Minibands and Wannier-Stark ladders in semiconductor superlattices studied by infrared spectroscopy

Abstract

We review the basic features of interminiband absorption in superlattices, focussing on the joint density of states, the oscillator strength and the associated sum rule. Then we will discuss infrared spectroscopic studies under application of an electric eld. With a eld in the plane of the layers, a hot-electron distribution can be generated. Using the temperature dependence of the interminiband absorption, energy loss and relaxation rates can be determined. A vertical electric eld leads to negative di erential resistance, domain formation and the break-up of the minibands into WannierStark ladders. We will present experiments showing the formation of interpenetrating WannierStark ladders in the continuum, which are strongly coupled by Zener resonances. This is the rst time to correlate transport and infrared absorption in a biased superlattice. I IntroductionSemiconductor superlattices are a fascinating model system for electrons in a periodic potential 1 . They have enabled researchers to observe long-sought p h ysical phenomena such a s W annier-Stark localization 2 and Bloch oscillations 3 . In the present paper we would like to review some of the basic properties of electrons in superlattices, in particular those related to optical transitions between minibands within the conduction band, which can be studied by infrared spectroscopy 4 . We will also present some recent absorption studies of superlattices under application of an electric eld, both parallel and perpendicular to the layers. Whereas in the former case information on the hot-electron relaxation is obtained 5 , the latter experiment reveals the formation of Wannier-Stark ladders far in the continuum and allows us, for the rst time, to correlate the current-voltage characteristic with the infrared absorption spectrum 6 . II Interminiband absorptionThe conduction band of a GaAs AlGaAs superlattice SL can be well described using the envelope function method, which, in the case of only one band, reduces to the Kronig-Penney model with di erent e ective masses in the well and barrier material. At rst we would like to discuss a superlattice consisting of 75 A wide GaAs quantum wells and 25 A wide Al 0:3 Ga 0:7 As barriers. The calculated band structure is shown in Fig. 1. The rst miniband has a width of 1 = 18 meV, the second of 2 = 70 meV approximately. If the superlattice is doped with electrons, optical transitions can occur between all lled states of the rst miniband and all empty states in the second miniband. It is well known that such transitions require the electric eld of the exciting radiation to possess a non-vanishing component perpendicular to the SL layers z-component 7 . In quantum wells such so-called intersubband transitions have been extensively studied and have found applications in infrared detectors quantum well infrared

Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models

“…where l = L b + L w and the coefficients a j and b j used in the approximations for all three superlattices are summarized in the appendix in tables A.3-A.5, respectively. Based on model (23) solved for k = 0, in figure 2 we present four lowest miniband energies as functions of the radius of GaAs/AlAs superlattices that correspond to the three cases of SSLs considered above. Here we use also the boundary condition for the radial equation J l(qR 0 ) = 0 (e.g., qR 0 = 0.240 48 for the first zero of J 0 , qR 0 = 3.8317 for the first zero of J 1 , and similarly for the third and fourth minibands).…”

“…In this work, our quantum mechanical/semiclassical approach in studying coherent oscillations and other transport phenomena in low-dimensional nanostructures, focusing on SSLs, will be exemplified for one-miniband SSLs. Miniband structures of SSLs have been studied extensively since the works of Esaki and Tsu on transport in these structures, and experimental results have frequently provided a good guideline for further theoretical progress and applications in the area [3,23]. Whenever required, extensions to multiple minibands can be developed based on the Wigner function description and the k • p theory (e.g., [24][25][26][27]).…”