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Barrier potential and width in a pn step junction, L-VI.

Today we will discuss about the depletion region in greater detail than before. We will derive a quantitative relation among barrier potential and its width which are created in the depletion region, as discussed before. We will also derive an expression for the electric field that is established due to this potential.

Lets first recall how electric field and electric potential are related to each other. Electric field is the negative potential gradient. Mathematically, in 1 dimension this is expressed by the following formula.

read more Barrier potential and width in a pn step junction, L-VI.

valence band and conduction band after diffusion of electrons takes place from n side to p side and creation of depletion layer.

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Energy levels in semiconductors. L-V.

Today we will discuss about energy levels and energy bands in semiconductors as well as breakdown in reverse bias.

This is because there is an attractive interaction between the nucleus and the electrons. Electrons must gain energy to go into higher energy levels. This is achieved by sources of heat, light or applied potentials. When the electrons fall from the higher energy levels they release their extra energy again in the form of heat, light or other radiation.

The energy of an electron is proportional to the size of the orbit it is found in. Thus specifying the radius of an orbit, of the electron, is equivalent to specifying its energy level. So electrons in the smallest or innermost orbit are in the first energy level. Electrons in the next higher orbit. i.e. second orbit belong to the second energy level, which is higher. Thee next orbit corresponds to the next energy level which is still higher, and so on for higher orbits and energy level.

read more Energy levels in semiconductors. L-V.

Forward and reverse bias of a pn junction diode.

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PN junction diodes (L-IV)

Today we will discuss about what are PN junction diodes and various conditions they can be subjected to, viz. the forward and reverse bias. We will discuss what is a depletion layer and whats a built-in potential barrier.

In our previous lecture we saw what are extrinsic semiconductors. We discussed that they are of two types, viz. p-type and n-type. By themselves the p-type and n-type semiconductors are not so useful.
But when crystals are doped so that one-half of the same is p-type and the other-half is n-type they serve very important purposes. They are now called PN-junction diode. The border or interface between the p-type part and n-type part is known as PN-junction. The PN junction finds application in almost all sorts of electronics through diodes, transistors and integrated circuits.

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Semiconductors and charge carriers: the silicon atom's electronic configuration. There are 14 electrons and 14 protons in the copper atom which makes it electrically neutral. Together with 10 electrons in the first 23 shells ( K, L ) and the 14 protons in the nucleus the copper atom's core has a net charge of + 4 e. The electron in the outermost M shell has 4 electrons, known as the valence electrons. Photo Credit: mdashf.org

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Conductivity and mobility in semiconductors, L-III

We will discuss in this lecture about drift velocity of electrons and holes in semiconductors which leads to the conductivity and mobility of free charge carriers in the same.

To smooth-sail through this lecture you might wanna first brush up the concepts discussed in the last two lectures: lecture I and lecture II.

Lets begin with Ohm’s law: I=V/R. — eqn 1

Here I is the electric current, V is the applied potential difference and R is the resistance of the material considered. The resistance R depends upon the length l and area of cross-section A of the given material. Let us cast Ohm’s law into a form which is independent of l and A.

read more Conductivity and mobility in semiconductors, L-III

To find the magnetic vector potential of a rotating, uniformly charged spherical shell. Vector potential, magnetic field intensity (mag induction) and current density are the most basic parameters of magnetostatics.

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Magnetic vector potential of a rotating uniformly charged shell.

Today we will solve the problem of finding magnetic vector potential of a rotating, uniformly charged spherical shell. We won’t discuss the general idea behind the vector potential (how it follows from Helmholtz theorem, and gauge freedom etc) and how its defined. That will be part of a conceptual lecture and will be available when the same would be created. The offline version is available, but the web version will call for a special priority to be assigned.

The problem is quite well defined. We just need to follow the straightforward method of implementing the basic definitions and carrying out the required steps. But we need to be mindful of the framework in which we need to accomplish these steps.

The framework I am talking about here is the coordinate system we need to set in order to solve the problem. Notice that the problem has been stated in the spherical coordinate system (which has been discussed couple of times in this website). But we need not worry about all the aspects of this coordinate system, we will only pick on those which are immediately applicable to our problem.

While this choice of the system where the polar axis (z-axis, wrt which the polar angle θ is measured in a r, θ, φ spherical coordinate system) coincides with the angular velocity vector ω is very natural, it isn’t the most convenient for carrying out the ensuing integral for the vector potential A.

read more Magnetic vector potential of a rotating uniformly charged shell.