The accurate numerical evaluation of half‐order Fermi‐Dirac Integrals

Mohankumar, N.; Natarajan, A.

doi:10.1002/pssb.2221880206

Cited by 25 publications

(11 citation statements)

References 14 publications

(13 reference statements)

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“…8c and 8d respectively). Numerical integration was performed using the function fermi.m in Matlab® [45]. Here, we see that the Seebeck, as calculated from Equation 3, fits the experimental data quite well when r=0, which is consistent with phononlimited scattering in 2D and captures the relative change in the Seebeck as a function of the carrier concentration induced by the backgate voltage.…”

Section: Calculation Of Seebeck Coefficient and Fermi Level (With Ressupporting

confidence: 70%

High thermoelectric power factor in two-dimensional crystals ofMoS2

et al. 2017

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The quest for high-efficiency heat-to-electricity conversion has been one of the major driving forces towards renewable energy production for the future. Efficient thermoelectric devices require high voltage generation from a temperature gradient and a large electrical conductivity, while maintaining a low thermal conductivity. For a given thermal conductivity and temperature, the thermoelectric powerfactor is determined by the electronic structure of the material. Low dimensionality (1D and 2D) opens new routes to high powerfactor due to the unique density of states (DOS) of confined electrons and holes. 2D transition metal dichalcogenide (TMDC) semiconductors represent a new class of thermoelectric materials not only due to such confinement effects, but especially due to their large effective masses and valley degeneracies. Here we report a powerfactor of MoS 2 as large as 8.5 mWm −1 K −2 at room temperature, which is amongst the highest measured in traditional, gapped thermoelectric materials. To obtain these high powerfactors, we perform thermoelectric measurements on few-layer MoS 2 in the metallic regime, which allows us to access the 2D DOS near the conduction band edge and exploit the effect of 2D confinement on electron scattering rates, which result in a large Seebeck coefficient. The demonstrated high, electronically modulated powerfactor in 2D TMDCs holds promise for efficient thermoelectric energy conversion.

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Section: Calculation Of Seebeck Coefficient and Fermi Level (With Ressupporting

confidence: 70%

High thermoelectric power factor in two-dimensional crystals ofMoS2

et al. 2017

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“…These equations are just the Einstein relation, written in a form that is valid at all temperatures. In three dimensions χ e must be evaluated numerically, 24 but in the non-degenerate limit Eq. 4 reduces to the familiar expression D e = µ e k B T /e.…”

Section: A Ambipolar Diffusionmentioning

confidence: 99%

Diffusion of degenerate minority carriers in a p-type semiconductor

Weber

Kittlaus

2013

Journal of Applied Physics

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We report ultrafast transient-grating experiments on heavily p-type InP at 15 K. Our measurement reveals the dynamics and diffusion of photoexcited electrons and holes as a function of their density n in the range 2 × 10 16 to 6 × 10 17 cm −3 . After the first few picoseconds the grating decays primarily due to ambipolar diffusion. While at low density we observe a regime in which the ambipolar diffusion is electron-dominated and increases rapidly with n, at high n it appears to saturate at 34 cm 2 /s. We present a simple calculation that reproduces the main results of our measurements as well as of previously published measurements that had shown diffusion to be a flat or decreasing function of n. By accounting for effect of density on charge susceptibility we show that, in p-type semiconductors, the regime we observe of increasing ambipolar diffusion is unique to heavy doping and low temperature, where both the holes and electrons are degenerate; in this regime the electronic and ambipolar diffusion are nearly equal. The saturation is identified as a crossover to ambipolar diffusion dominated by the majority carriers, the holes. At short times the transient-grating signal rises gradually. This rise reveals cooling of hot electrons and, at high photocarrier density, allows us to measure ambipolar diffusion of 110 cm 2 /s in the hot-carrier regime.

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“…Here, F j ͑͒ = ͐ 0 ϱ ͓x j / exp͑x − ͒ +1͔dx is the jth order Fermi integral and is evaluated numerically. 7 N, m d , and m refer to number of conduction valleys, density of states ͑DOS͒ effective mass, and conductivity effective mass, intrinsic to the material. D and a are the electron gas dimensionality factor ͑D =3,2,1 for bulk material, quantum well, and nanowire͒ and relevant length scale ͑e.g., quantum well/nanowire thick-ness͒ pertinent to the device under consideration, respectively.…”

Section: ͑4͒mentioning

confidence: 99%

The optimal Seebeck coefficient for obtaining the maximum power factor in thermoelectrics

Pichanusakorn

Bandaru

2009

Applied Physics Letters

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We propose the existence of an optimal Seebeck coefficient ͑S opt ͒ for three-, two-, and one-dimensional thermoelectric materials. This assertion is supported by an exhaustive comparison with experimental data of well characterized bulk thermoelectrics, all of which have shown that the power factor is maximized when S opt in the range of 130-187 V / K. Our study serves as a quick guideline for the optimization of thermoelectric materials, and makes the point that efforts should be focused on increasing the electrical conductivity ͑͒ at the given S opt .

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The accurate numerical evaluation of half‐order Fermi‐Dirac Integrals

Cited by 25 publications

References 14 publications

High thermoelectric power factor in two-dimensional crystals ofMoS2

High thermoelectric power factor in two-dimensional crystals ofMoS2

Diffusion of degenerate minority carriers in a p-type semiconductor

The optimal Seebeck coefficient for obtaining the maximum power factor in thermoelectrics

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