Alright, so I did some thinking about how I will go about finding the parameters for my simplified transistor models. 

To find the oxide capacitance, simply drive a known width, known length transistor with a current source. Tie the drain and source voltages to be appropriate to not have a body effect, and let the gate voltage have the appropriate starting condition.

The NMOS case is shown below:

The calculation for the ocide capacitance follows:

Then to find the other parameters, tie the drain, source, and gate voltages to bunches of different values and measure the drain source currents. 

We then find the best fit values for the x's based on our data points for a particular Vd. After that, the rest can be quite simple....

Now that I have Electric installed, I need to go through the various tutorials. 

Once that is done, the first order of business is to empirically find out a few values of great importance.

 

1. Critical Field Strength
   
2. Oxide Capacitance
   
3. Saturation Velocity
   
4. Effective mobility
   
5. Nominal Threshold Voltage
   

I will need to find these for both NMOS and PMOS.

I've decided I don't want to loose my circuit design skills, if my new job is software related. 

So I have conceived of the following project:

1. Design a super fast chip with multiple processors (perhaps with PDP-8 like instructions), with super fast, L1 and L2 caches made with 6-T SRAM, with many ports and queues. This will really test out my abilities. A lot of trade offs to consider for optimum circuit speed.
   
2. Have a PCI-E interface on chip, and have a really dumb driver that allows for direct access to the caches and code-streams for the processors. Cache coherency and instruction sequencing will be the responsibility of the programmer. 
   
3. Of course, I will then have to put it on a card, and that will refresh my PCB skills from a long time ago. 
   
4. Do a MOSIS run to create the chips, and I will need to get a cheap motherboard that supports PCI, with a cheap processor. I can then code programs to run massively parallel calculations like Black-Scholes, LU Factorization, Fast Fourier Transforms, SVD computations, and a whole school of such things on my PCI-E card. 
   
5. I will likely run Ubuntu on the system, meaning I will need to learn how to write Ubuntu drivers. 
   
6. Another nice challenge will be to see if I can convert some Apache Licence software to use my card to improve performance. I think the database, especially, can benefit from my MP-PCI card. 
   
7. Also, it will be fun to so some architectural modeling to see the trade offs between number of processors vs. cache etc. In addition, the circuit trade offs between power and speed, latch based design vs. domino vs CML vs. other logic families will be intense.
   

This is going to be very fun...but really expensive. Maybe I can take a class at Sac. State that puts runs through MOSIS.

I already downloaded Electric, MVSIS, and Dragon. I need to evaluate free simulators. I may just use the student version of Modelsim, but that would ruin any chance of me selling these cards. Making money isn't the point though.

Reviewing Basic Special Relativity

So, it didn't take very long to review the math needed to understand Maxwell's equations. I think I have a good grasp of the basic (though, as with mechanics, I will need more practice).

So on to special relativity. It has been a while since I took my modern physics course, but luckily Wikipedia, once again, has what I need for a basic review. 

Of course, let's start with the all-important Lorentz Factor:

Then the simple Lorentz Transformation for an inertial reference frame moving in the x direction...

Which yeilds time-dialation, and length-contraction in the direction of motion...

Which of-course has the inverse...

We also get the new way to add velocities...

And, we need definitions of Energy and momentum that'll be conserved...

We also need an reference frame invariant way to define "mass"...

If we try to relate the velocity four-vector  to the momentun four-vector  to get the analogous equation to the non-relativistic  we have...

Which leads to the famous equations...

Giving back our definitions of Energy and momentum. Cool huh?

But that was just a small digression from the straight summary of the basics (i.e. Special Relativity without the formalism)

So what do we have left? Force of course.  Which has quite a large number of forms.

We start with the definition that keeps...

...and just crank out from there...

Since , we have...

We can split that into components of acceleration, thus...

Well, that should cover the basics...well, there is Kinetic Energy. Real quick...

Let's look at the integral:

 

This allows us to conclude:

Well, that last bit was ugly, but the result was simple enough.

All this is a bit much for me to digest. But I think I got most of this (excepting maybe exactly knowing when to use inveriant mass, relativistic mass, or rest mass--but I'll figure it out).

After, I digest this stuff, it may be time to move to the formalism.

Re-Learning the Theories of Electricity and Magnatism

I am now in the process of changing from Engineer to Physicist. So, and reviewing a lot of my physics. It'll be a long road, and I will being going back to undergrad to do it. 

The laws of mechanics are straight forward enough.

Newton's second law:

Which is equivalent to the basic law in Lagrangian Mechanics:

Which is in-turn equivalent to the basic law's in Hamiltonian Mechanics:

Certainly, there are a lot of special cases to consider, the work energy theorem, the notion of conservative forces, etc. --I need plenty of practice, in addition.

But I will now focus on Electricity and magnetism, since it is used as a model to thing about many of the big problems in physics.  

The laws themselves are plenty....

There are the four equations for free charges:

Then the two new equations for total charge:

Beyond that each one has an integral form:

Beyond that, we need to comrehend that:

There is all that funkiness with the units of current density,  magnetizing field, electric displacement field, electric field, and magnetic field.  The accounting for that is something I don't have straight yet--not even conceptually.  

Mathematically, I need to review the meaning of the div and curl, as well as integrating over lines and surfaces. 

Beyond that, there is the task of learning how special relativity plays into things, and learning the covariant formlation of clasical electromagnatism.  But I suppose the last part can come while I try to tackle special relativity in full-form. 

So much to learn and so little time.