High-frequency impedance of driven superlattices

Abstract

The complex impedance of a semiconductor superlattice biased into the regime of negative differential conductivity and driven by an additional GHz ac voltage is computed. From a simulation of the nonlinear spatio-temporal dynamics of traveling field domains we obtain strong variations of the amplitude and phase of the impedance with increasing driving frequency. These serve as fingerprints of the underlying quasiperiodic or frequency locking behavior. An anomalous phase shift appears as a result of phase synchronization of the traveling domains. If the imaginary part of the impedance is compensated by an external inductor, both the frequency and the intensity of the oscillations strongly increase. 72.20.Ht, Semiconductor superlattices (SL) show pronounced negative differential conductivity (NDC)1 . If the total bias is chosen such that the average electric field is in the NDC region, stable inhomogeneous field distributions (field domains) 2 or self-sustained oscillations 3 with frequencies up to 150 GHz at room temperature 4 appear. Which of these scenarios occurs depends on bias, doping, temperature, and the properties of the injecting contact [5][6][7][8][9][10] . For a recent overview see Ref.11 . In order to apply the self-sustained oscillations as a high-frequency generator in an electronic device, it is crucial to know the response of the SL in an external circuit. A key ingredient for the analysis is the complex impedance of the SL in the respective frequency range. This is the subject of this paper where the complex impedance is evaluated numerically by imposing an additional ac bias to the SL. The interplay of the selfsustained oscillations and the external frequency causes a variety of interesting phenomena such as frequency locking, quasi-periodic and chaotic behavior which has been extensively studied both theoretically 12-14 and experimentally 15,16 . In contrast to those studies we focus on the response to the circuit and concurrent phase synchronization phenomena in this work.We describe the dynamical evolution of the SL by rate equations for the electron densities in the quantum wells, together with Poisson's equation for the electric fields. The current densities J j→j+1 between adjacent quantum wells are evaluated within the model of sequential tunneling, and Ohmic boundary conditions with a contact conductivity σ are used. For details see Refs.10,11 . Here we apply a periodic bias signal U (t) = U dc + U ac sin(2πν 1 t) and study the total current I(t) = A N j=0 J j→j+1 /(N + 1). In particular we consider the Fourier component I ac (ν 1 ) sin(2πν 1 t − φ) which gives the complex impedanceAs an example we consider the SL structure studied in Ref.16 . It consists of N = 120 GaAs wells of width 4.9 nm separated by 1.3 nm AlAs barriers. The sample is n-doped with a density of 8.7 × 10 10 cm −2 per period and the sample cross section is A = 64 (µm) 2 . We estimate the energy broadening Γ = 15 meV, which effectively gives the sum of phonon, impurity and interface roughness scattering rates. All cal...

Non-linear dynamics of semiconductor superlattices

“…The response of an ac driving voltage has also been investigated experimentally and theoretically for strongly coupled SLs with frequencies in the same range as the intrinsic oscillation frequency [270][271][272]. However, due to the much higher intrinsic frequency for strongly coupled SLs in comparison with weakly coupled ones, experimental results are only possible in the frequency domain and not in real time.…”

“…A separate theoretical investigation focused on the evolution of the impedance of the SL circuit with the frequency of the ac driving voltage [271,272], which exhibits strong variations of its amplitude and phase. In addition, Jappsen et al [271,272] found frequency-locked and quasiperiodic propagating dipole domains as well as a phase synchronization of the travelling dipole domains.…”