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Animation depicting a "photon conveyor belt" in a quantum well, an ultrathin layer of semiconductor material in which submicroscopic particles such as electrons are confined to move in two dimensions. Since these structures are extremely thin, the vertical axis in this schematic diagram is meant to represent energy, not space.
Sequence of movie:
(1) The rf-generator produces a radio-frequency sound wave which travels across the surface of the quantum well.
(2) A laser then creates excitons, pairs of electrons and holes, which are confined in the ultrathin layer of the quantum well.
(3)The sound wave mechanically compresses and expands the material, creating electric fields which serve to separate electrons (green) and holes (blue) into two distinct energy regions (Ec and Ev) of the quantum well. In addition, these electric fields separate the electrons and holes horizontally by half the wavelength of the sound wave.
(4) The electrons and holes, attracted to their respective points of low energy in the electric fields, move with the wave at the speed of sound.
(5) The electrons and holes are brought back together, emitting light which is recorded by a detector.
Researchers at the University of Munich in Germany constructed a 10-nanometer-thick indium gallium arsenide (InGaAs) quantum well which is sandwiched by a 20-nanometer thick GaAs layer on the top and a 1-micron thick gallium arsenide (GaAs) substrate on the bottom. This sample is a piezoelectric material, a solid that has the ability to generate an electric field when a mechanical stress is applied (and vice versa).
Using a device known as an "interdigital transducer," which converts electrical signals into mechanical vibrations, the researchers then apply a radio-frequency (840 megahertz) sound wave to their sample. This creates a "nanoquake on a chip" which propagates from one end of the sample to another.
In more technical terms, the "nanoquake" is really a "surface acoustic wave," (SAW), a packet of sound energy that propagates on the surface of a solid and then decays exponentially with depth. The typical decay depth is on the order of an acoustic wavelength (3 microns in the present experiment), but this depth is actually sufficient for this so-called surface wave to penetrate through the entire quantum well.
Shining a laser on the quantum well then generates excitons, pairs of electrons and holes. Holes can be thought of as the positively charged counterparts of electrons in a semiconductor crystal. They are "missing electrons" that can move from place to place in the crystal just like regular electrons do.
When the sound wave strikes these excitons, it separates the electrons and holes horizontally by half the wavelength of the sound wave. This is because the sound wave creates laterally polarizing electric fields as it mechanically compresses and expands the sample. These electric fields modulate the energy of the electrons and holes in a dynamical way.
Electrons in a semiconductor crystal can reside in one of two energy ranges. The valence band is the energy range corresponding to electrons that are connected to a particular atom in the crystal. Adding energy to any of these electrons can boost them to the conduction band, which describes the allowed energies for electrons that are free to move in the material. In crystals, there is always an energy gap between the valence band and the conduction band. (Materials with a high energy gap are insulators and electrons cannot typically flow freely through these materials; in metals, by contrast, there are always electrons in the conduction band even at very low temperatures and these electrons are free to move; materials with an intermediate band gap are semiconductors and their electrical properties can be greatly controlled with an external electric field.)
In the animation, Ec and Ev denote the "band edges" for the electrons and holes respectively in the quantum well. For the electron, the band edge Ec is the minimum energy in the conduction band (the upper boundary of the band gap) plus the lowest-energy state (the ground state) for the electron in the quantum well. Ev is the highest energy of the valence band (the lower boundary of the band gap) minus the minimum energy state (the ground state) for the hole.
Faced with the new electric fields introduced by the sound wave, the electrons and holes in the quantum well seek out their respective points of minimum energy in the presence of the fields. This causes the electron-hole pairs, which normally are extremely close together, to separate horizontally by half of the wavelength of the sound field.
The separated electrons and holes can be
thought of as horizontally separated "stripes" of charge on the quantum well. Like objects on a conveyor belt, the charges follow each other as they ride on the sound wave:
+ - + - + - + - + - + -
with adjacent positive and negative charges separated by 1.5 microns in the present experiment.
The vertical axis in the animation is not space, but energy. The electrons and holes actually reside in exactly the same depth; they are only separated laterally (horizontally). And it is also important to point out that there is really only a single sound wave. The two waves are there to show how the sound wave modulates the energy of the conduction and the hole band respectively. Like surfers at Sunset Beach, the electrons tend to settle at the low points of the conduction band, while the holes (like a bubble in water that is riding the ridge of the wave) settle to the top of the valence band (Ev). The electrons and holes move with the wave across the sample at the speed of sound (2865 meters/second in this case).
In the last step of the experiment, the electrons and holes are brought back together. This can be done, for example, by creating a second sound wave that travels in the opposite direction to cancel out the effects of the first. Or, placing a thin metal layer on the surface can nullify the effects of the electric field.
When the electrons and holes recombine, they release their energy in the form of light. The energy of this light (or its color) is given by the effective bandgap of the given quantum well structure and thus can be largely chosen at will, as is the case for semiconductor lasers and light emitting diodes.
This technique has a number of useful applications, for instance:
Animation courtesy of Achim Wixworth, University of Munich, Germany. Thanks to Dr. Wixforth for supplying much of the text.
This work is reported by C. Rocke, S. Zimmermann, A. Wixforth, J. P. Kotthaus, G. Bohm and G. Weimann, Physical Review Letters, 19 May 1997.