(c) Dr Paul Kinsler. [Acknowledgements & Feedback]

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Inter-subband Hole Lasers

This work was done within the Department of Applied Physics at Technical University Delft, and involved collaboration with Prof Tom Wenckebach.

Is this just Greek to you? Why not try looking at the IRC #physics channel information maze for some simple explanations of semiconductor physics.

Project Summary.


The operation of intersubband laser relies on a population inversion between the light and heavy hole (valence) subbands. This is achieved by confining the light holes in the lasing region (A) using the cyclotron orbits caused by crossed (perpendicular) electric and magnetic fields. Light holes that scatter out of this region due to either emitting a laser photon or some other scattering process usually end up in the heavy hole band (at (B)). If the electric and magnetic fields are correctly chosen, the heavy hole cyclotron orbit will sweep the hole far up the heavy hole band (to (C)), where its in-plane kinetic energy exeeds that of the LO phonon energy in the material, as well as being of a greater energy than the lasing region in the light hole band. From here a significant fraction of the heavy holes will scatter, ending up back in the lasing region (A), from whence they can emit a(nother) laser photon. Those that do not will scatter about in the bands until they are again in the lower part of the heavy hole band and will (again) be swept to higher energy.

This type of laser has been realised in p-doped Germanium (p-Ge), where their unusually broad gain spectrum makes them promising candidates for amplification and generation of far-infrared pulses on a picosecond time scale [2-4]. Their spectrum can be tuned by changing the applied fields; and mode locking enables us to generate a train of picosecond pulses of far-infrared radiation. These are about 1ns apart, and the entire length of the pulse train is limited to 1-10 us, due to the heating of the device.

Fig.1: Mechanism for population inversion in a (bulk) inter valence-band laser. The light and the heavy hole subbands are shown in an energy-momentum diagram, with the pumping cycle indicated by the heavy arrows.

I've just finished evaluating the potential of p-doped Gallium Arsenide (P-GaAs) and p-doped Indium Antimonide (p-InSb) as alternative materials. In particular, p-InSb has a very large heavy hole to light hole mass ratio, leading to greatly different cyclotron orbit ratios, which promises excellent performance -- assuming the other material parameters are at least as favourable as for Ge or GaAs. The evaluation is being done using Monte Carlo code, the original version of which which pre-dated my arrival at T.U.Delft in July 1999. I have made a range of improvements to the code, mainly for improved structure, usability, readability, and event logging. This was necessary to allow us to simulate the new InSb material system, and also for ease of modification.

The results, however, are rather surprising. Although the large mass ratio in InSb might seem promising, it is also a drawback. It makes it easier to get the combination of efficient heavy-hole streaming and light-hole cyclotron orbits; but the effect on the density of states makes it less likely that a hole will scatter from the heavy-hole to the light hole band. These results have been presented as a talk at the INTERACT meeting at Chateau de Bonas in July 2000; and written up into a paper that we have submitted to J. Appl. Phys.

I have recently got the Monte Carlo program working reliably in 2D for quantum well simulations. I did this by coding it so that can start by reading in a numerically calculated discretization of the bandstructure, which might be of any dimension. Currently I generate a quantum well bandstructure using slices through the bulk 3D bandstructure, which approximates an infinite quantum well. I have borrowed some code from a colleague, Bill Batty, which works out a quantum well bandstructure, but this is not yet properly integrated. However, all I need to do is relax his axial approximation and reformat his output files. In the meantime, though, I need to run some test cases in order to get results for the talk I am going to give at ICPS-25 in Osaka, Japan.


  1. P. Kinsler, W. Th. Wenckebach, "Hot-hole lasers in III-V materials", submitted to J. Appl. Phys.
  2. Opt. Quantum Electron. Vol. 23, Special Issue Far-infrared Semiconductor Lasers, (Eds. E. Gornik and A.A. Andronov, Chapman and Hall, London 1991).
  3. F. Keilmann and R. Till, Semicond. Sci. Technol. 7,B633(1992).
  4. E. Brundermann et al.,Infrared Phys. Technol. 36, 59 (1995).
  5. R.C. Strijbos et al., in Hot Carriers in Semiconductors, edited by K. Hess, J.-P. Leburton, and U. Ravaioli (Plenum Press, New York, 1996), pp. 631-633.

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Date=20020107 20000223 19990818 Author=P.Kinsler Created=1999