Device Model

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.

Figure 1: Floating-gate avalanche injection memory device FAMOS

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. 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.
Functional model of an NPN transistor
The operation of a transistor is difficult to explain and understand in terms of its internal structure. It is more helpful to use this functional model:

The base-emitter junction behaves like a diode.
A base current I_B flows only when the voltage V_BE across the base-emitter junction is 0.7V or more.
The small base current I_B controls the large collector current Ic.
Ic = h_FE × I_B (unless the transistor is full on and saturated)
h_FE is the current gain (strictly the DC current gain), a typical value for h_FE is 100 (it has no units because it is a ratio)
The collector-emitter resistance R_CE is controlled by the base current I_B:

I_B = 0 R_CE = infinity transistor off
I_B small R_CE reduced transistor partly on
I_B increased R_CE = 0 transistor full on ('saturated')

Additional notes:

A resistor is often needed in series with the base connection to limit the base current I_B and prevent the transistor being damaged.
Transistors have a maximum collector current Ic rating.
The current gain h_FE can vary widely, even for transistors of the same type!
A transistor that is full on (with R_CE = 0) is said to be 'saturated'.
When a transistor is saturated the collector-emitter voltage V_CE is reduced to almost 0V.
When a transistor is saturated the collector current Ic is determined by the supply voltage and the external resistance in the collector circuit, not by the transistor's current gain. As a result the ratio Ic/I_B for a saturated transistor is less than the current gain h_FE.
The emitter current I_E = Ic + I_B, but Ic is much larger than I_B, so roughly I_E = Ic.