Semiconductor-Metal Transition in Many-Valley Semiconductors

Charge degeneracy removal in the screened hydrogen atom

“…The finite number of states, which makes Z finite, is crucial for obtaining simple and analytical results, as well as to avoid lengthy calculations. Finally, the concept of screening is one of those ideas present in many applications such as semiconductors [51,52], metal-insulator transition [25][26][27][28][29], molecules [53], polymers [24], hydrogen under pressure [54][55][56] and almost all branches of solid state physics [1]. In particular, the old concept of Mott transition is still an active, broad and modern subject in physics [29].…”

“…We then denote the Thomas-Fermi parameter by q = (6πe 2 N /k B T f ) 1/2 , where k B and T f are the Boltzmann constant and the Fermi temperature, respectively. It is not surprising that many attempts to find accurate numerical solutions for this potential have been reported [24][25][26][27][28][29]. However it is still physically unclear how the screening phenomenon effectively occurs for the excited states of atomic structures where one has noted that a simplified and systematic analytical model is almost entirely absent.…”

Metal–insulator transition in many valley semiconductors in the spirit of the Hubbard model

“…Unlike the Thomas -Fermi function, which is strictly valid only in the long-wavelength limit, the Hartree function is valid at all values of k: The longwavelength part of the function in the potential energy term is separated here and the rest of the k-dependent part is used to renormalize the mass of the electron. This renormalization is similar to the mass enhancement in Fermi liquid theory in metals [17].…”

“…Note that Cð rÞ reduces to the hydrogenic ground state as l ! 0: Recently using renormalized Thomas -Fermi theory for the Mott transition in the absence of electron -electron interactions was found [17] and obtained the value of Mott constant as a p N 1=3 c ¼ 0:36n 21=3 : The values of Mott constant are 0.20 and 0.23 for Si and Ge, respectively [17].…”

“…When the different impurities are distributed randomly, with the effect on the potential seen by the carrier, Anderson localization comes into play [16]. Choosing the origin of coordinates at the position of an impurity, it is chosen for the probability of finding another impurity at r i as in an earlier work [17] a distribution of impurities given by Pðr i Þ ¼ A expð2ar i Þ was assumed and the impurity potential…”