Same maximum figure of merit ZT(=1), due to effects of impurity size and heavy doping, obtained in the n(p)type degenerate GaAscrystal (\mathbf{\xi}_{\mathbf{n}(\mathbf{p})}(\geqq\mathbf{1})), at same reduced Fermi energy \mathbf{\xi}_{\mathbf{n}(\mathbf{p})}(=\mathbf{1}.\mathbf{813}) and same minimum (maximum) Seebeck coefficient \mathbf{Sb}\left(=\left(\mp\right)\mathbf{1}.\mathbf{563}\times{\mathbf{10}}^{\mathbf{4}}\frac{\mathbf{V}}{\mathbf{K}}\right), at which same \bigm\left(\mathbf{ZT}\
DOI: 10.54647/physics140532 11 Downloads 272 Views
Author(s)
H. Van Cong, Université de Perpignan Via Domitia, Laboratoire de Mathématiques et Physique (LAMPS), EA 4217, Département de Physique, 52, Avenue Paul Alduy, F66 860 Perpignan, France.
Abstract
In our two previous papers [1, 2], referred to as I and II. In I, our new expression for the extrinsic static dielectric constant, \varepsilon\left(r_{d\left(a\right)}\right), r_{d\left(a\right)} being the donor (acceptor) d(a)radius, was determined by using an effective Bohr model, suggesting that, for an increasing r_{d\left(a\right)}, \varepsilon\left(r_{d\left(a\right)}\right), due to such the impurity size effect, decreases, and affecting strongly the critical impurity density in the metalinsulator transition and also various majority carrier transport coefficients given in the n(p)type degenerate GaAscrystal, defined for the reduced Fermi energy \mathbf{\xi}_{\mathbf{n}(\mathbf{p})}(\geqq\mathbf{1}). Then, using the same physical model and same mathematical methods and taking into account the corrected values of energybandstructure parameters, all the numerical results, obtained in II, are now revised and performed, giving rise to some important concluding remarks, as follows. (1) The critical donor(acceptor)density, N_{CDn\left(NDp\right)}(r_{d(a)}), determined in Eq. (3), can be explained by the densities of electrons (holes) localized in exponential conduction (valance)band (EBT) tails, N_{CDn\left(CDp\right)}^{EBT}(r_{d(a)}), given in Eq. (21). (2) In Tables 911, for a given d(a)density N [\geq2N_{CDn\left(NDp\right)}(r_{d(a)})] one notes here that with increasing temperature T(K): (i) for reduced Fermi energy \xi_{n(p)}(=1.813), while the numerical results of the Seebeck coefficient Sb present a same minimum (maximum) \left(=\left(\mp\right)1.563\times{10}^{4}\frac{V}{K}\right), those of the figure of merit ZT show a same maximum ZT\left(=\mathbf{1}\right), (ii) for \xi_n=1, those of Sb and ZT present same results: Sb\left(=\left(\mp\right)1.322\times{10}^{4}\frac{V}{K}\right) and 0.715, respectively, (iii) for \xi_{n(p)}=1.813 and \xi_{n(p)}=1, those of the wellknown Mott figure of merit give same \left(ZT\right)_{Mott}=\frac{\pi^2}{3\times\xi_{n(p)}^2}(\simeq1 and 3.290), respectively, and finally, (iv) we show here that in the degenerate semiconductor, the WiedemannFrank law, given in Eq. (25a), is found to be exact.
Keywords
Effects of the impuritysize and heavy doping; effective autocorrelation function for potential fluctuations; optical, electrical, and thermoelectric properties; figure of merit; WiedemannFranz law
Cite this paper
H. Van Cong,
Same maximum figure of merit ZT(=1), due to effects of impurity size and heavy doping, obtained in the n(p)type degenerate GaAscrystal (\mathbf{\xi}_{\mathbf{n}(\mathbf{p})}(\geqq\mathbf{1})), at same reduced Fermi energy \mathbf{\xi}_{\mathbf{n}(\mathbf{p})}(=\mathbf{1}.\mathbf{813}) and same minimum (maximum) Seebeck coefficient \mathbf{Sb}\left(=\left(\mp\right)\mathbf{1}.\mathbf{563}\times{\mathbf{10}}^{\mathbf{4}}\frac{\mathbf{V}}{\mathbf{K}}\right), at which same \bigm\left(\mathbf{ZT}\, SCIREA Journal of Physics. Vol.
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, No.
2
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2023
, pp.
133

157
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https://doi.org/10.54647/physics140532
References
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