FOUR LEVEL SIMULATION OF MOSFET

In this paper a software (MOSOFT) has been developed for 4-level simulation of MOSFETS. This software simulates the device characteristics up to micron channel length and includes long channel, short channel, subthreshold and field dependent mobility degradation models.


I. INTRODUCTION
Nowadays, IC designers have the opportunity to set or tune or adjust devices to circuit needs by using circuit simulation softwares which save considerable time in testing, optimising and verifying the performance of circuits. MOSOFT is one such simulation software.
We briefly explain Subthreshold Region and Short Channel Effects below as these play an important role in MOSOFT-Simulation Software.

Subthreshold Region
When gate voltage is below threshold voltage, the corresponding region is called subthreshold region.

Short Channel Effects
For a given channel doping concentration as the channel length is reduced, the depletion layer widths of the source and drain junctions become comparable to the channel length. Potential distribution in the channel now becomes Two-dimensional depending on both the transverse field (controlled by drain bias) and longitudinal field (controlled by gate bias). This resuls in: a) degradation of subthreshold behaviour; b) dependence of threshold voltage on channel length and biasing voltage. c) failure of current saturation due to punch through. Short channel effects complicate device operations and degrade device performance and hence should be minimized.
A particular approach concentrates on decreasing device dimensions while maintaining long channel behaviour in the subthreshold region. It has been empirically found that the minimum channel length for which such long channel behaviour is maintained fits in the relations: Zmin 0.4[r tox(Ws -+-Wz)2] 1/3 (1) where r: source and drain function Ws" depletion width at source Wz: depletion width at drain tox insular thickness MOSOFT is developed on 4 levels which are briefly explained below: Level is used solely for implementation of long channel MOSFETs.
It is based on the model proposed by shichmann and Hodges [...] and is usually not precise. Level 2 gives a better model for large and short channel MOSFETs, It in based an the model proposed by Ihantola and Moll [1].
where Qo is the charge at the oxide-silicon interface Cox is the capacitance per unit area of the thin oxide layer.
For VGB Vw, the carrier concentration is constant in the semiconductor and equals NA. When VGs > Vvs, the holes (majority carriers) are pushed away from the surface so that the negative charge of the fixed ions restores the balance with the gate charge. The carrier concentration near the surface is said to be depleted, The thickness of the depletion region Xs is given by Xn (2 s/qNA)l/20s (3) where Os is the potential across the depleted region. If Os is small enough to neglect the minority carriers in the channel, we get Os {IT 2 + 4(VcB-VFB) / T]:/4} (4) where T ((2 s qNa)/Z/Cox). These equations are valid as long as the carrier concentration remains negligible with respect to NA in the channel. When Os is sufficiently high, the concentration of electrons at the surface can exceed that of the holes in the substrate. From Boltzmann's distribution this happens when or i.e., when n NA niexp(Opq/KT) (6) Op (KT/q) In (NA/ni).
At Os 2Op, this theory assumes that the surface condition changes from depletion to one of inversion.  1) Gradual channel approximation, 2) Uniform doping throughout the P-region, 3) Constant mobility throughout the channel length, 4) Only drift transport occurs in the channel.
We get an expression for VD'sat as.
[V6s-  MOSFET Implementation for Level 2 The threshold voltage can be calculated from the physical parameters by the equation:  mobility was assumed constant. A variation of the parameter np has been introduced in MOSOFT. The modified expression is: Uc is the gate to channel critical field and the term (Vos-VxH)/tox represents the average electrical field perpendicular to the channel.    The model seen so far provides good results in the simulation of MOSFETs with a minimum channel length of 4-5 #m. 5. Effect of channel width on threshold voltage: In the MOSFETs with a small channel width IV, the value of the threshold voltage VTI is greater than that indicated by the previous theory. This effect is due to the 2-dimensional distribution of the QB at the edges of the channel. A modified equation is therefore VrH VF + 2Op + T'(2Op Vs) '/ + (s Tr/4Cox W)(2Op Vs).   The effect of gate voltage is dominant on the mobility. For this reason, it is sometimes said that eff "depends an the gate field". It is more correct to say that #eff depends on the normal field, which in turn, depends on all terminal voltages. Thus the following form has been Here VT-is the long channel threshold. The values of #o, 0 and 08 used in the above equation may have to be chosen empirically. By comparison to minimise the error. A typical value of #o is 60 m2/v ns for n-channel devices at room temperature 0 is of the form /0/tox, /3o is typically 0.001-0.004 m/v and tox is the oxide thickness, 08 is about a few hundred of lv-1. VT. This effect is assumed unrelated to pinch off and is present whether VDS is smaller or larger than Vs since even for VDS > V'DS the channel once is directly influenced by the field lines even in saturation, VT will continue to be an emanating from the nearby drain. Hence, function of VDS, not Vs. (42) /Dsat and GD.sat represent the current and conductance respectively for VDS VDsat-K is an empirical fitting parameter.
The results for MOSFET Level 3 are shown below (Fig.14):

VIII. PMOS TRANSISTORS IMPLEMENTATION
If the substrate is made of n-type material and the source/drain regions of P-type material, we have what is known as the p-channel MOS transistor or PMOS transistor.
The operation of the p-channel transistor is the 'dual' of the nchannel operation. The role of electrons played by holes and the role of ionised donor atoms. The value of the effective mobility for p-channel devices at low gate voltages is smaller than that in p-channel devices by a factor of 2 to 4; a typical value is 25 m2/vns. IX

X. CONCLUSION
The Level is not sufficiently precise because the theory is too approximated and the number of fitting parameters too small; its usefulness is in a quick and rough estimate of circuit performances.
The Level 2 Model can be used with differing complexity by adding the parameters relating to the effects needed to simulate with this model. But because of its inherent complexity a great amount of CPU time is required for the calculations. The Level 3 model is better off than the Level 2 an the CPU time required for the model evaluation is much lesser. The only disadvantage is the complexity in the calculation of some of its parameters.