Estabilidad de taludes

The experim ental data in the case o f non-U C L data has been accurately extracted using a scanner technique and gives a true representation o f the original published data (Fig. 8.5-8.8). The fits to the data from the m odel are show n as a sm ooth continuous line w here N E W P D E (x) is the nam e given to the equation.

Ghislotti data signal NEWPDE(x) 800 600 400 200 0 1.00 0.50 Energy shift eV

Fig. 8.5 Model fit to the Ghislotti d ata from reference [6]

Chapter Eight: Modelling o f photoluminescence due to the cpiantum confinement o f silicon nanoclusters Z h an g 55À d a ta 0.10 0.30 1000 signal NEWPDE(x) 800 600 S ig n a l (arb.) 400 200 0 0.50 Energy shift eV

Fig. 8.6 Model fit to the Zhang d ata from reference [7]

0.70 0.90

UCL SS27 looœc anneal data

S ign al (arb.) 300 1000 C NEWPDE(x) 200 100 0 0.75 1.25 0.25 Energy shift eV

Chapter Eight: Modelling o f photoliiminescence due to the quantum confinement o f silicon nanoclusters

UCL TEL2 EL data

S ig n a l (arb.) 8 0 0 0 EL NEWPDE(x) 4 0 0 0 2000 0 .5 0 1.00 Energy shift eV

Fig. 8.8 Model fit to the UCL electroluminescence d ata (see ch ap ter eleven)

The follow ing table details the im portant param eters derived from fitting the data. T he fitting technique used was a M onte C arlo routine using around 3000 iterations for each fit.

Sam ple M ean diam eter

 Standard D eviation a  G hislotti [6] 56.5 3.5 Zhang [7] 59.8 4.25 SS27 (1000 anneal) 48.5 4.9 TEL 2 EL data [8] 46.5 3.4

Tahle 8.0 Param eters derived from model

8.7 Discussion

T he G hislotti data (Fig. 8.5) used in this study was Si im planted S iO i layers. The spectrum used was from a sam ple annealed at 1000”C in vacuum . The m odel fitted this data reasonably but overestim ated the ‘b e ll’ part o f the photolum inescence spectrum . The Zhang data (Fig. 8.6) was from the photolum inescence o f m aterial fabricated by oxidising Si nanoparticles that were produced using m icrow ave plasm a gas phase synthesis. This study actually provided a m ean size for the sam ple o f 55 A and the m odel appears to agree reasonably well with this value.

C h apter Eight: M odelling o f photolum inescence due to the quantum confinem ent o f silicon nanoclusters

From a histogram of particle sizes provided [7] the standard deviation of the as- grown sample (i.e. prior to oxidising the particles) can be calculated to be around 38% of the mean. However, the model indicates a to be in the region of 4.5 Â or 8.1% of the mean cluster diameter. This discrepancy is thought to be due to changes in the cluster size brought as a result of the oxidising process.

The photoluminescence data from the UCL sample SS27 (Fig. 8.7) were taken from a measurement of a section of the as-grown film that was annealed at 1000° C for 90 minutes. The TEL2 sample electroluminescence spectrum is from an as- grown film (Fig. 8.8). The data from TEL2 is thought to be predominantly due to size effects, hence its inclusion in this study. The fit for this data is not as good as the other three. The tail in particular appears to be overestimated by the model. The fitting may be affected however since data for only one side of the peak is available, and so a close fit is less likely.

Most of the data is fitted well by the model but there is a scarcity of data for cluster size distributions available. Only the Zhang data [7] (estimated from TEM studies) provided this data and the mean value was reasonably well deduced by the model.

8.8 Conclusions

The model developed for the photoluminescence of Si clusters is only concerned with luminescence as a result of quantum confinement of the excitons in Si clusters by a high bandgap matrix. Experimental evidence in the main indicates that the photoluminescence spectra deviate from the Gaussian distribution. This is most likely to be due to the increase in electron-hole pairs in larger clusters making a greater contribution to the overall spectrum. In addition, the increase in oscillator strength due to the reduction of size also modifies the spectrum. The inclusion of further corrections to the effective mass approximation model (increase in oscillator strength for decreasing cluster sizes and increase in numbers of electron-hole pairs for increasing clusters sizes) has carried with it some approximations and assumptions. In particular it appears that the oscillator strength term is too high and a more rigorous treatment along with more size data

C h apter Eight: M odelling o f photolum inescence due to the quantum confinem ent o f silicon nanoclusters

will be required. However, it is still useful predict an approximate photoluminescence spectrum of Si clusters in a high bandgap matrix such as Si02« The effective mass approximation model overestimates the band gap energy for clusters smaller than 20 Â. However, the model used here is sufficient as an approximate technique for obtaining the modified bandgap of the Si clusters over the size range of 20-80 Â [9].

C h apter Eight: M odelling o f photolum inescence due to the quantum confinem ent o f silicon nanoclusters

References

1) I. M. Lifshitz, Adv. Phys. 42, 13,483, (1964)

2) X. Chen, J. Zhao, G Wang, X. Shen, Phys. Lett. A. 212, 285, (1996) 3) P. W. Atkins, ‘Quanta’ Oxford University Press (1991)

4) J. B. Khurgin, E. W. Forsythe, S. I Kim, D C. Morton, B. S. Sywe, B.A Khan, G. S. Tompa, B. S. Sywe. Mat. Res Soc. Proc. Symp 358, 193 (1995)

5) J. B. Khurgin, private communication

6) G. Ghislotti, B. Nielson, P. Asoka-Kumar, K.G. Lynn, A. Gambhir, L. F. Di Mauro, C.E Bottani, J. Appl. Phys. 79 ,11, 8660, (1996)

7) D. Zhang, R. M. Kolbas, P. D. Milewski, D. J. Lichtenwalner, A. I. Kingon, J. M. Zavada, App. Phys. Lett. 65 (21), 2684, (1994)

8) P. F. Trwoga, A. J. Kenyon, C. W. Pitt. Mat. Res. Soc. Proc. Symp. 1996, 424, 483-488

C h apter Nine: Lum inescence efficiency m easurem ents o f silicon-rich silica