One-dimensional Poisson Equation Research Articles

Metal-insulator-semiconductor studies of lead telluride∗

The capacitance and conductance-voltage characteristics were measured on metalinsulator-semiconductor capacitors fabricated with zirconium dioxide films on single-crystal lead telluride. At 77°K, on both n- and p-type substrates, evidence of surface potential control was obtained. Comparison of the measured capacitance-voltage characteristics with those calculated from the equilibrium solution of the one-dimensional Poisson equation indicates qualitative agreement, although the slope ( dC dV ) of the measured capacitance in the region near the capacitance minimum is less steep than calculated. The high-frequency response of the capacitance and position of the capacitance minimum were used to deduce the presence of an inversion layer on some n-type substrates of charge density approximately 5.0 × 10 13 cm −2. This layer was found to be dependent on surface preparation treatment prior to insulator deposition. Results of surface chemical studies indicate that inversion may be due to oxide formation during chemical etching. Conductance data obtained confirm the existence of a large interfacial state density.

Computer solution of one-dimensional Poisson's equation

The one-dimensional Poisson's equation for semiconductors doped with an ion-implanted profile (or any profile) is solved numerically using the mesh method of solution. The original equation is replaced by a set of finite difference equations. Solutions using a uniform mesh distribution together with the Störmer or the Cowell method are described. A variable mesh formulation of both the Störmer and the Cowell method is derived and is shown to give better accuracy for much smaller amounts of computation than the corresponding uniform mesh formulation.

Current-steering chip upgrades performance of d-a converter : E. Maddox. Electronics 125 (4 Apr. 1974)

The simple charge-transfer model usually applied to thin-film gas sensors is critically discussed and the fundamental difficulties are elucidated from a quantum-chemical point of view. In order to overcome the inconsistency of the charge-transfer model, a microscopic model of a thin-film gas sensor is developed in the framework of the electron theory of chemisorption. On the basis of Volkenstein's theory, two forms of chemisorption are introduced: the neutral weak-chemisorbed form and the charged strong-chemisorbed form. For the case of acceptor-like chemisorption and n-type metal-oxide semiconductors, the pressure dependence of the thin-film conductivity is derived, solving self-consistently the one-dimensional Poisson equation. Depending on the geometric and electronic structure of the thin-film gas sensor, relationships are derived in a consistent manner between the catalytic surface properties and the electronic bulk properties. It turns out that different types of adsorption isotherms can arise, depending on the bulk doping level. An interesting feature of the catalytic behaviour of the proposed microscopic model is the saturation effect of charged strong-chemisorbed species, which already arises at very low partial pressure (often known as the Weisz limitation in the sensor literature). In contrast to the charged strong-chemisorbed species, the neutral weak-chemisorbed species show a typical Langmuir behaviour. The main result is the power-law behaviour of the thin-film conductivity over a wide pressure region, σ(p) ∼ p−m. Whereas in the sensor literature the different power laws are explained by applying mass-action laws, it is shown that the power, m, is determined by different, fundamental parameters: ξ=D/LD (LD = Debye length), film thickness D, temperature and the surface-state energy. Hence it cannot be described by the stoichiometric coefficient alone. Furthermore, the theoretical values of the power vary between 0 and 1, in agreement with various experimental results. A modified Helmholtz equation is proposed, which can connect the change of the work function to both the change of the surface potential due to the charged strong-chemisorbed species and the change of the electron affinity due to the dipole moment of the neutral, weak-chemisorbed species. The effect of an external field on chemisorption is investigated for the case of a simplified one-dimensional ‘suspended’-gate MESFET (metal-semiconductor FET).

DIP inserter aims at low-volume users : G. Farrell. Electronics 155 (4 Apr. 1974)

The simple charge-transfer model usually applied to thin-film gas sensors is critically discussed and the fundamental difficulties are elucidated from a quantum-chemical point of view. In order to overcome the inconsistency of the charge-transfer model, a microscopic model of a thin-film gas sensor is developed in the framework of the electron theory of chemisorption. On the basis of Volkenstein's theory, two forms of chemisorption are introduced: the neutral weak-chemisorbed form and the charged strong-chemisorbed form. For the case of acceptor-like chemisorption and n-type metal-oxide semiconductors, the pressure dependence of the thin-film conductivity is derived, solving self-consistently the one-dimensional Poisson equation. Depending on the geometric and electronic structure of the thin-film gas sensor, relationships are derived in a consistent manner between the catalytic surface properties and the electronic bulk properties. It turns out that different types of adsorption isotherms can arise, depending on the bulk doping level. An interesting feature of the catalytic behaviour of the proposed microscopic model is the saturation effect of charged strong-chemisorbed species, which already arises at very low partial pressure (often known as the Weisz limitation in the sensor literature). In contrast to the charged strong-chemisorbed species, the neutral weak-chemisorbed species show a typical Langmuir behaviour. The main result is the power-law behaviour of the thin-film conductivity over a wide pressure region, σ(p) ∼ p−m. Whereas in the sensor literature the different power laws are explained by applying mass-action laws, it is shown that the power, m, is determined by different, fundamental parameters: ξ=D/LD (LD = Debye length), film thickness D, temperature and the surface-state energy. Hence it cannot be described by the stoichiometric coefficient alone. Furthermore, the theoretical values of the power vary between 0 and 1, in agreement with various experimental results. A modified Helmholtz equation is proposed, which can connect the change of the work function to both the change of the surface potential due to the charged strong-chemisorbed species and the change of the electron affinity due to the dipole moment of the neutral, weak-chemisorbed species. The effect of an external field on chemisorption is investigated for the case of a simplified one-dimensional ‘suspended’-gate MESFET (metal-semiconductor FET).

Stagnation Point Langmuir Probe in a Shock Tube-Theory and Measurements

Langmuir-type probes consisting of a flat-headed circular cylinder with a collecting electrode at the stagnation point are placed in a shock tube and exposed to supersonic ionized air flow at ion mass fractions less than 10−4 and initial shock tube pressure of 1 cm Hg. Stagnation point measurements of ion current density are obtained using negative electrode potentials. The exact gasdynamic stagnation point boundary layer equations and the one-dimensional Poisson equation are solved for an axially symmetric blunt body and ion mass fractions less than 10−2. Calculations of the ion-electron flow in the stagnation point boundary layer are presented for negative electrode potentials. The measurements and calculations agree within the experimental accuracy and the precision to which the physical constants are known.