Problem 12.47 noted that FeO (wüstite) may behave as a semiconductor by virtue of the tran...

Problem 12.47 noted that FeO (wüstite) may behave as a semiconductor by virtue of the transformation of Fe2+ to Fe3+ and the creation of Fe2 vacancies; the maintenance of electroneutrality requires that for every two Fe3+ ions, one vacancy is formed. The existence of these vacancies is reflected in the chemical formula of this nonstoichiometric wüstite as Fe(1-x)O, where x is a small number having a value less than unity. The degree of nonstoichiometry (i.e., the value of x) may be varied by changing temperature and oxygen partial pressure. Compute the value of x that is required to produce an Fe(1-x) O material having a p-type electrical conductivity of 2000 (Ω • m)–1; assume that the hole mobility is 1.0 × 10–5 m2/V s, the crystal structure for FeO is sodium chloride (with a unit cell edge length of 0.437 nm), and the acceptor states are saturated.

Problem 12.47

We noted in Section 5.3 (Figure 5.4) that in FeO (wüstite), the iron ions can exist in both Fe2+ and Fe3+ states. The number of each of these ion types depends on temperature and the ambient oxygen pressure. Furthermore, we also noted that in order to retain electroneutrality, one Fe2+ vacancy will be created for every two Fe3+ ions that are formed; consequently, in order to reflect the existence of these vacancies the formula for wüstite is often represented as Fe(1 x)O, where x is some small fraction less than unity.

In this nonstoichiometric Fe(1 x)O material, conduction is electronic, and, in fact, it behaves as a p-type semiconductor. That is, the Fe3+ions act as electron acceptors, and it is relatively easy to excite an electron from the valence band into an Fe3+ acceptor state, with the formation of a hole. Determine the electrical conductivity of a specimen of wüstite that has a hole mobility of 1.0 × 10 –5 m2/V s and for which the value of x is 0.060. Assume that the acceptor states are saturated (i.e., one hole exists for every Fe3+ ion). Wüstite has the sodium chloride crystal structure with a unit cell edge length of 0.437 nm.

Figure 5.4 Schematic representation of an Fe2+ vacancy in FeO that results from the formation of two Fe3+ ions.