Model equations, semiconductor devices

The above set of equations applies as shown to capacitively coupled systems. An identical set applies to the modeling of semiconductor devices [149]. Also, the similarity with the equations governing electrochemical systems (Section 8) is striking. The main difference is that continuity equations for electrons are not necessary, since there are no free electrons in the solution. 

As with all optoelectronic semiconductor devices, the current-voltage characteristics of an organic solar cell can be modelled using the continuity equations for each charge type. For electrons in the steady state we have... 

In order to model electron and hole transport in a semiconductor device, such as a transistor, we need solutions to a set of equations for the concentrations n and p, the electric current densities jn and jp, and for the electrostatic... 

The semianalytical model by Roichman et al. [42] is based on the mean medium approximation (MMA) and is probably the only one that shares the assumptions found in standard semiconductor models (for better or worse). A percolation-type model, which predicts that there are bottlenecks or small regions in which the current density is much larger than average, do not agree with the assumptions behind the semiconductor device model equations. The assumptions behind the MMA model include... 

In this paper our task is to determine the average lifetime t of the semiconductor devices at functioning temperature. There is applied the Arrhenius model while considering that the lifetime to failure at a temperature is proportional with the rate of the chemical degradation reaction, which takes place at that temperature. The equation of Arrhenius for the lifetime may be written as follows ... 

In any semiconductor device the charge densities are governed by three differential equations, Poisson s equation which expresses the minimization of electrostatic potential energy and continuity equations that express the conservation of charges. Typically, multilayer stacks of thin-film solar cells are simulated in the dimension parallel to the surface normal of the stack. For such a one-dimensional device model, these equations become... 

In Electrical Engineering, the semiconductor diode provides one of the most fundamental nonlinear devices. The current in die forward or conduction region is approximately an exponential function of diode voltage. Data for such a semiconductor diode is shown in Figure 9.48, along with a typical model equation of the form ... 

If a semiconductor element with negative differential conductance is operated in a reactive circuit, oscillatory instabilities may be induced by these reactive components, even if the relaxation time of the semiconductor is much smaller than that of the external circuit so that the semiconductor can be described by its stationary I U) characteristic and simply acts as a nonlinear resistor. Self-sustained semiconductor oscillations, where the semiconductor itself introduces an internal unstable temporal degree of freedom, must be distinguished from those circuit-induced oscillations. The self-sustained oscillations under time-independent external bias will be discussed in the following. Examples for internal degrees of freedom are the charge carrier density, or the electron temperature, or a junction capacitance within the device. Eq.(5.3) is then supplemented by a dynamic equation for this internal variable. It should be noted that the same class of models is also applicable to describe neural dynamics in the framework of the Hodgkin-Huxley equations [16]. 

First, we will briefly review the general conservation equations for mass and momentum, for continuous media. Then we will use these equations to describe the transport of electrons and holes in a semiconductor. The results will correspond to those which are used in device modeling, such as in the SEDAN ( ) and MINIMOS (4) programs, and will demonstrate the role of momentum conservation. 

The goal of the presentation in this section is to pose a generalized model comprising all the types of nonequilibrium detectors presented in the literature until now, and applicable to potential novel devices. When deriving the model we start from the semiconductor equations in their general form (Maxwell s equations and Boltzmann s transport equation.). 

Riess and coworkers at the University of Bayreuth proposed a Schottky barrier model for the operation of ITO/PPV/Al LEDs [70,71,94]. They argue that the current is predominantly carried by holes and that this hole current is limited by the Schottky barrier formed at the PPV/Al interface rather than by any barrier at the ITO/ PPV interface. They model the current-voltage characteristics using the equation for thermionic emission across a Schottky barrier from a semiconductor into a metal. It should be noted that the doping levels estimated for these devices are in the range 10 -10 cm, considerably higher than the values estimated by Marks et al. for their devices. 

Equations (10.2) and (10.3) describe the process when a pair of opposite charges encounter each other in space and recombine with the help of Coulomb attraction. According to the classical bimolecular recombination model, when the mean free path of charges in a material is smaller than the Coulomb capture radius bimolecular recombination will take place. The typical mean free path of organic semiconductors is about 1-2 nm, which is much smaller than r (10-20 nm at room temperature ), therefore bimolecular recombination is universally present in OSC devices. ... 

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