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

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 transmissi

Chapter 6

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

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 4 and consists of Sample A, B and C with Ge concentration estimated to be around 3, 10 and 15 at.%

6.2 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)

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 5 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

Figure 6.2: 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

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]

) 2 (

3 0 S11 S12

+

−

=

γω

ω ω

(6.1)

where ωembedded and ω etched 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

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

Figure 6.4: 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

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

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

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

Figure 6.7: 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

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

Figure 6.8: Hydrostatic pressure (P) experienced by Ge nanocrystals

embedded in a silicon oxide matrix as a function of annealing temperature for Sample A, B and C annealed for 15 minutes The inset is the typical Raman spectra of as-grown and free standing

Ge nanocrystals

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