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Semiconductors have been the subject of very extensive research over recent decades, because of ever more numerous and powerful applications. As conventional electronics, semiconductors are more appropriate than normal metals, since metal devices do not amplify current. Because of the complementary properties of semiconductor and ferromagnetic material systems, a growing effort is directed toward studies of semiconductor-magnetic nanostructures [1, 2].
Semiconductors and magnetic materials both play essential roles in modern electronic industry. Since the applications of semiconductors and magnetic have evolved independently, it appears logical to combine their properties for possible spin-electronic applications with increased functionalities [3]. This is known as spintronics, which utilizes both charge and spin of the electrons to process and store data. This is to control the spin degree of freedom of electrons in semiconductors. The direct method to introduce spin degrees of freedom in semiconductors is to introduce magnetic ions into semiconductors. Such semiconductors are referred to as diluted magnetic semiconductors (DMSs) [4]. The curie temperature of the DMS material and whether the ferromagnetism in the DMS material originates from free carrier mediation or purely from localized magnetic dopants limit DMS practical applications for devices [5].
For practical applications, increasing
For the ferromagnetic transition to occur in
The carrier-mediated spin–spin coupling is usually described in terms of the Ruderman-Kittel-Kasuya-Yosida (RKKY) model, which provides the energy
Where
Where
The interaction of localized spin
Where
Where
Where
Where
Eq. (7) can be considered as the matrix element of the operator
To determine the exchange coupling strength
Replacing the sum in Eq. (9) by an integral, using the quadratic dispersion relation valid for free electrons and the notations
Then the effective exchange interaction or the coupling exchange interaction constant between magnetic impurities and delocalized charge carriers is given by
Where
By using Eq. (11), we can determine the relaxation time
A better approximation can be obtained for the transition probability by replacing the matrix element of the scattering matrix
The scattering (transition) probability in Eq. (13) can be expressed in terms of the interaction Hamiltonian up to third order in the coupling constant. Then using the second-order correction to the
If the impurity spin goes over from the initial state
The first term in Eq. (15) is negligible since it is small; however, the second term is no longer small. The second term diverges logarithmically. Using this form, the transition probability Eq. (13) in
Where
We shall investigate the dependence of Eq. (16) on the energy of the initial state
By using Fermi-Dirac distribution,
Where
Then substituting Eq. (16) into collision integral, the relaxation time
The Fermi energy
In the presence of external perturbation due to the electric field or temperature gradient, there is a variation in the function
Then from standard theory, we can easily obtain the resistivity as
Where
Where V is the volume of the crystal. Then using some techniques, the total electrical resistivity becomes
Since substitutional
As mentioned in Section 2, the temperature dependence of electrical resistivity is calculated. The electrical resistivity of p-type
Electrical resistivity is the inverse of electrical conductivity of the material. The electrical resistivity of semiconductors decreases exponentially with increasing temperature in contrast to that of pure metals. The electrical resistivity of extrinsic semiconductor is decreased with increasing both the concentration of magnetic impurity and the temperature. From this concept the electrical resistivity of DMSs, in which magnetic impurities are incorporated into standard semiconductors, is decreased with temperature and concentration of magnetic ions. The temperature dependence of resistivity in
Electrical resistivity of
In this paper, we studied the theoretical temperature dependence of electrical resistivity of DMS specifically
First of all, I would like to thank the almighty God for keeping me safe and continually blessing me in all aspects of my life. I extend my heartful thanks to my parents for their encouragement and support both morally and psychologically.
The authors declare no conflicts of interest.
No data were used to support this study.
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\n\nThe Open Access Publishing Fee (OAPF) is payable only after your book chapter, monograph or journal article is accepted for publication.
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\n\nDuring the launching phase journals do not charge an APC, rather they will be funded by IntechOpen.
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