Increasing the concentration of nanocrystal dopants decreased
the distance between the Fermi level and the first hole transport level (increase in hole
concentration), and increased the activation energy of hopping (decrease in hole
mobility).
Another scope of this thesis focuses on the development of solution-processable
nanocomposite with enhanced thermopower via carrier energy filter. The conclusions
are summarized in the following.
1. Nancomposites composed of Pt nanocrystals embedded in a hydrazine-based
solution-processable Sb2Te3 semiconductor demonstrated an increase in thermopower
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2. Thermopower, van der Pauw resitivity and Hall effect measurements reveal an
increase in the thermoelectric power factor in Pt-Sb2Te3 nanocomposites compared to
that of the pure Sb2Te3 film.
3. The above work highlights the ability to choose different composition, size,
shape, and concentration of nanocrystals and embedding them either in n- or p-type semiconductor matrices to engineer both the carrier energy and phonon spectra with
the ease of material processing.
7.2 Future work: Electronic contributions to the thermal
conductivity
Electrons and holes, which are both charge and heat carriers, affect three
primary material parameters: electrical conductivity (charge), thermoelectricity
(charge and heat), and thermal conductivity (heat). In previous chapters, we have
theoretically and experimentally explored the first two terms in semiconductor
nanocrystal solids. As a last discussion of this thesis, we will focus on the electronic
contribution to the thermal conductivity. In metals or degenerate semiconductors, the
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Lorentz number (L = π2k
B2/3e2 = 2.45 x 10-8 WΩK-2). This is known as the
Widemann-Franz law (ke = LσT) which is commonly applied to bulk thermoelectric
materials to extract the electronic contribution to the thermal conductivity. However,
in nanostructures with a sharp distribution of density of states, the Lorentz number
can significantly deviate from the theoretical value and the Widemann-Franz law
loses its validity.[1] This is shown in an ideal electronic structure, as depicted in Figure
7.1(a), where the high energy portion of electrons that carries large amounts of heat
are cut-off due to the discontinuity of the density of states and therefore no longer
contributes to the thermal conductivity.[2] An accurate theoretical method to estimate
or an experimental method to practically measure electronic thermal conductivity may,
in combination with the strategy to achieve lowest lattice thermal conductivity, lead to
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Fig. 7.1 Failure of Wiedemann-Franz law and alternative methods to extract electronic thermal conductivity. (a) Schematic description of electron population in 3D and 0D material systems. Schematic illustration of (b) the Nernst and (c) the Ettingshausen effect.
One method, proposed as a future work of this thesis, is to directly measure
the electronic thermal conductivity exclusively via the Nernst and Ettingshausen
effects. The Nernst effect arises from the combination of Seebeck and Hall effects.
When the charge carriers thermally diffuse due to an applied temperature difference,
an applied external magnetic field (BZ) deflects the carrier perpendicular to the
direction of the current flow, causing the build up of an electric field. This electric
field is proportional to the applied temperature gradient (ΔT) as well as the magnetic
field (BZ) and the proportional constant is defined as Nernst coefficient, Qn in
y n Z
V =Q B TΔ . Similarly, the Ettingshausen effect is induced when the current is applied in the presence of a magnetic field. The deflected carrier causes a temperature
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proportional constant Pe is the Ettingshausen coefficient. These two effects are shown
in Fig. 7.1(b) and (c). The Nernst and Ettingshausen coefficients are related through
the Bridgeman relationship as P ke e =Q Tn , where ke is the electronic thermal
conductivity. Through measurements of these two magneto-thermal effects, electronic
contribution to thermal conductivity can be directly extracted.
Reference
1. Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G. Bulk Nanostructured Thermoelectric Materials: Current Research and Future Prospects. Energy Environ. Sci.,
2009, 2, 466-479.
2. Humphrey T. E.; Linke, H. Reversible Thermoelectric Nanomaterials, Phys. Rev. Lett.,