Normal Incidence Reflectance Data Research Articles

REFLECTANCE SPECTRUM AND OPTICAL PROPERTIES OF NANO-wBN IN THE VUV REGION OF SYNCHROTRON RADIATION

摘要 对冲击波法合成的纳米纤锌矿氮化硼（ｗＢＮ）进行了同步辐射真空紫外区的反射光谱测量，得到波长范围１００一２４０ｎｍ区间的反射光谱．利用Ｋｒａｍｅｒｓ－Ｋｒｏｎｉｇ关系计算获得了它的光学常数和介电函数谱，并导出了光电导谱．获得了纳米ｗＢＮ的光学禁带宽度实验值，为８．７±０．５ｅＶ．将以上结果和最新的理论计算进行了比较．观察到了经不同退火温度处理的纳米ｗＢＮ样品结构及尺寸变化对反射光谱和光学性质的影响． Abstract The reflectance spectrum of different wBN was measured. The sample were prepared by shock-wave method and heat-treated at 100℃ and 500℃. The measurement was performed in the wavelength range of 100-240nm at the time-resolved spectroscopy station of National Synchrotron Radiation Laboratory in Hefei. The optical constants of wBN have been determined in the VUV region by applying the Kramers-Kronig relation to normal incidence reflectance data. It was found that the average value of optical band gap determined from these constants is ８．７±０．５eV. The dielectric constants, optical conductivity of wBN were also obtained. The effet of the charges of particle size and structure of the nanometer-sized wBN on the optical reflectance spectrum were further studied. 作者及机构信息 苏夷希4, 巨新3, 魏坤4, 池元斌1, 韩正甫2, 石军岩2, 邓杰4, 施朝淑5 (1)吉林大学超硬材料国家实验室; (2)中国科学技术大学合肥国家同步辐射实验室; (3)中国科学技术大学近代物理系; (4)中国科学技术大学物理系; (5)中国科学技术大学物理系,中国科学技术大学合肥国家同步辐射实验室 基金项目: 国家自然科学基金 Authors and contacts SU YI-XI4, JU XIN3, WEI KUN4, CHI YUAN-BIN1, HAN ZHENG一FU2, SHI JUN-YAN2, DENG JIE4, SHI CHAO-SHU5 (1)吉林大学超硬材料国家实验室; (2)中国科学技术大学合肥国家同步辐射实验室; (3)中国科学技术大学近代物理系; (4)中国科学技术大学物理系; (5)中国科学技术大学物理系,中国科学技术大学合肥国家同步辐射实验室 参考文献 施引文献

Existence and construction of solutions of dissipative inverse problems

The problem considered here is that of simultaneously reconstructing spatially dependent velocity and dissipation profiles for a one-dimensional medium using a finite time trace of normal incidence reflection data measured on one side of the medium. It is shown that if the sup norm of the reflection data is bounded in a particular way, then this inverse problem is guaranteed to have a solution. A numerical algorithm which is based on this existence proof is used to illustrate the reconstruction process.

Goupillaud layers and construction of wave speed and density of a layered acoustic medium

The problem of finding the density and the wave speed of an acoustic medium from the observed reflection response at two different angles of incidence is studied. Based on results for finding impedance from normal incidence reflection data, existence of a modified Goupillaud method to our problem is motivated. A possible modified Goupillaud approach applicable to finding density and wave speed from reflection response at different angles of incidence is presented and studied.

Optical properties of semiconducting iron disilicide thin films

Iron disilicide thin films were prepared by furnace reaction of ion beam sputtered iron layers with single-crystal silicon wafers and with low-pressure chemical vapor deposition (LPCVD) polycrystalline silicon thin films. X-ray diffraction indicates the films are single-phase, orthorhombic, β-FeSi2. Impurity levels are below the detection limit of Auger spectroscopy. Normal incidence spectral transmittance and reflectance data indicate a minimum, direct energy gap of 0.87 eV. The apparent thermal activation energy of the resistivity in the intrinsic regime is about half of this minimum optical gap. With such a direct band gap, the material may be suitable for the development of both light-sensitive and light-emitting thin-film devices within the silicon microelectronics technology.

Variable Angle Submillimetre Laser Reflection Spectroscopy of Semiconductors

Power reflection coefficients in σ and π polarisation (Rσ and Rπ) have been obtained for silicon type semiconductors doped epitaxially with various concentrations of phosphorous. The coefficients Rσ and Rπ are obtained as a function of incidence angle ϕ for disks of semiconductor material doped on one side epitaxially. The Rσ(ϕ) and Rπ(ϕ) data are reported at four spot frequencies in the far infra-red. These data are not interpretable in terms of the simple band-edge equations of homogenously doped semiconductors in the far infra-red and contain more information than normal angle reflectivity (ϕ = 0), for which Rσ = Rπ. The differences between the measured Rσ and Rπ and the values given by the simple homogenous band edge theory vanish as σ → 90°, i.e., for glancing angles of incidence. The differences are at a maximum level for ϕ = 0°, i.e., for normal angles of incidence, especially in σ polarisation, but less so for π polarisation. This suggests that normal incidence reflectivity data probe more deeply into the structure of inhomogenously doped semiconductors or epitaxial layers.

Optical properties and interband transitions in the layered compounds SbI3

The optical constants of SbI3 single crystals, prepared from solution, were calculated from normal incidence reflectance data via a Kramers-Kronig analysis. The dependence of the absorption coefficient on the photon energy suggests the presence of a direct allowed interband transition whereE g d =2·225 eV at room temperature, as well as indirect phonon-assisted transition. The absorption coefficient follows Urbach's empirical relation in the range 2·08–2·34 eV near the intrinsic edge, and a Gaussian shape was obtained near the band maximum. This behaviour is indicative of its excitonic origin and may be contributed to localized excitons in the crystal.

Optical constants and interband transitions in the layer compound InSe

The relevant optical constants of InSe are obtained by applying the Kramers-Kronig relations to accurate near normal incidence reflectance data in the 1.5–5.5 eV energy range. In absence of band calculations, the observed structures are tentatively interpreted by analogy with GaSe ones.

Valence band state densities of tetrahedrally coordinated amorphous semiconductors

A novel technique, for obtaining the valence band state densities (VBSD's) of tetrahedrally coordinated amorphous semiconductors from normal incidence reflectance data, is applied to Si and Ge and GaP, GaAs and GaSb. The VBSD's of Si and Ge are similar to other published results, obtained by conventional techniques, and cannot be described by broadened crystalline VBSD's. On the other hand, the VBSD's of the 3–5's contain many of the crystalline features. The relation of these results to the structure of the amorphous phase is discussed.

Exciton dynamics in molecular solids from line shape analysis: An assessment of the extent of line shape distortion resulting from use of real crystals

For crystal absorption systems, the line profile of the frequency dependence of the dielectric permittivity ε(ω) contains information about the exciton dynamics that may be studied by the autocorrelation function generated by the Fourier transformation of ε(ω) into the time domain. However, ε(ω) obtained through transforming normal incidence reflectance data R (ω) of a real crystal when the photon-crystal eigenmodes are strongly coupled may be considerably distorted from ε(ω) of a perfect infinite crystal. In this paper, we consider the ways by which such distortions may arise and, by using a model for ε(ω) that might reasonably correspond to the 4000 Å b-polarized 0–0 absorption system at low temperatures of crystalline anthracene probed on the (001) face, we illustrate the dependence of the extent of distortions on the line profile of ε(ω) upon the following number of factors, viz., (i) spatial dispersion of the exciton bands; (ii) use of an oblique angle of incidence as an approximation to normal incidence in determining R (ω); (iii) thickness of the crystal slab used to determine R (ω); (iv) extent of roughness on the crystal surface; (v) mole fraction of defects in the crystal; and (vi) mole fraction of impurities in the crystal. The treatment allows definition of the condition [real ε(ω) < 0] under which various quasiparticles (longitudinal excitons, surface excitons, excitons bound to impurities) may be excited in a particular crystal system. The methods employed in this paper are of general applicability to strongly absorbing crystal systems and will be of use in understanding exciton dynamics in such systems. The data provide a firm foundation for interpreting reflectance data of a strongly absorbing crystal system, and thus we are able to discuss existing spectral data for anthracene crystals, especially narrow structure observed in low temperature reflection spectra, as well as suggest areas for both theoretical and experimental work.

Optical Properties ofa−MnSe

Near-normal-incidence reflectance measurements are reported on the face-centered-cubic (fcc) phase of MnSe from 0.006 to 16 eV. The complex index of refraction and complex dielectric constant have been obtained from a Kramers-Kronig phase-shift dispersion analysis of normal-incidence reflectance data. The first-order infrared absorption (reststrahl) has been analyzed to yield the transverse and longitudinal optical-phonon frequencies near $\ensuremath{\Gamma}$, the high- and low-frequency dielectric constants, and an "ionicity" parameter. The ultraviolet dispersion has been correlated with single-electron interband transitions and many-body excitations. In addition to the room-temperature reflectance measurements, transmission data are reported over the range 0.04-2.8 eV down to 80 \ifmmode^\circ\else\textdegree\fi{}K. In this energy range no exchange-related structure was detected. The N\'eel temperature was obtained from specific-heat measurements and confirmed by an independent optical technique. The value obtained 247 \ifmmode^\circ\else\textdegree\fi{}K agrees with a previous determination. The results of this work are compared in detail with earlier work on MnO and MnS.

A comparison of the optical properties of single crystal and liquid mercury in the energy range 0.5 to 8.25 eV

Normal incidence reflectance measurements were performed on single crystal Hg and liquid Hg in the energy range 0.5–8.25 eV. The reflectances of the solid and liquid are distinctly different below 2.0 eV but are of similar magnitude above. Evidence for the excitation of a surface plasmon has been found in crystal Hg but not in liquid Hg. Values for the real and imaginary parts of the dielectric function have been obtained by means of a least squares fit of the normal incidence reflectance data and they have been compared with values obtained from ellipsometric measurements.

Optical Properties of Amorphous Germanium Films

The optical constants of amorphous Ge films formed under well-defined conditions have been determined in the 0.1-25.0-eV spectral range. In the 0.1-1.8-eV range they were determined by analysis of precise reflectance and transmittance data ($\mathrm{RT}$), and in the 0.1-25.0-eV range by a Kramers-Kronig analysis of normal-incidence reflectance data. Both analyses gave the same results in the region of overlap. The absorption edge was found to be quite sharp (0.06 eV) and to occur usually at a photon energy of about 0.6 eV. The position of the edge was normally about 0.2 eV lower than the direct edge in crystalline Ge. No evidence was found for either the spin-orbit split valence band associated with crystalline Ge or a tailing and/or large number of states in the forbidden region. The smallest nonzero value of the absorption measured on the low-energy side of the absorption edge was about 10 ${\mathrm{cm}}^{\ensuremath{-}1}$. There was no evidence for free-carrier absorption further in the infrared. At 0.1 eV, the index of refraction was 3.99 \ifmmode\pm\else\textpm\fi{} 0.04 as determined by the $\mathrm{RT}$ analysis. This value was in excellent agreement with the value of 4.00 derived from the zero-frequency dielectric constant, which has been calculated using the sum rule. This is also the value determined for crystalline Ge in the infrared. Reflectance data for amorphous Ge films deposited and measured in ultra-high vacuum (in situ) are reported for the region 2.0-11.8 eV. The density, determined by weighing films of known thickness, was 12-15% less than the density of crystalline Ge.

Optical Properties of Platinum

The optical functions ${\ensuremath{\epsilon}}_{1}$, ${\ensuremath{\epsilon}}_{2}$, $\ensuremath{\alpha}$, and $\ensuremath{-}\mathrm{Im}(\frac{1}{\ensuremath{\epsilon}})$ have been deduced from reflectance data on electron-gun-evaporated Pt samples. They were obtained by two different methods: (1) the Kramers-Kroning analysis of the normal-incidence reflectance data, and (2) the analysis of reflectance at two different incident angles. The absorption coefficient $\ensuremath{\alpha}$ shows small peaks at $h\ensuremath{\nu}=0.4, 7.7, \mathrm{and} 10.5$ eV, and a broad peak centered about 4 eV. The imaginary part of the dielectric function, ${\ensuremath{\epsilon}}_{2}$, has structure at $h\ensuremath{\nu}=6.5$ and about 11 eV.

Kramers-Kronig analysis of reflection data

A method is given for using the Kramers-Kronig dispersion relations to evaluate optical and dielectric parameters of materials from normal incidence reflectance data when data over only a limited spectral range is available. No assumptions are needed concerning the behaviour of the reflectance data outside the experimental range, and no extrapolations of data are required. As an example, the extreme ultra-violet reflectance data of potassium iodide is analysed by this method.

Plasma–Interband Coupling in β′ CuZn†

Normal-incidence reflectivity data for β′ CuZn has been subjected to a Kramers–Kronig analysis for its optical constants in the spectral region 2 eV ≤ħω≤3 eV (4140 Å ≤λ≤6200 Å) in order to explain the nature of an observed reflectivity edge at 5000 Å. Extrapolations of the data into the infrared and ultraviolet were made. The frequency dependence of the optical constants indicates a plasma resonance at 2.52 eV (4920 Å), shifted and damped from its classically predicted value by the influence of interband transitions occurring at approximately the same energy. The spectral behavior of the optical constants in this region is not very sensitive to the exact nature of the extrapolation.

Optical Properties of Diamond in the Vacuum Ultraviolet

The optical constants of diamond have been determined in the range 5.5 to 23 eV by applying the Kramers-Kronig relation to normal incidence reflectance data. There are two salient features in the curve for optical absorption. First, the absorption rises rapidly near 7 eV, indicating the onset of strong direct transitions. Second, a relatively sharp peak occurs near 12.5 eV. These data are discussed in terms of the energy band picture for diamond and related materials which have a similar band structure.

Optical Constants of Silver

The optical constants for electrolytically polished silver samples were determined from normal-incidence reflectance data in the spectral region 2 to 10 ev. The sharp minimum in the curve for $k$ near 3.8 ev, which is associated with the onset of interband transitions, is deeper than in previous results. A second minimum is observed near 9.2 ev.