Silicon Nanocrystals
2.4 Optical Characterization of Depth Distribution
oxide include the optical excitation cross section (∼6 ×1016 cm2 at 488 nm) [80] and the single-triplet exchange energy gap for excitons (∼10 meV) [116]. The exchange splitting explains the temperature dependence of silicon nanocrystal photoluminescence intensity in terms of a slow recombination rate for the parity forbidden triplet-to-ground state tran- sitions (∼0.1–0.3% of the singlet-to-ground transition rate) and the probability that the exciton will be found in the more optically active singlet state in thermal equilibrium.
Figure 2.5. The custom-built dipping apparatus used to etch gradient profiles in oxide samples.
dilution of 48% hydrofluoric acid etches silicon dioxide at a rate of ∼2.5 ˚A s−1 [118]. This rate is slow enough to allow the immersion time to be used to control the removal of the oxide layer containing the silicon nanocrystals. After etching in the HF solution, spectro- scopic ellipsometry measurements can be used to determine the remaining oxide thickness.
Rather than measure one sample in many incremental cycles (etch oxide, measure remain- ing oxide thickness, measure photoluminescence, repeat), we instead begin with a long and narrow sample (∼1 cm× ∼10 cm) and etch a gradient in the oxide layer, effectively creating many samples simultaneously on the same substrate. We have designed and built a custom
“dipping” apparatus for this purpose, shown in figure 2.5. The sample is held vertically by a Teflon arm that can be raised or lowered under computer control. The immersion time is controlled to etch the desired “staircase” pattern into the sample. The precision of the
etched profile is limited only by the translation speed of the stepping motor and the etch rate of the solution. It is important to ensure that the acid solution is well mixed and to consider buffering the acid when etching at fast rates in more concentrated solutions. We have also sometimes encountered a gas phase or meniscus etching effect that tends to limit the thickness gradient that can be achieved between adjacent steps.
Silicon Substrate
Staircase etched oxide with Si nanocrystals
Figure 2.6. Two photoluminescence spectra collected at different positions along a staircase- etched sample. The nanocrystals are excited by∼1 W/cm2 pump illumination at 457.9 nm.
Figure 2.6 shows a schematic diagram of our optical depth profiling experiment. The implanted distribution of silicon nanocrystals is partially removed at each etch depth along the staircase sample. At each measurement position, the photoluminescence spectrum of the remaining nanocrystals shows a shift in intensity and in peak wavelength (figure 2.6 inset). The sample was cut from a large 300 mm wafer processed at Intel. The nanocrystals were fabricated by ion implantation (5 keV; 9.5×1015 ions/cm2 or 15% peak atomic excess Si) into an oxide layer that was grown to a thickness of∼15 nm. The nanocrystal formation anneal was performed in an RTA furnace at 1080◦C for 5 minutes. The calculated diffusion
∼1 W/cm2. The recorded photoluminescence data are then matched to the corresponding thickness map of the sample, which is collected in a similar automated fashion by translat- ing the sample under a spectroscopic ellipsometer. It is straightforward to collect hundreds of data points (spectra vs. oxide thickness) in a matter of minutes using this technique.
Spectroscopic ellipsometry (over the range 300 nm to 850 nm) cannot be expected to distinguish between pure SiO2 and SiO2 that is embedded with silicon nanocrystals in the very thin layers that we wish to study. We instead model the spectroscopic ellipsometry data by assuming that the oxide layer consists of pure SiO2. While this model fits the ellipsometry data perfectly, we know that the nanocrystals should modify the effective index of refraction within the oxide layer. In principle the ellipsometry data could be corrected using the Maxwell-Garnet effective medium model for inclusions (i.e., silicon nanocrystals) in a host matrix of SiO2. Unfortunately we can imagine many different mechanisms that could change the index profile or even the thickness of the implanted oxide layer. We instead show our photoluminescence data in figure 2.7 and figure 2.8 as a function of the equivalent pure SiO2 layer thickness that we directly measure.
If we assume that all of the implanted silicon ions are incorporated in the oxide matrix in silicon inclusions (including nanocrystals), we find that the initially 15 nm oxide layer should expand by ∼2.5 nm to incorporate the extra material. The added silicon content will then increase the index of refraction enough to make the layer appear another ∼2 nm thick when applying the pure SiO2 equivalent thickness model. In fact we see that our initially 15 nm thick oxide layer appears to be∼20 nm thick after the nanocrystal fabrication process. However, this could easily be a coincidence. Sputtering during the ion implantation could erode the oxide layer by a few nanometers. Oxide regrowth might increase the layer thickness while decreasing the silicon content. Such regrowth might preferentially occur near the substrate, as in the “anomalous swelling” effect observed in other work after ion implantation [84], or it could occur near the surface of the oxide layer. Due to extensive mixing near the interface, we might expect a large number of the implanted ions to be
incorporated into the substrate or a uniform background concentration of silicon throughout the layer. Finally, amorphous silicon clusters might account for a large fraction of the implanted silicon inclusions without contributing to the photoluminescence signal.
A separate issue is the possibility of native oxide regrowth that might thicken the remain- ing layer after the etching procedure and lead us to overestimate the remaining equivalent thickness at each etch step. This is apparent for samples that are completely etched down to the substrate that show no photoluminescence, for which we measure a native oxide thick- ness of ∼3 nm. The data points recorded for very thin oxide layers might be less reliable for this reason. We can also speculate that the etching process could damage a greater frac- tion of the nanocrystal distribution than the physically remaining oxide thickness reflects.
This would also tend to cause an overestimate of the remaining equivalent oxide thickness at any given etch depth. These effects could cause an artificial narrowing or shift in the distribution we find for optically active nanocrystals.
In spite of these difficulties, we estimate that the equivalent oxide thickness data can provide an accurate measure of the remaining physical layer thickness to within ∼3 nm.
Note that the precision of our measurement is higher (∼1 nm) and therefore relative dis- tances should have better than 3 nm accuracy. We are able to draw several important qualitative conclusions about the distribution of optically active nanocrystals from the op- tical characterization procedure.
Figure 2.7 shows the peak photoluminescence intensity, which is a measure of the inte- grated photoluminescence over the fraction of the depth distribution that remains at each equivalent oxide thickness. The drawn red line is the calculated differential photolumi- nescence intensity, which we interpret as a measurement of the optically active nanocrystal population depth distribution. Within our estimated∼3 nm thickness error, we see excellent agreement between the peak in the nanocrystal distribution and the simulated implantation depth. Notably, the width of the nanocrystal distribution is quite narrow in comparison to the implantation profile shown in figure 2.2.
We have plotted the peak wavelength of the photoluminescence spectra as a function of the remaining equivalent oxide thickness in figure 2.8. The data suggest that the large na- nocrystals are centrally located within the depth distribution and that smaller nanocrystals are more prevalent in the shoulders of the implanted distribution. We have included a scale bar indicating the corresponding nanocrystal sizes according to a phenomenological model
Figure 2.7. The depth-resolved differential peak photoluminescence intensity (drawn in red) suggests that the optically active nanocrystals are distributed in a region that is narrow in comparison to the implantation profile.
given by Ledoux [55]. Note that the spectra do not show a shift to shorter wavelengths until after the large nanocrystals at the peak of the distribution have been removed. The dashed line is drawn to suggest the actual depth distribution for nanocrystal diameters which may be symmetrical.
This optical characterization technique could easily be used in a comprehensive experi- ment correlating implantation or annealing conditions to the nanocrystal depth distribution or applied in the study of nanocrystals fabricated in thin films by other methods. Improve- ments that could be made include the use of ultraviolet ellipsometry that might allow the silicon concentration to be detected or the use of improved surface chemistry to limit pos- sible oxide regrowth after the staircase etching procedure.