Silicon device model

J. Lai and A. Majumdar, Concurrent Thermal and Electrical Modeling of Sub-Micrometer Silicon Devices, J. of Applied Physics (79) 7353-7361,1996. 

There are many excellent books and articles which discuss parameter extraction and device modeling of silicon and OFET devices in greater detail [112] [113]. This discussion will highlight the standard techniques for device characterization which have been used in OFETs, and also describe several of the newer techniques which are being developed which address the specific challenges that OFETs face. 

The IEEE 1620-2004 standard covers the testing of OFET devices. This standard is actively under review and is periodically revised [114] and lays out a procedure for OFET parameter extraction which fits device curves to a simplified large signal long channel crystalline silicon (c-Si) device model with some adaptations for dealing with the complications OFETs present. While this approach has some limitations (see Section 6.5.1), to first order this approach will at least approximately reproduce this characteristic. 

Curve fitting to c-Si device models poses several risks, because the assumptions inherent in the model are not necessarily valid in disordered semiconductor systems. Of particular note are the lack of a single uniquely definable mobility and the lack of a well defined threshold voltage. Both of these characteristics lead to inaccuracies in modeling which have led to the adoption of other transport models based on amorphous silicon (a-Si) or polysilicon (p-Si) device models. 

A one-dimensional model of stress buildup in silicon devices over a temperature range is given by the following equation ... 

Mathematical Modeling of Drug Delivery from Silicone Devices... 

Bovine estrus synchronization is an important field for the veterinary pharmaceutical industry. A description of the natural bovine cycle and methods to cycle control are presented. In addition, commercially available silicone devices for bovine estrus synchronization are listed. The mathematical modeling of progestagens release from such devices is a crucial tool in the development of novel and/ or optimized delivery systems. For this purpose, several in vitro models, approaches to explain the ADME processes and overall models are described. This type of mathematical modeling could help in the future to customize drug delivery systems to specific animals and/ or situations. 

Figure 11. Experimental and predicted differential conductance plots of the double-island device of Figure 10(b). (a) Differential conductance measured at 4.2 K four peaks are found per gate period. Above the threshold for the Coulomb blockade, the current can be described as linear with small oscillations superposed, which give the peaks in dljdVj s- The linear component corresponds to a resistance of 20 GQ. (b) Electrical modeling of the device. The silicon substrate acts as a common gate electrode for both islands, (c) Monte Carlo simulation of a stability plot for the double-island device at 4.2 K with capacitance values obtained from finite-element modeling Cq = 0.84aF (island-gate capacitance). Cm = 3.7aF (inter-island capacitance). Cl = 4.9 aF (lead-island capacitance) the left, middle and right tunnel junction resistances were, respectively, set to 0.1, 10 and 10 GQ to reproduce the experimental data. (Reprinted with permission from Ref [28], 2006, American Institute of Physics.)...

FIG. 72. Schematic cross-section of (a) a single junction p-i-n o-Si H superstrata solar cell and (b) a tandem solar cell structure. (From R. E. I, Schropp and M. Zeman. "Amorphous and Microcrystalline Silicon Solar Cells—Modeling, Materials and Device Technology," Kluwer Academic Publishers, Boston, 1998, with permission.)... 

R. E. I. Schropp and M. Zeman, Amorphous and Microcrystalline Silicon Solar Cells—Modeling, Materials and Device Technology. Kluwer Academic Publishers, Boston, 1998. 

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