A. T. Fromhold

Diffusion Currents in Large Electric Fields for Discrete Lattices

A derivation for the steady‐state current J produced by a large homogeneous electric field E0 in the presence of a concentration gradient is presented which includes explicitly the effects due to lattice discreteness. The resulting equation is J=4aν exp(−W/kBT) sinh(ZeE0a/kBT)[C(L)−C(0) exp(ZeE0L/kBT)]/[1−exp(ZeE0L/kBT)], where C(0) and C(L) are the boundary concentrations of the diffusing species at the interfaces of the planar film at positions x=0 and x=L; e, the electronic‐charge magnitude; Ze, the charge per particle of the diffusing species; 2a, the distance between adjacent potential minima; v, the frequency at which the ion attempts energy barriers which have height W in zero field; kB, the Boltzmann constant; and T, the absolute temperature. A derivation valid in the limit of a continuum model is also presented, and the results are compared numerically. The equations for the discrete and continuum models reduce to the results predicted by the ordinary linear diffusion equation for electric fields...

The interaction of atomic oxygen with thin copper films

A source of thermal, ground‐state atomic oxygen has been used to expose thin copper films at a flux of 1.4×1017 atoms/cm2 s for times up to 50 min for each of five temperatures between 140 and 200 °C. Rutherford backscattering spectroscopy was used to characterize the oxide formed during exposure. The observations are consistent with the oxide phase Cu2O. The time dependence and the temperature dependence of the oxide layer thickness can be described using oxide film growth theory based on rate limitation by diffusion. Within the time and temperature ranges of this study, the growth of the oxide layers is well described by the equation L(T,t)=3.6×108 exp(−1.1/2kBT)t12, where L, T, and t are measured in angstroms, degrees Kelvin, and minutes, respectively. The deduced activation energy is 1.10±0.15 eV, with the attendant oxidation rate being greater than that for the corresponding reaction in molecular oxygen.

The oxidation of polycrystalline silver films by thermal, ground-state atomic oxygen

Abstract Experimental results indicate a linear relationship between oxide layer thickness and exposure time for thin Ag films exposed to thermal, ground-state atomic oxygen fluxes of the order of 10 17 atoms/(cm 2 s). Exposure times ranged between 10 and 120 s, and all exposures were made at ambient temperature. The techniques of scanning electron microscopy (SEM) and Auger electron spectroscopy (AES) were used to characterize stress-induced damage in the thickest oxide layers. This damage was also observed using RBS (Rutherford backscattering spectroscopy) techniques which were applied to determine oxide layer thicknesses as a function of exposure time. Results are compared with data recently obtained from similar measurements using thin, polycrystalline Cu films.

Hauffe—Ilschner Transition during Thermal Oxidation

Numerical computations together with physical considerations are used to argue that a transition proposed by Hauffe and Ilschner from electron tunneling to nonlinear ionic diffusion as rate‐limiting mechanisms during thermal oxidation is not to be expected. The results indicate instead that the reverse transition is likely to occur. This in turn has serious implications regarding the oxidation kinetics and limiting thicknesses as a function of temperature deduced from the Mott—Cabrera theory.

Electric Fields in Thin‐Film Dielectrics on Metal Surfaces

Electrostatic fields in oxides and similar compounds formed on metals by thermal reaction with ambient gases are deduced for the case in which rate is determined by charged‐particle diffusion through the compound. Specifically, the limiting case where the macroscopic electrostatic potential leads to a condition approximating local charge neutrality is examined. The position‐dependent electric field in the compound leads to an electrostatic potential across the layer which is independent of thickness.

Space Charge in Growing Oxide Films. V. Perturbation Coefficients and Second‐Order Treatment

The coefficients in a previously developed perturbation treatment of space‐charge effects for growing oxide films are explicitly evaluated in terms of the boundary concentrations of the diffusing species. The quadratic forms for the coefficients in terms of concentrations of ions and electrons makes quantitative comparison of theory and experiment possible, and facilitates the development of analytical approximations for limiting cases. The perturbation treatment itself is extended to include higher‐order terms. The resulting equations reduce to quadratures; numerical computations for a specific example are presented to compare first‐ and second‐order results. An approximate equation L(t)=L∞′(1−exp{−(t/τ′)−[L(t)/L∞′]}) is thereby obtained relating film thickness L(t) to time t for the later stages of growth, with the parameters L′∞ and τ′ determined by the space‐charge concentrations in the film. Dimensionless curves are presented which illustrate the relationship between this equation and the first‐order...

Recombination and local equilibrium in growing oxide films

The possibility of a recombination of certain diffusing point defects in growing oxide films is examined within the framework of a simple collision model. Local equilibrium between diffusing cation interstitials and cation vacancies (or between diffusing anion interstitials and anion vacancies, or between electrons and electron holes) can represent a viable approximation for 100 A oxide films when the average diffusing point defect density exceeds 1021/cm3; for a 100 μ thick oxide layer, the minimum defect density for such reduces to 1017/cm3. On the other hand, arguments are presented on the basis of physical considerations which indicate that local equilibrium between the diffusing cation and anion point defect species within the growing oxide film is not to be expected; likewise, local equilibrium between the diffusing electronic and ionic species giving rise to new oxide growth is not to be expected.

Theorems relating to space-charge retardation and enhancement of current transport in solids

The following theorem regarding charge transport in solids is proved: The current of a single mobile species given by the linear diffusion equation under constant voltage and fixed values for the conductivity at the interfaces is retarded by the space charge of that mobile species. Two related theorems, likewise proved, show that dominant space charge of opposite sign to a given mobile species enhances the current of the mobile species, while dominant space charge of the same sign as a given mobile species retards the current of the mobile species.

Transient Nuclear Magnetic Resonance Studies of Dilute Copper‐Base Alloys

Data are presented for the nuclear spin–spin and spin–lattice relaxation rates for the 63Cu and 65Cu resonances in dilute copper‐base alloys with the following atomic percent of the solute metals: 0.1% Ag, 0.2% Ni, 0.25% Al, 0.25% Au, 0.4% Ni, 1.0% Ni, and 5.0% Ag. The data reflect the sizable electric field gradients due to local strains introduced by alloying and the spatial rearrangement of conduction‐band electrons in the vicinity of individual solute atoms.