Thermal Conductivity of N-Type Si-Ge
- PDF / 513,752 Bytes
- 8 Pages / 420.48 x 639 pts Page_size
- 23 Downloads / 199 Views
THERMAL CONDUCTIVITY OF N-TYPE Si-Ge
PAUL G. KLFMENS University of Connecticut, Institute of Materials Science, Storrs, CT 06269-3136
ABSTRACT The lattice thermal conductivity of 80-20 Si-Ge is treated theoretically for the case of the Fermi energy positioned for optimum figure of merit. The spectral distribution of the lattice conductivity is limited by anharmonic interactions, by the randomness of the Si-Ge lattice and, at low frequencies, by the interaction with free carriers and neutral donors. The two latter processes dominate over grain boundary scattering. The spectral conductivity is sharply peaked around 0.1 of the Debye frequency. A further reduction in lattice conductivity can be obtained by small insulating inclusions. This is partially offset by a reduction in electronic conductivity, but results in some improvement in the figure of merit. INTRODUCTION Thermoelectric materials for energy conversion require a large Seebeck coefficient and a low ratio of thermal to electrical conductivity. The coefficient of performance, which should be maximised, and which determines the conversion efficiency as fraction of the Carnot efficiency, is ZT = S 20T()e+X)- = (S 2/L)(1+ -A /A e) where S is the Seebeck coefficient, a- the electrical conductivity, T the absolute temperature, while ?e' are the electronic and lattice components of the thermal conductivity. The Lorenz ratio L is defined by
L =
ee/(7 T
(2)
In a solid which conducts electricity, one can at any temperature regard the conductivity to be made up of contributions from electrons of different energies E, so that 0- = Id-(E)(dfo/dE) dE
(3)
Here 0r(E) is the product of the density of states and mobility as function of E, and dfu/dE is the derivative of the FermiDirac distribution function f=
exp(E -)/kT
+ i]-1
(4)
where S is the Fermi energy, k the Boltzmann constant. The integrand in (3) peaks at an energy of order kT from the band edge. )/kT, and define One can introduce a reduced energy 9 =(Emoments of the conductivity integral Mat. Res. Soc. Symp. Proc. Vol. 234. 01991 Materials Research Society
88
Mn = f7(E)(df°/dE) En dE
(5)
one can then show [i] that
(6)
S = (k/e) M1 /M0 and
L = (k/e)2[M2/M
- (MI/M
2
0
) ]
(7)
Thus M1 /M0 depends on the position of ; with respect to the band edge and is the mean energy of conduction, in units of kT,, measured from S. The Lorenz ratio L depends on the second momeni of the 'conductivity integral about that mean; thus M0-(MI/M0) -A has a value ranging from 1 to 3. If it were not for the parasitic lattice conductivity Ag, ZT would increase the further the Fermi energy ! were moved from the band edge, even though this would lower both or andl. However, ?g is often larger than -A e, in which case ZT S 2aT/X g $= (8) erefore, to increase ZT one aims to maximize the power factor S o and to minimize 'kg. There is an optimum carrier concentration to maximize the power factor; correspondingly % should lie close to the band edges just above it at low T, which would place it just below the band edge at hi
Data Loading...
