Thermoelectric power factor of nanoporous semiconductors

Journal of Applied Physics

Volumn 101, Issue 1, 2007, Pages

  Mingo, N ^a   Broido, D A ^b  

^a NASA Ames Center for Nanotechnology   (United States)

^b BOSTON COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BULK EFFECTIVE MASS; NANOPOROUS MATRIX MATERIALS; PARABOLIC BAND MATERIALS; THERMOELECTRIC POWER FACTOR;

ELECTRIC POWER GENERATION; OPTIMIZATION; POROUS MATERIALS; SEMICONDUCTOR MATERIALS; THERMAL CONDUCTIVITY; THERMOELECTRIC POWER PLANTS;

NANOSTRUCTURED MATERIALS;

EID: 33846273114     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2405232     Document Type: Article

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9. These relations are directly obtained from the Schrödinger equation with infinite barrier boundary conditions. They are strictly valid only if the confining potential is infinite outside the material. A proof goes as follows: inside the material, the wave function corresponding to the set of quantum numbers α, with kz =0 satisfies Eα ψα = (2 2 m⊥) (2 x2 + 2 y2) ψα, subject to the condition ψ=0 at the pore boundaries. Trivially, for a material with different effective mass, m⊥′ and the same pore size and aspect ratio, the energy of the corresponding state α changes as E′ = m⊥ m⊥′ E. Substituting this in the definition of ρ 2D, Eq., one obtains Eq.. A change in the pore separation, d, keeping the aspect ratio dδ constant, is analogous to a change in length units. Let ψ be the wave function corresponding to the case with pore separation d, and ψ′ be the one with pore separation d′. At any point inside the material (excepting the pores) the wave function satisfies Eα = (2 2 m⊥) [(2 l x2 + 2 y2) ψα] ψα. Since the wave functions in the d and d′ cases are related by ψα (x, y) ψ′ α (x d′ d, y d′ d), this implies that their energies are related as Eα′ = (d d′) 2 Eα. Substituting this into Eq. and taking into account the change in the Brillouin zone size, one obtains Eq..
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