Modeling the MOSFET's Inversion Layer and Its Universal Mobility: A New Experimental Method

<div>We formulate a simple, yet accurate, model for a non-uniform mobile charge density ρ(z) giving rise to a mean potential Ψ* across an inversion layer of finite extent, which we measure by means of a novel, sensitive, experimental method involving nulls of harmonic distortion components (D2 ≈ D3 ≈ 0) of the drain current under sinusoidal excitation below saturation. We thus establish analytically and experimentally, that the low-field, "universal" effective mobility µ_eff varies as ~(E*_T)^-1/3for transversal fields E_T*= <b>-</b>(1/ε_si)<b>·</b>[ɳQ_i + Q_b] <b>≤ </b>0.5 MV/cm, wherein ɳ varies continuously between 1/2 and 1/3. We also establish and observe that the higher order, derivative, parameter θ_T quantifying µ_eff’s modulation by E*_T varies as ~(E*_T)^-5/3 under laminar flow conditions, thereby further corroborating the foregoing effects and interpretations thereof.</div>

Modeling the MOSFET's Inversion Layer and Its Universal Mobility: A New Experimental Method

<div>We formulate a simple, yet accurate, model for a non-uniform mobile charge density ρ(z) giving rise to a mean potential Ψ* across an inversion layer of finite extent, which we measure by means of a novel, sensitive, experimental method involving nulls of harmonic distortion components (D2 ≈ D3 ≈ 0) of the drain current under sinusoidal excitation below saturation. We thus establish analytically and experimentally, that the low-field, "universal" effective mobility µ_eff varies as ~(E*_T)^-1/3for transversal fields E_T*= <b>-</b>(1/ε_si)<b>·</b>[ɳQ_i + Q_b] <b>≤ </b>0.5 MV/cm, wherein ɳ varies continuously between 1/2 and 1/3. We also establish and observe that the higher order, derivative, parameter θ_T quantifying µ_eff’s modulation by E*_T varies as ~(E*_T)^-5/3 under laminar flow conditions, thereby further corroborating the foregoing effects and interpretations thereof.</div>

On two kinds of the reverse half-discrete Mulholland-type inequalities involving higher-order derivative function

By means of the weight functions, Hermite–Hadamard’s inequality, and the techniques of real analysis, a new more accurate reverse half-discrete Mulholland-type inequality involving one higher-order derivative function is given. The equivalent statements of the best possible constant factor related to a few parameters, the equivalent forms, and several particular inequalities are provided. Another kind of the reverses is also considered.

GENERATION OF NEW OPERATIONAL MATRICES FOR DERIVATIVE, INTEGRATION AND PRODUCT BY USING SHIFTED CHEBYSHEV POLYNOMIALS OF TYPE FOUR

While solving the fractional order differential equation the requirement of the higher-order derivative is obvious therefore, this paper gives a definite expression for constructing the operational matrices of derivative which is the direct method to find the derivative of higher-order according to the requirement of the total differential equation. The proposed work expands the Chebyshev polynomial of type four up to six degrees that could help get the accuracy for the numerical solution of a given differential equation. Previously Chebyshev polynomial of the third type has been used by cutting the domain from [-1, 1] to [0, 1]. This study also generates the integrational operational matrix for solving the integral equation as well as an integrodifferential equation by using the Chebyshev polynomial of type four and expand it up to six order and generate the matrix by cutting the domain from [-1, 1] to [0, 1]. This is the first attempt to generate an integrational operational matrix that has never been highlight nor generate by any researcher. Another contribution of this paper is the generation of categorical expressions for the product of two Chebyshev vectors that will help in solving the differential equation of several kinds.

On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect

The main purpose of this paper is to study the global existence and uniqueness of solutions for three-dimensional incompressible magnetic induction equations with Hall effect provided that ∥u0∥H32+ε+∥b0∥H2(0<ε<1) is sufficiently small. Moreover, using the Fourier splitting method and the properties of decay character r*, one also shows the algebraic decay rate of a higher order derivative of solutions to magnetic induction equations with the Hall effect.