MOS Transistors

Learn how MOS transistors work, and how to model them. The understanding provided in this course is essential not only for device modelers, but also for designers of high-performance circuits.

About The Course

The MOS transistor (MOSFET) is the workhorse of the microelectronic revolution. It is estimated that there are currently over 1 billion transistors per human being in the world. Part of the MOS transistor's success lies in its very small size (you can fit 1,000 of them within the width of a human hair!), part lies on some amazing things this device can do. However, the descriptions of MOS transistors in basic electronics courses cannot begin to do justice to this device. If you want to really know how the MOSFET operates, and how to model it, you need to study it carefully and systematically. This course will help you do just that. 

The course starts with a review of basic physical principles, and expands into a detailed treatment of MOS transistor phenomena, in a logical and systematic fashion, enhanced by intuitive discussions. We discuss a hierarchy of models - from the simple to the sophisticated - clearly identifying the connections between them, and encompassing many aspects of modeling, including dc, large-signal transient operation, quasi-static operation, non-quasi-static operation, small-signal operation, noise, and structural effects. We discuss the concepts on which the most popular CAD (computer-aided design) MOS transistor models are based.

Frequently Asked Questions

  • Will I benefit from this course if I am an integrated circuit designer?
If you are designing analog or high-performance digital and mixed-signal circuits, the answer is certainly yes. The modern MOSFET is a device with complex and idiosyncratic behavior; you cannot treat it as a black box and hope to develop efficient, high-performance circuits with it. It is no longer sufficient to treat it as a textbook "square-law device"; modern devices are not square-law. It is no longer sufficient to think that the device is off if its gate voltage is below the threshold; your watch contains many transistors operating with their gate voltage below the threshold, and they are certainly not off! To design high-caliber circuits, you need a high-caliber understanding of your transistors.

  • What computing resources are required for this course?
All you need is a math package, such as Matlab, MathCad, Mathematica, or any other package that can help you quickly evaluate algebraic expressions and make plots. Such packages often have inexpensive student versions available. There is also math freeware, such as GNU Octave, available on the Web. 

  • How easy is it to get by in this course without reading the textbook?
Some students could get by without it, depending on their background and their learning style; but reading the textbook will really help. The textbook provides detailed explanations for everything we cover in the lectures, including parts  which, due to lack of time, are just mentioned and taken for granted. At Columbia, students taking a similar course spend about half of their time reading the textbook, and half doing the homework.

  • Do I need a background in semiconductor devices? 
You do not need a background beyond what is provided in many basic electronics courses, concerning electrons and holes, intrinsic and extrinsic semiconductors, drift and diffusion, etc. However, even these concepts will be reviewed at the beginning of the course. If you have not seen such material before, this review, together with reading the first chapter of the textbook, should be enough to allow you to follow the rest of the course.

Recommended Background

This course assumes a background in basic calculus and in basic circuits and electronics. The course will include a quick refresher of basic semiconductor concepts (electrons and holes, intrinsic and extrinsic semiconductors, drift and diffusion, etc.).