Germanium electron concentration

Impurity Semiconductors, n-Type andp-Type. The discussion has been restricted so far to pure intrinsic semiconductors exemplified by germanium and silicon. In these substances, there is a low concentration of charge carriers (compared with metals). Further, the hole and electron concentrations are equal, and their product is a constant given by the law of mass action... 

A typical featnre of reactions involving the minority carriers are the limiting currents developing when the snrface concentration of these carriers has dropped to zero and they mnst be snpplied by slow dilfnsion from the bulk of the semiconductor. A reaction of this type, which has been stndied in detail, is the anodic dissolution of germanium. Holes are involved in the first step of this reaction Ge — Ge(II), and electrons in the second Ge(ll) —> Ge(IV). The overall reaction equation can be written as... 

Refined X-ray methods have also been applied to other types of crystal [7—9). In some metals, for example, the inter-ionic electron minimum density corresponds to some few electrons spread over the lattice (2 for Mg, 3 for A1 for example). And in covalent crystals like diamond there are non-spherical interatomic concentrations corresponding to the chemists covalent bonds, although such effects are small even for germanium (7). 

Germanium used for transistors has a resistivity of 2 cm and an electron hole concentration of 1.9 x 10 holes/cm. (a) What is the mobility of the electron holes in the germanium (b) What impurity element could be added to germanium to create electron holes ... 

Semiconductors like silicon or germanium are an intermediate case. Their electrons are not as tightly bound as in insulators so that at any given time a small fraction of them will be mobile. In a perfect germanium crystal, for instance at 25°C, about 3 x 1019 electrons per m3 are free. This corresponds to a concentration of 5 x 10-8 M or 50 nM. It is much lower than the concentration of charge carriers (cat- and anions) in an aqueous electrolyte solution. Despite this small concentration, the conductivities are of the same order of magnitude, because the electrons in a semiconductor are typically 108 times more mobile than ions in solution. 

If, however, the electrode is a semiconductor, the distribution of charges in the solid will be similar to that in the electrolyte, for the concentration of carriers in semiconductors is significantly smaller than in metals, hi pure germanium for example the concentration of electrons and holes at room temperature is 2.5 x 10 cm or 4 x 10 mole/1 i.e., the... 

In practice, nothing is absolutely pure, so the word substance is an idealization. Among the purest materials ever prepared are silicon (Fig. 1.5) and germa-ninm. These elements are used in electronic devices and solar cells, and their electronic properties require either high purity or else precisely controlled concentrations of deliberately added impurities. Meticulous chemical and physical methods have enabled scientists to prepare germanium and silicon with concentrations less than one part per billion of impurities. Anything more would alter their electrical properties. 

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