Temperature dependence of the band parameters of bismuth

Vecchi, M.P.; Dresselhaus, M. S.

doi:10.1103/physrevb.10.771

Cited by 120 publications

(57 citation statements)

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“…5 The T point effective-mass values are not expected to have a strong temperature dependence. 6 The valence band at the T point is well approximated by a parabolic dispersion relation:…”

Section: ͑1͒mentioning

confidence: 99%

“…3 is characterized by its effective-mass tensor The L point band structure, in contrast to that of the T point, has a strong temperature dependence for temperatures above 80 K due to coupling between the nonparabolic L point valence and conduction bands. 6,8 As a result, the L point effective-mass components have been found to vary with temperature approximately according to the empirical relation As noted above, the L point valence and conduction bands are very strongly coupled due to the small band gap between them ͓E gL = 36 meV at 300 K ͑Ref. 6͔͒, and a parabolic dispersion relation is therefore not appropriate.…”

Section: ͑1͒mentioning

confidence: 99%

“…The L point band gap and the L-T band overlap have been estimated to be E gL = 36 meV and E 0 = 98 meV, respectively, but since only one study measures these values, it is not clear how accurate these values are. 6 Since the value of E gL is likely to be more accurate than the value of E 0 , we will use the published value of E gL = 36 meV, and we will find E 0 using our model.…”

Section: ͑16͒mentioning

confidence: 99%

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Indirect L to T point optical transition in bismuth nanowires

Levin

Black²,

Dresselhaus

2009

Phys. Rev. B

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An indirect electronic transition from the L point valence band to the T point valence band has been previously observed in Bi nanowires oriented along the ͓0112͔ crystalline direction ͑used by Black et al. and by Reppert et al.͒ but not in ͓1120͔-oriented nanowires ͑used by Cornelius et al.͒ or in bulk bismuth. Here we measure the Bi nanowire samples from each of these prior experimental studies on the same Fourier transform infrared apparatus, confirming that the differences are indeed physical and are not associated with the experimental setup. We develop an analytical model for the threshold energy of the indirect L to T point valence-band transition that takes as parameters the nanowire diameter and crystalline orientation. Our model shows good agreement with experimental results, and demonstrates that the nonparabolic nature of the L point bands is essential for calculating the energy of this transition. Finally, we propose a mechanism based on symmetry lowering to explain why this indirect transition is observed for ͓0112͔-oriented but not for ͓1120͔-oriented nanowires.

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“…5 The T point effective-mass values are not expected to have a strong temperature dependence. 6 The valence band at the T point is well approximated by a parabolic dispersion relation:…”

Section: ͑1͒mentioning

confidence: 99%

Section: ͑1͒mentioning

confidence: 99%

Section: ͑16͒mentioning

confidence: 99%

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Indirect L to T point optical transition in bismuth nanowires

Levin

Black²,

Dresselhaus

2009

Phys. Rev. B

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“…As noted earlier, according to band structure parameters [17], the position of the scattering onset ! is too low to derive from a direct interband process.…”

Section: Prl 99 016406 (2007) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Charge Carrier Interaction with a Purely Electronic Collective Mode: Plasmarons and the Infrared Response of Elemental Bismuth

et al. 2007

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We present a detailed optical study of single-crystal bismuth using infrared reflectivity and ellipsometry. Large changes in the plasmon frequency are observed as a function of temperature due to charge transfer between hole and electron Fermi pockets. In the optical conductivity, an anomalous temperature dependent midinfrared absorption feature is observed. An extended Drude model analysis reveals that it can be connected to a sharp upturn in the scattering rate, the frequency of which exactly tracks the temperature dependent plasmon frequency. We interpret this absorption and increased scattering as direct optical evidence for a charge carrier interaction with a collective mode of purely electronic origin, here electron-plasmon scattering. The observation of a plasmaron as such is made possible only by the unique coincidence of various energy scales and exceptional properties of semimetal bismuth. DOI: 10.1103/PhysRevLett.99.016406 PACS numbers: 71.45.ÿd, 78.20.ÿe, 78.30.ÿj, 78.40.Kc Elemental semimetals, such as graphite and bismuth, are materials of much long term interest due to their exceptional properties, including large magnetoresistive and pressure dependent effects [1][2][3]. In the case of bismuth, these properties derive from its low carrier number ( 10 ÿ5 electrons per atom), reduced effective masses ( 10 ÿ2 electron masses), small Fermi wave vector ( 40 nm), and long mean free path ( 0:1 mm).A number of recent results are causing an increased interest in these materials, both from the side of fundamental solid-state physics as well as applications potential. For instance, field dependent crossovers reminiscent of a metal-insulator transition have been observed in both graphite and bismuth [4,5]. Isolated single layers of graphene have been shown to have novel transport properties and an anomalous quantization of the quantum Hall effect resulting from their exceptional zero mass Dirac cone dispersion relation [6,7]. Moreover, there continues to be interest in bismuth for quantum confinement studies [8]. On the technical side, advances in film growth [9], anomalously long spin diffusion lengths, and very large magnetoresistive response make bismuth useful for possible incorporation in nanomagnetometers, magnetooptical devices, and spintronics applications [10,11].In principle, transport phenomena in bismuth should be well described by the conventional metals theory, but due to the exceptionally low Fermi energy, effective masses and charge densities there are substantial departures from standard metallic behavior. Moreover, the material's very low carrier density opens up the possibility for novel plasmonic effects and strong electron-electron interactions due to the relative scales between potential and kinetic energy at low charge densities [12].In this Letter, we present detailed temperature dependent optical measurements over the full optical range from farinfrared (FIR) to UVof single-crystal bismuth. We observe a narrow Drude peak and a plasmon energy consistent with the low carrier number...

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“…In reality, the electronic energy dispersion at the L points for bulk Bi is highly nonparabolic and temperature dependent. 19,20 However, at the optimal structure of the superlattice, the energy for the lowest conduction subband edge is always higher than the Fermi energy of bulk Bi (E F e ϭ23 meV͒, and in this energy range the mass variations with respect to energy and temperature are relatively weak. Therefore, the values given above, which correspond to the effective mass tensor at the Fermi energy of bulk bismuth at low temperatures, are a conservative approximation for the values of the effective mass tensor components of the lowest conduction subband of the superlattice.…”

Section: -28mentioning

confidence: 99%

Thermoelectric figure of merit ofBi/Pb1−xEu<

2000

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An enhanced thermoelectric figure of merit Z 3D T is predicted for Bi/(111)Pb 1Ϫx Eu x Te superlattices. The values of Z 3D T obtained for xϷ1 superlattices are 2.31, 1.55, and 1.61 at 300, 150, and 77 K, respectively, showing that they are promising candidates for thermoelectric elements in the temperature range 77-300 K.Even with x as small as 0.1, where the conduction-band offset ⌬E c is estimated to be 0.25 eV, the predicted Z 3D T values are 1.75, 1.16, and 1.18 at 300, 150, and 77 K, respectively. It is proposed that other families of Bi-based superlattices, such as Bi/͑111͒CdTe superlattices, should also be good candidates for low-temperature thermoelectric elements.The use of superlattice structures to design useful thermoelectric materials with a large thermoelectric figure of merit ZT (ϭS 2 T/ , where S, , , and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively͒ has attracted significant interest in the thermoelectric materials community. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] The basic strategies for enhancing ZT using low-dimensional structures are based on ͑1͒ the use of an enhanced density of states for electrons ͑or holes͒ near the band edge to increase the magnitude of the Seebeck coefficient ͉S͉ at a given carrier concentration and ͑2͒ the use of increased boundary scattering of phonons at the quantum well-barrier interfaces in the superlattice to reduce the lattice thermal conductivity ph relative to the bulk values. 11,16 Recently, the original proposal by Hicks et al. 7,11,13,16 has been extended to more realistic systems, such as GaAs/AlAs ͑Refs. 1-3͒ and Si/Ge ͑Refs. 1,4͒ short-period superlattices, and an enhanced threedimensional figure of merit (Z 3D T) for the whole superlattice was predicted relative to the ZT's for the corresponding bulk materials.The key strategy for the successful design of thermoelectric materials using a superlattice structure is to find materials with highly anisotropic constant energy surfaces for the quantum well layers and materials for the barrier layers that are chemically ͑and structurally͒ compatible with the quantum well material and have large values for the energy band gaps to provide sufficient conduction-and valence-band offsets for the superlattices. Bismuth ͑Bi͒ is a semimetal that has various unique properties, such as a highly anisotropic Fermi surface, large electron and hole mobilities, and a small lattice thermal conductivity. [17][18][19][20][21] These features of Bi make it potentially a very desirable material for thermoelectric applications, especially in its semiconducting form. 7,8,17 A semimetal-semiconductor transition in Bi has been predicted and experimentally demonstrated using low-dimensional structures, such as quantum wells and wires. [22][23][24][25] The twodimensional nature of the electron transport in Bi/͑111͒PbTe superlattices has also been reported experimentally. [26][27][28] Here we report a theoretical investigation of the thermoelectric p...

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Temperature dependence of the band parameters of bismuth

Cited by 120 publications

References 7 publications

Indirect L to T point optical transition in bismuth nanowires

Indirect L to T point optical transition in bismuth nanowires

Charge Carrier Interaction with a Purely Electronic Collective Mode: Plasmarons and the Infrared Response of Elemental Bismuth

Thermoelectric figure of merit ofBi/Pb1−xEu<

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