Optical properties of photodetectors based on wurtzite quantum dot arrays P. Tronc* Laboratoire d’Optique Physique, Ecole Supérieure de Physique et Chimie Industrielles, 10 rue Vauquelin, 75005 Paris, France K. S. Zhuravlev and V. G. Mansurov Institute of Semiconductor Physics, Prospekt Lavrentieva 13, 630090 Novosibirsk, Russia G. F. Karavaev and S. N. Grinyaev Kuznetsov Siberian Physicotechnical Institute, Tomsk State University, Pl. Revolyutsii 1, Tomsk 634050, Russia I. Milosevic and M. Damnjanovic Faculty of Physics, University of Beograd, P.O. Box 368, Beograd 11001, Serbia Received 7 March 2007; revised manuscript received 6 February 2008; published 21 April 2008 We show that two types of wurtzite quantum dots can be grown with the C 3v symmetry. Their symmetry axis coincides with a threefold proper rotation and a 6 3 improper rotation axis of the wurtzite lattice, respectively. One-, two-, and three-dimensional periodic structures made of such dots are considered. Most of them have the C 3v point symmetry except some one- and three-dimensional structures that have the C 6v one. The symmetry planes and possible glide planes for the dots and dot structures are those of the wurtzite matrix. It is shown that, under incident light propagating along the growth direction, the absorption is strong for valence-to-conduction- band transitions but, on the contrary, the absorption is weak in infrared detectors based on transitions within the conduction band. It makes it necessary to draw a grating to change the light direction within the device as is also the case for infrared detectors based on wurtzite quantum wells or superlattices. DOI: 10.1103/PhysRevB.77.165328 PACS numbers: 68.65.Hb, 78.67.-n I. INTRODUCTION Numerous optoelectronic devices involving quantum dot QD arrays are currently under study. For example, in the GaN / AlN system, both intraband and interband transitions are of interest, the former in the infrared wavelength range including fiber-optic telecommunication wavelengths at 1.3 and 1.55 m, 1–3 the latter in the blue and UV range. In ad- dition, due to the Froelich interaction in highly ionic wurtzite materials, the absorption recovery time is extremely short, of the order of few hundreds of femtoseconds, for intersubband transitions in the GaN / AlGaN system. 4,5 Infrared photode- tectors based on conduction intersubband transitions in GaN / AlN QD structures have been proposed. 6,7 Dispersion of QD dimensions naturally arising from growth broadens the detector response range. The devices are generally based on multilayered QD structures. Indeed, QDs cover only a small percentage of the plane surface in a layer and it is useful to increase the number of layers to improve the cou- pling with the light. 8 In addition, the structures can be of better quality than those involving a single layer when the few first layers are of lower quality than the following ones. 9 Last, it is noteworthy that the wurtzite lattice is a polar one. The nanostructures grown along the c axis direction can present a huge built-in electric field arising from the piezo- electric effect and the difference in spontaneous polarizabil- ity between the dot and matrix materials. 10 It will be shown hereafter that the wurtzite lattice allows growing two types of high-symmetry dots. Both types have the C 3v symmetry. Orientation of the dots is imposed by the matrix lattice that dramatically reduces the number of pos- sible configurations for the QD structures. We consider here- after the three types of structures, namely, a single chain of dots stacked one over the other along the c axis of the wurtz- ite lattice that is chosen as the z axis, a single layer with a regular trigonal or hexagonal distribution of dots within the layer plane, and last, a multilayered structure made of such layers with dots stacked along the c axis and forming chains. Determining the exact symmetry of the dot structures allows deriving the optical selection rules and relative intensities of the transitions. It makes it possible to optimize the design of the photodetectors even if the structures considered hereafter have a rather high symmetry, sometimes higher than that of some grown QD structures. In addition, it will be shown that the possible space-symmetry groups of high-symmetry dot arrays are identical to those of wurtzite quantum wells QWs or superlattices SLs. Therefore, the optical selection rules and hence, in particular, the relative intensities of con- duction intersubband transitions are the same. The present paper is organized as follows. In Sec. II, we analyze the space symmetry of the various QD-based struc- tures as well as the site symmetry of atoms in the lattices and the symmetry lowering by an applied magnetic or electric field. Section III is devoted to establishing the selection rules for dipolar transitions, exciton recombination, infrared ab- sorption, and Raman scattering. Particular attention is paid to infrared photodetectors based on conduction intersubband transitions. It is shown that the transitions between the ground state and the first-excited states are weak with inci- dent light propagating perpendicular to the layers, which makes it necessary to use a grating to change the direction of the light within the device. That is also the case for infrared photodetectors based on conduction intersubband transitions in wurtzite QWs or SLs. The next section deals with the envelope function approximation. Section V considers a few topics such as built-in electric field, distinguishing structures PHYSICAL REVIEW B 77, 165328 2008 1098-0121/2008/7716/1653287 ©2008 The American Physical Society 165328-1