Simple conduction

Our initial studies will more or less be a review of topics in electricity that you may have seen before in physics. However,if experience is any guide, there is no great harm in going back over this material, for it seems that for many students, thewhole concept of just how electricity actually works is just a little hazy. Considering that you hope to be called anelectrical engineer one of these days, this might even be a good thing to know!

Most of the "laws" of how electricity behaves are really just mathematical representations of a number of empiricalobservations, based on some assumptions and guesses which were made in attempt to bring the "laws" into a coherent whole.Early investigators (Faraday, Gauss, Coulomb, Henry etc....all those guys) determined certain things about this strange"invisible" thing called electricity. In fact, the electron itself was only discovered a little over 100 years ago. Even beforethe electron itself was observed, people knew that there were two kinds of electric charge, which were called positive and negative . Like charges exhibit a repulsive force between them and opposite chargesattract one another. This force is proportional to the product of the absolute value of positive and negative charge, andvaries inversely with the square of the distance between them. Different charge carriers have different mass, some are verylight, and others are significantly heavier. Electrical charges can experience forces, and can move about. Since force timesdistance equals work, a whole system of energy ( potential as well as kinetic ) and energy loss had to be described. This has lead to our currentsystem of electrostatics and electrodynamics, which we will not review now but bring up along the way as things are needed.

Just to make sure everyone is on the same footing however, let's define a few quantities now, and then we will see how theyinteract with one another as we go along.

The total charge in some region is defined by the symbol $Q$ and it has units of Coulombs. The fundamental unit of charge (that of an electron or a proton)is symbolized either by a little $q$ or by $e$ . Since we'll use $e$ for other things, in this course we will try to stick with $q$ . The charge of an electron , $q$ , has a value of $1.6E-19$ Coulombs.

Since charge can be distributed throughout a region with varyingconcentrations, we will also talk about the charge density , $\rho (\nu )$ , which has units of $\frac{\mathrm{Coulombs}}{\mathrm{cm}^3}$ . (In this book, we will use a modified MKS system of units. In keeping with most workers in the solid-state devicefield, volume will usually be expressed as a cubic centimeter, rather than a cubic meter - a cubic meter of silicon is just fartoo much!) In most cases, the charge density is not uniform but is a function of where we are in space. Thus, when we have $\rho (\nu )$ distributed throughout some volume, $V$