|
|
|
Modulated reflectivity monitors the change in the reflectivity, R, that results from a change in the electric field distribution within a semiconductor (due, for instance, to surface electric fields, which are usually sufficiently strong). In conventional PR, a laser beam of photon energy above the band gap is used to excite free carriers that partially screen the internal field. Since the energies of the excitonic transitions are sensitive to the field, these are shifted when the light is applied. The laser beam is chopped and the resulting modulation in the reflectivity, DR, is measured using CW broadband illumination, with the reflected light being collected, analysed via a monochromator and detected using a photodiode or photomultiplier. The normalised modulated signal (DR/R, of order 10-5 to 10-4) is obtained via phase sensitive detection linked to the chopping frequency. The normalisation corrects for the variations of source and spectrometer characteristics with wavelength. Many different types of lineshape (related to different derivatives of the excitonic line) are obtained depending on whether, e.g., excitons within epilayers or in quantum well structures are being observed. The phase shift between excitation and modulated signals also contains information and is easily measured.
Schematic diagram of a photomodulated reflectivity set-up (PJ Klar, PhD thesis).
The figure below shows the different components of a PR spectrum. The dots represent the measured data points and the lines serve as a guide to the eye. On the top left the in-phase modulated AC signal with laser and white light on the sample, top right on the same scale the corresponding AC background signal (mainly PL) with the laser on the sample and the white light off. The graphs on the bottom are the DC reflectivity signal R and the derived dR/R signal on the left and right respectively. The DC background signal is not shown (PJ Klar, PhD thesis).
A subgroup of the dilute magnetic semiconductors (DMS) comprises alloys consisting of an AIIBVI host material with Mn2+ ions incorporated randomly in cation positions. The s, p-d exchange interaction between the Mn2+ ions and the carriers in the band states leads to an enhanced Zeeman splitting of the electron and the hole states in an applied magnetic field at low temperature. These magnetic effects and their theoretical understanding can be used to investigate fundamental properties of semiconductor structures containing DMS in novel ways by magneto-optical experiments. Series of MBE grown multiple quantum well samples and quantum dot samples (dot diameter < 200 nm) prepared from the Cd1-xMnxTe / CdTe, the Zn1-xMnxTe / ZnTe and the Zn1-xMnxSe / ZnSe systems have been studied by photoluminescence, photoluminescence excitation, reflectivity, photomodulated reflectivity and spin-flip Raman scattering spectroscopy. Data obtained by different magneto-optical experiments on the same DMS structures have been compared with calculations that combine models for the electronic and excitonic states with models for the paramagnetism of the Mn2+ ions. All experiments can be interpreted simultaneously and consistently in terms of strain, interface roughness and the chemical valence band offset (VBO). The values for the VBO of 35% and 30% for the Cd1-xMnxTe / CdTe and the Zn1-xMnxTe / ZnTe systems respectively were confirmed and a VBO of 20% (x > 15%) was determined for the Zn1-xMnxSe / ZnSe. For the Cd1-xMnxTe / CdTe and the Zn1-xMnxSe / ZnSe samples the degree of interface roughness was also determined. Similar analyses of the magneto-optical results for the quantum dots gave insight into the effects of the nanofabrication process e.g. a strain relaxation towards a freestanding structure, the damage induced by different etching procedures and effects due to the reduction of the lateral size of the nanostructures.
In the magneto-optical studies of the MQW samples several problems have been addressed. Some of those are general problems in heterostructures. Others are specifically related to the unique magnetic properties of the DMS. It was thought in previous studies that the possibility of performing magneto-optical experiments offers additional, independent ways of determining non-magnetic heterostructure parameters such as the chemical VBO. It appears that this is not the case. The main reason is the strong correlation between interface roughness and enhanced paramagnetism of the Mn2+ ions at the interfaces of the heterostructure. Because of the difficulty of determining interface roughness directly in any optical experiment and because its effects on the energy positions of excitonic transitions are usually small in conventional semiconductors, this problem was usually ignored. However, experimental and theoretical studies have shown that the effects related to the enhanced paramagnetism are not negligible in DMS heterostructures. Whereas in zero-magnetic field optical experiments only the strain state, the value of the chemical VBO and probably the exciton binding energy need to be taken into account, a fourth quantity, the enhanced paramagnetism at the interfaces plays a major role in the interpretation of magneto-optical experiments on DMS heterostructures. To make use of the additional information contained in magneto-optical experiments it is therefore essential to interpret sets of data from zero-magnetic field and magnetic field experiments together. This requires one, firstly, to carry out different experiments on the same specimens and, secondly, to combine conventional models for excitons and electrons in semiconductor heterostructures with models for the enhanced paramagnetism at the interfaces. This has been attempted for the Cd1-xMnxTe / CdTe system and the Zn1-xMnxSe / ZnSe system. By combining results of zero-magnetic field a-PR experiments and SFR experiments and by comparing them with calculations using models derived from the combinations of the interface model of Stirner et al. with the exciton model of Hilton et al. and with the SFR model of Halsall et al. it was possible to confirm the established value for the chemical VBO of 35% in the Cd1-xMnxTe / CdTe system and simultaneously to determine the degree of interface roughness of each individual sample according to the model of Stirner et al. It should be pointed out that the situation for this system is made simple because strain effects only play a minor role. This is not the case for the other two systems, the Zn1-xMnxSe / ZnSe and the Zn1-xMnxTe / ZnTe. However, for the former the strain parameters, in particular the absolute deformation potentials av and ac, are known by experiment, which is not the case for the latter, where only theoretical values for av and ac are available. Using a simultaneous analysis of zero-field and magnetic field R, PLE and SFR spectroscopic data it was possible for the series of Zn1-xMnxSe / ZnSe samples to determine the chemical VBO to be about 20% and the degree of roughness to be c = 0.1; the strain state of the samples was also found. The analysis of the zero-field experiments allowed only a determination of the strain state. The models used in the calculation were the model of Stirner et al. combined with a model similar to the one of Halsall et al., but excluding additional donors, in the case of the SFR data, and a combination of the interface model of Stirner et al. with the exciton model of Peyla et al. in the case of the PLE data. It was only possible to eliminate finally the effects of the enhanced paramagnetism in the determination of the chemical VBO by magnetic field experiments because two complementary sets, the experimental data for SFR and for PLE, were available. These are complementary in two senses: firstly, in SFR electrons are probed whereas in the PLE excitonic states are probed and, secondly, the electrons probed in SFR are sensitive to the magnetic splitting in the conduction band, whereas the magnetic field splitting between the excitons in the PLE is dominated by the valence band splitting. For the determination of the chemical VBO in the Zn1-xMnxTe / ZnTe system, zero-magnetic field and magnetic field dependent b-PR data were available. From the zero-magnetic field b-PR data it was (as for the Zn1-xMnxSe / ZnSe samples) only possible to determine the strain state of the samples. The magnetic field dependent b-PR data have been analysed only using a value of the chemical VBO of 30% as determined by Cheng et al. assuming ideal interfaces and the validity of the theoretical values for av and ac calculated by van der Walle. It was not possible to separate the effects of interface roughness, i.e. enhanced paramagnetism at the interfaces, mainly because the complementary set of SFR data was not available for the analysis. However, the agreement between experimental data and calculated data confirmed that the set of assumptions i.e. a chemical VBO of 30%, the theoretical strain parameters of van der Walle and ideal interfaces as used by Cheng et al. give a good description of the net potential situation present in these four Zn1-xMnxTe / ZnTe MQWs. The effects of the magnetic-field induced type I - type II transition for the Jz = -3/2 heavy hole state in the valence band on the s+ component of the e1hh1 exciton was studied in detail for the series of Zn1-xMnxTe / ZnTe MQWs. The analysis of the results focused on the transition from a spatially direct to a spatially indirect exciton. It was found that, due to exciton binding energy effects, the type I - type II transition for the free hole does not coincide with the transition from a spatially direct to a spatially indirect exciton for the s+ component of the e1hh1 exciton; instead, the former occurred at a lower magnetic field than the latter. This finding has been theoretically validated by a discussion of effective potentials which include exciton binding energy effects calculated using the model suggested by Peyla et al. In agreement with other work, it is observed that exciton binding energy effects smear out the direct evidence (such as drastic changes of the transition energy and the oscillator strength as a function of magnetic field) for a magnetic-field induced type I -type II transition. The main evidence for the occurrence of a type I - type II transition is the cross over between the ZnTe buffer excitonic transition and the s+ component of the e1hh1 quantum well exciton together with the sidebands which occur on the main signal of the s+ e1hh1 exciton in the magnetic field region around the flatband situation in the potential of the Jz = -3/2 heavy hole state in the valence band. In the Cd1-xMnxTe / CdTe system the magnetic-field induced type I - type II transition was not addressed. However, the effects of the magnetic-field induced type I - type II transition on the transition energies of the e1hh1 quantum well exciton played a major role in the analysis of the PLE data on the Zn1-xMnxSe / ZnSe which led to the determination of the chemical VBO for this heterostructure system. All Q-dot samples had lateral sizes (100 nm to 200 nm) which are in a size regime (>50 nm) where no additional lateral confinement effects are expected. However, the comparison with the corresponding parent heterostructures revealed differences in the optical spectra for the Q-dots in all three heterostructure systems. These differences can either be related to effects induced by the nanofabrication process, such as changes in the strain state, changes in the surface electric field and damage caused by the etching, or even be related to the reduction of size, such as the change of the intensity ratio of the bound exciton compared to the free exciton in quantum well emission. A strain relaxation towards a freestanding Q-dot structure was observed in Q-dots prepared in the two strongly strained heterostructure systems. In the series of 200 nm Q-dot samples prepared in the Zn1-xMnxTe / ZnTe system, an inversion of the energetic order of the e1hh1 and the e1lh1 quantum well excitons was easily observable by b-PR. In the Zn1-xMnxSe / ZnSe, energy shifts in the quantum well PL emission were due to a strain relaxation. In this case the strain relaxation was detectable by PL because the PL emission was related to the lowest light-hole quantum well transition e1lh1, which is more sensitive to changes in strain than its heavy-hole counter part e1hh1. It is remarkable that a strain relaxation occurred even in the Zn1-xMnxSe / ZnSe Q-dots whose height is only half of their diameter. In the a-PR spectra of the 200 nm and 100 nm Cd1-xMnxTe / CdTe Q-dots, strain related shifts of the transition energies could not be detected. However, strain effects play only a minor role in these specimens and are expected to give rise only to small shifts of the excitonic transitions (such shifts are within the experimental error of the a-PR experiment). It therefore is possible to draw the general conclusion that Q-dots usually relax towards a freestanding structure. Direct studies of the damage induced by the etching in the nanofabrication process were carried out only for the Cd1-xMnxTe / CdTe system. Here, the magneto optical experiments (i.e. SFR) proved to be a useful tool to detect the induced damage. It was even possible to locate the depth down to which the Q-dot sample was damaged in comparison to the MQW parent structure. To achieve this, it was again necessary to include the effects of interface roughness in the models used to analyse the experimental data and to combine the results of the magneto-optical experiment with the results of the zero-magnetic field a-PR experiments. It was shown that the 100 nm Q-dots etched solely by Ar+ ion etching show considerable damage e.g. the top quantum wells of the MQW structure were also damaged by the etching. This was not the case in the 200 nm Cd1-xMnxTe / CdTe Q-dot samples, whose undamaged core reaches the original surface of the MQW structure. Thus, the value of at least 30 nm for the depth of the damage rim around Q-dots prepared by Ar+ ion etching found by Gourgon et al. is indirectly confirmed. The PL spectra of the 200 nm Zn1-xMnxTe / ZnTe Q-dots reveal an additional emission band which is not present in the PL of the parent MQWs and which is therefore a result of the nanofabrication process. This is the only indication for induced damage in the Q-dots prepared in this system. Thus, like the 200 nm Cd1-xMnxTe / CdTe Q-dot sample, the four 200 nm Zn1-xMnxTe / ZnTe Q-dots are of good quality and it can be assumed that the undamaged core of the Q-dots extends right to the top surface of the original structure. In the two Zn1-xMnxSe / ZnSe Q-dots, no signs of damage induced by the nanofabrication are observed, not even for the 100 nm Q-dot sample. This is a particularly satisfying result because this 100 nm Q-dot sample was prepared by a combined etching procedure in which the specimen was first etched by Ar+ ion etching to dot diameters of 200 nm and then, in a second step, by wet-chemical etching reduced further in size down to 100 nm in diameter. This shows that with the combined etching method good quality Q-dots of sizes smaller than 200 nm can be fabricated, which is not possible by solely using Ar+ ion etching where the lower limit is a diameter of about 200 nm. In the PL spectra of the Zn1-xMnxTe / ZnTe and the Zn1-xMnxSe / ZnSe Q-dot samples, a reduction of the PL intensities compared to the LO phonon intensities is observed. This can be explained as being due to the presence of non-radiative recombination centres created either as a result of the band bending by the surface electric field in the sidewalls or by damage induced by the nanofabrication process. A genuine size effect was observed only in the PL spectra of the two Zn1-xMnxSe / ZnSe Q-dots and their parent SQW structure. A decrease in the relative intensity of the donor bound quantum well emission compared to the intensity of the free exciton quantum well emission was observed with decreasing Q-dot size, which can be explained by an increase with decreasing Q-dot size of the number of dots without donors in the well region.
As a by-product of studies on Zn1-xMnxTe / ZnTe, it was found that the new technique, b-PR spectroscopy, gives the same spectroscopic information as the conventional a-PR spectroscopy, but offers some advantages. As far as the aims given in the preface of the thesis are concerned the work was successful. It is possible, by simultaneously analysing results obtained by different spectroscopic methods and by including the theoretical knowledge about the magnetic properties of the Mn2+ ions in the models for the excitonic and electronic states, to gain additional information about heterostructure parameters, changes caused by nanofabrication etc. In DMS heterostructure systems, this can be achieved by magneto-optical experiments in ways which are not applicable in non-magnetic semiconductor heterostructures. A very important result in this context is that it is possible to achieve a consistent interpretation of the properties of the samples even when data of several different experiments are analysed simultaneously so that, in effect, the problem is overdetermined. This shows that the theoretical understanding of the physical properties of the DMS systems as well as the quality of the grown DMS structures has reached a high standard. Therefore, DMS heterostructures and nanostructures are ideal model systems for semiconductor technology. Several final concluding remarks about the DMS Q-dots are appropriate. Firstly, it was shown that magneto-optical experiments on DMS nanostructures are possible and lead to interesting new results. Secondly, useful information can be gained from the study of 'big' nanostructures of dimensions for which no additional confinement effects are expected. The occurring effects in such structures are not only interesting from an applicative point of view but will also play a major role in studies of nanostructures of even smaller sizes where similar effects will occur together with new effects such as additional lateral confinement. Finally, as far as the fabrication of smaller DMS structures is concerned, the essential limit at the moment is the etching procedure. However, the combined etching procedure used to fabricate the 100 nm Zn1-xMnxSe / ZnSe Q-dots seems to be a possible step in this direction. The potential of DMS heterostructures and nanostructures as good model systems in semiconductor technology offers interesting research possibilities for the future, for example, in making contributions to the development and improvement of growth and nanofabrication processes: special heterostructures and nanostructures can be designed to address specific questions that can only be answered by using the magnetic properties of DMS, in particular, in cases where the interaction between Mn2+ ions and excitons or free carriers can be used as a probe. It should not be forgotten, that, apart from questions of applications, there are still many other fundamental physical questions where DMS heterostructures and nanostructures and their unique magnetic properties can offer novel ways of providing answers.
|
