Germanium hole conductivity

In addition, there exist two great classes of semiconductors characterized by the presence of local energy levels (to the account of different admixtures) in the forbidden energy gap. If these levels lie close to the top of the valence band (Figure 9.12a) (this is called the acceptor level), electrons of the valence band occupy them and release some levels in this band. The so-called hole conduction appears (on account of vacancies near the top of the valence band). Such materials are semiconductors of p-type. Germanium crystals with indium admixture can be numbered amongst them. 

We discuss the dissolution of surface atoms from elemental semiconductor electrodes, which are covalent, such as silicon and germanium in aqueous solution. Generally, in covalent semiconductors, the bonding orbitals constitute the valence band and the antibonbing orbitals constitute the conduction band. The accumulation of holes in the valence band or the accumulation of electrons in the conduction band at the electrode interface, hence, partially breaks the covalent bonding of the surface atom, S, (subscript s denotes the surface site). 

In general, the activation energy for the release of electrons from surface atoms into the conduction band increases with increasing band gap of the semiconductor electrode with this increase the capture of holes by the surface atoms and radicals predominates. Except for germanium, most covalent semiconductors have been found to dissolve anodically through this valence band mechanism [Memming, 1983]. 

The mobilities of holes are always less than those of electrons that is fXh < Me- In silicon and germanium, the ratio [ie/[ih is approximately three and two, respectively (see Table 6.2). Since the mobilities change only slightly as compared to the change of the charge carrier densities with temperature, the temperature variation of conductivity for an intrinsic semiconductor is similar to that of charge carrier density. 

Some examples of intrinsic semiconductors are silicon and germanium. These materials do not contain any impurities. The conduction mechanism can be represented in a simplified way by means of a projection diagram of a silicon or germanium crystal (fig. 11.4.6) By supplying energy to the material, the electrons are torn free from their atoms and positively charged electron holes (+) arise. Placing the material in an electric field will result in the transport of holes ... 

It is clear, from the above model and from Fig. 44(a) and (b), that, if 0 ,red is closer to Ec than °E0X is to Ev, then electron transfer involving the conduction band Eox is closer to Ex than °Ered to Ec, hole transfer involving the VB will be the main vehicle of the redox process. An example of this is shown for Germanium in Fig. 44(c) where a fairly clear-cut division can be made. 

Solid state detectors consist of three layers, a layer of pure silicon sandwiched between a p-type and an n-type conductor. We recall that an example of an n-type conductor is germanium to which is added P or As, an impurity. The extra electron in the phosphorus or arsenic atoms is thought of as being in an energy level close to the conduction band. These electrons are readily thermally excited into the conduction band increasing the conductivity. A p-type semiconductor may be silicon to which a trivalent element such as boron or aluminum is added as an impurity. This creates holes close to the valence band. Electrons are readily promoted to these holes leaving positive holes in the valence band that provide for a conduction pathway. 

Consider a pure crystal of germanium. Like silicon it will have a low intrinsic conductivity at low temperatures. If we now dope some gallium atoms into this crystal, we shall have formed holes because each gallium atom contnbutes only three electrons rather than the requisite four to fill the band. These holes can conduct electricity by the process discussed above. By contrulling the amount of gallium impurity, we can control the number of carriers. 

Interestingly, the anodic dark current at n-Ge electrodes increases considerably upon addition of the oxidized species of a redox system, for instance Ce" ", to the electrolyte, as shown in Fig. 8.4 [7]. The cathodic current is due to the reduction of Ce. The latter process occurs also via the valence band (see Chapter 7), i.e. since electrons are transferred from the valence band to Ce", holes are injected into the Ge electrode. Under cathodic polarization these holes drift into the bulk of the semiconductor where they recombine with the electrons (majority carriers) and the latter finally carry the cathodic current. In the case of anodic polarization, however, the injected holes remain at the interface and are consumed for the anodic decomposition of germanium, as illustrated in the insert of Fig. 8.4. Accordingly, the cathodic and anodic current should be compensated to zero. Since, however, the anodic current is increased upon addition of the redox system there is obviously a current multiplication involved, similarly to the case of two-step redox processes (see Section 7.6). Thus, in step (e) (Fig. 8.1) electrons are injected into the conduction band. This experimental result is a very nice proof of the analytical result presented by Brattain and Garrett [3]. 

This expression is derived from the more general case where the electron and hole concentrations in the conduction and valence bands are n and p with np = n2. At RT, taken as 300 K, the intrinsic carrier concentration n is 1.1 x 10111 cm in silicon, but it increases to about 4 x 1013 cm 3 in germanium to reach 2 x 1016 cm-3 in intrinsic InSb. 

The fact that shallow p- and n-type dopants of germanium could be considered as H-like atoms emerged at the end of the 1940s to explain the electrical conductivity of this material, and this was clearly expressed by William Shockley in his monograph Electrons and holes in semiconductors , first published in 1950. 

We consider, for instance, germanium in aqueous solution. The anodic dissolution of germanium occurs by either donating electrons into the conduction band or accepting holes out of the valence band of germanium as follows ... 

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