By growing a periodic sequence of thin layers of different
semiconductors as suggested by Nobel Laureate Leo Esaki together with
Raphael Tsu [1],
one is able to make artificial semiconductors whose electric
properties can, at least to some extent, be engineered.
This unique degree of freedom makes semiconductor superlattices
a model system for a wealth of phenomena in solid state physics [2].
One of these phenomena are Bloch oscillations [3, 4], which are oscillations of particles in a periodic potential under a constant force at a frequency, which is proportional to the applied force and lattice period (see the theory page). Such kind of oscillations cannot be observed in usual semiconductors because the scattering frequency is typically much larger than the Bloch frequency. However, the lattice period in superlattices can be made significantly larger, so that the electrons can perform several Bloch oscillations between the scattering events [5, 6]. This means that if a superlattice is connected to a dc voltage, we can observe transient current oscillations during a time scale determined by the scattering time. Finally each electron still performs oscillations, which are interrupted by scattering events, but because the phases of the oscillating electrons are different only a constant dc current is flowing in the superlattice. The Bloch oscillations manifest themselves in the stationary transport as a negative differential conductivity (NDC) if the Bloch frequency is larger than the scattering frequency [1]. In reality, the space-charge density fluctuations grow up in conditions of NDC leading to formation of electric domains i.e. regions with different internal fields. These (usually) moving domains (Gunn domains) complicate the simple picture presented above.
Since
the invention of superlattices one of the main goals has been
to build amplifiers and oscillators operating at high-frequencies [7]. The
Bloch oscillator is a device, where a dc-biased superlattice is
connected to a resonator whose resonance frequency is the desired alternating
field frequency (see schematic figure above). According to an interesting
theoretical work [8],
a weak ac field will syncronize the Bloch oscillations resulting in a
particularly shaped dispersive Bloch gain profile, where a crossover from gain
to loss occurs approximately at the Bloch frequency (see the figure right,
negative absorption corresponds to gain). This means that generation of
radiation at frequencies below the Bloch frequency can be achieved in the Bloch oscillator
if the formation of the electric domains can somehow be circumvented. However,
the Bloch gain occurs only in conditions where the Bloch frequency is larger
than the scattering frequency, resulting in NDC at the operation point, and the domain formation has destroyed all the
attempts to realize a Bloch oscillator operating in cw mode.
By introducing an auxiliary pump field in addition to the resonator field (probe field), we have found several new approaches to obtain THz gain at stable operation point. One of our ideas in the development of THz Bloch oscillator is a modification of a scheme proposed by Nobel Laureate Herbert Kroemer in order to stabilize the large-amplitude operation of the Bloch oscillator [9]. In our suggestion a strong THz pump field creates new transport channels which help to suppress the formation of electric domains while a probe field at another frequency is amplified [10]. Recently we have also found that instead of a monochromatic high-frequency pump field, one can also stabilize the Bloch gain profile by using a polychromatic low-frequency field [11, 12]. There one periodically harvests the Bloch gain during a reasonably short time intervals, so that domains do not have enough time to grow up. We have also studied the parametric up- and down-conversion of electromagnetic radiation from the available frequencies to the desirable THz frequency range [13-17]. We have shown that an action of ac pump field causes oscillations of electron's effective mass in the miniband, which result in parametric resonances at harmonics and half-integer harmonics of the pump frequency. Moreover, the parametric amplification does not require operation in conditions of negative differential conductivity.
Our most recent work focuses on the influence of the magnetic field on the small-signal absorption and gain [18]. Our results demonstrate exciting new possibilities to control the gain profile with the help of magnetic and electric fields. We have predicted a very large and tunable THz gain due to nonlinear cyclotron oscillations in crossed electric and magnetic fields. In contrast to Bloch gain, here the superlattice is in an electrically stable state. Moreover, the magnetic field can also significantly enhance the magnitude of the THz Bloch gain. In tilted magnetic field geometry, the Bloch gain can be realized at stable operation point.
References
[1] L. Esaki, R. Tsu, IBM J. Res. Dev. 14, 61 (1970).
[2] A. Wacker, Phys. Rep. 357, 1 (2002).
[3] F. Bloch, Z. Phys. 52, 555 (1928).
[4] C. Zener, Proc. R. Soc. London, Ser. A 145, 523 (1934).
[5] J. Feldmann et al., Phys. Rev. B 46, 7252 (1992).
[6] C. Waschke et al., Phys. Rev. Lett. 70, 3319 (1993).
[7] R. Tsu, Microelectron. J. 38, 959 (2007).
[8] S. A. Ktitorov et al., Sov. Phys. Solid State 13, 1872 (1972).
[9] H. Kroemer, cond-mat/0009311.
[10] T. Hyart, K. N. Alekseev, and E. V. Thuneberg, Bloch gain in dc-ac-driven semiconductor superlattices in the absence of electric domains, Phys. Rev. B 77, 165330 (2008).
[11] T. Hyart, N. V. Alexeeva, J. Mattas and K. N. Alekseev, Terahertz Bloch oscillator with a modulated bias, Phys. Rev. Lett. 102, 140405 (2009).
[12] T. Hyart, N. V. Alexeeva, J. Mattas and K. N. Alekseev, Possible THz Bloch gain in dc-ac-driven superlattices, Microelectronics Journal 40, 719 (2008).
[13] T. Hyart, A. V. Shorokhov, K. N. Alekseev, Theory of parametric amplification in superlattices, Phys. Rev. Lett. 98, 220404 (2007).
[14] T. Hyart, N. V. Alexeeva, A. Leppänen and K. N. Alekseev, THz parametric gain in semiconductor superlattices in the absence of electric domains, Appl. Phys. Lett. 89, 132105 (2006).
[15] K. N. Alekseev, M. V. Gorkunov, N. V. Demarina, T. Hyart, N. V. Alexeeva, A. V. Shorokhov, Suppressed absolute negative conductance and generation of high-frequency radiation in semiconductor superlattices, Europhys. Lett., 73 (6), 934-940 (2006).
[16] T. Hyart, A. V. Shorokhov, K. N. Alekseev, Teraherz parametric gain in semiconductor superlattices, Conference digest of IRMMW-THz 2007, Vol. 1, 472 (2007).
[17] T. Hyart, K. N. Alekseev, Nondegenerate parametric amplification in superlattice and the limits of strong and weak dissipation, Int. J. Mod. Phys. B 23, 4403 (2009).
[18] T. Hyart, J. Mattas, K. N. Alekseev, Model of the Influence of Magnetic Field on the Gain of Terahertz Radiation from Semiconductor Superlattices, Phys. Rev. Lett. 103, 117401 (2009).
Back to theory page
08.10.2009, Timo Hyart