Investigating Seebeck Coefficients in Bi2Se3 Films

Categories: Physics

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The theoretically calculated and experimentally measured Seebeck coefficients, showing the Seebeck coefficients as a function of film thickness. It should be noted that the theoretically calculated Seebeck coefficients are for bulk orthorhombic and rhombohedral phase Bi2Se3 with corresponding Fermi levels. It can be seen that the experimental Seebeck coefficients match with the theoretically calculated Seebeck coefficients of the rhombohedral phase when the film thicknesses are less than 1µm and the experimental Seebeck coefficients fall between the theoretically calculated Seebeck coefficients of rhombohedral and orthorhombic phases when the film thicknesses are larger than 1µm as expected.

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Future Works

The primary goal of my research will be to find the optimum SSTI device structures theoretically considering the effects of asymmetry, effects of the defect on the structure and the secondary goal will be to investigate the effects of electron-phonon interaction on electron transport in highly correlated bulk materials.

The aim of the first research area is to theoretically investigate the effect of asymmetry in the 2DvdW based SSTI devices.

In our preliminary work, we have considered identical metallic contacts in the heterostructure based devices (metal-2D materials-metal) and evaluated their performance. Typically, in a vacuum thermionic device, the metal in the cathode side and anode side are non-identical. In my proposed work, I want to evaluate the same concept in the case of SSTI devices. In these devices the 2DvdW heterostructure will be sandwiched between two dissimilar metallic electrodes and the effect of asymmetry on the device performance will be investigated.

A fair portion of the dissertation work will be devoted to investigating the effect of different combinations of metallic contact as well as different energetically aligned 2D layered materials on the performance of heterostructure based SSTI devices. The second area will theoretically investigate the effect of the defect on the performances of the SSTI device. It is well known that defects work as the scattering center and lower the thermal conductance as well as the electrical conductance but the overall effect of the defect on the performance of SSTI devices is not known. The main challenge in the theoretical calculation is to include the effect of imperfections in the formalism.

The most important defects are lattice mismatch and impurities such as vacancies and foreign atoms or molecules or eventual oxide layers that can exist at interfaces. The third area shifts focus from SSTI devices to the effect of electron-phonon coupling on bulk materials. In this area of research, we will investigate the effect of electron-phonon interaction on electron transport in different highly correlated bulk materials from first principle calculations using the EPW code.

The key research questions (RQ) to drive the proposed works are:

RQ-1: What is the effect of structural asymmetry on the performance of SSTI devices based on 2DvdW heterostructure?
RQ-2: What is the overall effect of the defects on the performance of the SSTI device?
RQ-3: How electron-phonon interaction modifies the electronic transport in highly correlated bulk materials?

Work Plan and Implications

Find Suitable Metallic Contacts and 2D Materials

The thermionic current density of electron flux from the cathode side to the anode side in an SSTI device can be represented by Richardson’s law for the thermionic current J=AT^2 e^(-E_b/k_B T), where A=em^* k_B^2 τ ̅/(2π^2 ħ^3) is the Richardson constant, e is the electron charge, m* is the effective mass, τ ̅ is the averaged electron transmission denoting the fraction of electrons transmitted from the metal to the semiconductor, k_B is the Boltzmann constant, ħ is the reduced Plank’s constant, T is the absolute temperature and E_b is the thermionic barrier height which is usually taken as a parameter to optimize the thermionic energy conversion efficiency (2, 6, 7, 10). For a single barrier thermionic energy converter, the optimum value for E_b is found to be several k_B T (6).

In case of the SSTI converter, the energy barrier height can be found by Anderson rule as E_b=φ_c-χ_S, where φ_c is the cathode work function and χ_S is the electron affinity of the semiconductor. The first step of my work will be to find a combination of suitable metallic contacts and 2D material so that the energy barrier height is in the desirable range. The large database of 2D semiconductor with different electron affinity will help me to find suitable 2D material (49). Moreover, the quantum confinement effect leads to layer dependent band alignment in 2D materials which helps to tune the energy barrier height by changing the number of layers (50).

However, the determination of the exact energy barrier height of 2DvdW heterostructure based thermionic devices is challenging due to the Fermi level pinning effect in the metal-2D material interface (51). Fortunately, this difficulty can be overcome by the parameter-free density functional theory (DFT) based on first-principles calculations. The barrier height for DFT calculation can be represented as E_b^n=CBM-E_F and E_b^p=E_F-VBM for n-type and p-type barriers respectively, where CBM and VBM stand for the conduction band minimum and valence band maximum (10). Therefore, the Anderson rule will help to initially screen the 2D materials and the DFT calculations will help to find the accurate energy barrier height.

DFT Band Structure and DOS Calculation

Structure relaxation calculations will be performed using the Quantum Espresso package (41). We will use the generalized gradient approximation for the exchange and correlation functional, as proposed by Perdew–Burke–Ernzerhof (PBE) (55) and the GBRV (56) ultrasoft pseudopotential to treat the ion-electron interactions. To correctly deal with the van der Waals interactions, we will employ the non-local van der Waals DFT functional (optB88-vdW) (57, 58) to relax the structure along the cross-plane direction. The band structures and local density of states (LDOS) will be calculated using the SIESTA package (54).

SIESTA uses the standard Kohn-Sham (59) self-consistent density functional method in the local density (LDA-LSD) (60) and generalized gradient (GGA) (55) approximations, as well as in a non-local functional that includes van der Waals interactions (VDW-DF). It uses norm-conserving pseudopotentials (61, 62) in their fully nonlocal (Kleinman-Bylander) (63) form and atomic orbitals as a basis set, allowing unlimited multiple-zeta and angular momenta, polarization and off-site orbitals. SIESTA also includes scalar-relativistic effects and the nonlinear partial-core correction to treat exchange-correlation in the core region (64). It projects the electron wave functions and density onto a real-space grid in order to calculate the Hartree and exchange-correlation potentials and their matrix elements.

Electron Transport Calculation

The electronic transport properties of the SSTI devices will be studied by using density functional theory (DFT)-based first-principles calculations combined with real-space Green’s function (GF) transport formalism. The electron transmission function will be calculated using real-space Green’s function method as in the TranSiesta implementation (52). TranSIESTA deals fully with the atomistic structure of the whole system, treating both the contact and the electrodes on the same footing. The effect of the finite bias is considered using nonequilibrium Green’s functions. After calculating the electron transmission function using TranSIESTA, the transport coefficient can be obtained using the linear response approximation (53):

Conductance, G=q^2 L_0

Seebeck coefficient, S=L_1/qTL_0

Electronic thermal conductance, κ_el=(L_2-L_1^2/L_0)/T

L_n=2/h∫(dET(E)(E-µ)^n (-δf/δE))

where q is the electron charge, and f is the Fermi-Dirac distribution function.

Preliminary Results (Band structure, DOS, Electronic transport)

Applying the same recipe as Dr. Xiaoming Wang4*, I studied Sc-WSe2-Sc structure, previously studied by Dr. Wang, computationally using first-principles calculations combined with real-space Green’s function formalism and successfully reproduced band structure, the local density of states (LDOS) and electronic transport properties.

The structural relaxation calculations were performed using the Quantum Espresso package (41). The generalized gradient approximation for the exchange and correlation functional, as proposed by Perdew–Burke–Ernzerhof (PBE) was used. The non-local van der Waals DFT functional (optB88-vdW) (57, 58) was employed to relax the structure along the cross-plane direction to correctly deal with the van der Waals interactions. To study the electronic properties of the Sc-WSe2-Sc van der Waals heterostructure, I used the state-of-the-art density functional theory based first-principles calculations, as implemented in the SIESTA package (54).

The exchange-correlation functional of Perdew-Burke-Ernzerhof (55) revised for solids (43) and standard basis set, namely, double zeta plus polarization (DZP) was used. Real-space mesh cutoff energy was set to 300 Ry. A single k point in the cross-plane direction and a 24×24 k mesh in the basal plane was used for the Brillouin zone sampling. The cross-plane direction was relaxed without any constraint. The forces of all the atoms were relaxed within 0.01 eV/Å. The calculated band structure and local density of states (LODS) are shown in Figure 13. The ballistic transport properties as shown in Figure 14 were calculated using the real-space Green’s function method as in the TranSIESTA implementation (52).

Conclusion

Investigating Seebeck coefficients in Bi2Se3 films provides valuable insights into the thermoelectric properties of materials. Future research aims to optimize SSTI device structures and understand the influence of factors like asymmetry, defects, and electron-phonon interaction, contributing to advancements in thermoelectric technology.