Barrier Height Eb Research Articles

Exactly solvable double-well potential in Schrödinger equation for inversion mode of phosphine molecule

The reduced mass of the effective quantum particle for the inversion mode ν2 of phosphine molecule PH3 is known to be a position dependent one. In the present article the inversion spectrum of PH3 is considered with the help of the Schrödinger equation (SE) with position dependent mass and corresponding modified double-well potential. The SE is shown to be exactly solvable. The results are used for the analysis of the pertinent experimental data available in literature. We are based on the reliable value ν2=E2-E0=992.1cm-1 (2ν2=E4-E0=1972.5cm-1; 3ν2=E6-E0=2940.8cm-1; 4ν2=E8-E0=3895.9cm-1) obtained by Špirko et al. Also we use the value for the barrier height Eb=12300cm-1 that seems to be commonly accepted at present and the hypothetical value for the energy splitting of the 11-th doublet of the 10ν2 band s10=E21-E20≈7.2cm-1 suggested in the literature. Definite predictions are derived for the energy splitting of the 4-th doublet of the 3ν2 band s3=E7-E6 that is a test one for the observation in the experiment of Okuda et al. SE with position dependent mass provides self-consistently the required values of {ν2;Eb;s10} yielding s3=6.21·10-12cm-1.

Influence of flexible substrate in low temperature polycrystalline silicon thin-film transistors: temperature dependent characteristics and low frequency noise analysis

The carrier transport of p-type low temperature polycrystalline silicon (LTPS) thin-film transistors (TFTs) on flexible substrate has been intensively studied and compared to that on glass substrate in order to improve device performance. To investigate the origin of carrier transport on different substrates, temperature dependent characterizations are carried out for electrical device parameters such as threshold voltage (VTH), subthreshold swing (SS), on-current (Ion) and effective carrier mobility (μeff). The poly-Si grain size Lgrain and the barrier height EB between grain boundaries are well known to be the main parameters to determine transport in polycrystalline silicon and can be extracted based on the polycrystalline mobility model. However, our systemic studies show that it is not grain size but EB that has more influence on the degradation of LTPS TFT on flexible substrates. The EB of flexible substrate is roughly 18 times higher than glass substrate whereas grain size is similar for both devices on different substrates. Compared to the LTPS TFT on glass substrate, higher EB degrades approximately 24 % of Ion, 30 % of SS and 21 % of μeff on the flexible substrate at room temperature. From low frequency noise (LFN) analysis, it is observed that the total trap density (Nt) for flexible substrate is up to four times higher than that of glass substrate, which also supports the high value of EB in the device fabricated on the flexible substrate.

Decomposition of substituted alkoxy radicals—part I: a generalized structure–activity relationship for reaction barrier heights

An update and expansion of our readily applicable structure-activity relationship (SAR) for predicting the barrier height E(b) to decomposition by beta C-C scission of (substituted) alkoxy radicals is presented. Such alkoxy radicals are key intermediates in the atmospheric oxidation of volatile organic compounds, and a correct description of their chemistry is vital to the understanding of atmospheric chemistry; nevertheless, experimental data on these reactions remain scarce. The SAR is based on quantum chemical characterizations of a large set of alkoxy radicals, and accommodates alkoxy radicals with alkyl- (-R), oxo- (=O), hydroxy- (-OH), hydroperoxy (-OOH), alkoxy (-OR), alkylperoxy- (-OOR), nitroso- (-NO), nitro- (-NO2), nitrosooxy- (-ONO), and nitroxy- (-ONO2) functionalities, as well as 3- to 6-membered rings and some unsaturated side chains. The SAR expresses the barrier height to decomposition, E(b) = 17.9 kcal mol(-1) + Sigma N(s) x F(s), as a linear function of the number N(s) of these substituents on the relevant carbons, and the substituent-specific activities F(s) derived from the quantum chemical calculations, allowing facile predictions based solely on the molecular structure. For low barriers, < or = 7 kcal mol(-1), a simple curvature correction is required. The SAR-predicted barrier height E(b) can be used to predict the high-pressure rate coefficient for alkoxy decomposition k(diss) at or around 298 K.

A Generalized Structure-Activity Relationship for the Decomposition of (Substituted) Alkoxy Radicals

A novel and readily applicable Structure-Activity Relationship (SAR) for predicting the barrier height Eb to decomposition by β C-C scission of (substituted) alkoxy radicals is presented. Alkoxy radicals are pivotal intermediates in the atmospheric oxidation of (biogenic) volatile organic compounds, and their fate is therefore of crucial importance to the understanding of atmospheric VOC degradation mechanisms. The SAR is based on available theoretical energy barriers and validated against barriers derived from experimental data. The SAR is expressed solely in terms of the number(s) Ni of alkyl-, hydroxy- and/or oxo-substituents on the α- and β-carbons of the breaking bond: Eb(kcal/mol) =17.5 − 2.1 × Nα(alk) − 3.1 ×Nβ(alk) − 8.0 × Nα,β(OH) − 8.0 × Nβ(O=) − 12 × Nα(O=). For barriers below 7 kcal/mol, an additional, second-order term accounts for the curvature. The SAR reproduces the available experimental and theoretical data within 0.5 to 1 kcal/mol. The SAR generally allows conclusive predictions as to the fate of alkoxy radicals; several examples concerning oxy radicals from prominent atmospheric VOC are presented. Specific limitations of the SAR are also discussed. Using the predicted barrier height Eb, the high-pressure rate coefficient for alkoxy decomposition kdiss∞ (298 K) can be obtained from kdiss∞ (298 K) = L ×1.8 × 1013 exp(−Eb/RT) s−1, with L the reaction path degeneracy.

Photoconductivity in polycrystalline semiconductors: Grain boundary effects

Photoconductivity of polycrystalline Zn x Cd 1− x Se films (0< x<1.0)with direct band gap ( E g) is reported here. The experimental data were analyzed for h ̷ ω < E g in order to obtain the grain boundary parameters (e.g., barrier height Eb, density of trap states Q t and the capture cross-section σ 1 of the majority carriers). The variations of Eb with intensity Φ and energy ħω of the incident photon indicated an excellent agreement with the theoretical plot obtained on the basis of the existing models considering monovalent trapping states.

Influence of illumination on the grain boundary recombination velocity in silicon

The variation with illumination of the grain boundary (GB) barrier height EB and of the effective recombination velocity Seff is calculated by means of a self-consistent procedure which takes into account the bending of the minority carrier quasi-Fermi level in the GB space-charge region and in the GB quasi-neutral region. The GB interface states have been assumed to be uniformly distributed in a half-filled band whose width and position in the band gap can vary. Seff is nearly proportional to exp(EB/kT), only when EB is sufficiently low. For high EB, Seff is limited by the thermal velocity. The influence of the density of interface states and the grain doping concentration has been studied. The experimental results obtained with Silso–Wacker polycrystalline silicon show that the grain boundaries present different behaviors.

Dependence of electrical properties of polycrystalline cvd si films on grain size and impurity doping concentrationa,b

The electrical properties of sets of simultaneously grown p-type polycrystalline Si films, deposited by SiH4 pyrolysis on polycrystalline high-purity alumina substrates and B-doped during growth, were determined by Hall-effect measurements in the temperature range 77-420K as functions both of impurity doping concentration N (~10l5 to ~1020cm−3) and average grain size (≈1 to ≈125μm) in the film. Room temperature data showed rapidly increasing resistivities and rapidly decreasing free-carrier concentrations for doping below a critical concentration Nm and distinct mobility minima at that concentration, with the value of Nm being larger the smaller the average grain size. Measurements as a function of sample temperature showed the intergrain barrier height Eb, decreasing from a maximum value of ~0.4eV at the critical concentration to very small values (~0.01eV) for concentrations above 1019cm−3, with a functional dependence close to Eb ∝l/N1/2 and Eb for any given concentration being larger the smaller the average grain size. Results are interpreted in terms of the grain-boundary trapping model. Trapped carrier densities in the grain boundaries were calculated to range from ~5×l011cm−2 at N≈Nm to ~5×l012cm−2 for N>1019cm−3, the density being higher the smaller the grain size, and evidence was found for an energy distribution of traps in the Si bandgap, rather than a fixed density at a single discrete energy level. The observed relationship between Nm and average grain size nearly coincides with that of the model for films with ~lμm grain size but sharply departs from it for larger grain sizes, indicating probable applicability of the model for grain sizes up to that range.

The reaction X+Cl2→XCl+Cl (X=Mu,H,D). I. A new inversion procedure for obtaining energy surfaces from experimental detailed and total rate coefficient data

A new inversion method has been developed which uses detailed vibrotational and total rate coefficient data in order to obtain the potential energy surface for a chemical reaction. The method is applied to the reaction X+Cl2→XCl+Cl (X=Mu,H,D). The philosophy of the method is to separate the dynamical effects due to the collinear and the noncollinear parts of the potential surface, which are then treated independently, and to reduce a large amount of experimental data to a few informative quantities. These are then related to a small number of potential surface parameters. This compaction of data is carried out in an iterative scheme starting from a potential surface assumed to be sufficiently similar to the correct one. In the present case, the collinear part of the potential surface is constrained to be of the extended LEPS variety with correct asymptotic properties and two adjustable Sato parameters. Information theoretic techniques are used to obtain the fraction of reactive reagents and then the vibrotational product distribution for ground state reagents P(J′,v′ ‖ v=0) in a thermal reactant distribution. Next, these three dimensional P(J′,v′ ‖ v=0) are projected onto the corresponding collinear vibrational distribution PC(v′ ‖ v=0). This distribution is then further reduced to its most informative moment 〈fv′〉C to 𝒜⊥, the attractivity of the potential surface. An estimate of the barrier height Eb of X+Cl2 is made from the isotopic ratios of thermal rate coefficients, which are assumed to be dominated by collinear potential surface properties. We thus compact the original experimental data into two parameters 𝒜⊥ and Eb which determine the Sato parameters characterizing the collinear part of the potential surface. With Eb=1.5 kcal mol−1, the collinear part of the extended LEPS surface which best reproduces 〈fv′〉C for the H+Cl2 and D+Cl2 reactions has Sato parameters of S(XCl)=0.067 and S(Cl2)=−0.113. We have not explicitly derived the noncollinear part of the potential surface due to the present unavailability of simple parametrized models for the angular behavior.