Electron focusing in metals and semimetals

J. Heil, A. Böhm, A. Gröger, M. Primke, P. Wyder, P. Keppler, J. Major, H. Bender, E. Schönherr, H. Wendel, B. Wolf, K. U. Würz, W. Grill, H. Herrnberger, S. Knauth, J. Lenzner

Research output: Contribution to journalReview article

6 Citations (Scopus)


Partly ballistic propagation of carriers and phonons in single crystals of the metals Ag and W and the semimetal Bi is studied in real space. The carriers are excited by heating a small surface area of the sample by illumination or electron beam irradiation. Alternatively they are injected through point contacts. They spread out from this point-like source setting up a characteristic anisotropic current pattern representing some kind of fingerprint of the material's band structure. If the sample thickness is comparable to the mean free path of the carriers, they produce a potential pattern on the opposite sample surface. We present images of these patterns revealing the phenomenon of electron focusing, i.e. caustics produced by a diverging density of trajectories in specific directions. The influence of magnetic fields is studied. We give some basic theoretical analysis of the data in terms of fully ballistic transport. An outlook into possible future developments and applications of the technique and the completion of the theoretical model is given.

Original languageEnglish
Pages (from-to)387-455
Number of pages69
JournalPhysics Report
Issue number5
Publication statusPublished - Jan 2000


  • Ballistic transport
  • Electron focusing
  • Electronic transport
  • Thermopower

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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    Heil, J., Böhm, A., Gröger, A., Primke, M., Wyder, P., Keppler, P., Major, J., Bender, H., Schönherr, E., Wendel, H., Wolf, B., Würz, K. U., Grill, W., Herrnberger, H., Knauth, S., & Lenzner, J. (2000). Electron focusing in metals and semimetals. Physics Report, 323(5), 387-455. https://doi.org/10.1016/S0370-1573(99)00044-7