Akira Hori

Optical absorption edge and photoluminescence spectra in amorphous and crystalline boron-rich solids

Optical absorption spectra for amorphous B, B 4 C and B 13 P 2 films are fitted by α h ω = A(h ω − E 0 ) n where n is not 2 but 3. Temperature dependence of the spectrum shows that the origin of n=3 may be linear densities of states at both band edges. Photoluminescence (PL) spectrum for β -rhombohedral boron has a peak at 1.14 eV and temperature independent broad width. This corresponds to recombination between a hole in the intrinsic acceptor level and an electron in the conduction band bottom or in the trapping level. Thermal quenching of the PL intensity is analyzed by two activation process, activation energies of which are 0.12 and 0.004 eV. The former may be escape process of hole or electron from the acceptor or the trapping level.

Optical properties of quasicrystalline approximant boron-rich solids

Abstract The photoluminescence (PL) spectrum of a single crystal of β -rhombohedral boron, which is a rhombohedral crystalline approximant of the icosahedral quasicrystal, has a peak around 1.14 eV. This is assumed to correspond to recombination between a hole in the intrinsic acceptor level originated from B 12 icosahedral cluster, and an electron in the highest trapping level. Thermal quenching of the PL intensity is analyzed by two activation processes, whose activation energies are 0.12 and 0.004 eV. The former is considered to be an escape process of an electron from the trapping level.

Absorption Edge Spectra of Boron-Rich Amorphous Films Constructed with Icosahedral Cluster

Optical absorption edge spectra of amorphous B, B 4 C and B 13 P 2 films, prepared by electron-beam deposition, were measured with a spectrophotometer in the wave length range of about 300∼700 nm. These were fitted by \(\alpha \hbar \omega =\)A\((\hbar \omega -E_{\rm opt})^{\rm n}\), where α , \(\hbar \omega\) , A and the constant E opt are the absorption coefficient, the photon energy, a constant and the optical gap energy, respectively. The exponent n was found to be 3 for the amorphous boron-rich films, though n was 2 for the usual amorphous semiconductors. From a comparison of the temperature dependence with that of crystalline β-rhombohedral boron (β- B ), the usual selection rule of indirect forbidden type transition did not hold in the amorphous solids of these boron-rich systems. Therefore the origin of n=3 was concluded to be the linear distribution of the densities of states. The value of the exponent n and the relatively small value of A were related to the complicated atomic and electronic str...

Selberg-Ihara's Zeta function for p-adic Discrete Groups

This chapter focuses on Selberg–Iharas zeta function for p -adic discrete groups. In [SeI], a zeta function Z Γ ( s ) has been introduced and proved to have many important properties that resemble those of usual L -functions, such as Euler product, functional equation, and analogue of Riemann hypothesis. This function, called with the name of Selberg, is generalized to any discrete subgroup Γ of a semi-simple Lie group of R -rank one. An analogue of Z Γ ( s ) was introduced by Ihara, for a cocompact torsion-free discrete subgroup Γ of PSL(2, K ) or PL(2, K ), where K is a p -adic field. The chapter presents an extension of Iharas results to the case when G is a semi-simple algebraic group over a p -adic field K and Γ is a discrete subgroup of G . The chapter discusses p -adic algebraic groups and the structure of the discrete subgroups Γ .

Crystalline structures as an approximant of quasicrystal and distortion of B12 icosahedron in boron-rich solids: Search for semiconducting quasicrystal

Abstract Analyzing the crystalline structure of α- and β-rhombohedral boron as an approximant structure of a quasicrystal, atomic structures of two unit cells (prolate and oblate rhombohedra) of icosahedral quasicrystal are constructed. According to molecular orbital calculation, a neutral B 12 H 12 icosahedral cluster is distorted to a cubic or rhombohedral type by the Jahn–Teller effect. The distortion of B 12 in the β-rhombohedral boron and K2B12H12 has the same sign as the lowest energy distortion in the calculation. Among the α-rhombohedral type structures, the distortion of B12 is correlated with the rhombohedral axis angle, and the angle is the closest to the icosahedral angle for B6O and the distortion is the smallest for B–C. A meta-stable phase has been found on the way towards crystallization of amorphous B–C films.

Photoluminescence Spectra of β-Rhombohedral Boron

We report the detailed features of the photoluminescence (PL) spectra of a single crystal of β-rhombohedral boron (β-B) in the range of 900–1700 nm (0.73–1.38 eV). Broad spectra whose peak energy was 1.14 eV were observed. The peak energy corresponds to the recombination of an electron in a trapping level with a hole in the intrinsic acceptor level, which is characteristic of β-B and originates from the unique electronic structure of an icosahedral cluster B 12 . Temperature dependence of the PL intensity indicates that there are two thermal escape processes of electrons whose activation energies are about 0.10 and 0.004 eV. The former is attributed to the escape process of an electron from the electron trapping level to the conduction band. These results agree with the proposed band structure model based on the electronic structure of B 12 . PL decay measurement shows that there are two components with lifetimes of 4×10 -7 s and 5×10 -5 s.

Possibility of semiconducting quasicrystal in boron-rich solids

Analyzing the crystalline structure of α- and β-rhombohedral boron as approximants of a quasicrystal, atomic structures of two unit cells (prolate and oblate rhombohedra) of an icosahedral quasicrystal are constructed. Based on the molecular orbital calculation, as the cohesive energy for the α-boron type quasicrystal has a value between those for α- and β-boron, such a structure can be realized. A neutral B12H12 icosahedral cluster is distorted to a cubic or rhombohedral one by the Jahn-Teller effect. The distortions of B12 cluster in the K2B12H12 and β-rhombohedral boron have the same signs as the lowest energy distortions in the calculation. Among the α-rhombohedral-type structures, the distortion of B12 is correlated with the rhombohedral axis angle, and the angle is the closest to the icosahedral angle for B6O and the distortion is the smallest for B-C. A search for semiconducting quasicrystal has been experimentally done in the B-C system. A meta-stable phase has been found on the way to crystallization of the B95C5 amorphous phase.

MOLECULAR ORBITAL CALCULATIONS FOR ICOSAHEDRAL BORON-RICH SOLIDS

Icosahedral boron-rich solids are unique semiconducting materials whose crystalline structures are composed of icosahedral clusters (B 12 ). Molecular orbital calculation was performed for the B 12 whose 12 outer bonds were terminated by 12 hydrogen atoms, i.e. B 12 H 12 . The results account for the Jahn-Teller effect in the B 12 which is closely related to electronic structures and some properties in boron-rich solids. The dipole matrix element was also calculated using the molecular orbitals. Anisotropy in optical absorption observed in some boron-rich solids can be explained with it. Some of them are considered to be candidates for semiconducting quasicrystals which have icosahedral symmetry. Using molecular orbital calculations, cohesive energies of crystals and quasicrystals have been estimated. They suggests that realization of the quasicrystalline structure is possible.