APPLIED PHYSICS LETTERS 93, 031105 共2008兲
Transient carrier transfer in tunnel injection structures V. G. Talalaev,1,2,3 J. W. Tomm,1,a兲 N. D. Zakharov,2 P. Werner,2 U. Gösele,2 B. V. Novikov,3 A. S. Sokolov,3,4 Y. B. Samsonenko,5,6,7 V. A. Egorov,6,7 and G. E. Cirlin5,6,7 1
Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, 12489 Berlin, Germany Max-Planck-Institut für Mikrostrukturphysik, 06120 Halle (Saale), Germany 3 Fock Institute of Physics, Saint-Petersburg State University, 198504 St. Petersburg, Russia 4 Fakultät für Physik und Astronomie, Universität Heidelberg, 69120 Heidelberg, Germany 5 Ioffe Physico-Technical Institute RAS, 191021 St. Petersburg, Russia 6 Physics and Technology Centre for Research and Education RAS, 195220 St. Petersburg, Russia 7 Institute for Analytical Instrumentation RAS, 190103 St. Petersburg, Russia 2
共Received 12 June 2008; accepted 3 July 2008; published online 23 July 2008兲 InGaAs tunnel injection nanostructures consisting of a single quantum well as injector and a quantum dot layer as emitter are studied by time-resolved photoluminescence spectroscopy. The quantum dot photoluminescence undergoes substantial changes when proceeding from direct quantum dot excitation to quantum well excitation, which causes an indirect population of the dot ground states. This results in a lowered effective carrier temperature within the dots. Results on the carrier transfer versus barrier thickness are discussed within the Wentzel–Kramers–Brillouin approximation. Deviations for barrier thicknesses ⬍5 nm are assigned to the formation of nanobridges that are actually detected by transmission electron microscopy. © 2008 American Institute of Physics. 关DOI: 10.1063/1.2963973兴 Tunnel injection structures are interesting for applications in diode lasers since they offer additional degrees of freedom for the design of the gain region. This is given by the spatial separation of carrier source 共injector兲 and light emitter. In case of quantum well 共QW兲 and quantum dot 共QD兲 devices, a selective population of the lasing ground state allows for reducing the electron heating within the emitter by direct injection of cold electrons from the separated carrier source into the ground state by tunneling. Potentially this results in reduced gain suppression, increased quantum efficiency, decreased diffusion capacitance, and lower low-frequency roll-off and high-frequency chirp.1 Furthermore the expected preferential population of QDs of a particular size eventually leads to reduced inhomogeneous broadening of the gain 共emission兲 spectrum.2 These predictions have been verified in QW- and QD-based devices that demonstrate an improved high-speed behavior; see Ref. 3 and additional references on other device implementations therein. In this letter, we report on the analysis of the transient carrier transfer between a QW and QDs in a special type of tunnel-injection nanostructures, where QW and QDs are serving as injector and emitters, respectively. Such a structure has been suggested by Evtikhiev et al.4 First we characterize these structures and point to a unique feature of them, namely an “inverted energy band offset” within the conduction bands. Then we analyze the kinetics of the carrier transfer between the vertically stacked QW and the QDs by timeresolved photoluminescence 共PL兲 spectroscopy by measuring a set of structures with different barrier thicknesses. Finally, we discuss the results within the framework of the Wentzel– Kramers–Brillouin 共WKB兲 approximation and assign the observed deviations of the data from this model for barrier thicknesses ⬍5 nm to the formation of nanobridges between QW and QDs. Evidence for the formation of such bridges is a兲
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provided by transmission electron microscopy 共TEM兲. InGaAs tunnel injection structures are grown by solidsource molecular beam epitaxy with the following sequence of layers: InAs QDs 共2 ML兲, GaAs spacer 共thickness determined by TEM兲, and a single 11 nm thick In0.15Ga0.85As QW, all embedded into a GaAs matrix. This layer sequence is rather unusual and is expected to promote the formation of nanobridges. Reference samples containing either exclusively QDs or QWs are grown as well. Structural information 共morphology of QD and QW, local chemical composition兲 was received by TEM investigation techniques 共i兲 by diffraction contrast mode 共Phillips CM20 microscope, acceleration voltage U = 200 kV兲 and 共ii兲 by image processing and analysis of high-resolution lattice structure micrographs 共JEM 4010, U = 400 kV兲. The In0.6Ga0.4As QDs have a diameter of 18 nm, a height of 4 nm, and an array density of ⬃5 ⫻ 1010 cm−2 共standard deviation of these parameters is ⬇10%兲. Using this information, calculations within the framework of the effective mass approximation are performed, providing a conduction band structure as follows: QWs, EA0 = 58 meV; disk-shaped QDs, EA0 = 109 meV and EA1 = 43 meV. Here EA denotes the energetic distance between the quantum-confined electron state 共0 or 1兲 and the conduction band edge of the adjacent barrier. These values have been experimentally confirmed by Arrhenius analysis of continuous wave 共cw兲 PL intensities providing activation energies of EA0 = 55⫾ 3 meV for the QW and EA0 = 105⫾ 7 meV and EA1 = 35⫾ 2 meV for QDs. A scheme representing these facts is depicted in Fig. 1共d兲. Time-resolved PL measurements are performed at 10 K with sub-100-fs excitation pulses using a mode-locked Ti:sapphire laser operating at 82 MHz. The photon energies and excitation power density are 1.33– 1.60 eV and ⬃5 ⫻ 1011 photons pulse−1 cm−2, respectively. The PL is dispersed in an imaging monochromator and detected by a synchro-scan streak camera equipped with an infraredenhanced cathode. The time resolution of the total system is
0003-6951/2008/93共3兲/031105/3/$23.00 93, 031105-1 © 2008 American Institute of Physics Downloaded 24 Jul 2008 to 62.141.169.250. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
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FIG. 1. 共Color online兲 TEM cross-section images of two different tunnel injection structures: 共a兲 barrier thickness 6.5 nm, 共b兲 barrier thickness 3.1 nm, 共c兲 high-resolved TEM of the latter. The contour was drawn over the contrast corresponding to x ⬃ 0.15. The letter z denotes the growth direction. 共d兲 Level scheme of the structure 共not to scale兲. Full 共red兲 arrows mark ground state transitions, whereas the dashed 共blue兲 arrow denotes excited state transitions. 共e兲 PL spectra of a structure with 6.5 nm GaAs barrier for above barrier excitation: full black line represents cw excitation 共50 W cm−2兲, black symbols stand for pulse excitation 共5 ⫻ 1011 photons pulse−1 cm−2兲, red open circles denote the PLE spectrum with the monitor set to the QD ground state energy at 1.2 eV. The spectroscopic measurements are done at T = 10 K.
at best ⬃10 ps. PL cw measurements are done with a standard setup, whereas the PL excitation 共PLE兲 experiment was done by using a KOHERAS SuperK power source. Figure 1 provides selected results from a basic characterization of the samples. Cross-sectional dark field images of samples with barrier thickness 6.5 and 3.1 nm are shown in Figs. 1共a兲 and 1共b兲, respectively. These micrographs were taken by applying the chemically sensitive 共200兲 reflection. Thereby In containing regions 共QW and QDs兲 appear as darker areas. As visible in Fig. 1共a兲, the QW is well separated from QDs, whereas in Fig. 1共b兲 the QD touches the QW. This type of nanobridge is presented as an image processed high-resolution micrograph in Fig. 1共c兲. Inside the contour, the In content exceeds 15%, see Ref. 5. Figure 1共e兲 presents PL and PLE spectra from a sample with 6.5 nm barrier thickness. Tentative assignments of the optical transitions are given, with the subscripts 0 and 1 standing for ground and excited state transitions. These attributions are confirmed by both the calculations and the evolution of the PL intensities when increasing the population density by switching from cw to impulsive excitation. Figure 2 shows transient PL data. PL maps as detected by the streak camera system are shown
Appl. Phys. Lett. 93, 031105 共2008兲
FIG. 2. 共Color online兲 Transient PL from a structure with 6.5 nm barrier for two excitation energies: 共a兲 1.33 eV, 共b兲 1.42 eV, corresponding to excitation energetically below and above the QW ground state transition energy, respectively. 关共c兲 and 共d兲兴 PL transients for two structures with barrier thickness of 6.5 nm 共black full circles兲 and 3.1 nm 共red open兲. 共c兲 QW emission at 1.36 eV after excitation into the barrier with 1.6 eV; 共d兲 QD ground state emission at 1.2 eV after excitation into the QW ground state with 1.3 eV. Time zero corresponds to the maximum of the fs excitation laser pulse as detected by the setup 共full width at half maximum ⬃10 ps兲. All measurements are done at T = 10 K and excitation density is 5 ⫻ 1011 photons pulse−1 cm−2.
in Figs. 2共a兲 and 2共b兲, whereas Figs. 2共c兲 and 2共d兲 show vertical cuts from maps, i.e., PL transients at particular photon energies. We compare the PL transients in the spectral channels of QW0 共c兲 and QD0 共d兲 ground state recombination, respectively, for two different samples with barrier widths of 3.1 nm 共black full circles兲 and 6.5 nm 共red open circles兲 barrier thickness. Figure 3 summarizes the tunneling
FIG. 3. Tunneling time between QW and QDs vs barrier thickness deduced from the decay of the QW PL 共full squares兲 and the rise of the QD PL 共full circles兲. Open circles mark data that can not be assigned to meaningful t-values, because of the limitations set by the QD PL rise time. Triangles are taken from Refs. 6 and 7. The dashed line correspond to the WKB approximation, whereas the doted lines represent the border cases for the time constants as measured at the reference samples containing either a single QW or QD layer. Downloaded 24 Jul 2008 to 62.141.169.250. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
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times as derived from such transient PL data measured from the whole sample set. It is worthwhile to address the implications of our results. First, we point to the band structure. According to Fig. 1共e兲 the spectral positions of the QW ground state and the QD excited and ground state transitions are at about 1.36, 1.27, and 1.2 eV, respectively. According to calculations and Arrhenius analysis, the electron states 共in the conduction band兲 do not follow this order 共on the absolute energy scale兲; see Fig. 1共d兲. Figures 2共a兲 and 2共b兲 show the result that proves this tentative assignment. The only difference between both measurements is an increase of the excitation photon energy by 90 meV from 1.33 to 1.42 eV. For an excitation energy below the QW absorption edge, the QDs get predominantly populated by their own ground and first excited state absorption, resulting mainly in “hot” luminescence via the QD1 state with a decay time of about 150 ps; see Fig. 2共a兲. For an only slightly increased excitation photon energy that exceeds the QW0 ground-state transition energy 共and thus allows for efficient QW absorption兲, we observe a substantial increase of the QD0 luminescence 共decay time ⬃750 ps兲; see Fig. 2共b兲. The increased QD0 PL is likely to be caused by the efficient population of the electronic QD ground states by tunnel injection from the QWs. Thus we show that in this particular structure pumping at increased photon energies results in “colder” luminescence. The term colder points here to the fact that the ratio of the populations of ground and excited states is altered in favor of the ground state population. Basically, the result shown in Figs. 2共a兲 and 2共b兲 is a clear demonstration of the functionality of a tunnel injection structure. This is also a necessary condition for the following analysis of the PL transients. Tunneling times t are obtained by fitting transient PL curves such as shown in Figs. 2共c兲 and 2共d兲. Both the QW PL decays and the QDs PL rises are impacted by t since they involve the depopulation of the injector and the population of the emitters, respectively. The actual transients, however, are formed additionally by the recombination lifetime QW, and QD, which are determined separately at the reference samples to 420 and 750 ps, respectively. Thus the transient depleting of the QW ground state is described by two competing processes and produces a QW PL decay curve IQW that is shaped according to
冉 冊 冉 冊
IQW共t兲 = Imax exp −
t
QW
t exp − . t
共1兲
Here Imax corresponds to the maximum of the profile. The QD PL rise is well-described by two noncompeting processes. Taking into account the instantaneous population, the rise is described by
冉 冊 冉 冊册
IQD共t兲 = I0 exp − − exp −
t
QD
t t
,
+
冋 冉 冊
Imax ⫻ QD t exp − QD − t QD
共2兲
where I0 corresponds to the intensity where the excitation pulse peaks. Thus there are two independent PL data sets, namely QW PL decay and QD PL rise, which provide information on t. Therefore the excellent agreement between the two obtained t-data sets 共see circles and squares in Fig. 3兲 provides
additional evidence for the supposed carrier transfer scenario. On the other hand the actual values of QW, as well as the rise time of the QD PL set limits for the applicability of the two approaches; see open circles in Fig. 3. All these results are summarized in Fig. 3 together with t values that have been obtained for the carrier transfer between differently sized QDs.6,7 As long as the barrier thickness exceeds about 6 nm, remarkable agreement with the data from Ref. 6 and the WKB approximation is visible. For this thickness range, we also do not find any systematic dependence of QD-transition energies on the barrier thickness. For lower barrier thicknesses, however, our actual t-values fall substantially shorter and approach the time resolution limits of our setup. We assume that the significant reduction of the transfer time is explained by the formation of point-contactlike channels 共nanobridges兲 between the apexes of some QDs and the QW. The high resolved TEM image of a structure with a barrier width of 3.1 nm, see Fig. 1共c兲, shows such an contact nanobridge with a width of about 1 nm. These nanobridges are expected to form channels that allow for ultrafast carrier exchange between QDs and the QW. A very similar type of such contacts was previously observed for closely stacked InAs QD layers.7 A complementary analysis of the tunnel-injection mechanism as well as the determination of reliable t-values for the barrier thickness range below 5 nm, in particular in presence of nanobridges, represent tasks for ongoing investigations. Summarizing, we report on the transient carrier transfer in tunnel-injection nanostructures containing a QW and a QD layer, which are coupled through a barrier. A set of structures with barrier thickness in the 2 – 9.5 nm range is analyzed. For QW excitation substantial cooling of the carriers confined within the QDs is demonstrated, compared to the situation when the QDs are populated exclusively by their own absorption. The carrier transfer from the QW into QDs is measured and the results are discussed within the framework of the WKB approximation for tunneling. Observed deviations from this model for barrier thicknesses ⬍5 nm are assigned to the formation of nano-bridges across the tunneling barriers. Evidence for the existence of such bridges is provided by TEM analysis. Helpful discussion with M. Ziegler and expert technical assistance by R. Hoffmann is gratefully acknowledged. This work has been supported by the Russian Foundation for Basic Research 共08-02-00954兲 and Program RAS “Quantum Nanostructures.” 1
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