- Transistor models
Transistor s are complicated devices. In order to ensure the reliable operation of circuits employing transistors, it is necessary to scientifically model the physical phenomena observed in their operation using**transistor models**. There exists a variety of different models that range in complexity and in purpose. Transistor models divide into two major groups: models for device design and models for circuit design.**Models for device design**The modern transistor has an internal structure that exploits complex physical mechanisms. Device design requires a detailed understanding of how device manufacturing processes such as

ion implantation , impurity diffusion, oxide growth, annealing, and etching affect device behavior. Process models simulate the manufacturing steps and provide a microscopic description of device "geometry" to the device simulator. By "geometry" is meant not only readily identified geometrical features such as whether the gate is planar or wrap-around, or whether the source and drain are raised or recessed (see Figure 1 for a memory device with some unusual modeling challenges related to charging the floating gate by an avalanche process), but also details inside the structure, such as the doping profiles after completion of device processing.With this information about what the device looks like, the device simulator models the physical processes taking place in the device to determine its electrical behavior in a variety of circumstances: DC current-voltage behavior, transient behavior (both large-signal and small-signal), dependence on device layout (long and narrow versus short and wide, or interdigitated versus rectangular, or isolated versus proximate to other devices). These simulations tell the device designer whether the device process will produce devices with the electrical behavior needed by the circuit designer, and is used to inform the process designer about any necessary process improvements. Once the process gets close to manufacture, the predicted device characteristics are compared with measurement on test devices to check that the process and device models are working adequately.Although long ago the device behavior modeled in this way was very simple - mainly drift plus diffusion in simple geometries - today many more processes must be modeled at a microscopic level; for example, leakage currents in junctions and oxides, complex transport of carriers including

velocity saturation and ballistic transport, quantum mechanical effects, use of multiple materials (for example, Si-SiGe devices, and stacks of different dielectrics) and even the statistical effects due to the probabilistic nature of ion placement and carrier transport inside the device. Several times a year the technology changes and simulations have to be repeated. The models may require change to reflect new physical effects, or to provide greater accuracy. The maintenance and improvement of these models is a business in itself.These models are very computer intensive, involving detailed spatial and temporal solutions of coupled partial differential equations on three-dimensional grids inside the device.cite book

author=Carlo Jacoboni, Paolo Lugli

title=The Monte Carlo Method for Semiconductor Device Simulation

year= 1989

publisher=Springer-Verlag

location=Wien

isbn=3211821104

url=http://books.google.com/books?id=3cWnyhKmACEC&pg=PP1&dq=isbn:3211821104&sig=TCFY-o_l5gLj8OblcwGgQeB4Xts] cite book

author=Siegfried Selberherr

title=Analysis and Simulation of Semiconductor Devices

year= 1984

publisher=Springer-Verlag

location=Wien

isbn=3211818006

url=http://books.google.com/books?id=EE4HlRZTYi4C&pg=PA97&dq=isbn:3211818006&sig=19_iT2-C0gy8WdBIPcLc7gRAXw8#PPP1,M1] cite book

author=Tibor Grasser (Editor)

title=Advanced Device Modeling and Simulation (Int. J. High Speed Electron. and Systems)

year= 2003

publisher=World Scientific

isbn=9812386076

url=http://books.google.com/books?id=HBkA3_pZMp4C&dq=%22MOSFET++simulation%22&as_brr=0] cite book

author=Kramer, Kevin M. and Hitchon, W. Nicholas G.

title=Semiconductor devices: a simulation approach

year= 1997

publisher=Prentice Hall PTR

location=Upper Saddle River, NJ

isbn=0-13-614330-X] cite book

author=Dragica Vasileska, Stephen Goodnick

title=Computational Electronics

year= 2006

page=p .83

publisher=Morgan & Claypool

isbn=1598290568

url=http://books.google.com/books?id=DBPnzqy5Fd8C&printsec=frontcover&dq=%22gate+tunneling%22&as_brr=0#PPA83,M1] Such models are slow to run and provide detail not needed for circuit design. Therefore, faster transistor models oriented toward circuit parameters are used for circuit design.**Models for circuit design ("compact" models)**Transistor models are used for almost all modern

electronic design work.Analog circuit simulators such asSPICE use models to predict the behavior of a design. Most design work is related tointegrated circuit design s which have a very large tooling cost, primarily for thephotomask s used to create the devices, and there is a large economic incentive to get the design working without any iterations. Complete and accurate models allow a large percentage of designs to work the first time.Modern circuits are usually very complex. The performance of such circuits is difficult to predict without accurate computer models, including but not limited to models of the devices used. The device models include effects of transistor layout: width, length, interdigitation, proximity to other devices; transient and DC

current-voltage characteristic s; parasitic device capacitance, resistance, and inductance; time delays; and temperature effects; to name a few items. cite book

author=Carlos Galup-Montoro, Mǻrcio C Schneider

title=Mosfet Modeling for Circuit Analysis And Design

year= 2007

publisher=World Scientific

isbn=9812568107

url=http://books.google.com/books?id=yrrDcRm9bfUC&pg=PA293&dq=%22gate+tunneling%22&as_brr=0&sig=SJv5PSqaLbMdw10sEQPFd3ykN8E#PPA1,M1]**Large-signal nonlinear models**Nonlinear, or large signal transistor models fall into three main types:cite book

author=Narain Arora

title=Mosfet Modeling for VLSI Simulation: Theory And Practice

year= 2007

page=Chapter 1

publisher=World Scientific

isbn=981256862X

url=http://books.google.com/books?id=SkT2xOuvpuYC&dq=%22table+lookup+model%22&as_brr=0] cite book

author=Yannis Tsividis

title=Operational Modeling of the MOS Transistor

year= 1999

edition=Second Edition

publisher=McGraw-Hill

location=New York

isbn=0-07-065523-5

url=http://worldcat.org/isbn/0070655235]**Physical models**: These are models based upon device physics, based upon approximate modeling of physical phenomena within a transistor. Parameters within these models are based upon physical properties such as oxide thicknesses, substrate doping concentrations, carrier mobility, etc. In the past these models were used extensively, but the complexity of modern devices makes them inadequate for quantitative design. Nonetheless, they find a place in hand analysis (that is, at the conceptual stage of circuit design), for example, for simplified estimates of signal-swing limitations.

**Empirical models**: This type of model is entirely based upon

curve fitting , using whatever functions and parameter values most adequately fit measured data to enable simulation of transistor operation. Unlike a physical model, the parameters in an empirical model need have no fundamental basis, and will depend on the fitting procedure used to find them. The fitting procedure is key to success of these models if they are to be used to extrapolate to designs lying outside the range of data to which the models were originally fitted. Such extrapolation is a hope of such models, but is not fully realized so far.**Tabular models**: The third type of model is a form of

look-up table containing a large number of values for common device parameters such as drain current and device parasitics. These values are indexed in reference to their corresponding bias voltage combinations. Thus, model accuracy is increased by inclusion of additional data points within the table. The chief advantage of this type of model is decreased simulation time (see articlelook-up table for discussion of the computational advantages of look-up tables). A limitation of these models is that they work best for designs that use devices within the table (interpolation ) and are unreliable for devices outside the table (extrapolation ).The use of nonlinear models, which describe the entire operating area of a transistor, is required for digital designs, for circuits that operate in a large-signal regime such as

power amplifier s and mixers, and for the large-signal simulation of any circuit, for example, for stability or distortion analysis. Nonlinear models are used with a computer simulation program, such asSPICE . The models in SPICE are a hybrid of physical and empirical models, and such models are incomplete unless they include specification of how parameter values are to be extracted, especially as "unrealistic" (that is, unphysical) values can be made to fit the measured data without such a prescription. An incorrect set of fitting parameters results in wild predictions for devices that were not part of the originally fitted data set.Large-signal computer models for devices continually evolve to keep up with changes in technology. To attempt standardization of model parameters used in different simulators, an industry working group was formed, the

Compact Model Council , to choose, maintain and promote the use of [*http://www.geia.org/index.asp?bid=1333 standard models*] . An elusive goal in such modeling is prediction of how circuits using the next generation of devices should work, to identify before the next step which direction the technology should take, and have models ready beforehand.**mall-signal linear models**Small-signal or linear models are used to evaluate stability,

gain , noise and bandwidth, both in the conceptual stages of circuit design (to decide between alternative design ideas before computer simulation is warranted) and using computers. A small-signal model is generated by taking derivatives of the current-voltage curves about a bias point orQ-point . As long as the signal is small relative to the nonlinearity of the device, the derivatives do not vary significantly, and can be treated as standard linear circuit elements. A big advantage of small signal models is they can be solved directly, while large signal nonlinear models are generally solved iteratively, with possible convergence or stability issues. By simplification to a linear model, the whole apparatus for solving linear equations becomes available, for example,simultaneous equations ,determinant s, andmatrix theory (often studied as part oflinear algebra ), especiallyCramer's rule . Another advantage is that a linear model is easier to think about, and helps to organize thought.**mall-signal parameters**A transistor’s parameters represent its electrical properties. Engineers employ transistor parameters in production-line testing and in circuit design. A group of a transistor’s parameters sufficient to predict circuit

gain , input impedance, and output impedance are components in its small-signal model.Parameters used in small-signal circuits (two ports) adopt names related to the names of these circuits such as

*Transmission parameters (T-parameters),

*Hybrid-parameters (h-parameters),

*Impedance parameters (z-parameters),

*Admittance parameters (y-parameters), and

*Scattering parameters (S-parameters).These parameters all can be evaluated using measured scattering parameter data. Scattering parameters, or S parameters, can be measured for a transistor at a given bias point with a vector network analyzer.

**Popular models***

Gummel–Poon model

* Ebers–Moll model

* [*http://www-device.eecs.berkeley.edu/~bsim3 BSIM3*] (seeBSIM )

* [*http://www-device.eecs.berkeley.edu/~bsim3/bsim4.html BSIM4*]

* [*http://www-device.eecs.berkeley.edu/~bsimsoi BSIMSOI*]

*EKV MOSFET Model ( [*http://legwww.epfl.ch/ekv/ its web site at EPFL*] )

* [*http://pspmodel.asu.edu/ PSP*]

* [*http://www.iee.et.tu-dresden.de/iee/eb/hic_new/hic_start.html HICUM*]

* [*http://mextram.ewi.tudelft.nl/ MEXTRAM*] .

*Hybrid-pi model

* H-parameter model**References****External links***"Agilent EEsof EDA, IC-CAP Parameter Extraction and Device Modeling Software http://eesof.tm.agilent.com/products/iccap_main.html

**ee also***

Bipolar junction transistor#Theory and modeling

*S-parameters

*Small-signal model

*SPICE

*Two-port network

*Safe operating area

*Electronic design automation

*Electronic circuit simulation

*Semiconductor device modeling

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