Solid-state physics

Surprising movements in solids

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A process as simple as diffusion should be easy to understand. Butour knowledge of the movements of atoms in semiconductors is still far fromcomplete.

The natural movements (diffusion) of atoms in a solid are made possibleby defects in the crystal lattice. So studies of diffusion in technologicallyimportant materials, such as semiconductors, help engineers to make smallerand better microelectronic and optoelectronic devices. On page 69 of this issue Bracht et al.1report that in the semiconductor compound gallium antimonide the antimonyatoms move a thousand times slower than the gallium atoms. This result contradictsearlier measurements, and was not expected from the diffusion behaviour ofother semiconductor compounds.

Gallium antimonide is used to make infrared lasers and photodetectors,night-vision devices, solar cells and some special transistors. These areniche applications compared to those of the ubiquitous silicon, or galliumarsenide and indium phosphide, which are mostly used in lasers and high-speedtelecommunications devices. The significance of Bracht and colleagues' resultdoes not stem from the technological importance of gallium antimonide. Rather,it is because the finding is another in a long line of unexpected differencesand similarities encountered in the history of understanding diffusion insemiconductors.

It was first suggested by the Russian scientist Frenkel2in 1924 that the movement of atoms in a crystalline material may not justoccur through two neighbouring atoms exchanging positions, but that defectsare required. In metals, these defects were shown to be missing lattice atoms,known as vacancies. How fast a lattice atom can move depends on the concentrationof these vacancies — which, for thermodynamic reasons, are present inincreasing concentrations with increasing temperature — and on themobility of the vacancies.

When semiconductors came along in the 1940s, germanium was used to makethe first transistors. Germanium atoms were also found to diffuse with thehelp of germanium vacancies, as happens with metals. Technological interestsoon shifted to crystalline silicon, which has several advantages over germaniumfor making electronic devices: for example, it can form a high-quality electricallyinsulating oxide, and it can be grown as large single crystals (Fig. 1).

Figure 1: One of the largest available single crystals of silicon, presentedat an exhibition of the German Physical Society.

It symbolizes a modern-day version of the 'Stone of Wisdom', the topicand theme of the exhibition. (Photo courtesy of Research Center Jülich.)

Unexpectedly, the mechanism of diffusion of silicon atoms in silicon crystals— also known as 'self-diffusion' — turned out to be differentfrom that in metals and germanium. As well as the usual vacancy mechanism, extra silicon atoms called self-interstitials play a prominent role3. But even though Frenkel had already discussed self-interstitialsin his early papers, the idea of vacancies dominating diffusion processeswas so engrained that it took more than 20 years for the role of self-interstitialsto be accepted and finally incorporated into computer models used to designmicroelectronic devices.

Experiments using silicon later showed that the coefficients of self-diffusion(the rates of self-diffusion) for both of these defect mechanisms are extremelysimilar in magnitude over an extended temperature range of several hundreddegrees Celsius. This would have been astonishing enough, but we also learnedthat the individual factors determining self-diffusion in silicon —the defect concentrations at a given temperature, and the mobility of thesedefects — are almost unbelievably similar. For example, at the meltingpoint of silicon the concentrations of vacancies and self-interstitials differby only about 30%. This surprising fact is at the heart of the observationthat, during growth of silicon crystals, either vacancies or self-interstitialscan agglomerate, and so both are responsible for forming undesirable defects4.

It also offers the possibility of growing the crystals in such a way thatalmost all the vacancies and self-interstitials annihilate each other, sothat practically no defects remain. This feat of engineering is key to producingthe almost perfect silicon wafers required for the next generation of computerchips. From a scientific point of view we still do not know whether theseunexpected similarities in silicon are purely accidental or whether some deeperscientific truth lies behind them.

The situation is more complex for semiconductor compounds, however, becausethere are two sublattices — in gallium arsenide, one for gallium atomsand one for arsenic. How do gallium and arsenic atoms move in these sublattices?Fortunately, what we have learned in the case of silicon can also be appliedto semiconductor compounds, in an appropriately modified form. There are vacanciesand self-interstitials in both sublattices, and both types of defect playa role in diffusion processes. One of the first unexpected observations wasthat the movement of atoms on both sublattices is generally similar in magnitude.One possible reason for this is that one atom on one sublattice (say, gallium)is typically surrounded by four atoms of the other sublattice (arsenic) andvice versa. Although the binding between the atoms is not symmetric, the wholediffusion process seems to involve some kind of averaging over the differentconfigurations and local atomic environments, ultimately favouring similardiffusivities on both sublattices.

Earlier self-diffusion measurements for gallium and antimony in galliumantimonide5 found the diffusivities of gallium and antimonyto be similar, as expected. But Bracht et al.1 now reportexperiments showing that antimony diffuses 1,000 times slower than gallium.Immediately two questions arise. First, are the new results more reliablethan the earlier ones? And second, supposing the new results are true, whatmakes this material different from other semiconductors?

The first question can be answered easily. Previous measurements were basedon radioactive elements diffusing in from the surface, whereas the techniqueof Bracht et al. involves growing semiconductor structures containingspecific non-radioactive isotopes. The existence of these isotopes throughoutthe structure avoids the undesirable surface effects associated with radioactiveprobes, and leads to more accurate measurements. Because most of the self-diffusion data from other semiconductor compounds are also based on radioactivetracers, perhaps we should also worry about the reliability of these otherestablished data.

Concerning the second question, Bracht et al. speculate that someof the gallium atoms move into empty antimony sites, thereby blocking thevacancy-assisted movement of antimony atoms, and at the same time increasingthe concentration of gallium vacancies. This process would require unusualinteractions of native defects. The model proposed by Bracht et al.should be investigated by quantum-mechanical calculations of these diffusionprocesses, and might inspire new thinking on diffusion mechanisms in semiconductors.This could lead to new insights into the behaviour of materials other thangallium antimonide.


  1. 1

    Bracht, H. et al. Nature 408, 69–72(2000).

  2. 2

    Frenkel, Y. Z. Physik 26, 117–138 (1924).

  3. 3

    Seeger, A. & Chik, C. P. Phys. Stat. Sol. 29, 455–542 (1968).

  4. 4

    Voronkov, V. V. J. Cryst. Growth 59, 625–643(1982).

  5. 5

    Weiler, D. & Mehrer, H. Phil. Mag. A 49, 309–325 (1984).

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Correspondence to Ulrich Gösele.

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