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INTRODUCTION OF LOCAL CONDUCTIVITY CENTERS (LEVELS) IN SEMICONDUCTORS BY NUCLEAR BOMBARDMENT
“Monoatomic” semiconductors, germanium and silicon (let us call them so, in contrast to semiconductors that are chemical compounds), belong to group IV of the periodic table and have a crystalline lattice of the diamond type. In 1 cm³ of crystalline Ge and Si there are, respectively, \(4.5 \cdot 10^{22}\) and \(5.2 \cdot 10^{22}\) atoms. It is known that the addition of impurities from group III elements, for example boron, aluminum, gallium, and indium, gives rise to “hole” conductivity in Ge and Si. Impurities of group V elements—nitrogen, phosphorus, antimony, and arsenic—produce excess (electronic) conductivity\(^{1,2,3}\).
The conductivity of a semiconductor can be expressed as the sum of intrinsic and impurity components:
\[ \sigma = \sigma_{\text{intrinsic}} + \sigma_{\text{impurity}} . \]
At temperatures of the order of \(300^\circ\) K, the first is usually negligibly small compared with the second. The intrinsic conductivity of pure silicon is about \(4 \cdot 10^{-6}\,(\Omega \cdot \text{cm})^{-1}\); the addition of 1 boron atom per \(10^6\) silicon atoms increases it almost to \(1\,(\Omega \cdot \text{cm})^{-1}\), i.e., by \(2 \cdot 10^5\) times. One may take
\[ \sigma = \sigma_{\text{intrinsic}} + nq\mu , \tag{1} \]
where \(n\) is the number of carriers released by impurity atoms.
From the example given above of the influence of impurity atoms on the conductivity of silicon, it is clear that the usual methods of chemical or spectral analysis are inapplicable for a quantitative study of the distribution of such small amounts of impurity in a sample.
In this case, however, the method of radioactive indicators may be applied (see \(^{4,5}\)), i.e., active isotopes of impurity atoms (for example, P or Sb)\(^{6}\). In experiments with germanium, 0.054, 0.00081, and 0.00078% antimony were added to the pure semiconductor. Autoradiographs showed—
They showed that in an ingot of germanium the impurity is distributed exponentially with depth, with maximum concentration at the surface. Measurement of the activity by means of Geiger counters made it possible to determine the concentration of impurities.
A particularly important fact from the standpoint of the zone theory of solids is the coincidence of the data on the concentration of the impurity and on the electrical conductivity determined by it: one antimony atom in the germanium lattice gives one conduction carrier (Fig. 1).
The principal difficulty in the experimental verification of the theory of semiconductivity consists in obtaining semiconductors with properties predicted in advance upon addition of an impurity.
Fig. 1.
This difficulty would be resolved if impurity atoms could be “inserted” into the sites of a crystal lattice occupied earlier by atoms of the parent substance, without disrupting its structure. In principle this problem can be solved by irradiating pure semiconductors with a flux of slow thermal neutrons, which, as the result of a nuclear reaction of the type \((n,\gamma)\), produce \(\beta\)-active nuclei; these, after their decay, become stable atoms of a new element (an impurity) in the lattice of the semiconductor under study.
In the case of germanium, the number and type of isotopes are known. Nuclear reactions here lead to the formation of gallium atoms, which give rise to \(p\)-conductivity, and arsenic atoms, which give donor levels and produce electronic conductivity.
The ratio of the numbers of impurity levels and, consequently, the conductivity arising after irradiation, is ultimately determined by the effective activation cross sections (see, for example, \(^{7}\)). In general, the number of acts of nuclear interaction is
\[ N_e = n v t \cdot \sigma_p \cdot n_A - P_t \cdot w, \tag{2} \]
where \(n \cdot v\) is the number of bombarding particles incident per second on unit area, \(\sigma_p\) is the effective cross section in \(\text{cm}^2\), \(n_A\) is the number of atoms in \(1\ \text{cm}^3\) of the specimen (target), \(P_t\) is the isotopic abundance of the nuclei participating in the process, and \(w\) is a coefficient accounting for secondary effects,
accompanying the process. For nuclear reactions \(w = 1\), but, for example, for elastic collisions \(w\) may reach several hundred.
For germanium it was established that bombardment in a nuclear reactor ultimately always leads to a predominance of hole conductivity. If \(n\)-type specimens are irradiated in the reactor, then their conductivity at first decreases and then, when all conduction electrons are captured by the acceptors that have arisen, the sign of the carriers changes and \(p\)-conductivity increases (Fig. 2).
The transition to hole conductivity agrees, according to the author of the experiments,^8 with Pomeranchuk’s measured values of the capture cross sections of
\(A\) — increase in the conductivity of \(p\)-germanium under irradiation with slow neutrons
\(B\) — change in the conductivity of \(n\)-germanium
Fig. 2.
slow neutrons by the separated isotopes of germanium. It turned out that, at a neutron flux density of the order of \(10^{18}\) concentrations, the number of \(p\)-centers arising in pure germanium during irradiation for several hours is of the same order as that for the impurity in crystals used in practice.
The difference is that the impurity semiconductor obtained by the method of nuclear reactions can be “ideal” (provided pure single crystals are used).
As in experiments with the introduction of radioactive antimony \(\mathrm{Sb}^{124}\), the most essential conclusion from the experiments on irradiating germanium with slow neutrons is the fact that the total number of atoms of the neighboring element arising in the bulk of the semiconductor agrees, to an accuracy of \(10\%\), with the number of impurity levels that arise (esta-
determined from measurement of the Hall effect). This confirms the prediction of the theory that one atom of a neighboring element in a lattice site gives one conductivity carrier.
In contrast to the changes in a semiconductor caused by slow neutrons, bombardment by charged heavy particles, for example deuterons, produces a number of additional effects: displacement of lattice atoms upon collision with a fast particle and ionization. In some cases “avalanche” perturbations of the lattice are possible. These phenomena are expressed in temporal changes of the semiconductor conductivity, depending mainly on the ionizing ability of the incident particles. Bombardment of germanium by deuterons and α-particles in a cyclotron showed that here the effect of nuclear reactions is small in comparison with secondary changes (ionization of atoms and perturbations of the lattice).
A difficulty in such experiments is the preparation of a sufficiently thin specimen so that the bombardment effect takes place uniformly throughout its entire volume.
Of very great interest is the possibility, by irradiating sharply limited regions of the surface of a semiconductor, of obtaining “contactless” \(n\)-\(p\) boundaries possessing rectifying properties. Such boundaries, as is known, can be used as photocells and “contactless” semiconductor amplifiers\(^{9}\).
V. Vavilov
CITED LITERATURE
- Torrey and Whitmer, Crystal Rectifiers (monograph), McGraw Hill (1948).
- Lark-Horovitz, Electrical Engineering 68, 1047 (1949).
- Mott, P. I. E. 96, I, 253 (1949).
- M. Ardens, Physical Principles of the Use of Radioactive and Stable Isotopes as Indicators, GIIL, Moscow (1948).
- Preparation and Determination of Labeled Atoms, collected articles, GIIL, Moscow (1948).
- Lark-Horovitz, NDRC Report 14—585 (March 1942—November 1945).
- Goodman, Scientific and Technical Foundations of Nuclear Power Engineering, GIIL, 1949.
- Johnson and Lark-Horovitz, Phys. Rev. 76, 442 (1949).
- Shockley, Bell System Techn. Journal 28, 435 (1949).