part2lecture1

8/7/2019 PART2LECTURE1

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Semiconductors

Semiconductors

Dr DC Hendry

Course EG1501

1 Semiconductors

There is overlap between this material and earlier material in EG1008. Youmay wish to review the relevant lectures in EG1008 as part of your study of thislecture.

Semicondutors are materials constructed from elements such as silicon (by farthe most important currently), germanium (the main element used in the earlyyears of semiconductors) and also compounds such a GaAs (gallium arsenide). Anumber of compounds are also used for LEDs and for specialised photodetectors(PbTe and SnTe for example). In this course we will consider only silicon,although most of the material presented applies to other semiconductors too.

A semiconductor typically consists of elements (such as silicon or germanium)with four electrons in the outermost shell of the atom. You may remember thatwhen atoms bond together to form a solid (a crystal in this case) one form ofbond is a covalent bond. Adjacent atoms share one electron from each atom toform a bond consisting of two electrons. And we get the following two dimen-sional view, the bonds are really arranged tetragonally in three dimensions:

Revision Page 1 of 7 Dr DC Hendry


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1.1 Intrinsic Semiconductor Semiconductors

The real structure in 3D looks like this:

1.1 Intrinsic Semiconductor

This view, where each bond consists of two electrons, is accurate for low temper-atures. As temperature increases however, a very small number of these bondsbreak apart and an electron can then move freely about the crystal. Such freeelectrons are then able to conduct current. In a semiconductor, the hole leftbehind in the lattice is also able to conduct current.

X

A pure semiconductor as described here is referred to as an intrinsic semiconduc-tor. The alternative, as we shall see later is a doped or extrinsic semiconductor.In an instrinsic semiconductor then, conduction is due to a small number offree electrons and holes. The density of such holes and electrons is equal, andhighly dependent upon temperature. Let n be the density of free electrons, pthe density of free holes, then for an intrinsic semiconductor:



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1.2 Extrinsic Semiconductor Semiconductors

n = p = ni (1)

where ni is referred to as the intrinsic carrier concentration. Note that of coursenp = n2

i. For silicon, the value of ni at 300K is 1.4 10

16m3, but note thatindustry practice often quotes this figure as 1.4 1010cm3.

1.2 Extrinsic Semiconductor

The density of charge carriers in a semiconductor can be increased substantiallyby doping the semiconductor. A semiconductor is doped by adding a very small

amount of an element with one more, or one less, electron in the outermostshell. Such elements are then referred to as dopants. Dopants with an additionalelectron are called donors, those with one less electron are called acceptors.

When we add a small amount of donors to a semiconductor the same bonds form,but for every donor atom added to the lattice, there is, at room temperature, onefree electron. Such a semiconductor is referred to as an n-type semiconductor.Typical donor atoms used in silicon or germanium are phosphorus (P) andarsenic (As).

When we add a small amount of acceptors to a semiconductor again the samebonds form, but for every acceptor atom added to the lattice, there is, at roomtemperature, one free hole. Such a semiconductor is referred to as a p-type

semiconductor. Typical acceptor atoms used in silicon or germanium are boron(B), aluminium (Al) and gallium (Ga).

The additional charge carriers introduced by dopants (the free electrons, or thefree holes), mean that the density of free electrons is no longer equal to thedensity of free holes. Consider first the case of an n-type semiconductor, onewith a density ND of added donors. Assuming that each donor releases onefree electron then the density of donors (assuming ND >> ni) will be ND.The additional electrons mean that there is a much greater chance of a holerecombining with an electron and both become part of a bond. Neither therecombined electron or hole are then available for conduction. The density ofholes in an n-type material is therefore less than the density of holes in anintrinsic semiconductor.



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1.3 Holes Semiconductors

1.3 Holes

What is a hole? The simple explanation is that it is really a broken covalent bondmoving from atom to atom on the crystal. This would seem to be consistent withfor example the fact that holes move slower in an electric field than do electronsin the same field. But that is far from the entire story. The Hall Effect showsthat holes actually behave as if they were positive charges moving (whereas theexplanation above is based on negative charges, the electrons, moving). For afull explanation of this, we would need to learn first quantum mechanics (thewave theory of matter), and then a substantial part of the theory of solid statephysics. All in all, with the mathematics needed to support such study anotherthree courses!

But here is something closer to the truth. Electron motion needs to be described

really as a wave (you may have encountered the Bohr model of an atom). Infree space, even with this wave model, electrons then behave much as a particlemodel would suggest. In a crystal however, when the wavelength of an electronis equal to the spacing of the atoms in a lattice, rather strange effects occur. Inthat situation the electron can be thought of as having a negative mass. Theeffect is that when an electric field is applied it goes in an opposite direction tothat expected.

In an insulator it turns out that for every positive moving electron there isan electron moving in the opposite direction, so no current flows. In a p-typesemiconductor, one of the negative mass electrons is missing, and this is whatwe mean by a hole.

2 The Mass-Action Law

It can be shown in fact, that if n is the total density of free electrons, and p isthe density of holes, then by the mass action law:

np = n2i (2)

even in the presence of dopants. So taking the density of electrons in an n-type

semiconductor as ND, and the density of holes as p we have that:

NDp = n2

i (3)

p =n2i

ND(4)



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Semiconductors

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Figure 1: PN Junction

So if ND >> ni, the p


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Semiconductors

are remember thermally generated minority carriers present (electrons in thep-type, holes in the n-type) and these cause a small current to flow. It may be

shown that the current through a diode is given by:

ID = IS(exp(VD

nVT) 1) (5)

In this equation:

ID is the current through the diode from anode to cathode

VD is the voltage applied to the diode with the anode as the positive terminal,the cathode as the negative terminal

n is the emission coefficient (also referred to as the quality factor) and depends

upon the semiconductor fabrication process. n is ideally 1, and usually inthe range 1 to 2.

IS is the diode saturation current and is determined by the doping densitiesand temperature of the diode.

VT is the thermal voltage, given by:

VT =kT

q(6)

where k is the Boltzmann constant, T is the absolute temperature inKelvin, and q is the charge of the electron.

Ensure that you understand:

1. What is meant by an intrinsic and an extrinsic semiconductor.

2. How an extrinsic semiconductor is made (dopants).

3. The mass action law and how to apply it.

4. Construction of the diode and naming of the terminals.

5. Why the diode conducts in one direction only.

6. How to apply the diode equation.


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