Техническое чтение для энергетиков. Бухарова Г.П. - 49 стр.

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51
charge, and there will be, a strong tendency for the extra electrons to be held to this
centre, and this combination, the electrons trapped in the anion vacancy, is the donor
centre. If, by some means, any of these trapped electrons can be released, they enter
the conduction band of the crystal and increase the electrical conductivity.
In the case of arsenic in germanium, it is apparent that the fifth electron lies in
a higher energy state than the normal valence electrons, so that the localized extra
level associated with the arsenic lies above the top of the filled band. At the same
time, since there is some binding energy for an electron in this state to remain on the
arsenic, the level lies below the lowest "free" electron state in the conduction band.
The extra state must therefore lie in the forbidden y gap, as shown in Fig. The energy
required to remove this electron may be estimated by noting the similarity to the
removal of an electron from a hydrogen atom. The coulombic attraction between the
arsenic and the electron, as compared with the hydrogen atom, is reduced by the
dielectric constant of the medium, since the electron orbit in the solid encompasses
several atomic distances. The reduction in ionization energy depends on the square of
the dielectric constant, which is 15.8 for germanium. The ionization energy for the
free hydrogen atom is 13.6 eV, so one expects the ionization energy for arsenic in
germanium to be reduced by a factor (15.8)², thus 13.6/(15.8)²= 0.05 eV.
A further reduction is expected because the effective mass for electrons should
be used, rather than the actual electronic mass, in computing the energy. This
reduction leads to good agreement with the experimental values, which lie near 0.01
eV. This, then, is the energy difference between the bottom of the conduction band
and the localized energy level at an arsenic. Similar considerations show that an
acceptor like boron provides levels just above-the top of the filled band, as shown in
Fig. Centers like these: are often called "hydrogen-like".
At room temperature, the thermal excitation energy of the electrons is
sufficient to ionize almost completely arsenic centers in germanium, so there is an
increased concentration of electrons in the conduction band nearly equal to the
arsenic concentration, and these give rise to an increase in the electrical conductivity.
Such behavior is called "extrinsic", as it depends on the concentration of
imperfections in the lattice. The case of boron in germanium provides #n example of
an extrinsic semiconductor where an excess of holes has been introduced. At room
temperature the boron levels are nearly all ionized, that is to say, the holes have been
removed from them and have entered the valence band, leaving an electron trapped
on each acceptor center.
Not all donors and acceptors in germanium have as small ionization energies as
do boron and arsenic, and larger ionization energies are encountered in other
materials also. When both acceptors and donors are present in material – and for
practical reasons this will almost always occur to some degree – there is a
"compensation" effect. The difference between donor and acceptor concentration will
determine the carrier concentration. Thus, in Fig. with five arsenic and two boron
atoms present, the boron levels are filled by two of the available electrons from the
arsenic and only three conduction electrons are supplied.

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