Photoluminescence and AFM characterization of silicon nanocrystals prepared by low-temperature plasma enhanced chemical vapour deposition and annealing Lara Lama laral@kth.se Axel Nordström axenor@kth.se Supervisors: Jan Linnros Ilya Sychugov Bachelor of Science Thesis in Engineering Physics, SA104X School of Information and Communication Technology Stockholm, Sweden 2012
Abstract When studying quantum dots one of the most important properties is the size of the band gap, and thus also their physical dimensions. We investigated these properties for silicon quantum dots created by means of plasma-enhanced chemical vapour deposition and annealing. To determine the band gap size we measured photoluminescence for ten different samples and to determine the physical dimensions we used an atomic force microscope. The photoluminescence measurements indicated that the intensity of the emitted photons varied across the samples, but did not indicate any shift in peak wavelength between samples nor any time-dependence of the luminescence. The peak wavelength was in the order of 600 to 620 nm, corresponding to a band gap of 2.0 to 2.1 ev and a physical size of approximately 3 nm. The AFM scans revealed densely packed quantum dots, where few single objects could be distinguished. In order to be able to perform a better statistical analysis, efforts would have to be taken to separate the quantum dots. 1
Contents 1 Introduction 4 1.1 Background................................... 4 1.2 Purpose and question formulation....................... 4 2 Quantum dots 4 2.1 Background theory............................... 4 2.2 Surface passivation for silicon quantum dots................. 6 2.3 Potential applications............................. 7 2.3.1 Medical applications.......................... 7 2.3.2 Applications in solar cells....................... 7 2.3.3 Applications in lasers and LEDs................... 8 3 Plasma enhanced chemical vapor deposition and annealing 8 4 Photoluminescence measurements 8 4.1 Theory...................................... 9 4.2 Experimental setup............................... 9 4.3 Results...................................... 10 4.4 Discussion.................................... 10 5 Atomic Force Microscopy measurements 13 5.1 Theory...................................... 13 5.2 Experimental setup............................... 14 5.3 Results...................................... 15 5.4 Discussion.................................... 15 6 Conclusions 16 References 18 2
Acknowledgements We would like to thank our supervisors Jan Linnros and Ilya Sychugov for starting us up on this project and aiding us in its realization. Furthermore, we thank Benjamin Bruhn for his help with annealing and etching of the samples in the clean room; Mahtab Sangghaleh for helping us get started on the photoluminescence measurements; Torsten Schmidt for helping us with the AFM measurements; and Fatjon Qejvanaj for helping in the attempt at performing AFM measurements on single quantum dots. 3
1 Introduction 1.1 Background In the early 1980 s Dr. Louis Brus and his team of researchers discovered that nanosized crystal semiconductor materials - quantum dots - made from the same substance exhibited different colours when exposed to ultraviolet light. This discovery contributed to the understanding of the quantum confinement effect which explains the relationship between size and colour of the quantum dots[2]. Due to the small size of the quantum dots they have discrete energy levels, like those of single atoms. The electrons can make transitions between these energy levels, thus absorbing photons or emitting photons of a specific wavelength. A change in size of the quantum dots would therefore - due to the quantum confinement effect - result in changed energy levels allowing emission of photons in a different colour. Quantum dots have the potential to revolutionize the efficiency of solar cells, improve medical diagnostics and treatment by providing efficient biological markers and targeted drug delivery. They also have the potential to advance the development of optical devices such as lasers and light emitting diodes (LEDs) (see section 2.3). 1.2 Purpose and question formulation To be able to use quantum dots in new applications one would first have to overcome the difficulties of manufacturing quantum dots with the desired characteristics. Therefore it is of interest to measure the wavelengths where the quantum dots have photon emission and to measure of the physical sizes of quantum dots manufactured by different methods. Our quantum dots were created using plasma enhanced chemical vapor deposition and annealing (see section 3) and in our research the following questions are investigated What is the size of the band gap of our quantum dots? What is the size of a single quantum dot and what does the size-distribution look like across different samples? Can a relationship between the physical size and the size of the band gap be observed? How do the properties of our samples change with time? 2 Quantum dots 2.1 Background theory Quantum dots are nanocrystals made of semiconductor materials e.g. Si, CdSe, GaAs with typical dimensions of 1-10 nm. Compared to bulk semiconductor material, quantum dots have different properties due to their small size. For instance the size of their band gap is strongly dependent on the physical dimensions of the quantum dot. 4
(a) Electrons in the valence band are excited by photons with at least the band gap energy. (b) Electrons returning to the valence band, emitting photons with energy corresponding to the band gap. Figure 1: Direct transitions in a bulk semiconductor, k is the wave number[3]. Bulk materials have electrons distributed in continuous bands separated by the band gap as seen in Figure 1. However, in reality the bands are not actually continuous. Consider the conduction electrons of a quantum dot as a free fermi gas confined to a spherical crystal with radius R[4]. If we solve the time-independent Schrödinger equation h2 2m ψ(r) + V (r) = E nψ(r) (1) in spherical coordinates r, φ, θ for this problem, i.e. for the potential V (r) = { 0 for r < R, (2) otherwise (3) one finds solutions only for specific values of E n, that is E n = h2 π 2 n, for n = 1, 2, 3... (4) 2mR2 The mass m is here taken as the reduced mass of the effective electron and hole masses, m e = 0.26m e and m h = 0.386m e respectively - m e is the free electron mass - and thus the reduced mass is m = 0.155m e [6]. For bulk silicon the effects of this quantum confinement is totally neglectable. For a silicon sphere with radius R = 1 mm, the difference in energy between the ground state (n = 1) and the first excited state (n = 2) is merely 7.3 10 12 ev, which differs from the band gap of bulk silicon at room temperature, which is E g = 1.12 ev[1], by twelve 5
orders of magnitude. However, if we go down in size and consider silicon nanocrystals with R = 3 nm, the energy difference between the ground state and the first excited state is 0.81 ev. If we go down in size even more to R = 1 nm we get 7.3 ev. These last values are not neglectable at all but will have a large impact on the size of the band gap. A somewhat more refined model for the resulting band gap in a quantum dot is the so-called Brus equation[4] Eg dot = E g + h2 π 2 ( 1 2R 2 m + 1 ) e m 1.8e2 h 4πɛ r ɛ 0 R (5) where the last term is a correction due to the coulomb interaction between the electron and the hole[4]. Using this equation for the silicon quantum dot with radius R = 3 nm, we get a band gap of Eg dot = 1.32 ev - significantly higher than the bulk silicon E g = 1.12. When shining with a laser upon the quantum dots with high energy photons ultraviolet light electrons are excited from the valence band to the conduction band, leaving holes in the valence band. When the electrons returns to their resting state in the valence band they emit light of a specific colour, depending of the size of the band gap. Since decreasing the size of the dots will result in an increasing band gap it will also cause the emission of higher energy photons of shorter wavelength. 2.2 Surface passivation for silicon quantum dots The quantum confinement model describes the behaviour of quantum dots very well under certain circumstances. However, when considering silicon quantum dots which have been exposed to oxygen, effects due to surface passivation may have to be accounted for. As long as the band gap is smaller than 2.1 ev - that is the diameter is larger than 3 nm - the quantum confinement model agrees with experiments[5], but when when the diameter is further reduced the band gap does not increase as much as predicted by the theory. This is due to the formation of Si=O covalent double bonds when the silicon quantum dots are exposed to oxygen. These Si=O bonds can trap electrons and holes, and as the energy gap between these surface states get smaller than the band gap from the quantum confinement they come to dominate the recombination process[5]. There are three different possible recombination mechanisms for the oxygen-passivated quantum dots, indicated by the three different zones in Figure 2. In zone I the experiments agree with the quantum confinement model and the recombination is between free electrons and free holes. When the diameter is below 3 nm - in zone II - however, the band gap does not increase as much as predicted by quantum confinement because the recombination is now dominated by trapped electrons and free holes. Finally, in zone III, the recombination is between trapped holes as well as trapped electrons[5]. As the trapped states display no dependence on the physical dimensions of the quantum dot, the band gap will remain basically constant when reducing the diameter further. 6
Figure 2: The three zones describe three different recombination mechanisms for oxygenpassivated quantum dots. In zone I, recombination is via free electrons and holes, in zone II a trapped electron is involved along with a free hole and in zone III the recombination is between trapped electrons and trapped holes[5]. 2.3 Potential applications 2.3.1 Medical applications When injected to living organisms quantum dots can be used for tracking of cell development, detection of diseases and for delivering drugs to diseased areas - such as cancer tumours - without damaging healthy tissue. The quantum dots can bind to cells in several ways. For instance, they can be coated with a lipid bilayer that makes them water soluble and enables attachment of biomarker-binding antibodies. Each quantum dot would then only bind to one biomarker protein on the surface of a single cell [7]. It is possible to detect several kinds of diseases using this technique due to the biomarker protein being unique for each type of diseased cell. By further using quantum dots that emit light of several distinct colours, they can be enabled to detect different types of diseases simultaneously. The coated quantum dots could also be used as drug carriers for targeting specific areas, when attached with drug molecules. The drug would then be released to the cell as the quantum dots binds to it. 2.3.2 Applications in solar cells In conventional solar cells - made with semiconducting bulk material - the efficiency of the cells depends on the conversion of photons into electricity. In the solar cell, photons with energy as the band gap of the material or higher excites electrons, forming an electric current in a circuit. The excess energy of the high-energy photons is lost as heat[8]. By using quantum dots as the photovoltaic material instead of bulk material 7
the efficiency of the cells can be increased. This is possible by two means; quantum dots of certain semiconductors can emit more than one electron for every photon absorbed[9], thus increasing the electrical current. The quantum dots can also be tuned to match the solar spectrum, which would decrease the high-photon energy loss. 2.3.3 Applications in lasers and LEDs Due to their light emission quantum dots can be used as the active light-emitting medium in lasers, operating at their characteristic wavelength. In LEDs quantum dots are used for enhancing the colour and efficiency. Today s white-light LEDs consists of a blueemitting LED coated with a phosphor that is excited by the LED, emitting yellow and orange light. The combination of blue and yellow produces a white light lacking in red photons. By choosing a certain material and a certain size of the quantum dots in the LEDs they can be adjusted to radiate in a specific colour[10]. 3 Plasma enhanced chemical vapor deposition and annealing Our quantum dots were created using a method based on the annealing of silicon oxide wafers. We had wafers upon which were deposited oxide and silicon by use of lowtemperature plasma enhanced chemical vapour deposition (PECVD). Basically, chemical vapour deposition (CVD) is performed by allowing a gas to react with the surface of a heated wafer[13]. PECVD - unlike CVD - also uses a plasma, from which ions are accelerated onto the surface. The reaction is thus not only initiated by temperature, but also by the impact of these ions and hence this method can yield good results at significantly lower temperatures than CVD[13]. On our wafers, there was approximately twice as much oxide as silicon as if we were to form SiO 2. However, the amount of silicon was increased a bit beyond this so that there was a slight excess of silicon on the wafers. This excess amount of silicon was varied across ten different samples. When later annealing - heating - the samples at 1100 C, the silicon and oxide on the wafers formed a SiO 2 matrix and the excess silicon gathered in tiny nanoclusters - quantum dots. In the end, we had ten different samples labeled 26, 28, 30, 31, 32, 33, 34, 35, 36 and 37. The exact differences between these samples were not known to us as the manufacturing specifications were unavailable. Thus we can only say that the samples differed in their composition but not exactly how they differed and comparing samples quantitatively is not possible. 4 Photoluminescence measurements When using the method described above for creating the quantum dots we wanted to investigate various properties of the quantum dots generated this way. First there was the question of the effect of the ratio of silicon and oxide. Does this parameter change the size - and thus the emitted wavelength - of the created quantum 8
Figure 3: Schematic picture of the photoluminescence measuring equipment. dots? What does the size distribution look like? Secondly, there was the issue of time-dependence. How do the properties of the samples change from only a few hours after annealing to a few days or weeks after annealing? To answer these questions we carried out a series of photoluminescence (PL) measurements on the ten differently composed samples. We performed four measurements during a period of two weeks. 4.1 Theory By shining a laser on a semiconductor substrate, electrons will be excited - provided that the photon energy is sufficient - from the valence band to the conduction band of the substrate. When the electrons return to the valence band, they lose an amount of energy corresponding to the band gap by emitting a photon. The wavelengths of these photons can be measured using a spectrometer and thus one can determine the band gap. Since the band gap size has a great size-dependence for quantum dots, a photoluminescence spectrum will yield information about the size and size-distribution of the quantum dots. 4.2 Experimental setup For the PL measurements, the substrate was placed upon an inverted optical microscope. After setting the magnification at 50x and focusing the microscope on the surface, the UV laser of wavelength 405 nm was switched on, directed by mirrors towards the substrate. The emitted light was then directed through a slit into the spectrometer where it was directed by more mirrors onto a grating, which deflected different wavelengths on different areas of the detector. To remove stray light from the laser reflected off the sample s surface, the signal passed a high-pass filter before entering the spectrometer, designed so that visible light would pass, but UV light would not. 9
4.3 Results From the setup we got a spectrum for each measurement (Figure 4b). When analysing the spectra, the samples labeled 26 and 28, showed only very weak - if any - luminescence. The background was clearly dominant in these measurements and therefore we decided to use the sample 26 measurement as an estimation of the background for the other samples (Figure 4c). Subtracting the background, we plotted the other signals and fitted each to a gaussian distribution (Figure 4d) from which we then extracted the peak size, the corresponding wavelength and the full width half maximum - see table 1. (a) The image from the detector (b) Measured spectrum (c) Error with curve fit (d) Compensated spectrum with gaussian fit Figure 4: Plotted data for the sample labeled 35. 4.4 Discussion How do the results relate to the questions posed beforehand? Concerning variations across different samples, we can safely say that the intensity of the emitted light strongly depends of the silicon-oxide ratio - the 36 and 37 samples are far more luminescent than the other samples, whereas the luminescence of the 26 and 28 samples cannot be 10
Table 1: Data from the photoluminescence measurements fitted to a gaussian distribution from which the quantities peak size, peak wavelength and the full width half maximum could be extracted. Sample/Date of measurement Peak (counts) Peak wavelength (nm) Full width half maximum (nm) Standard deviation (counts and % of maximum amplitude) Sample 31 2012-02-23 62.7 609.5 14.3 4.1 (7%) 2012-02-28 61.0 606.1 11.6 12.2 (20%) 2012-03-01 52.4 621.9 13.9 15.0 (29%) 2012-03-06 61.3 614.9 13.9 16.5 (27%) Sample 32 2012-02-23 77.1 610.8 15.7 9.1 (12%) 2012-02-28 80.6 623.1 12.8 13.1 (16%) 2012-03-01 85.9 619.5 13.7 16.0 (19%) 2012-03-06 94.8 611.7 15.4 18.2 (19%) Sample 33 2012-02-23 96.2 621.1 14.8 7.3 (8%) 2012-02-28 126.9 625.6 13.1 14.0 (11%) 2012-03-01 103.2 624.1 13.9 16.7 (16%) 2012-03-06 114.8 618.9 15.2 17.4 (15%) Sample 34 2012-02-23 106.5 618.4 14.5 6.7 (6%) 2012-02-28 195.9 623.1 12.9 11.1 (6%) 2012-03-01 155.3 622.1 13.9 17.3 (11%) 2012-03-06 168.8 618.8 14.5 18.8 (11%) Sample 35 2012-02-23 275.8 611.9 13.8 12.2 (4%) 2012-02-28 308.9 614.3 12.4 14.2 (5%) 2012-03-01 390.9 613.0 13.3 23.6 (6%) 2012-03-06 465.7 611.2 13.4 25.8 (6%) Sample 36 2012-02-23 775.1 606.4 13.1 25.2 (3%) 2012-02-28 790.7 613.9 13.8 32.3 (4%) 2012-03-01 844.3 606.8 13.0 38.7 (5%) 2012-03-06 1030.8 605.3 13.0 42.5 (4%) Sample 37 2012-02-23 1274.9 598.7 13.1 45.5 (4%) 2012-02-28 1505.1 598.3 13.0 39.8 (3%) 2012-03-01 1531.3 598.4 13.0 38.7 (3%) 2012-03-06 1651.1 597.5 13.0 52.9 (3%) 11
distinguished from the background. However, we cannot say the same for the emitted wavelengths corresponding to the band gaps and thus the sizes of the nanocrystals. All peak wavelengths seem to be around 600 to 620 nm and no systematic wavelength shift can be determined. The peak wavelengths vary back and forth within samples with as much as 15 nm which should be due to random and fitting errors. Consider for example the measurements in Figure 5. In Figure 5a we have a measurement of the 37 sample where the data does not quite follow the presumed normal distribution. The curve-fitted peak wavelength seems to be some five nanometers shorter than the measured peak and therefore the measured peak is within the same wavelength region as the peaks of the other samples. In 5b we see a measurement and curve-fit of the 33 sample. Due to plentiful noise - the standard deviation between the data and the normal distribution is in this case 16% of the maximum amplitude - there are evidently some difficulties associated with determining a definite peak wavelength, and thus the margin of error is quite large. (a) The 2012-02-23 measurement of the 37 sample with curve-fit. (b) The 2012-03-06 measurement of the 33 sample with curve-fit. Figure 5: Plots describing the difficulties with getting an exact peak wavelength from the measured data. Not only seems the most common size to be the same across samples, but also the distribution of sizes. The calculation of the full width half maximum - or linewidth - differs only little, which tells us that the size-distribution is basically the same. As the linewidth is quite large, it is probably due to approximately normal distributed variations in size between the quantum dots and not due to random errors from equi-sized quantum dots. Concerning the time-dependence of the luminescent behaviour, the results seem equally inconclusive. We can see no evidence of a red-shift as time progresses, nor can we see any change in the size-distribution of the quantum dots - the full width half maximum stays the same. Although we can see no time-dependence it does not mean that there is no time-dependence. Since we started measuring hours after annealing, something could have already happened. Indeed, Wolkin et al.[5] found that as silicon 12
quantum dots were exposed to oxygen a red-shift was observed for quantum dots smaller than 3 nm only three minutes after exposure to oxygen due to the effects discussed in Section 2.2. If we try to theoretically approximate the size of the quantum dots from the measured peak wavelengths using the Brus equation (equation 5 in Section 2.1) we get a radius of approximately 1.5 nm. To get more conclusive results we could improve the measurements in the following ways. First, we could increase the exposure time quite drastically. This would yield more statistically certain results, especially for the less luminescent samples, where 30 seconds seems far too short judging by the results for these samples. To easier distinguish these less luminescent samples from the background, we should have performed a measurement of the background prior to the actual photoluminescence measurements. To be able to say anything quantitative about the relation between sample composition and the measured intensity we would need samples where the specifics of the manufacturing process were known. 5 Atomic Force Microscopy measurements Having measured photoluminescence, we wanted to measure the size of single quantum dots to see if the sizes differed between samples. For this task we used an Atomic Force Microscope (AFM). 5.1 Theory Atomic Force Microscopy uses a cantilever with a tiny tip to measure the surface profile of a substrate. The AFM can run in a few different modes depending on the sample one wants to investigate. In contact mode, the tip follows the surface. When the surface exerts a force on the tip - i.e. the surface s height profile changes - the cantilever will bend according to Hooke s law F = kz, where F is the force exerted on the tip, k is the spring constant of the cantilever and z is the vertical displacement of the tip. Using a laser directed at the cantilever and reflected onto a detector, one can measure the displacement of the tip. This method requires only forces in the range of pn[11] to yield measurable results. Measurements in contact mode has a relatively high scan rate compared to other methods, but as the tip touches the sample there is a risk that the tip will damage the sample - especially a softer one such as a biological sample - or vice versa, that is the surface damages the tip[12]. For our measurements we used non-contact mode, which means that the tip does not actually touch the sample, but rather oscillates above it at a frequency slightly above the resonance frequency of the cantilever[12]. As the tip is situated slightly above the substrate, the forces on the tip are mostly long range ones such as van der Waals forces[12]. When the tip is brought closer to the surface, these van der Waals forces will cause the frequency of the oscillations to decrease[12], and thus a measurement of the frequency will yield a height profile of the surface. Due to being able to measure as small 13
Figure 6: Due to the width of the tip, the horizontal resolution of the AFM is not as good as the vertical resolution[15]. forces as pn, the limit on the vertical resolution - on the axis orthogonal to the surface of the sample - is governed by electronic and thermal noise and is thus in the order of an Å[11]. The horizontal resolution, however, is limited by the size of the tip. The tip is generally in the form of a pyramid or a tetrahedron[12]. If the surface suddenly changes height, the upper part of the tip will come too close to the sample and force the tip upwards before the tip actually reaches the height change. Thus a steep ascent will be smoothed out and the heightened area will seem larger than it actually is, as in Figure 6. Typically, the horizontal resolution is in the order of a few nm and thus when measuring nanocrystals, the resolution in the plane is not enough and we must look on the height of the quantum dots rather than the measured width. 5.2 Experimental setup After annealing the samples, the quantum dots were covered by the SiO 2 matrix. To be able to measure the height profile of the quantum dots, we had to etch the SiO 2 cover away using hydrogen fluoride (HF). Having done this, the substrate was placed with the etched area beneath the tip of the AFM. The laser was then focused onto the back surface of the cantilever and reflected onto the photodetector, which has four sectors. This can be seen in Figure 7. The laser had to be positioned so that the signal received by the photodetector was as strong as possible. Then the detector had to be positioned so that the laser was aimed at the intersection between all four sectors of the detector. This is because the vertical deflection of the cantilever is determined by the difference in the light intensity measured by the upper and lower sectors[12]. Before doing the measurements, the feedback system a PI-controller connected to the cantilever had to be set so that the trace and retrace scans of the surface topography overlaped each other. When they do not overlap it means that the tracking is poor which results in blurred images. To prevent poor tracking two parameters of the feedback system was mainly changed, the setpoint and the I-gain. The setpoint is the value of the deflection of the cantilever that the feedback circuit attempts to maintain[12], the 14
Figure 7: A schematic diagram of the AFM setup[12]. smaller it is set the less are the oscillations in the scans. The higher the value of the feedback gains are set, the faster will the feedback system react. If the gains are too high the system becomes unstable which causes high frequency noise in the scans. 5.3 Results The surface profile from an AFM scan of a five-by-five microns area of the sample labeled 37 is shown in Figure 8a. The software allowed us to draw a line in this image and would then give us the cross section along this line as in Figure 8b. Looking at these cross sections in a few different areas of the images, we tried to determine the sizes of the quantum dots from the samples labeled 26, 34 and 37. The quantum dots of the 26- sample seems to have a diameter in the order of approximately 3 nm. The diameter for the 34-sample is somewhere around 5 to 8 nm and for the 37-sample it is somewhere between 2.5 and 5 nm. 5.4 Discussion The AFM measurements revealed a large density of quantum dots upon the sample surfaces, which proved it difficult to distinguish single quantum dots from layers upon layers of quantum dots. To measure their sizes we had to try to find the smallest height differences in the height profile that we can say is not due to disturbances of some kind. Considering the sensitivity to mechanical vibrations - such as sound waves - of the AFM, noise is plentiful. Accordingly, our results consists of approximate values of what we consider might be single quantum dots. To further improve the accuracy we would have to measure the surface profile of a sample with single quantum dots or at least with a very low density of them. We did attempt this by using ultrasonic waves on an etched sample in a solvent of isopropanol. The quantum dots would thus detach from the surface and dissolve in the solvent. We then placed a drop of this solution upon a clean sample holder and waited for it to evaporate, leaving only quantum dots on the sample holder. When doing this the solvent did not evaporate completely and left several microscopic droplets of fluid on the sample holder. In our measurements these droplets how microscopic they may 15
(a) The surface profile of the 37-sample from an AFM scan, 5-by-5 microns in size. Brighter areas represent elevated areas. (b) The cross section along the line in this 500-by-500 nm scan. Figure 8: Measurement results from the AFM scans. have been were significantly larger than what any of the quantum dots would have been. They were therefore completely obscuring the image and probably concealing most quantum dots. However, we could eventually see something that may have been a quantum dot - the size was approximately what one might expect but since we at the time had no possibility to investigate this single object further, we could come to no conclusion. To achieve conclusive results from this kind of measurement, we would need to measure photoluminescence and surface profile simultaneously, so that we can confirm the existence of a quantum dot when we find a candidate with the AFM. This is a quite complicated and lengthy search because a single silicon quantum dot does not emit a great amount of photons, and thus the exposure time required would be large indeed. 6 Conclusions To compare the results from the photoluminescence measurements and the AFM scans we can use the Brus equation (equation 5 in Section 2.1. The sample labeled 37 seemed to have dimensions of 2.5 to 5 nm. This would correspond to luminescence in wavelengths between 500 nm and 870 nm according to the quantum confinement approach. While this interval covers the measured spectrum - which was from approximately 540 nm to 660 nm - it is also significantly larger. However, the expected photoluminescence would not contain wavelengths beneath 590 nm (2.1 ev) due to the surface-passivation effects described in Section 2.2. The 34-sample seemed to have quantum dots with dimensions 16
(a) Sample 26. (b) Sample 37. Figure 9: The density of quantum dots seem to vary across samples according to the AFM scans. Here are AFM scans of the 26- and 37-samples, 20-by-20 microns in size. of approximately 5 nm to 8 nm, corresponding to wavelengths of 870 nm to 1020 nm, which is well above the measured photoluminescence spectrum - probably due to that we cannot distinguish between single and clustered quantum dots in the AFM scans. Finally, the 26-sample with dimensions of some 3 nm would yield luminescence around 590 nm. It is possible that this is correct - we cannot tell from the photoluminescence spectrum, since we could detect no luminescence from the 26-sample. To conclude, and return to our initial questions, the photoluminescence measurements tells us that the band gap for all the samples - where luminescence could be distinguished - is approximately 2.0 ev, which is significantly larger than that of bulk silicon, i.e. 1.12 ev. According to these same measurements and the Brus equation the size of the quantum dots is approximately 3 nm for all the samples. The AFM measurements were too difficult to interpret to aid us in determining the size and the actual sizes could be smaller due to the size-dependence of the band gap is expected to almost disappear for quantum dots smaller than 3 nm. Furthermore the size distribution is the same across the samples - the diameters of the quantum dots vary with approximately 0.3 nm around the most common size of 3 nm, according to the photoluminescence. Finally, we could see no evidence of any time-dependence for any of these properties. However, we could observe a large difference in the intensity of the luminescence from the different samples. The reason for this could be varying density of quantum dots between the samples. Fewer quantum dots would mean weaker luminescence. Lower density for the 26-sample than for the 37-sample seems to be implied by the AFM scans in Figure 9 - though admittedly, the horizontal resolution of the AFM is not good enough to say anything definite from these images. Such a difference in amount of quantum dots 17
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