Gauss’ electric field law

Taking into account the continuity equation in the frequency domain V J —j ujp = 0, we may express the Maxwell-Ampere law and the Gauss electric field law as... 

Next, for evaluating the composed polarizability and total energy in the electrostatic AC-complex one should relay on the basic principles of electrostatic, starting from the Gauss electric flux law linking the total (source) charge with the electrostatic field created through a closed surface... 

In Eq. (14.16), the sign of the right hand side equals that of the applied bias. The total charge in the semiconductor, Qt, is related to the electric field at the insula-tor-semiconductor interface, F according to Gauss s law ... 

For spherically symmetric nuclear charge distribution (Gaussian, Fermi, or point nucleus), the electric field at a point r outside the nucleus can be evaluated from Gauss law as... 

Gaussian probability, linear thermodynamics quadratic expansion, 12-13 regression theorem, 17-20 Gaussian-type orbitals (GTOs), 257-258 Gauss s law, diatomic molecules, internal electric field computations, 249-250... 

In order to give an example of oxide charge induced MOS behaviour, let us consider the case of fig. 6 where a sheet of charge Qox is inside the oxide at x t and where the corresponding electric field is drawn according to Gauss law ... 

An electric field is generated in the depletion region due to ionized donors and a gradient in electron concentration. From Gauss s law we find... 

Gauss s law states that if an imaginary enclosed surface of area S is drawn around a uniform density of charge, the component of the electric field at the surface, which is perpendicular to the surface, is proportional to the total charge enclosed. Hence, Gauss s law is expressed as... 

Let d be the thickness of a monolayer and n the total number of layers (that is, the thickness of the film divided by d). The layers are numbered starting from the insulator-semiconductor interface. To estimate the density n (per unit area) of charge-carriers in the ith layer we apply Gauss s law to a cylinder of unit cross section limited by the boundaries between the ith layer and each of its neighboring layers. For a long channel device, the electric field F is perpendicular to the film, and we have ... 

Figure 6. The photorefractive effect. Top in an idealized hole transport material, the net charge density is ti radians out of phase with the intensity pattern. Middle the electric field, E, due to this net charge density, p, is given by Gauss law, dEjdx = p/e, and is shifted in phase by njl radians relative to the charge density distribution. Bottom the refractive index will then follow the phase of the electric field. In real materials the charge distribution is not always n radians out of phase relative to the intensity pattern, as competition between drift and diffusion currents leads to a reduced phase shift. The refractive index contrast might therefore be shifted by only n/lO radians relative to the intensity pattern in some polymers.

Under the assumption that there are no surface states or specific adsorption of charged species, the space charge hi a semiconductor in contact with an electrolyte is balanced by the charge in the diffuse part of the double layer thus, (]sc = cfd- Gauss s law can therefore be used to provide a boimdary condition for the electric field at the surface of the semiconductor as... 

Another expression of the Coulomb law is the Gauss law, which states that the electric field associated with a charge distribution p (r) satisfies the relationship... 

The electron densities and the electric fields are coupled by the following discrete version of Gauss s law... 

The Gauss law of electrostatics is used to calculate the electric field produced by the total charge distribution obtained in the previous step. The new function V(r) generally differs from the estimation made in the first step. The procedure is repeated until two consecutive values of V(r) become essentially the same. Then the obtained self-consistent solution describes the electrons in the ground state of the multi-electron atom. 

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