Conduction intersubband transitions at normal incidence in Si_1−xGe_xquantum well devices

Abstract

We show theoretically that it is possible to design SiGe-based quantum well structures in which conduction intersubband transitions are induced by normal incidence infrared radiation. A sp(3)d(5)s(*) tight binding model has been adopted to evaluate the electronic states and optical transitions between lowest conduction confined states of a superlattice composed of one pure Ge quantum well separated by SiGe alloys, grown along the [001] direction. We find that significant optical coupling between confined states in the Ge wells is achieved at normal incidence radiation by the off-diagonal elements of the mass tensor. The minimum energy Ge conduction valleys are, in fact, tilted with respect to the [001] growth axis. For comparison we show that no such coupling can be realized for the conduction states confined in a similar structure composed by Si quantum wells because the ellipsoids of the lowest conduction valleys are oriented along the growth direction.

Valley splitting and optical intersubband transitions at parallel and normal incidence in [001]-Ge/SiGe quantum wells

“…In contrast, in Ge-rich ͓001͔-SiGe QWs the lowest conduction states near the L point have essentially equal p x , p y , and p z components, and electric-dipole transitions are allowed. From the effective-mass perspective, the same conclusions follow observing that, in Si-rich ͓001͔-SiGe QWs, normal incident radiation does not stimulate conduction intersubband transitions because the electric field oscillates in the QW plane which is a free direction for the motion of the ⌬ electrons; in Ge-rich ͓001͔-SiGe QWs, the in-plane field is coupled to the motion along the confined direction by the off-diagonal terms of the mass tensor at L. 43 To evidence the effect of these selection rules on the intersubband absorption spectrum, we have evaluated ␣͑͒ in n-type QW systems with different values of the doping concentrations and QW widths, both in the presence and in the absence of electric fields superimposed along the growth direction. For the investigated doping concentrations ͑n + =10 −6 -10 −5 Å −2 ͒ and in the low-temperature regime, only electronic states in a small neighbor of the U point are populated and the sampling of the quasi-2D BZ can be reduced to the gray shaded region depicted in Fig.…”

“…42 Finally, it is worth mentioning that, in Ge-rich ͓001͔multilayer structures, intersubband transitions can be stimulated both in TE and TM modes of the incident radiation. 43 This fact is due to the presence of off-diagonal terms in the mass tensor at the L point ͑the constant energy ellipsoids have principal axes along the ͗111͘ directions while the considered systems are grown along the ͓001͔ direction͒ which guarantees coupling between electronic states and radiating fields of arbitrary polarization. We exploit this possibility to suggest experimental arrangements for optical detection of IS.…”

Quantum-confined Stark effect inGe∕SiGequantum wells: A tight-binding description

“…The same approach has been successfully adopted also for tight-binding simulations of nanostructured systems. [22][23][24][25][26] Ren and Harrison 21 have shown that if the basis wave functions are not explicitly known ͑as is the case for the parametrization of Ref. 15͒, the dipole matrix elements can be reasonably approximated by the following relation:…”

Terahertz intersubband absorption and conduction band alignment inn-type Si/SiGe multiple quantum wells

“…Since the Si mass tensor is diagonal in the reference system of the growth direction, intersubband transitions are only allowed for incidence radiation with electric field in the growth direction, i.e., they are forbidden for normal-incidence radiation. 19 Therefore, in order to observe intersubband absorption, the samples were cut in a waveguide shape with lateral facets at 45°, as depicted in the sketch of Fig. 1.…”

“…19,[26][27][28] In fact this atomistic approach allows taking into account the geometric details of the whole structure, the chemical composition of the substrate and of the deposited materials, the strain within each layer and the spin-orbit coupling. The method provides the energy-band structure over the whole Brillouin zone, the spatial and orbital compositions of the states and the optical matrix elements for inter- 26,28 and intraband 19,27 optical transitions. Furthermore, band alignments, 9 band folding, and intervalley interactions 27 have been also described within the same formalism.…”