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April 4, 2019
Amplifier for terahertz lattice vibrations in a semiconductor crystal
by Forschungsverbund Berlin e.V. (FVB) <http://www.fv-berlin.de/index.html>
(a) Phonon (wavy lines) absorption and (b) stimulated emission of so
called longitudinal optical (LO) phonons schematically explained in the
conduction band structure (black parabola: electron energy vs. its
momentum) of the semiconductor gallium arsenide (GaAs). (a) The blue
circles of different size represent a thermal electron distribution at
room temperature. A phonon is absorbed (removed) by lifting an electron
from a state with a higher occupation probability to one with a lower.
(b) A strong THz field (green double arrow) shifts the electron
distribution to an inversion situation. Now, stimulated emission of a
phonon increases the number of phonons by the inverse electron
transition. (c) Sketch of the sample architecture covered by an array of
metallic dogbone resonators (orange). The latter enhance electric fields
(along the dashed lines) close to the electrically charged arms of the
resonators. (d) Measured amplitude (area under peaks) of coherent
phonons as a function of time showing a 10-fold increase within a period
of 1.5 picoseconds. Credit: MBI Berlin
In analogy to the amplification of light in a laser, vibrations of a
semiconductor crystal, so-called phonons, were enhanced by interaction
with an electron current. Excitation of a metal-semiconductor
nanostructure by intense terahertz (THz) pulses results in a 10-fold
amplification of longitudinal optical (LO) phonons at a frequency of 9
THz. Coupling such lattice motions to propagating sound waves holds
potential for ultrasound imaging with a sub-nanometer spatial resolution.
The fundamental principle of laser light can be adopted for phonons via
the vibrational quantum in a crystal. Phonons can be absorbed or emitted
by electrons in the crystal lattice. A net amplification of phonons
requires that their number emitted per second via stimulated emission is
larger than that absorbed per second. In other words, there must be more
electrons emitting than absorbing a phonon
<https://phys.org/tags/phonon/>. This condition is illustrated
schematically in Fig. 1, in which the electron energy is plotted as a
function of the electron momentum k, following roughly a parabolic
dependence.
For a thermal equilibrium distribution of electrons at room temperature
[sketched by filled blue circles of different size in Fig. 1(a)],
electron states at higher energies have a smaller population than those
at lower energies, resulting in a net phonon absorption. Stimulated
emission of a phonon can only prevail if a so-called population
inversion exists between two electronic states separated by both the
energy and the momentum of the corresponding phonon in the crystal [Fig.
1(b)]. For optical phonons, this condition is very difficult to fulfill
because of their comparatively high energy.
Researchers from the Max-Born-Institute in Berlin, Germany, the Sandia
National Laboratories, Albuquerque, New Mexico, and the State University
of New York at Buffalo, New York, have now demonstrated the
amplification of optical phonons in a specially designed
metal-semiconductor nanostructure [Fig. 1(c)]. The system consists of a
metallic dog-bone antenna on top of a layered semiconductor structure
consisting of GaAs and AlAs. This structure is irradiated with an
ultrashort pulse at THz frequencies.
On the one hand, the THz pulse excites longitudinal optical (LO)
phonons; on the other hand, it drives an electron current in the thick
GaAs layer. The LO phonons oscillating with a frequency of 9 THz (9 000
000 000 000 Hertz, about 450 million times the highest frequency humans
can hear) are amplified by interaction with the electrons. The strength
or amplitude of the phonon oscillations is monitored via the concomitant
change of the refractive index of the sample. The latter is measured
with the help of a second ultrashort pulse at higher frequency. In Fig.
1(d), the time evolution of the phonon excitation is shown. During the
peaks of the curve, there is a net phonon amplification with the yellow
area under the peaks being a measure of the phonon oscillation
amplitude. The movie attached shows the spatiotemporal evolution of the
coherent phonon amplitude which displays both periods of phonon
attenuation [situation Fig. 1(a)] and phonon amplification [situation
Fig. 1(b)] depending on the phase of the THz pulse.
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Left: Amplitude of GaAs optical phonons at the interface between the
thin AlAs layer and the thick GaAs layer [Fig. 1(c)]. Red curve: LO
phonon oscillations with a THz-driven electronic current in the thick
GaAs layer. Blue curve: phonon oscillations without the amplifying
mechanism. Right: Spatiotemporal evolution [cf. moving circles in the
left panel] of the LO phonon amplitude as a function of the penetration
depth from the AlAs/GaAs interface into the thick GaAs layer [Fig.
1(c)]. The movie clearly shows alternating periods of phonon attenuation
[situation Fig. 1(a)] and phonon amplification [situation Fig. 1(b)]
depending on the phase of the driving THz pulse. Credit:
Forschungsverbund Berlin e.V. (FVB)
The present work is a proof of principle. For a usable source of
high-frequency sound waves, it is necessary to further increase the
amplification <https://phys.org/tags/amplification/>. Once such a source
is available, it can be used for extending the range of sonography
towards the length scale of individual biological cells. While the
non-propagating optical phonons cannot be directly used for imaging, one
can transform them into acoustic phonons with the same frequency in
another material and apply the latter for sonographic imaging.