Naomi Hirayama

Linking probabilities of off-lattice self-avoiding polygons and the effects of excluded volume

We evaluate numerically the probability of linking, i.e. the probability of a given pair of self-avoiding polygons (SAPs) being entangled and forming a nontrivial link type L. In the simulation we generate pairs of SAPs of N spherical segments of radius rd such that they have no overlaps among the segments and each of the SAPs has the trivial knot type. We evaluate the probability of a self-avoiding pair of SAPs forming a given link type L for various link types with fixed distance R between the centers of mass of the two SAPs. We define normalized distance r by where denotes the square root of the mean square radius of gyration of SAP of the trivial knot 01. We introduce formulae expressing the linking probability as a function of normalized distance r, which gives good fitting curves with respect to χ2 values. We also investigate the dependence of linking probabilities on the excluded-volume parameter rd and the number of segments, N. Quite interestingly, the graph of linking probability versus normalized distance r shows no N-dependence at a particular value of the excluded volume parameter, rd = 0.2.

First-Principles Study on Structural and Thermoelectric Properties of Al- and Sb-Doped Mg2Si

We theoretically investigate the structural and thermoelectric properties of magnesium silicide (Mg2Si) incorporating Al or Sb atoms as impurities using first-principles calculations. We optimized the structural properties through variable-cell relaxation using a pseudopotential method based on density functional theory. The result indicates that the lattice constant can be affected by the insertion of impurity atoms into the system, mainly because the ionic radii of these impurities differ from those of the matrix constituents Mg and Si. We then estimate, on the basis of the optimized structures, the site preferences of the impurity atoms using a formation energy calculation. The result shows a nontrivial concentration-dependence of the site occupation, such that Al tends to go into the Si, Mg, and interstitial sites with comparable formation energies at low doping levels (<2 at.%); it can start to substitute for the Mg sites preferentially at higher doping levels (<4 at.%). Sb, on the other hand, shows a strong preference for the Si sites at all impurity concentrations. Furthermore, we obtain the temperature-dependence of the thermoelectromotive force (Seebeck coefficient) of the Al- and Sb-doped Mg2Si using the full-potential linearized augmented-plane-wave method and the Boltzmann transport equation.

Theoretical analysis of structure and formation energy of impurity-doped Mg2Si: Comparison of first-principles codes for material properties

We theoretically investigate the impurity doping effects on the structural parameters such as lattice constant, atomic positions, and site preferences of impurity dopants for Al-doped magnesium silicide (Mg2Si) crystal using the first-principles calculation methods. We present comparison between several codes: ABCAP, Quantum Espresso, and Machikaneyama2002 (Akai KKR), which are based on the full-potential linearized augmented plane-wave method, the pseudopotential method, and KKR/GGA Greens function method, respectively. As a result, any codes used in the present study exhibit qualitative consistency both in the dependence of the lattice constants on the doping concentration and the energetic preference of the Al atom for the following sites; substitutional Si and Mg sites, and interstitial 4b site; in particular, ABCAP, which is based on the all-electron full-potential method, and Quantum Espresso, which is a code of the pseudopotential method, produce closely-resemble calculation results. We also discuss the effects of local atomic displacement owing to the presence of impurities to the structural parameters of a bulk. Using the analytical method considering the local atomic displacement, moreover, we evaluate the formation energy of Na- and B-doped systems as examples of p-type doping in order to examine the possilbility of realizing p-type Mg2Si.

Comparison between theoretical and experimental results for energy states of two-dimensional electron gas in pseudomorphically strained InAs high-electron-mobility transistors

The energy states of a two-dimensional electron gas (2DEG) in high-electron-mobility transistors with a pseudomorphically strained InAs channel (PHEMTs) were analyzed rigorously using a recently established theory that takes into account the nonparabolicity of the conduction band of the channel layer. The sheet density of the 2DEG in InxGa1−xAs-PHEMTs and the drain I–V characteristics of those devices were calculated theoretically and compared with the density and characteristics obtained experimentally. Not only the calculated threshold voltage (VTH) but also the calculated transconductance agreed fairly well with the corresponding values obtained experimentally. When the effects of the compositions of the InxGa1−xAs subchannel layer in the composite channel and the channel layer on energy states of 2DEG were investigated in order to establish a guiding principle for a design of the channel structure in PHEMTs, it was found that VTH is determined by the effective conduction-band offset energy ΔEC between the InAlAs barrier and the channel layers.

Temperature distribution in nano-devices under a strong magnetic field

The thermoelectric and thermomagnetic phenomena of two-dimensional electron gases at low temperatures are numerically examined using the finite-difference method. The temperature and the voltage are calculated from transport equations describing thermoelectric and thermomagnetic effects. The results demonstrate that a magnetic field distorts equipotential lines and generates an uneven distribution of the temperature, which can cause inhomogeneous heating of experimental systems. In particular, a part of the system is found to be colder than the temperature of the heat baths.

Analysis of energy states of two-dimensional electron gas in pseudomorphically strained InSb high-electron-mobility transistors taking into account the nonparabolicity of the conduction band

We propose a high electron mobility transistor with a pseudomorphically strained InSb channel (InSb-PHEMT) having an InSb composite channel layer in which the Al y In1− y Sb sub-channel layer is inserted between the InSb channel and the Al x In1− x Sb barrier layers to increase the conduction-band offset (ΔE C) at the heterointerface between the InSb channel and the Al x In1− x Sb barrier layers. The energy states for the proposed InSb-PHEMTs are calculated using our analytical method, taking account of the nonparabolicity of the conduction band. For the proposed InSb-PHEMTs, putting the sub-channel layers into the channel is found to be effective for obtaining a sufficiently large ΔE C (~0.563 eV) to restrain electrons in the channel and increase the sheet concentration of two-dimensional electron gas to as high as 2.5 × 1012 cm−2, which is comparable to that of InAs-PHEMTs. This also leads to a large transconductance of PHEMTs. In the proposed InSb-PHEMTs, electrons are strongly bound to the channel layer compared with InAs-PHEMTs, despite the effective mass at the conduction band (0.0139 m 0) of InSb being smaller than that of InAs and ΔE C for the InSb-PHEMTs being 25% smaller than that for the InAs-PHEMTs. This is because the bandgap energy of InSb is about one-half that of InAs, and hence, the nonparabolicity parameter of InSb is about twice as large as that of InAs.

General Polygonal Length Dependence of the Linking Probability for Ideal Random Polygons

The linking probability that two closed random walks (i.e., random polygons: RPs) are mutually entangled, Plink, is investigated numerically quite accurately. Here, Plink is a function of the distance between two RPs, R, and the number of polygonal segments, N . In a previous paper, we numerically estimated Plink precisely in the wide region of 0 ≤ ξ ≤ 3.0 where ξ denotes the normalized distance, i.e., the ratio of R to the radius of gyration Rg : ξ = R/Rg. We have also shown that the N and R-dependence of Plink can be well approximated by a simple function: Plink(ξ;N) = exp (−κ1ξ1) − C exp (−κ2ξ2), where κ1, ν1, κ2, ν2 and C are fitting parameters which depend on N . In this paper we extract the general N -dependence of Plink. We evaluate numerically the five fitting parameters as functions of N , i.e., κ1(N), ν1(N), κ2(N), ν2(N) and C(N). Considering physical requirements of Plink, we impose constraints on these functions. By taking account of both the numerical data from N = 32 to 512 and the constraints, we propose good approximate functions of N for the above fitting parameters. We find that they are valid from N = 32 to 512. We expect that they should also be effective for approximating the linking probability at least in some region of N > 512, although it is not clear how effective it is for large values of N . This result enables us not only to estimate Plink for an arbitrary N at least roughly, but also to predict the possible asymptotic behavior of Plink at N = ∞.

Analysis of energy states where electrons and holes coexist in pseudomorphically strained InAs high-electron-mobility transistors

In strained high-electron-mobility transistors (HEMTs) with InAs as the channel, excess electrons and holes are generated in the drain region by impact ionization. In the source region, electrons are injected to recombine with accumulated holes by the Auger process. This causes the shift of the gate potential, V GS,shift, for HEMTs. For a system where electrons and holes coexist, we established a theory taking into account the nonparabolicity of the conduction band in the InAs channel. This theory enables us to rigorously determine not only the energy states and the concentration profiles for both carriers but also the V GS,shift due to an accumulation of holes. We have derived the Auger recombination theory which takes into account the Fermi–Dirac statistics and is applicable to an arbitrary shape of potential energy. The Auger recombination lifetime τA for InAs-PHEMTs was estimated as a function of the sheet hole concentration, p s, and τA was on the order of psec for p s exceeding 1012 cm−2.

Comparison between theoretical and experimental results for energy states of two-dimensional electron gas in pseudomorphically strained InAs-HEMTs

Comparison between theoretical and experimental results for energy states of the two-dimensional electron gas has been made for pseudomorphically strained InAs-HEMTs. Not only the threshold voltage but the transconductance of HEMTs calculated using the non-parabolic energy band model agreed fairly well with those obtained experimentally. In addition, the effect of composition of the InxGa1-xAs barrier layer on energy states of 2DEG was investigated. It was found that VTH does not depend on the structure of the buffer layer used.

Current-Induced Cooling Phenomenon in a Two-Dimensional Electron Gas Under a Magnetic Field

We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential ϕ and the temperature T in a 2DEG enclosed in a square area surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with ϕleft<ϕright and Tleft=Tright), using a pair of nonlinear Poisson equations (for ϕ and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.