MOSFET Simulation ECE 417

George Vartanov

Introduction MOSFETs are the most ubiquitously used semiconductors in the electrical engineering field. In this project we will be exploring the various aspects of the MOSFET through simulation in three different software applications. The parameters that we calculate initially will help us see the behavior of the MOSFETs through I-V curves.

Part 1: MATLAB Finding the Threshold Voltage:

Finding these parameters required a few key equations. The first parameter is the bulk potential. In this case the bulk is mostly p-type. This means it is expected to be positive and is consistent with the value that I found above. In addition to this, the capacitance of the oxide should be quite small due to the very small value of GOX.

This small capacitance corresponds to the flat band voltage relatively well due to the fact that the C-V curve for a NMOS shows a small capacitance for negative voltage values. The M parameter is a scalar that takes into account the bulk potential for improved accuracy. That value should be greater than 1 so my value makes sense. Finally, the threshold voltage is the turn-on point for the MOSFET, and should be relatively low and positive.

Developing the Output Curve:

The curve at the left depicts the output characteristics of the MOSFET at some specific gate biases. It is somewhat difficult to see the cutoff curve, but the value is at a constant current value of 0A. The reason that the blue curve is in cutoff is because the value of Vg is below the threshold voltage for this MOSFET. These curves do not take into account any channel length modulation because the saturation region looks completely

ideal. The saturation region exists to the right of each of the voltage values marked Vdsat on the curves. The pre-saturation region is located to the left of those voltage values. It is clear that the drain current increases with the gate voltage.

Paramter Value B .4165 V Cox 3.4531e-07 F VFB -1.0693 V M 1.2903 VT0 .247 V

Developing the Transfer Curve: The plots at the right depict the transfer characteristics of the MOSFET. The upper figure has the data plotted with a logarithmic scale used for the current while the lower figure uses a linear scale. The logarithmic plot is the most effective at revealing where the current plateau occurs. This is the region where the change in gate voltage does not have much influence on the drain current. There is definitely an increase in current when the drain voltage increases. As the drain voltage values increase, there is not as much of a difference in the drain current at high gate voltage values. The linear graph is useful for seeing which values of drain voltages would increase the drain current at the most dramatic rate. In addition to this, the linear graph reveals where the threshold voltage is as the current is only non-zero at values higher than .247 Volts.

Part 2: HSPICE Developing the Output Curve:

The figure to the left is the HSPICE representation of the output curves. This plot is very similar to the one generated by MATLAB with one significant difference. The HSPICE model does take the channel length modulation into account when creating the curves. The blue line still represents the cutoff region. The black line divides the saturation region (right side) from the pre-saturation region (left side).

Developing the Transfer Curve and estimating VT: The figures to the right are the HSPICE representations of the transfer curves. These are very similar to the results I acquired in MATLAB. This result seems more accurate than the initial plot that I found earlier and also has a slightly higher current overall. I am not sure what HSPICE is accounting for that was not included in MATLAB. The overall trend is the same in both graphs, which is reassuring. In order to calculate the threshold voltage from these plots, the drain voltage value of .1 Volts was used. Using the trace tool on the logarithmic plot, I found the point where the curves began to split and estimated the voltage to be approximately .272 Volts. The linear model was slightly more difficult to use, but I found a value of approximately .276 Volts. This makes sense, as the calculated value earlier was .274 Volts.

Part 3: ATLAS

Energy Band Diagrams at Various Locations: The figure at the right shows the band energy at Y = 0.6 microns. This makes sense because the poly-silicon layer should not have a difference between valence and conduction bands. At the oxide there should be a rapid change of the energy due to the capacitance found in the region and is also what the two black bars are representing. In the p-substrate, there is a difference in the valence and conduction energies and according to this plot the MOSFET is in accumulation region of operation.

The figure to the left depicts the energy levels laterally across the device. Because there are no biases on the device, there will be equivalent n-type regions and a flat p-type region. The energy should be higher in the p-type region so this diagram makes sense. The device would be at equilibrium at this point.

Developing the Output Curve: The figure to the right is the ATLAS representation of the drain current using a slow sweep over the drain voltages. The different curves depict the drain current at different gate voltages. This figure is more relatable to the HSPICE simulation than the MATLAB output curves. The current is also quite low on this graph.

You mentioned this in the project description, but I could not figure out how to account for it in ATLAS. Developing the Transfer Curve: The curves to the right are the ATLAS representations of the drain current when preforming a sweep over gate voltages. The three different curves are the three different values of drain voltage biases we tested. The biggest difference that is visible in these plots is the rate of increase in slope. It is clearly much slower when using ATLAS due to the accuracy of the software. There were many more parameters being taken into account when developing the curve. The gaps between the curves are much more defined in this linear representation. However, it would be very difficult to estimate VT using these curves.

Biasing the Device: 1) Cutoff: The figure at the top includes the energy bands in red and blue. The green curve is the potential energy. The potential energy is exactly mirrored by the valence band energy across the Fermi energy level. The potential energy should be lower in the p substrate due to the lower number of electrons. The following figure represents the electric field at cutoff. The electric field should be much larger in the p substrate since it is in the accumulation region. The oxide has an electric field, which causes this increase, while the n regions do not have anything causing an electric field. The peaks of the electric field are likely due to abrupt changes in doping in the device. The final figure is the representation of the hole and electron concentration along the device. This makes perfect sense since this is an NMOS device, and has a high number of holes in the center with large quantities of electrons on the left and right side of the substrate. Because this device is in cutoff, the figures are all expected to be symmetrical and in equilibrium.

2) Pre-Saturation: The figure at the left displays the energy bands and potential of the MOSFET when it is in pre-saturation mode. There is not a very large gate to surpass which will allow current to flow much more easily. The electric field is higher towards the drain due to the high voltage being applied to the gate. This also causes much more electrons carrying current to be present near the drain. In comparison to the device in cutoff, there are much fewer holes present and many more electrons present over the whole device.

3) Saturation: The figures at the left represent the device in saturation. The energy bands are very close together due to the high biasing on the gate and the drain. This makes sense due to the clear ease of the current to flow from the source to the drain. This amount of current flow causes a serious spike in the electric field. The electric field has two valleys where the concentration changes in slope. The electric field is mostly negative and is much different from the pre-saturation electric field. The concentration of holes is very close to zero because of how heavily doped the MOSFET is. The electron concentration changes with the hole concentration at the gate drain interface due to recombination generation occurring at the junction.