By Emilio Scalise
Ge and III–V compounds, semiconductors with excessive provider mobilities, are applicants to interchange Si because the channel in MOS units. 2nd fabrics – like graphene and MoS_2 – also are expected to exchange Si within the future.
This thesis is dedicated to the first-principles modeling of the vibrational homes of those novel channel materials.
The first a part of the thesis makes a speciality of the vibrational homes of varied oxides on Ge, making it attainable to spot the vibrational signature of particular defects which may bog down the correct functioning of MOSFETs.
The moment a part of the thesis studies at the digital and vibrational homes of novel 2nd fabrics like silicene and germanene, the Si and Ge 2nd opposite numbers of graphene. The interplay of those 2nd fabrics with metal and non-metallic substrates is investigated. It was once expected, for the 1st time, and later experimentally proven, that silicene will be grown on a non-metallic template like MoS_2, a leap forward which may open the door to the prospective use of silicene in destiny nanoelectronic devices.
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Extra info for Vibrational Properties of Defective Oxides and 2D Nanolattices: Insights from First-Principles Simulations
Example text
The ingenuity of the method developed by Kohn–Sham (KS) consists in the formulation of the Hohenberg–Kohn universal functional in two separated terms for the independent particle Kinetic energy and the Hartree one, including the remaining entities in an exchange-correlation functional E xc [n] (which can reasonably be approximated as a local functional of the density). 21) The exact ground state density of a N-electrons system which minimizes the universal functional of Eq. 23) with HK S that can be expressed as: HK S = Ts + VH ar tr ee + Vext + Vxc .
36) LR Thus, the Coulomb potential is substituted with a screened potential by using the error function in Eq. 36, since it leads to computational advantages in evaluating the short range HF exchange integrals [20]. Numerical tests indicate that the HF and PBE LR exchange contributions to the functional in Eq. 35 are rather small and tend to cancel each other. One can neglect these terms, obtaining the HSE hybrid density functional in the form: H SE = a E xH F,S R (ω) + (1 − a)E xP B E,S R (ω) + E xP B E,L R (ω) + E cP B E .
15, one can satisfy the condition of minimum ground state energy by using the Lagrange multiplier εi [3, 4]. The resulting expression in the form of eigenvalue equations, called Hartree–Fock equations, is: − 2 2m N /2 2 i e2 |ψ j (r )|2 dr |r − r | + Ven (r) + 2 j=1 h(r) N /2 − j=1 ψi (r) Vc (r) e2 ψ ∗j (r )ψi (r ) |r − r | Vx (r) dr ψ j (r) = εi ψi (r). 1 Methods for Electronic Structure Calculation 15 Fig. 2 Self consistent field method In fact, this equation is the one electron SE in which the electron interaction potential (Vee (ri , rj )) is replaced by the self-consistent (or Hartree) potential (r) which contains the Coulombic potential (Vc ) from all electrons (with both spin directions) and the exchange potential from all electrons with same spin (Vx ).