Claude A. Klein

Bandgap Dependence and Related Features of Radiation Ionization Energies in Semiconductors

The problems dealt with concern the production of electron‐hole pairs in a semiconductor exposed to high‐energy radiation. The goal is to develop a simple phenomenological model capable of describing the present experimental situation from the standpoint of yield, variance, and bandgap dependence. We proceed on the premise that e, the average amount of radiation energy consumed per pair, can be accounted for by a sum of three contributions: the intrinsic bandgap (EG), optical phonon losses r(ℏωR), and the residual kinetic energy (9/5) EG. The approach differs from prior treatments in the sense that the residual kinetic energy relates to a threshold for impact ionization taken to be 32EG in accordance with indications stemming from studies of avalanching in p‐n junctions. This model is subjected to three quantitative tests: (a) Fano‐factor variations are found to reflect the relative weight of phonon losses [K=r(ℏωR)/EG], but residual energy fluctuations govern the statistical behavior for K2 ≲0.3. An appl...

How accurate are Stoney’s equation and recent modifications

Stoney’s equation has been—and still is—extensively used to evaluate the macrostress acting in a coating deposited on a thick substrate. In principle, the formula applies only in the “thin-film approximation,” that is, for coatings much thinner than the substrate. The main purpose of this communication is to demonstrate that, based on a general theory of elastic interactions in multilayer laminates, the correct formula for the stress can be expressed in terms of Stoney’s equation and a correction factor equal to (1+γ δ3)/(1+δ), where γ designates the ratio of the biaxial moduli and δ is the ratio of the layer thicknesses. In this light, it is shown that (a) Stoney’s equation does not cause serious errors for thickness ratios δ⩽0.1; (b) Atkinson’s recently proposed modification, which does not require information on the coating’s modulus, yields much improved results for thickness ratios up to δ≃0.4; and (c) Brenner–Senderoff-type expressions can be very misleading and should be avoided.

Young's modulus and Poisson's ratio of CVD diamond

Abstract The elastic modulus E of diamond is often set equal to 1 s 11 = 1050 GPa , which assumes that it does not vary much with orientation, and many authors use v = 0.2 as an appropriate average value of Poissons ratio, which is incorrect. In fact, since the elastic constants of diamond are known with great accuracy, it is a straightforward matter to derive exact numbers for E and v that take into consideration the stress direction and the intrinsic anisotropy as well as the crystalline configuration. For diamonds synthesized by chemical vapor deposition (CVD) we find that in a first approximation the Hershey-Kroner-Eshelby averaging procedure yields acceptable numbers, E = 1143 GPa and v = 0.0691 , which are quite compatible with available experimental evidence. Our measurements of the biaxial modulus E′ = E (1 − v) make use of the bulge test method to characterize the elastic behavior of both microwavepower- and hot-filament-assisted CVD diamond films. High quality deposits yield ′E ≈ 1180 and 1220 GPa for randomly orientated and (110)-textured deposits respectively; these results confirm that state-of-the-art deposits exhibit elastic properties that are in accord with the measured stiffnesses of natural single-crystal diamond. The residual hydrogen content strongly impacts the elastic behavior and appears to be responsible for the degradation of the modulus observed in this and previous work.

STB Model and Transport Properties of Pyrolytic Graphites

We propose to demonstrate that a coherent description of pyrolytic graphite (PG) layer‐plane phenomena can be based on a parabolic two‐band system with cylindrical equal‐energy surfaces. In this simple two‐band model (STB model), band overlap and effective mass must be interpreted as phenomenological parameters to be derived from experiments on highly heat‐treated pure PG. With p‐type (boron‐doped) specimens, the objective is to describe the situation from the shift of the Fermi level, on the assumption that the presence of trapping centers would not inject major perturbations in the band structure. (1) Galvanomagnetic effects: As derived from zero‐field resistivity and magnetoresistance mobility, the intrinsic carrier concentration and its variation with temperature in the range 0° to 1500°K implies that past a given graphitization stage band‐structural features may no longer be seriously affected by the size of the carbon networks. Above room temperature the carrier concentration increases almost linear...

Strains and stresses in multilayered elastic structures: The case of chemically vapor-deposited ZnS/ZnSe laminates

Solid structures consisting of layers of different materials created at elevated temperatures usually exhibit substantial residual stresses. These stresses are caused by intrinsic strains in addition to thermal strains, and originate from the bonding of the layers, which generates internal forces and moments that must be balanced to achieve mechanical equilibrium. It is shown that the solution proposed by Townsend et al. [P. Townsend, D. Barnett, and T. Brunner, J. Appl. Phys. 62, 4438 (1987)] for describing elastic interactions in multilayered, elastically isotropic structures provides a powerful tool for evaluating the strains, the normal stresses off the edges, and the curvature of chemically vapor-deposited (CVD) laminates. The residual stresses acting in each layer are best expressed as follows: σi(z)=Ei′[(ei,0−e0¯)+(zN−z)K], where z measures the distance from the bottom surface, Ei′ is the biaxial modulus of the layer, (ei,0−e0¯) characterizes the strain mismatch prior to any mechanical relaxation, ...

Anisotropy of Young's modulus and Poisson's ratio in diamond

The elastic modulus E of diamond is often set equal to 1s11 = 1050 GPa, which assumes that it does not vary much with orientation, and many authors use v = 0.2 as an appropriate average value of Poissons ratio, which is incorrect. In this paper, we show that, since the elastic constants of diamond are known with great accuracy, it is a straightforward matter to derive exact numbers for E and v that take into consideration the stress direction, the intrinsic anisotropy, as well as the crystalline configuration. For textured CVD diamond deposits, we find that, in a first approximation, the Hershey-Kroner-Eshelby averaging procedure yields acceptable numbers, E = 1143 GPa and v = 0.0691, which are quite compatible with available experimental evidence; this confirms that high-quality deposits have elastic constants similar to those of single-crystal natural diamond.

Optical distortion coefficients of high-power laser windows

This paper concerns the problem of describing and evaluating thermal lensing phenomena that occur as a result of the absorption of laser light in solid windows. The aberration function expansion method is applied for deriving the two optical distortion coefficients x+ and xthat characterize the degradation in light intensity at the Gaussian focus of an initially diffraction-limited laser beam passing through a weakly absorbing stress-birefringent window. In a pulsed mode of operation, the concept of an effective optical distortion coefficient Xeff, which properly combines the coefficients x+ and x- in terms of potential impact on focal irradiances, then leads to the definition of a figure of merit for distortion. The theory and calculations presented in this and earlier papers provide simple analytical tools for predicting the optical performance of a windowmaterial candidate in a specific systems environment.

Further remarks on electron beam pumping of laser materials.

This article demonstrates that recently completed studies on the energy dissipation of kilovolt electron beams in solids provide readily applicable methods for assessing the situation in electron beam pumped lasers.

Diamond windows and domes: flexural strength and thermal shock

Ring-on-ring flexural strength measurements performed on free-standing specimens of chemically vapor-deposited (CVD) diamond indicate that if fracture originates at the nucleation surface, the strength is thickness independent and best described as follows: characteristic strength of approximately 300 MPa; and a Weibull modulus of approximately three. In a test configuration that puts the growth surface in tension, the strength decreases with increasing thickness and drops to less than 100 MPa for specimens thicker than 0.5 mm. These strengths are much lower than anticipated and therefore, invalidate earlier speculations on the thermal shock resistance capability of CVD-diamond windows and domes. The purpose of this contribution is to evaluate the results of strength measurements and to provide an updated assessment of the thermal shock performance. In this context, it is essential to keep in mind that the transient stress intensity critically depends on the nature of the heat flow as characterized by the Biot number. Considering that any viable sensor window must also be able to withstand the mechanical stresses induced by aerodynamic pressure, it is demonstrated that in a thermally thin regime, CVD-diamond plates or shells have unmatched figures of merit, which is of significance because presently available infrared-transmitting window/dome materials for the long-wavelength IR may not be able to handle the thermo-structural loads encountered on projected flight trajectories.

Thermochemical heat of ablation of solid carbon

The thermochemical heat of ablation of carbon, HA, is usually set equal to 32 kJ/g as derived from the JANAF tables. There is, however, some uncertainty since JANAF‐recommended values for heats of vaporization and partial vapor pressures differ from the results of a detailed analysis that was carried out at the Lawrence Livermore National Laboratory (LLNL). We find that the LLNL model yields carbon‐vaporization enthalpies that are appreciably lower than the JANAF‐based values. In this light, we examine experimental data generated in the course of a comprehensive investigation of laser‐interaction effects in graphite and conclude that our experiments are indicative of an HA equal to 31.0±1.6 kJ/g.