Physical model

Numerical analysis based on the fundamental equations governing semiconductors has become necessary in IC technology development, and is often referred to as "device simulation”. MEDICI is part of a technology computer-aided-design (TCAD) package, which includes process simulation, device simulation, and parameter extraction programs[1]. The use of a device simulator or TCAD tools in general, requires substantially more knowledge of the internal workings of the simulator than the use of, say, a circuit simulator such as SPICE. For instance, users must choose which mobility model to use, which statistics (Fermi-Dirac or Boltzmann) to use. The default physical models are usually the simplest ones, and often give inaccurate results, particularly for advanced device technologies such as SiGe.

As was mentioned earlier, choosing the right model in the simulation is fundamental in the calibration process. Each device has its own mobility model that is suitable to its operation method. Mobility is a measure of the time interval between collisions for a carrier moving through a semiconductor lattice. The two most important collision mechanisms in bipolar transistors are lattice and impurity scattering, and the total mobility is given by the sum of the probabilities of collision due to these individual mechanisms. Lattice scattering is caused by collision between carriers and the atoms of the semiconductor lattice. These lattice atoms are displaced from their lattice site by thermal vibration, since thermal motion increases with temperature, the mobility decreases with temperature. However, as the doping concentration increases beyond 1015 cm-3 - 1016 cm-3, which is the case in bipolar transistors, the lattice scattering mechanism becomes less important and impurity scattering becomes the major factor in defining the carrier mobility.

The impurity scattering is caused by collisions between carriers and impurity atoms in the semiconductor lattice. An increase of doping will increase the number of collision which will lead to further decrease in the mobility. This impact has been confirmed by experiment and was reported for different semiconductors such as Si, Ge and GaAs [2, 3]. Therefore, it is important to choose the mobility model that reflects the impact of the impurity (doping) on the mobility. The model chosen was the Concentration Dependent Mobility model and it has been added to the simulation by adding the term CONMOB to the model statement.

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In lightly doped semiconductors, the dopant atoms are sufficiently widely spaced in the semiconductor lattice, therefore it is reasonable to assume that the dopant atoms have little effect on the perfect periodicity of the semiconductor lattice and therofore on the edge of the valence and conduction bands. However this is not true at heavy doping, where the dopant can perturb the perfect periodicity of the semiconductor and reduce its band-gap. This effect is known as band-gap narrowing. The important effect on the operation of bipolar transistors is that it affects the intrinsic carrier concentration as illustrated by the following equation [4]:

_(4.1)

where ni is the intrinsic carrier concentration at low doping levels, nie is the intrinsic carrier concentration at high doping level and ∆EG,H is the band-gap narrowing caused by the doping. Various band-gap narrowing models have been developed for use in bipolar transistor simulation. However, the Slotboom BGN model is the most widely used band-gap narrowing model. This model has been implemented in nearly every major commercial device simulator, including MEDICI [5]. The following equation represents Slotboom model:

(4.2)

With ∆EG,L=6.92 meV, 1.3×1017 cm-3 and C=0.5 and N is the doping level.

It is important to mention that based on the above equation the band-gap narrowing in Silicon will occur at doping levels which are higher than about 1.3×1017 cm-3. Since the doping level in the device is higher than this value, then it is important to include this effect for an accurate simulation [6].

It is obvious that the incorporation of Ge into Si bipolar transistors, to produce SiGe HBTs and sSi HBTs, has improved the performance of bipolar technology. However, it leads to more defects present in the device. These defects cause energy states to be introduced into the forbidden gap. These energy states act as a stepping stones for the generation and recombination (G-R) of electrons and holes. As was reported in chapter 3, the ideality factor of the base current at low voltage (VBE <0.4 V) is higher than 1. This increase of the ideality factor is caused by the generation recombination phenomenon. Therefore, the AUGER and

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CONSRH models have been used to account for the generation–recombination processes, which are only important for the base current at low base voltages (VBE < 0.4 V).

Generally, drift and (or) diffusion mechanism are responsible for the transport of electrons and holes in semiconductor. However, this is true only in continuous media (in the absence of band discontinuity). The energy bands in both the SiGe HBTs and the strained Si HBTs exhibit a discontinuity at the base-collector junction. The electrons must pass this discontinuity through thermionic-field emission or tunnel phenomenon. Therefore, including these phenomena in the simulation is necessary.