ABSTRACT

An increasing need for effective thermal sensors, together with dwindling energy resources, have created renewed interests in thermoelectric (TE), or solid-state, energy conversion and refrigeration using semiconductor-based nanostructures. Effective control of electron and phonon transport due to confinement, interface, and quantum effects has made nanostructures a good way to achieve more efficient thermoelectric energy conversion.

This thesis studies the two well-known approaches: confinement and energy filtering, and implements improvements to achieve higher thermoelectric performance. The effect of confinement is evaluated using a 2D material with a gate and utilizing the features in the density of states.  In addition to that, a novel controlled scattering approach is taken to enhance the device thermoelectric properties.

The shift in the onset of scattering due to  controlled scattering with respect to sharp features in the density of states creates a window shape for transport integral. Along with the controlled scattering, an effective utilization of Fermi window can provide a considerable enhancement in thermoelectric performance.

The conclusion from the results helps in selection of materials to achieve such enhanced thermoelectric performance. In  addition to that, the electron filtering approach is studied using the Wigner approach for treating  the carrier-potential interactions, coupled  with Boltzmann transport equation which is solved using  Rode’s iterative method,  especially in periodic potential structures. This study shows the effect of rapid potential variations in materials as seen in superlattices and the parameters that have significant contribution towards the thermoelectric performance.

Parameters such as period length,  height and smoothness of such periodic potentials are studied and their effect on thermoelectric performance is discussed. A combination of the above two methods can help in understanding the effect of confinement and key requirements in designing a nanostructured thermoelectric device that has a enhanced performance.

A Thermoelectric Device with p-type and n-type Semiconductor Legs.

OVERVIEW ON ENHANCEMENT IN THERMOELECTRIC PERFORMANCE

Low-Dimensional Thermoelectric Structures:

Seminal early work by Hicks and Dresselhaus reported the possibility of improved ZT when moving from higher to lower dimensional materials using the change in the shape of density-of-states (DOS). They concluded that the sharp features in reduced-dimensional materials provide energy filtering and push the carrier energies upward (Since S∝(E−Ef)) relative to their bulk counterparts, resulting in enhanced thermopower. There has been enormous research and innovations in the field over years mainly on nanostructured materials and devices.

Thermionic Energy Conversion:

To enhance the thermoelectric efficiency another approach called hot electron filtering can also be  used. In this method potential barriers are introduced in the material to allow only high energy electrons to participate in the transport, thereby improving the Seebeck coefficient. These heterostructures can have single and multi barrier structures. In single barrier devices, an optimum height barrier is used in one direction and a large barrier is used in other direction to prevent the reverse current.

Calculation of Thermoelectric Performance Parameters:

To evaluate the efficiency of thermoelectrics, Figure-of-merit (ZT) is the commonly used parameter.  Calculation of ZT requires the calculation of Seebeck co-efficient (S), electrical conductivity (σ) and Thermal conductivity of both electrons (κe) and phonons (κp). This thesis deals only with the electron transport, so only Seebeck coefficient (S), electrical conductivity (σ) and Thermal conductivity of electrons (κe) is focused.

Trade-off between Electrical Conductivity and Seebeck coefficient:

As discussed earlier, to improve power factor, both Seebeck and electrical conductivity has to be improved. But, improving one of them results in the decrease of the other so a balance has to be maintained to maximize both in a material. The differential electrical conductivity function or Transport distribution function (TDF) can be used to study the trade-off between electrical conductivity and Seebeck coefficient.

ENHANCEMENT IN A GATED 2-D MATERIAL USING FEATURES IN DENSITY OF STATES

The initial work on improving the thermoelectric properties of materials suggests moving from higher  to lower dimensional  material and  tuning  the  TDF to make it a delta shaped function helps to achieve higher conversion efficiency.

Thermoelectric refrigeration using Si-based nanowires and nanoribbons is an attractive approach for targeted cooling of local hotspots due to the ease of on chip integration and the nanowires’ enhanced TE Figure-of-merit. Silicon-on-insulator (SOI) membranes and membrane-based nanowires and ribbons show  promise for application as efficient thermoelectrics,  which requires both high power factor and low thermal conductivity.

Overview of Our Approach:

Mahan and Sofo studied the optimal conditions for thermoelectric conversion and  proposed  that  a delta shaped transport distribution  function  (TDF) Ξ (E)  =τ(E)g(E)v2(E), where τ (E) represents the relaxation time, g(E) represents the DOS,andv(E) is velocity of carriers, can significantly improve S thereby improving the overall ZT through electron filtering.  Zhou et.  al. re-investigated this idea to determine the best electronic structure for materials in terms of energy filtering band width (Wα) by studying the transport properties using different scattering models of carriers.

Transport Model:

To explore the practical possibility of achieving the delta shaped TDF in a confined nanostructure,  a back gated undoped silicon nanoribbon of 20 nm thickness on an oxide of 10 nm thickness is simulated. The oxide acts as a capacitor which induces carriers that participate in the transport of  both charge and energy, by applying the bias to the gate. The subband energies in the nanoribbon are obtained by self-consistently solving the coupled one-dimensional Schr ̈odinger and Poisson equations in the direction of confinement.

Schematic Depiction of the Simulated Silicon Nanoribbon.

Results and Discussion:

To check the proposed approach in silicon nanoribbons towards the possible enhancement in Seebeck coefficient (S), we implement the elastic mechanisms, phonon acoustic and surface roughness scattering has to be minimized; thus making the inelastic intervalley optical phonon scattering as dominant mechanism. A reduced acoustic phonon scattering is implemented by using a deformation potential which is 10% of the normal value.

All the transport integrals and the Seebeck coefficient S are calculated. As expected,  there is a little or no change in S in the presence of surface roughness in normal or reduced acoustic phonon scattering conditions, indicating that the elastic surface roughness (SR) is the dominant scattering mechanism when large roughness is present.

ENHANCEMENT OF SEEBECK COEFFICIENT IN RAPID VARYING PERIODIC STRUCTURES USING WIGNER FORMALISM

Introduction:

Electron filtering is one of the approaches that can provide an improved thermoelectric performance.  In electron filtering ”cold” electrons (low energy electrons) are restricted from participating in transport using a potential barrier as the Seebeck coefficient (S)∝(E−Ef).

There have been several studies done by implementing this approach using nanocomposites [25], superlattices, single and multiple barrier structures.  Zide et al. demonstrated an increase in thermoelectric efficiency using a nanocomposite consisting of III-V semiconductors (more specifically, InGaAlAs) containing nanoparticles of erbium arsenide as energy dependent scatterers.

The Graphene Device Used by D. Dragoman and M. Dragoman to Observe the Effect of Periodic Potential Being Applied Using a Series of Gates.

Wigner Formalism:

The semi-classical approach of the Boltzmann transport equation (BTE) is widely used in the device simulations.  But, in semi-classical approach, electrons are considered as point particles moving  with a velocity of their wave packet center and the spread of wave packet to be unchanged during  their propagation.  Hence the electrons are assumed to be well localized wave packets of Gaussian typical form.

Implementation of Transport Model:

In this thesis, Rode’s approach of Wigner-Boltzmann transport formalism is implemented in bulk silicon. To maintain a more realistic approach to the implementation, the full band structure silicon is used for modeling the thermoelectric properties. To calculate the band structure, the empirical pseudopotential model is implemented and energy E (k) values are calculated fork-space corresponding to 1/8 th of the Brillouinzone, which can be extended to full BZ using symmetry.

Results:

Validating the Model

Our initial implementation of the Rode’s method is completed, and thermoelectric parameters are calculated. At first, to validate the model, bulk silicon thermoelectric properties are compared with the experimental results in the literature.

It shows the mobility and Seebeck coefficient  dependence on impurity concentration that has been calculated from Rode’s implementation, compared with the literature. These thermoelectric parameters are in good agreement with the literature, thus validating the model.

Effect of boundaries on bulk silicon:

The aim of this thesis is to study the effects of nanostructuring on thermoelectric properties, now with the model validated the effect of confinement or boundaries is studied.  In Nanostructures, material dimensions confine the electron transport and considerably change the electrical characteristics. Our model captures the effect of boundaries on transport through boundary scattering, which evaluates the boundary as either diffuse or specular based on the surface roughness.

Dependence of Mobility of Electrons on Impurity Concentration in Bulk Silicon at Room Temperature T= 300 K and Compared With Results From Literature C. Jacobini Et Al., W. J. Patrick [38] and I. Grancher .

Electron filtering is one of the approaches that has been used to improve thermoelectric efficiency. Seebeck coefficient (S) is calculated in Silicon with periodic potentials using the potential operator in Wigner approach. Rode’s iterative method is used to calculate the perturbed distribution function (gi) due to the applied electricfield and the quantum evolution due to the rapid varying potentials.

Thermoelectric parameters of bulk silicon are calculated to validate the model by comparing it with the literature.  Then the confinement or boundary effects are simulated which showed a reduction in conductivity of electrons at low dimensions of silicon and no effect of surface roughness on transport.  Then the thermoelectric parameters are calculated for square potential with smoothening and perfectly smooth cosine potential.

The effect of tunneling and the energy filtering along with the interplay between them when the potential period and barrier height is changed. Along with that the effect of smoothening is also studied which showed an increase in quantum reflections due to barriers thereby providing more energy filtering. Thus we studied the effect of rapid varying periodic potentials and their shape parameters on thermoelectric parameters in semiconducting nanostructures.
Source: University of Massachusetts
Author: Adithya Kommini

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