This post contains a derivation of a recurrence relation that can be used to calculate $\pi$. While it's not useful for the purpose of calculating to any decimal place imaginable, what's notable is that it only uses the Pythagorean thereom and should therefore be easy to follow. Unsurprisingly, the recurrence relation is neither original nor unique because it falls under the category of using polygons to compute $\pi$ (attributed to Archimedes). At the end of the notebook, the derived recurrence relation is implemented in code and run.
read moreAutomated drawing of the MOS band diagram
The MOS capacitor's band diagram can be drawn using results from the one-dimensional solution of Poisson's equation. This post uses the results from the MOS capacitor analysis to automate drawing of the band diagram. Written in an IPython notebook so that the code is shown alongside the discussion.
read moreMOS surface potential equation
A derivation of the surface potential equation of the idealized MOS capacitor. The resulting equation is used by the MOS capacitor derivation post in order to relate applied voltages to semiconductor band-bending.
read moreGauss's law as used in MOS derivations
There are two applications of Gauss's Law used in MOS derivations for computing the surface potential equation (SPE). One of the applications is also used in the formulation of semiconductor charge per unit area from the surface field that is found during the solution of Poisson's equation. This post presents both applications of Gauss's law, which are required to complete the MOS capacitor analysis.
read moreElectrical characteristics of the MOS capacitor
An IPython notebook showing the derivation of the electrical characteristics of the idealized MOS capacitor by using the one-dimensional solution of Poisson's equation. The results of the derivation are entirely physics-based and are coded in Python. The code is used to generate plots showing the derived quantities.
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