Synthesis and stress analysis of germanium nanocrystals embedded in dielectric matrices 3

Chapter Results & Discussions III Chapter Results & Discussions III: Analysis of Stress Development of Ge Nanocrystals in Silicon Oxide Matrix 6.1 Introduction There has been an intense interest in nanocrystals embedded in a silicon oxide matrix in the hope that the quantum confinement effect will make the indirect bandgap semiconductors (e.g Si or Ge) become more efficient light emitters Recently, Takeoka et al had demonstrated the strong size dependence of the photoluminescence (PL) spectra from the Ge nanocrystals embedded in a silicon oxide matrix and suggested it to be linked to electron-hole pairs confined in the nanocrystals [1] However, there is a relatively unexplored area in the research of Ge nanocrystals in silicon oxide matrix, namely, the stress development of the nanocrystals in such a system Wellner et al [2] had concluded from their Raman results of Ge nanocrystals in silicon oxide that it was strongly affected by compressive stress The Ge nanocrystals were obtained from annealing silicon oxide layers implanted with Ge In our earlier work, it is also noticed the that the Raman peak position - 124 - Chapter Results & Discussions III changed in our co-sputtered samples when rapid thermal annealed under different conditions [3] Moreover, in the pervious chapter, we have pointed out that the changes in the Raman peak position of samples are associated with the mechanical stress experienced by the nanocrystals This stress occurs mainly because the SiO2 is unable to accommodate the growing Ge nucleus Wellner et al and Borany et al have argued that the compressive stress might be explained by the fact that Ge undergoes a volume expansion of about 6% during the liquid to solid phase transition [2,4] Yi et al [5] agreed with Wellner et al and suggested that the observed pressure exerted on the nanocrystals are mainly attributed to a volumetric difference as the nanocrystals reside in a matrix cavity that is too small In this chapter, we report results of a study on the development of mechanical stress experienced by Ge nanocrystals in a silicon oxide matrix using a combination of Raman and transmission electron microscopy techniques We have followed the procedure outlined by Sharp et al [6,7] to secure free-standing Ge nanocrystals from those originally embedded in the silicon oxide matrix This enables us to examine the effect of the compressive stress exerted on the nanocrystals on the Raman spectra that is independent of the size effect and discuss the origin of such stress The samples used in this work are the same as those used in Chapter and consists of Sample A, B and C with Ge concentration estimated to be around 3, 10 and 15 at.% - 125 - Chapter 6.2 Results & Discussions III Liberating the Ge nanocrystals Recently, Sharp et al has shown in his work that a mixture solution of 1:1 HF:H2O is able to selectively etch away the oxide while retaining a substantial amount of the nanocrystals on top of the substrate as free-standing nanocrystals Moreover, it was also found this etching process does not significantly affect nanocrystal size and that the structure of the Ge nanocrystals remains stable even after prolonged exposure to the environment [5-7] We followed such procedure and dipped the samples in the HF:H2O solution with occasional shaking of the sample holder to enhance the etching process After ensuring that the oxide film has been successfully removed (which can be judged by a colour change of the film), the sample was removed from the solution and left to dry in air Figure 6.1: (a)-(c) Schematic diagrams of the process of obtaining free standing Ge nanocrystals from the annealed co-sputtered samples via our careful etching experiments (d) XTEM micrograph of Sample A annealed at 1000°C in forming gas (10% H2, 90% N2) for 15 minutes after selective removal of oxide matrix and (e) high magnification TEM of 6.1(d) - 126 - Chapter Results & Discussions III The above mentioned process is shown in a schematic in Figure 6.1 As the oxide is being etched away, the embedded nanocrystals will be released from the oxide film The nanocrystals are found to accumulate at the surface after a complete removal of the SiO2, as can be seen in Figure 6.1(d) The nanocrystals retain their crystallinity, showing clear lattice fringes as can be seen from Figure 6.1(e) The attractive van der Waals forces are likely to be responsible for the build-up of nanocrystals It has also been shown that these nanocrystals remain crystalline and un-oxidized up to at least months even when directly exposed to air [5] 6.3 Calculation of stress experienced by the Ge nanocrystals Typical Raman spectra of pre- and post etched annealed samples are shown in Figure 6.2 The frequency of the phonon Raman band depends on the masses and positions of the atoms, the inter-atomic forces (i.e force constants of the bonds) and the bond length Therefore, any effects altering these features will produce a change in the frequency of the band For instance, a tensile stress will result in an increase in the lattice spacing and, hence, a decrease in the wavenumber of the vibrational mode In the case of compressive stress, the decrease of the lattice parameter yields a corresponding increase of the vibrational frequency From the downward shift towards relatively lower frequency in the Raman peaks between the pre- and post-etched samples, it suggests that the nanocrystals experienced compressive stress - 127 - Chapter Figure 6.2: Results & Discussions III A set of typical Normalized Raman spectra of samples annealed for 15 minutes at 900°C before and after selective oxide matrix removal Several effects can contribute to the stress state of the nanocrystal: the surface tension between the matrix and nanocrystal, the different thermal expansion coefficients of Ge and silicon oxide, and the equilibrium size of the matrix cavity in which the nanocrystal resides In order to account for the temperature changes during processing and characterization, one must consider the thermal expansion coefficients of silica and Ge, the latter being an order of magnitude higher than the former The differential expansion contributes to a tensile stress that reduces slightly the compressive stress state of the nanocrystal when quenched to room temperature - 128 - Chapter Results & Discussions III However, considering all these sources of stress, one may conclude that the observed pressure is mainly attributable to a volumetric difference, i.e the nanocrystal resides in a matrix cavity that is too small This volumetric difference may arise from the matrix atoms not being able to move rapidly enough to accommodate the nanocrystal as it is growing due to the fast growth rate experienced by the nanocrystals as a result of enhanced diffusivity at elevated annealing temperatures, or the stress could be caused by the volumetric expansion of Ge (~6%) [2,4] when it solidifies from the liquid phase to the solid phase By comparing the Raman spectra of our pre- and post-etched annealed samples, the hydrostatic pressure, P, in the nanocrystals can be estimated as [8] P= ω embedded − ω etched γω ( S11 + 2S12 ) (6.1) where ωembedded and ωetched are the Raman peak positions of the nanocrystals embedded in silicon oxide and free-standing Ge nanocrystals respectively, and ω0 is the Raman peak position of bulk Ge, γ = 0.89 cm-2 is the mode-Grüneisen parameter [8], S11 and S12 are components of the elastic compliance tensor with S11 + 2S12 = 0.44 ×10-12 dyn-1 cm2 6.3.1 Effect of annealing time on the stress state of the nanocrystals In order to study the influence of annealing time on the formation and the stress state of the nanocrystals, samples A were subjected to the conventional furnace annealing between 700 to 1000°C for 15 and 60 minutes, and their Raman spectra are shown in Figures 6.3 and 6.4, respectively Figure 6.3 shows that a small peak at 305 cm−1 is observed for sample annealed at 700°C, indicating the - 129 - Chapter Results & Discussions III growth of Ge nanocrystal in the oxide matrix The peak intensity increases and the peak position moves to higher wavenumber as the annealing temperature increases from 800 to 900°C The peak intensity reduces drastically coupled with a shift to a lower wavenumber for the peak position when the sample was annealed at 1000°C Figure 6.4 shows that when annealing time increases to 60 minutes, the variation of the peak intensity and position with respect to annealing temperature follows exactly those shown in Figure 6.3 except that nanocrystal growth can be observed at a lower temperature of 600°C with an increase in annealing time Figure 6.3: Raman spectra of Sample A annealed between 700°C to 1000°C for 15 minutes - 130 - Chapter Figure 6.4: Results & Discussions III Raman spectra of Sample A annealed between 600°C to 1000°C for 60 minutes The values of P for our Samples A annealed under different temperatures for 15 minutes are plotted in Figure 6.5 It can be seen from this figure that P increases from a very insignificant value gradually to 0.32 GPa as the annealing temperature increases from 600 to 800°C There is a sharp increase in the value of P to 1.52 GPa when the annealing temperature increases to 900°C, followed by a drastic reduction to 1.04 GPa at an annealing temperature of 1000°C It is reasonable to expect the compressive stress to be lower at low temperature (i.e 800°C) in Sample A due to the small size and the sparse distribution of the nanocrystals, as observed in the TEM micrograph of Figure 4.2 As temperature increases, the Ge diffusivity increases leading to an increase - 131 - Chapter Results & Discussions III in growth rate and size of nanocrystals As the nanocrystals become larger in size, it becomes more difficult for the silicon oxide matrix to accommodate them, leading to an increase in stress until 900°C Figure 6.5: Hydrostatic pressure (P) experienced by Ge nanocrystals embedded in silicon oxide matrix from Sample A and annealed for 15 and 60 minutes in forming gas (10% H2, 90% N2) as a function of annealing temperature Beyond 900°C, Ge starts to become molten and its diffusivity increases tremendously As temperature continues to increase to 1000°C, the rate of diffusion of Ge away from the matrix starts to dominate over the nucleation rate of the nanocrystals At this stage, more and more Ge atoms will be able to escape into the Si substrate causing a reduction in the density of the Ge nanocrystals as shown in Figure 4.4 It is also worthwhile to point out that our HRTEM image of Sample A annealed at 1000°C (see Figure 6.6(a)) shows that the nanocrystals had - 132 - Chapter Results & Discussions III multiple twinning defects The formation of such defects can help in alleviating the compressive stress experienced by the nanocrystals These factors help to bring about a net decrease in the compressive stress at 1000°C despite the large size of the nanocrystals On the other hand, the HRTEM image of Sample A annealed at 900°C (Figure 6.6 (b)) shows nanocrystals of good crystallinity with no defects This means that there is one less route for stress relief for Sample A annealed at 900°C as compared to the same sample annealed at 1000°C Note that when annealed at 1000°C, the viscosity of the silicon oxide would decrease and this will also assist in the stress relief for the nanocrystals This will also contribute to the reduction in P for the sample annealed at 1000°C Figure 6.6: High magnification TEM micrographs of Sample A annealed at (a) 1000°C and (b) 900°C in forming gas (10% H2 + 90% N2) for 15minutes When the annealing time was increased further to 60 minutes, as can be seen in Figure 6.5 that, the hydrostatic pressure experienced by the nanocrystals - 133 - Chapter Results & Discussions III increased quite significantly at 800°C It had been pointed out that, the diffusion length (∝ t1/2) would be doubled when the annealing time was increased from 15 to 60 minutes As such, the nanocrystals would grow and increase in number as the annealing duration increases, which causes an increase in P shown in Figure 6.5 Note that, there is no significant increase in P has been noticed for temperatures below 800°C due to the fact that nucleation is stifled by the limited diffusivity of Ge at the relatively lower temperatures The increase in Ge diffusion towards the Si substrate, when annealing is performed at elevated temperatures of 800°C, 900°C and 1000°C for longer annealing duration can result in Si–Ge bonds being formed at the Si surface This accounts for the very clear Raman peaks at 410–440 cm−1 shown in Figure 6.7 The intensity of these peaks becomes more prominent as the annealing temperature increases As mentioned in Section 4.2, these peaks are due to the localized Si-Si phonon mode (from the substrate) in the near vicinity of Ge atoms and they occur due to the diffusion of Ge into the Si substrate - 134 - Chapter Figure 6.7: Results & Discussions III Raman spectrum showing the low frequency Si peak between 300 to 500 cm-1 for Sample A annealed for 60 minutes in forming gas (10% H2, 90% N2) At 900°C, two competing factors affecting the stress state of the nanocrystals seem to be in place when the annealing duration is increased The first is the increase in size of the nanocrystals as they grow which would lead to an increase in the stress while the second is the significant diffusion of Ge into the Si substrate which would reduce the number of nanocrystals and hence the stress The slight increase in the value of P means that the growth of the nanocrystals has dominated slightly over the diffusion of Ge into the substrate Therefore, with a longer annealing time of 60 minutes, the change in the hydrostatic pressure is obtained in Figure 6.5 - 135 - Chapter Results & Discussions III At 1000°C, an increase in annealing duration will result in even more Ge diffusing away from the silicon oxide matrix and thus further reducing the number of nanocrystals This explains the reduction in the P value when one compares the samples annealed at 1000°C for 15 and 60 minutes 6.3.2 Effect of Ge concentration on the stress state of the nanocrystals It could be seen from Figure 4.7 that, the significant blue shift of the Raman band for sample C annealed at 1000°C implies that the Ge nanocrystals were under the most compressive stress at this temperature This is in contrast to the case of sample A where the most compressive stress occurred when the sample was annealed at 900°C The calculated hydrostatic pressure experienced by the nanaocrystals is shown in Figure 6.8 It can be seen that, unlike sample A, P of sample B decreases gradually from 0.39 to 0.18GPa as the annealing temperature increases from 800 to 900°C before a significant increase to 1.23GPa at 1000°C In addition, for the highest Ge concentration sample (i.e sample C), P starts from 0.33GPa at 800°C and decrease to 0.19GPa at 900°C and then increase further to 1.4GPa at 1000°C - 136 - Chapter Figure 6.8: Results & Discussions III Hydrostatic pressure (P) experienced by Ge embedded in a silicon oxide matrix as a function temperature for Sample A, B and C annealed for 15 inset is the typical Raman spectra of as-grown and Ge nanocrystals nanocrystals of annealing minutes The free standing As mentioned in Section 4.3, Figures 4.8 and 4.11 show that, for samples B and C annealed at 800°C, even though the size of the nanocrystals is small, they are closely spaced and the density of the nanocrystals is much higher than those found in sample A annealed at the same temperature (see Figure 4.2) This accounts for the higher values of P obtained at 800°C As the annealing temperature increased to 900°C, the diffusivity of Ge will increase This, coupled with a higher Ge concentration in the silicon oxide matrix, will lower the barriers to nucleation and result in a smaller critical nucleus size for samples B and C as compared to sample A The nanocrystals in samples B and C are able to overcome - 137 - Chapter Results & Discussions III kinetic limitations and form facets which minimize interfacial energy In the process of faceting, it would be energetically favourable for the nanocrystals to grow along planes that exerted the least pressure on the silicon oxide matrix thus minimize stress for the nanocrystals At 1000°C, the Ge would become molten and lose their atomic ordering This resulted in a significant increase in the diffusivity of the Ge atoms Again, due to the high concentration of Ge in the oxide matrix, nanocrystals will form rapidly which gives rise to a large compressive stress exerted on the nanocrystals This large compressive stress will cause the nanocrystals to adopt a spherical shape in order to minimize the surfaceto-volume ratio of the nanocrystals and thus minimize the strain energy of the nanocrystals It should be noted that, with higher Ge concentration, sample C may start to facet at a lower annealing temperature as compare to sample B Therefore, the observed stress is slightly lower for the sample C than sample B at 800°C anneals However, when the annealing temperature increased to as high as 1000°C, the higher Ge supersaturation will result in larger and denser Ge nanocrystal (see Figures 4.10 and 4.13) This may account for the higher stress experienced by the nanocrystal in sample C at 1000°C 6.4 Summary Synthesis of Ge nanocrystals via annealing co-sputtered SiO2 + Ge films induces large compressive stresses in the as-grown nanocrystals under certain conditions of annealing time, annealing temperature, Ge concentration and - 138 - Chapter Results & Discussions III annealing ambient This compressive stress can be determined quantitatively by evaluating the Raman peak shift with respect to the peak position of free-standing nanocrystals The magnitude of the stress depends strongly on the annealing temperature, annealing time and the Ge concentration in the co-sputtered films It was found that the size, shape, density and quality of the nanocrystals are factors that will determine the amount of the compressive stress exerted on the nanocrystals - 139 - Chapter Results & Discussions III References [1] S Takeoka, M Fujii, S Hayashi, and K Yamamoto, “Size-dependent near-infrared photoluminescence from Ge nanocrystals embedded in SiO2 matrices”, Phys Rev B, vol 58, pp 7921-7925, 1998 [2] A Wellner, V Paillard, C Bonafos, H Coffin, A Claverie, B Schmidt and K H Heinig, “Stress measurements of germanium nanocrystals embedded in silicon oxide”, J Appl Phys., vol 94, pp 5639-5642, 2003 [3] W K Choi, V Ng, S P Ng, H H Thio, Z X Shen and W S Li, “Raman characterization of germanium nanocrystals in amorphous silicon oxide films synthesized by rapid thermal annealing,” J Appl Phys., vol 86, pp 1398-1403, 1999 [4] J V Borany, R Grotzschel, K H Heinig, A Markwitz, A.; W Matz, B Schmidt and W Skorupa, “Multimodal impurity redistribution and nanocluster formation in Ge implanted silicon dioxide films”, Appl Phys Lett., vol 71, pp 3215-3217, 1997 [5] D O Yi, I D Sharp, Q Xu, C Y Liao, J W Ager III, J W Beeman, Z Liliental-Weber, K M Yu, D Zakharov, E E Haller and D C Chrzan, “Modeling the Stress Evolution of Ion Beam Synthesized Nanocrystals”, Mater Res Soc Symp Proc., vol 821, pp 8.16.1-6, 2004 [6] I D Sharp, D O Yi, Q Xu, C Y Liao, J W Beeman, Z LilientalWeber, K M Yu, D Zakharov, J W Ager III, D C Chrzan and E E Haller, “Mechanism of stress relaxation in Ge nanocrystals embedded in SiO2”, Appl Phys Lett., vol 86, pp 063107-1-3, 2005 - 140 - Chapter [7] Results & Discussions III I D Sharp, Q Xu, C Y Liao, J W Ager III, J W Beeman, K M Yu, D Zakharov, Z Liliental-Weber and E E Haller, “Liberation of Ion Implanted Ge Nanocrystals from a Silicon Dioxide Matrix via Hydrofluoric Acid Vapor Etching”, Mater Res Soc Symp Proc., vol 777, pp T7.6.1-6, 2003 [8] F Cerdeira, C.J Buchenauer, F H Pollack and M Cardona, “StressInduced Shifts of First-Order Raman Frequencies of Diamond- and ZincBlende Type Semiconductors”, Phys Rev B, vol 5, pp 580-593, 1972 - 141 - ... annealed for 15 inset is the typical Raman spectra of as-grown and Ge nanocrystals nanocrystals of annealing minutes The free standing As mentioned in Section 4 .3, Figures 4.8 and 4.11 show that,... a tensile stress will result in an increase in the lattice spacing and, hence, a decrease in the wavenumber of the vibrational mode In the case of compressive stress, the decrease of the lattice... annealing time was increased from 15 to 60 minutes As such, the nanocrystals would grow and increase in number as the annealing duration increases, which causes an increase in P shown in Figure 6.5