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This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differential‐algebraic initial value problem for the electric circuit with multidimensional parabolic‐elliptic boundary value problems for the devices. We prove an existence and uniqueness result and the asymptotic behavior of this mixed initial boundary value problem of partial differential‐algebraic equations. [ABSTRACT FROM AUTHOR]

We consider an elliptic partial differential-algebraic model which arises in the modeling of an electric network that contains semiconductor devices. In this context, the electric network is described by linear differential-algebraic equations, while the semiconductor devices are described by nonlinear elliptic partial differential equations. The coupling takes place through the source term for the network equations and the boundary conditions for the device equations. Under the assumption that the fully coupled model has tractability index 2, we prove an existence result for this system. The extension of the notion of tractability index to a specific class of coupled systems is a further result of this paper. [ABSTRACT FROM AUTHOR]

We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC. [ABSTRACT FROM PUBLISHER]

Abstract: We consider a system of partial differential–algebraic equations which model an electric network containing semiconductor devices. The zero-dimensional differential–algebraic network equations are coupled with multi-dimensional elliptic partial differential equations which model the devices. For this coupled system we prove an existence result. [Copyright &y& Elsevier]

Abstract: In integrated circuit modeling, a general framework is presented for an RCL electric network with a detailed description of the semiconductor devices contained in it. The network part is described by modified nodal analysis, which leads to a system of differential-algebraic equations. The semiconductor devices are described by distributed models, namely, generic systems of partial differential equations with some key features common to all semiconductor models. The network part and the device part are coupled by means of applied potential and electric currents at the contacts of the devices. To take into account devices with more than two contacts, a multigraph description is used for the branches with devices. [Copyright &y& Elsevier]

In refined network analysis, a compact network model is coupled with distributed models for interconnects and semiconductor devices, linking differential-algebraic equations to partial differential equations, thus creating PDAEs. This paper deals with linear RLC networks containing one-dimensional diodes as distributed devices, modeled by the stationary drift-diffusion equations. For the resulting mixed initial boundary value problem we prove a uniqueness result for solutions close to equilibrium, i.e., with small initial data and electrical sources, based on a contraction argument. [ABSTRACT FROM AUTHOR]

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multidimensional approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that joins the differential-algebraic initial value problem for the electric circuit with parabolic-elliptic boundary value problems modeling the diodes. For this mixed initial boundary value problem of partial differential-algebraic equations a first existence and uniqueness result is given, and its asymptotic behavior is discussed. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents. [ABSTRACT FROM AUTHOR]