## Semiconductors and Diodes – Soham Ghosh

As all of the world would agree, semiconductors are one of the major creations of Physics in the field of electronics. Semiconductors are almost an essential part of every circuit and integrated circuit today.  So this week’s fact of the week is about this exciting area of Physics!

Semiconductors, by definition, are material in which the current flow is an intermediate between conductors and insulators. Firstly, let’s take a look at how conductors and insulators work to better understand the situation for semiconductors.

## Energy bands in solids:

In the case of a single isolated atom, there are single energy levels (1s2 2s2 2p6 3s2….). These energy levels are discrete (due to electron containing orbitals being degenerate) and far apart, as you can see in the figure below:

(Note that this is also used in the explanation of photon absorption, in which only an photon with the energy E = hf is absorbed where E refers to the energy difference between the lowest unfilled orbital and the one next to it.)

However, as we know, in the case of solids the atoms are arranged in a systematic space lattice and hence an atom is greatly influenced by its neighbouring atoms. Hence the energy level diagrams of the outer shells (which are not strongly bounded by the nucleus) differ very slightly from one atom to another. As a result, on the whole, due to the intermixing of the number of permissible energy levels increases. Even though the permissible energies are actually still discrete, the difference between the closest ones is minute and for most purposes may be considered to be non-existent. Hence the result is that instead of discrete lines, now bands of energy exist.  And the two bands that we will be examining today are the valence band and the conduction band. As you can see in the figure below, the conduction band is the lowest unfilled energy band. The band below that is the valence band, which contains the valence electrons, and is the band having the highest occupied band energy.

The energy gap shown between the valence band and the conduction band is also known as the forbidden energy gap.

How conduction works:

Electrons present in the conduction band are able to move about freely and conduct electricity, and hence electrons existing in this region are known as conduction electrons. Electrons may jump from the valence band to the conduction band in order for electricity to be conducted.

In metals/conductors, the conduction band and the valence band overlap. Hence plenty of electrons are available to conduct electricity as electrons in the valence band can freely enter the conduction band. Even the slightest potential difference can cause the free electrons to move. The most important characteristic of conductors is that charge carrying is simply by electrons as holes are not present in the system.

In insulators, a large forbidden energy gap exists. The gap is typically of the order of 10 eV. The valence band is completely full at 0 K, hence no possibility of conduction of electricity. Increasing the temperature (hence supplying thermal energy) or by applying a high electric field may result in some electrons being able to jump across the forbidden gap, however  the current generated is minimal. Only above the breakdown voltage, may a substantial current be obtained. But you will probably end up burning stuff or destroying stuff, like in the two videos here:

Now, let’s move on to the topic that we wanted to discuss: semiconductors. As mentioned before, semiconductors are somewhere in between conductors and insulators.

In semiconductors, the forbidden gap does exist, but is much smaller. For example in Si it is 0.7 eV and in Ge it is 1.1 eV. Hence, like insulators, at 0 K there are no electrons in the conduction band. However, when a small amount of energy is supplied (for example thermal energy at room temperature), electrons easily jump from valence to the conduction band. Actually, when the thermal energy is increased, the forbidden gap decreases. Click on the link to the gif file for a graph for a demonstration of this. As you can see, the electrons gain energy and move to higher energy levels (the x axis parameter F is actually a probability distribution function). For those interested, this has been obtained using Fermi Dirac statistics (http://en.wikipedia.org/wiki/Fermi-Dirac_statistics)

## Semiconductors:

There are two kinds of semiconductors: intrinsic semiconductors, or extrinsic semiconductors.

### Intrinsic semiconductors:

Intrinsic semiconductors are pure semiconductors such as pure Ge or Si. Note that both the compounds are tetravalent, with 4 valence electrons. Both of these materials exist in a crystalline state where the bonds are covalent bonds. (recall J1 chemistry). Hence the crystal structure is tetrahedral.

Refer to the above diagram for easy reference. o refers to an electron. Each Si atom is bonded to another via a single covalent bond. However, at 0 K all these bonds are intact and hence no electrons are available for the conduction of electricity.

However, at a higher temperature, for example at room temperature, a few of these bonds might actually break, resulting in some of the bonding electrons being released. The result is the diagram below. One of the electrons breaks away from the bond. The dissociated electron (in red) is now able to conduct electricity, as it is free to move.

The + sign at where the bond was broken refers to a hole. A hole is basically the absence of an electron from where it was supposed to be present. Hence, by symmetry, it has a unit positive charge. At room temperature, for every such bond broken, a hole is formed. Therefore, in semiconductors, the flow of electricity is due to the drift of electrons , as well as the drift of holes. The mechanism for drift of holes is described below.

Drift of holes: (dissociated electrons not shown)

When electrons are liberated on breaking the bonds, they move about randomly, conducting electricity. But how do holes move? Holes are not physically occurring objects, just a concept. However, in the presence of an electric field these holes are said to move.

Let’s say a hole is formed at (A). A positive charge can be considered to exist at that site. This then strongly attracts bonded electrons from nearby Si atoms. One of the bonds breaks (let’s say at B). The electron at that site then fuses with the hole (with slight release of energy) to complete the Si-Si bond at A. Now the hole exists at B and from here the hole travels to C by the same mechanism. Hence the net effect is the drift of the holes.

Such is the case for an intrinsic semiconductor which is purely made of one element.

## Semiconductors

### Extrinsic semiconductors:

There are mainly two types of simple extrinsic semiconductors, the first of which is N type semiconductor.

In the N type semiconductor, a small amount of pentavalent impurity is inserted into a pure semiconductor crystal during crystal growth. This process is known as doping, and usually the element Arsenic (As) is used.

The As atom having five valence electrons, after the tetrahedral structure has been formed using special manufacturing techniques, it still has a lone electron that is loosely attracted to the nucleus of the As atom. Slight appliance of thermal energy causes this electron to dissociate and be able to conduct electricity. Hence for a small amount of the N type semiconductor a larger amount of electrons are available. This is to increase the conductivity of the semiconductor, and also to manufacture diodes (discussed later).

In the same line of thought the P type semi conductor is produced. In the P type semiconductor, instead of pentavalent atoms, the pure crystal is doped with trivalent atoms, usually Boron (B). Now instead of there being an extra electron, a hole exists at the place where an extra Si bond cannot be formed because all the valence electrons in B have already been used for bonding with 3 other Si atoms. Hence in the P type semiconductor, the conduction of electricity is mainly due to drift of holes.

Now, you may be wondering how do the P-N junctions work which are widely used as diodes as many of the circuits in the world today.

### P-N junctions:

Diodes usually consist of P-N junctions which consist of a P-type material is joined to an N-type. Now, as we know, (ideally) diodes conduct electricity only and only when it is forward biased (let’s take it to be the correct way of joining it in the circuit for now).

Now let’s recap P and N type material. P contains more holes (hence apparently* more ‘positive’) and N contains more electrons (hence apparently more ‘negative’). Shown above is a schematic of P and N type material NOT joined together. (Electron, Hole)

When they are joined together, the most obvious happens. The electrons from N type material flow to the P type and the holes in the P type flow to N type by diffusion. Due to this diffusion, there is an interchange of particles between the P and N type materials and the electrons combine with holes in each side and become neutral. The represents slight emission of energy (the electron falls back to the valence band from the conduction band across the forbidden energy gap).

(joined P and N junctions)

This basically results in the accumulation of neutral charges in the middle in a layer known as the depletion layer, or the charge free region where there are no charges to conduct electricity. The diffusion of holes and electrons continues until a potential barrier is developed in the depletion layer which prevents further diffusion or neutralisation. This potential barrier is due to the accumulation of the electric charges of opposite polarities in this region (basically an opposing electric field is generated.

### So how does the diode work?

When the diode is forward biased, that is the p side is connected to the positive terminal of the battery, the junction voltage VB (typically of the order of 0.6 V)can be overcome due to the applied electric field by the battery. Hence current can now flow as the junction voltage has been demolished and the electrons and holes can move, conducting electricity.

However, when the diode is reverse biased, that is the n side is connected to the positive terminal, the junction voltage is only aggravated by the connection of the battery, and hence there cannot be flow of charges again.
The I-V curve of a diode is given below. Please note that the reverse current is really small, in the µA range. The breakdown voltage is also quite big, around -40-50 V. Usually that kind of voltage is not used in usual circuits.

I guess that’s a lot of information. Contact me at 93510048 if you wish to know how transistors work, unless you have not figured it out yourself by now. It’s actually quite easy.

Semiconductor design is a very coveted job, and in the future some of you might want to consider it! (: