PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH

The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.

Zero-Magnetic-Field Spin Splitting of Polaron＇s Ground State Energy Induced by Rashba Spin-Orbit Interaction

We study theoretically the ground state energy of a polaron near the interface of a polar-polar semiconductor by considering the Rashba spin-orbit （SO） coupling with the Lee-Low-Pines intermediate coupling method. Our numerical results show that the Rashba SO interaction originating from the inversion asymmetry in the heterostructure splits the ground state energy of the polaron. The electron area/density and vector dependence of the ratio of the SO interaction to the total ground state energy or other energy composition are obvious. One can see that even without any external magnetic field, the ground state energy can be split by the Rashba SO interaction, and this split is not a single but a complex one. Since the presents of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the polaron are more stable than electron＇s.

Graphene as Gas Sensors

The triatomic and tetratomic gas molecule adsorption effects on the electrical conductivity of graphene areinvestigated by the tight-binding model,Green’s function method,and coherent potential approximation.We find thatthe electrical conductivity of graphene sheet is sensitive to the adsorption of these gases.

Low Frequency Dispersion Law for Two-Dimensional Metallic Photonic Crystals

Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic （EM） waves in two dimensional dielectric photonic crystals （PCs） and metallic photonic crystals （MPCs） in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation （CPA）, which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.

Ionization in an intense field considering Coulomb correction

We derive a simple ionization rate formula for the ground state of a hydrogen atom in the velocity gauge under the conditions：ω〈〈1 a.u.（a.u.is short for atomic unit） and γ〈〈1（ω is the laser frequency and y is the Keldysh parameter）.Comparisons are made among the different versions of the Keldysh-Faisal-Reiss（KFR） theory.The numerical study shows that with considering the quasi-classical（WKB） Coulomb correction in the final state of the ionized electron,the photoionization rate is enhanced compared with without considering the Coulomb correction,and the Reiss theory with the WKB Coulomb correction gives the correct result in the tunneling regime.Our concise formula of the ionization rate may provide an insight into the ionization mechanism for the ground state of a hydrogen atom.

A modified simplified coherent potential approximation model of band gap energy of III-V ternary alloys

Based on the modification of the simplified coherent potential approximation （SCPA）, a model is developed to calculate the composition dependence of the band gap energy of Ⅲ-V ternary alloys with the same anion. The derived equation is used to fit the experimental band gap energy of InxAl1-xN, InxGa1-xN and A1xGal xN with x from 0 to 1. It is found that the fitting results are better than those done by using SCPA. The fitting results are also better than those obtained by using the formula with a small bowing coefficient, especially for InxAl1-xN. In addition, our model can also be used to describe the composition de- pendence of band gap energy of other Ⅲ-V ternary alloys.

A surface potential-based non-charge-sheet core model for undoped surrounding-gate MOSFETs

A surface potential based non-charge-sheet core model for cylindrical undoped surrounding-gate （SRG） MOSFETs is presented. It is based on the exact surface potential solution of Poisson＇s equation and Pao-Sah＇s dual integral without the charge-sheet approximation, allowing the SRG-MOSFET characteristics to be adequately described by a single set of the analytic drain current equation in terms of the surface potential evaluated at the source and drain ends. It is valid for all operation regions and traces the transition from the linear to saturation and from the sub-threshold to strong inversion region without fitting-parameters, and verified by the 3-D numerical simulation.

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation(CPA)within full counting statistics(FCS)formalism is shown to be a suitable method to investigate average electric conductance,shot noise as well as higher order cumulants in disordered systems.We develop a similar FCS-CPA formalism for phonon transport through disordered systems.As a byproduct,we derive relations among coefficients of different phonon current cumulants.We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders.For binary disorders as well as Anderson disorders,we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method.The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio.Collective features of phonon current cumulants are also revealed.

From parabolic approximation to evanescent mode analysis on SOI MOSFET

Subthreshold conduction is governed by the potential distribution. We focus on full two-dimensional（2D） analytical modeling in order to evaluate the 2D potential profile within the active area of Fin FET structure.Surfaces and interfaces, which are key nanowire elements, are carefully studied. Different structures have different boundary conditions, and therefore different effects on the potential distributions. A range of models in Fin FET are reviewed in this paper. Parabolic approximation and evanescent mode are two different basic math methods to simplify the Poisson＇s equation. Both superposition method and parabolic approximation are widely used in heavily doped devices. It is helpful to learn performances of MOSFETs with different structures. These two methods achieved improvement to face different structures from heavily doped devices or lightly doped devices to junctionless transistors.