The motivation for this investigation stems from three main concerns:
1. The usual parameterization of device models for device and circuit simulation causes problems due to the interdependence of the parameters.
It is not physically realistic to change any one parameter without determining the change in the process technology that would produce such a change in the parameter.
Then all the other parameters which also depend on this change in the technology must be adjusted accordingly.
In addition, it is quite difficult to determine the effect of a specific change in a new technology since the available parameters each depend on a number of technology parameters.
2. The predictive performance of present models is not good. It has usually been necessary to fabricate devices in any chosen technology, and extract parameters, and then fit the model to this specific technology by use of additional “adjustment” parameters.
Of course, this procedure is reasonable and useful once a technology has been chosen. However, it would be useful if the model could produce fairly accurate results if only the process specifications are used.
Without such predictive accuracy it is difficult to make an initial choice of technology.
3. Most models have been developed for digital applications where devices operate above threshold and therefore are not strongly temperature sensitive.
This causes problems for modeling analog circuits which use sub threshold operation. In particular, the temperature dependence of sub threshold behavior has not been fully explored. In many models some parameters which are temperature dependent have been assumed to be constant.
Device and circuit models are all based on the physical properties of semiconductor materials, the dimensions of the devices, and on theoretical and empirical equations which are intended to model electrical behavior.
The distinction between theoretical and empirical equations is often unclear. Most of the equations are substantially empirical.
Of all the equations, one of the most fundamental, and problematic, is the equation for ni, the intrinsic carrier concentration of asemiconductor.
The definition of ni derives from the thermodynamic equilibrium of electron and hole formation, based on the fact that the energy gap is a Gibbs energy. The equilibrium equation is
where n is the electron concentration, p is the hole concentration, Nc is the density of effective states in the conduction band, Nv is the density of effective states in the valence band, Eg is the band gap, k is Boltzmann’s constant and T is the absolute temperature.
The carrier concentration is then given by It would appear to be a simple matter to substitute Si values for Nc, Nv, Eg, and the value of the constant kT to obtain an accurate value of ni.
However, the theoretical and experimental knowledge required for accurate values of Nc and Nv is even now incomplete. In the early 1960’s, when Si-based circuits were beginning to be designed and fabricated very little was known about Nc and Nv, but estimates were required for practical use. This led to approximations based on work. The key approximation was that chosen by Grove in . This approximation is the still widely used
1. Determination of Intrinsic Carrier Concentration (ni)
The empirical expressions for Eg from Bludau and for Nc and Nv from Sproul and Green provide the values needed for equation (2.1). Our derivation of the equation for ni follows Green. Therefore, the exciton binding energy term, using the value Exb = 14.7meV, is included in the band gap, Eg.
In the past, this term has either been neglected, or in some cases a value of 10meV has been used. Green  and Sproul and Green are by far the best references for the history, theory, and experimental measurements leading to reliable values for ni. Thus, the equations are: