Quantum Physics: A Beginner's Guide by Alastair I.M. Rae

Author:Alastair I.M. Rae
Language: eng
Format: mobi
Published: 2008-06-19T14:47:03+00:00

Ch5.qxp 1/28/2008 11:37 AM Page 114

114 Quantum Physics: A Beginner’s Guide

Figure 5.1 In a semiconductor, the gap between the top of the highest full band and the foot of the lowest empty band is small enough for some electrons to be thermally excited across the gap. This is illustrated in the above diagram, where continuous lines represent completely filled states (i.e. each contains four electrons indicated by filled circles), broken lines indicate empty states and dot-dash lines indicate partially filled states.

Current can be carried both by the excited electrons and by the empty states or ‘holes’ (open circles) left in the valence band. The positions of the symbols on the lines have no significance.

the metal, carrying electric current, since there are plenty of available empty states to move into. Secondly, the empty states left behind in the lower band (known as the ‘valence band’) are available to the electrons in this band, so these are also able to move freely and carry current. Thus, both bands contribute to current flow and the material is no longer a perfect insulator.

We now consider the behaviour of the nearly full lower band in a little more detail. We will find that its properties are just the Ch5.qxp 1/28/2008 11:37 AM Page 115

Semiconductors and computer chips 115

same as those of a nearly empty band, containing positively charged particles rather than negative electrons. To see how this works, we first recall that in a full band an equal number of electrons move in opposite directions. Referring to Figure 5.2(a), we see that if one of these electrons is removed, an imbalance results and the net result is a current equal but opposite to that associated with the missing electron; however, this is just the current that would result from a single positive charge moving with the same velocity as that of the missing electron.

In Figure 5.2(b) we illustrate the effect of applying an electric field to the system: this exerts the same force on all the electrons, causing their velocities to change by the same amount, so the net change is again equal and opposite to what would have been experienced by the missing electron. Thus, the behaviour of a set of electrons with one removed is the same as that expected from a particle that possesses all the properties of a single electron, except that its electrical charge is positive.

Deeper study confirms that all the relevant properties of a nearly full band are identical to those of a nearly empty band containing a number of positively charged particles equal to the number of the missing electrons. As it is much easier to envisage the behaviour of a small number of positively charged particles than it is to consider the properties of a huge number of electrons, we will follow usual practice and employ this model from now on. These fictitious positive particles are conventionally known as ‘holes’, for reasons that should be pretty obvious.

However, we should not forget that this is a convenient model

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