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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 16296–16304
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Experimental setup for investigating silicon solid phase crystallization at high temperatures

Thomas Schmidt, Annett Gawlik, Henrik Schneidewind, Andreas Ihring, Gudrun Andrä, and Fritz Falk  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 16296-16304 (2013)
http://dx.doi.org/10.1364/OE.21.016296


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Abstract

An experimental setup is presented to measure and interpret the solid phase crystallization of amorphous silicon thin films on glass at very high temperatures of about 800°C. Molybdenum-SiO2-silicon film stacks were irradiated by a diode laser with a well-shaped top hat profile. From the relevant thermal and optical parameters of the system the temperature evolution can be calculated accurately. A time evolution of the laser power was applied which leads to a temperature constant in time in the center of the sample. Such a process will allow the observation and interpretation of solid phase crystallization in terms of nucleation and growth in further work.

© 2013 OSA

1. Introduction

Polycrystalline silicon thin films offer a wide range of scientific and technical applications. Dependent on the grain size the material is suitable e.g. for thin film-transistor fabrication [1

1. D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett. 27(7), 564–566 (2006). [CrossRef]

] or for crystalline silicon thin film solar cells [2

2. A. Aberle, “Progress with polycrystalline silicon thin-film solar cells on glass at UNSW,” J. Cryst. Growth 287(2), 386–390 (2006). [CrossRef]

, 3

3. N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 74(1-4), 295–303 (2002). [CrossRef]

]. Silicon with crystals of sub-micrometer scale can be directly deposited by plasma enhanced chemical vapor deposition [4

4. A. Matsuda, “Microcrystalline silicon. Growth and device application,” J. Non-Cryst. Solids 338-340, 1–12 (2004). [CrossRef]

]. To get larger grains, amorphous silicon (a-Si) deposition followed by crystallization is necessary [5

5. G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C 5(10), 3221–3228 (2008). [CrossRef]

]. Using high power energy sources such as lasers or flash lamps this can be done by melting and recrystallization of the a-Si with, however, some disadvantages such as high temperature load and dopant diffusion.

Due to the metastable character of amorphous silicon, crystallization can also be achieved by a solid phase process (SPC). Depending on crystallization temperature and on some film parameters (e.g. deposition conditions, interfaces to adjacent materials) nucleation and growth take place at different rates [6

6. T. Chaki, “Solid-phase-epitaxy – Effects of irradiation, dopant, and pressure,” Phys. Status Solidi A 142(1), 153–166 (1994). [CrossRef]

, 7

7. C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys. 84(10), 5383–5414 (1998). [CrossRef]

]. For temperatures below 700°C kinetic parameters of SPC were studied intensively by various groups [8

8. U. Köster, “Crystallization of amorphous silicon films,” Phys. Status Solidi A 48(2), 313–321 (1978). [CrossRef]

11

11. Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells 101, 186–192 (2012). [CrossRef]

]. Crystallization in this temperature range takes several minutes up to several hours so that constant processing temperatures can be reached before relevant crystallization processes start.

To get more efficient and cheaper processes, SPC at temperatures up to 1000°C is useful but difficult to investigate [12

12. T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films 520(24), 7087–7092 (2012). [CrossRef]

]. Some measurements of SPC at temperatures of about 800°C by cw laser heating in the millisecond range were performed by Olson et al. [13

13. G. Olson and J. Roth, “Kinetics of solid phase crystallization in amorphous silicon,” Mater. Sci. Rep. 3(1), 1–77 (1988). [CrossRef]

]. They determined the temperature indirectly from measuring the reflectivity which is not so easy since the optical functions of amorphous silicon are not well known at these temperatures and since a-Si converts to c-Si during the measurements. They also stated that no steady-state temperature could be achieved in their experiments due to the rapid heating by a constant laser power. This makes it very difficult to interpret the crystallization kinetics. Nucleation and growth parameters have to be calculated from a transient temperature evolution which is very critical due to the strong temperature dependence of the kinetic parameters. Moreover, a direct fit of the crystallization curves, for example in terms of classical nucleation theory, is not possible. Mannino et al. crystallized amorphous silicon under millisecond laser irradiation and calculated a non-steady temperature profile. They simulated the appropriate crystallization process but only for a fixed set of kinetic parameters determined from low temperature stationary crystallization experiments [14

14. G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett. 97(2), 022107 (2010). [CrossRef]

].

In this work a diode laser with a homogenized top hat profile is used to irradiate a molybdenum-SiO2-silicon film stack deposited on borosilicate glass. From the known thermal parameters of the substrate and the optical parameters of the absorbing metal we can calculate the temperature evolution in the silicon layer very accurately. Furthermore, we could determine a transient laser power leading to a constant temperature over time in the center of the irradiated area. Time resolved reflectivity (TRR) measurements were carried out to observe the crystallization processes in situ.

2. Experimental

Figure 1
Fig. 1 Scheme of experimental setup for laser crystallization.
shows the scheme of the used experimental setup to crystallize and to observe the samples.

A high power diode laser (λ = 808 nm) is homogenized by two consecutive microlens arrays with subsequent focusing on the sample. This leads to a square shaped 1x1 mm2 top hat profile with an intensity variation of less than 6% across the area which covers 87% of the total energy. For TRR measurements a helium neon laser was focused on the backside of the film stack. The 1/e2-size of the circular focus was about 150 µm, which is small enough to observe an area of nearly constant temperature on the irradiated sample. The intensity of the diagnostic laser is approximately 100 times lower than that used for diode laser irradiation, so that no additional heating has to be considered. The intensity of the reflected beam was determined by a silicon photo diode.

In Fig. 2
Fig. 2 Layout of the used samples.
the layout of the samples is illustrated. Amorphous silicon was deposited by electron beam evaporation on 1”x1” square Schott Borofloat33 glass substrates 3.3 mm thick. The substrates were cleaned with a surfactant solution, acetone, and isopropanol. Before deposition the samples were heated in the deposition chamber up to 420°C to remove water from the surface. The temperature during deposition was 250°C and the deposition rate was about 300 nm/min at a working pressure of 10−7 mbar. The thickness of the silicon was fixed to one micrometer, so that the incident helium neon laser for TRR is fully absorbed in the silicon and no optical effects from the SiO2 layer above have to be taken into account.

On top of the silicon 50 nm of SiO2 was deposited by plasma enhanced chemical vapor deposition (PECVD) to prevent the silicon from forming silicides at the Mo-Si interface and to avoid metal induced crystallization [15

15. W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films 516(15), 4946–4952 (2008). [CrossRef]

] during irradiation.

Then 500 nm of molybdenum were sputtered onto the samples. This layer is very essential to accurately determine the temperatures which can be achieved by the laser heating. Direct absorption of the diode laser within the silicon would give many uncertainties in the simulation of the process. Since the extinction coefficient of a-Si and of crystalline silicon (c-Si) for a wavelength of 808 nm is very small, a big amount of the laser radiation would reach the silicon-substrate interface and would be reflected. So interference effects which depend on the optical constants and the thickness of the film must be taken into account. Moreover, the complex refractive index of a-Si strongly depends on temperature and on the preparation conditions, so that literature data cannot be easily used. Even if one has complete knowledge on the optical functions of amorphous and crystalline silicon with the appropriate temperature dependence as described in [16

16. Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran. 40(7), 1591–1600 (1997). [CrossRef]

, 17

17. J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express 20(S6), A856–A863 (2012). [CrossRef]

], the phase change of the material during irradiation has to be considered since the indices of refraction of a-Si and c-Si differ. Therefore, heating of the silicon by direct laser light absorption should be avoided since an accurate simulation of this process is not possible. Molybdenum as absorbing layer offers the advantages of a high extinction coefficient [18

18. B. T. Barnes, “Optical constants of Inandescent Refractory Metals,” J. Opt. Soc. Am. 56(11), 1546–1549 (1966). [CrossRef]

] and high heat conductivity [19

19. E. P. Mikol, “The thermal conductivity of molybdenum over the temperature range 1000-2100°F,” Oak Ridge National Laboratory (1952). http://www.ornl.gov/info/reports/1952/3445603609021.pdf.

], so that the underlying silicon is heated by conduction independent of its phase state. Additionally, the melting and the boiling point of Mo is much higher than that of silicon, so that no destruction of the film in the desired temperature range is to be expected. After irradiation the molybdenum film can be easily removed by hot nitric acid without damaging the silicon layer.

On top of the sample a second SiO2 film of 50 nm thickness is deposited to prevent the molybdenum from oxidation during laser heating in ambient air. The interference effects caused by this layer have to be taken into account in the simulation but are non-critical since the index of refraction is real, well known and only slightly temperature dependent, which can be neglected [20

20. T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys. 16(5), L97–L100 (1983). [CrossRef]

, 21

21. B. Brixner, “Refractive-Index Interpolation for Fused Silica,” J. Opt. Soc. Am. 57(5), 674–676 (1967). [CrossRef]

].

3. Simulation of the temperature

For calculating the temperature evolution numerically the finite element software environment Comsol Multiphysics was used. The typical irradiation times in this work were between 10 ms and several seconds. Convective and radiative cooling at the sample surface are negligible and only heat conduction must be taken into account. Inside the glass substrate the three dimensional heat conduction equation
ρ(T)cp(T)Tt=(κ(T)T)
(1.1)
has to be solved, whereρis the mass density,cpis the specific heat capacity, andκthe heat conductivity of the substrate. Due to the high absorption coefficient of the molybdenum on top no laser radiation is transmitted through the film stack into the substrate and therefore no heat source occurs within the glass volume. The simulated geometry consists of a simple block. The dimensions of the block were chosen smaller than the sample size to minimize the effort of memory but were big enough to make sure that the bottom and lateral boundaries were on room temperature at any time. So at these boundaries there is no heat flow to the outside represented byn(κT)=0, with n the normal vector of the boundary.

The boundary on top of the block is represented by the film stack. During the relevant time scales any temperature gradient within the stack depth is negligible. This is because the characteristic length for heat conduction within the times under consideration is very large compared to the thickness of the films (e.g. for molybdenum >100 µm within 0.1 ms). So the heat conduction equation for the film stack must only be solved in the lateral directions. This is very useful computationally since it would be very demanding to resolve the different length scales of film and glass substrate in a single mesh. The heat loss of the film stack into the glass can be attributed by a cooling term in the 2-d heat equation for the stack according to
dρf(T)cp,f(T)Ttt(κf(T)tT)=n(κ(T)T)+I
(1.2)
The first term on the right hand side is the heat loss into the substrate determined by the temperature gradient at the glass surface. I is the absorbed laser intensity which depends on the spatial coordinates according to the beam profile of the laser. Additionally it can vary in time due to a given power evolution and is temperature dependent since the optical constants of molybdenum and therefore the absorbance change with temperature. The index f stands for the appropriate property of the film stack whereastmeans the 2-d gradient operator in the plane of the stack. This equation at the same time acts as boundary condition for the 3-d heat equation in the glass substrate. For the material parameters of the stack effective values were used, calculated from the thickness weighted sums of the particular films. For the contribution of the silicon simply the thermal properties of crystalline silicon were used. Changing these to that of amorphous silicon the simulation showed temperature deviations of only 1 K to 6 K which is very small compared to the covered temperature range of about 1000 K. This is because the lateral heat conduction in the stack is dominated by the molybdenum layer.

The spatial intensity distribution of the diode laser was measured with a beam profiler camera (Fig. 3
Fig. 3 Measured intensity distribution of the diode laser in the focal plane.
) and was included in the model directly. Since no absolute values can be achieved from this the overall laser power was measured calorimetrically and was set as the spatial integral of the imported intensity distribution.

The absorbance of the sample depends only on its reflectivity, due to the opaque molybdenum layer. The reflection was calculated by using interference formulas for a thin SiO2 film on an infinitely thick substrate (Mo). Therefore the complex indices of refractionn+ikof SiO2 and of molybdenum enter. Both materials were carefully characterized at room temperature with spectroscopic ellipsometry and in an UV/VIS spectrometer. For SiO2 the optical functions agreed very well with literature values and its very weak temperature dependency were neglected [20

20. T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys. 16(5), L97–L100 (1983). [CrossRef]

, 21

21. B. Brixner, “Refractive-Index Interpolation for Fused Silica,” J. Opt. Soc. Am. 57(5), 674–676 (1967). [CrossRef]

]. For pure molybdenum published data are given only for bulk material, which showed strong deviations from our data of the sputtered material. These differences are not fully understood. Nevertheless the values measured on our material were used together with a linear fit to the temperature dependency from [18

18. B. T. Barnes, “Optical constants of Inandescent Refractory Metals,” J. Opt. Soc. Am. 56(11), 1546–1549 (1966). [CrossRef]

]. All parameters used in the simulation are given in Table 1

Table 1. Optical and thermal parameters used in the simulation. TR=289K. Tis in K.

table-icon
View This Table
.

For accurate simulations it is essential to know the time response of the laser on a given external controlling voltage. This is important since the time constants of the laser electronics are in the same order of magnitude as the desired heating times. Figure 4
Fig. 4 Controlling voltage together with laser power output.
shows the time evolution of the laser power under a step change of the controlling voltage, measured by a photo diode. It is obvious that the signal rises and falls in a few milliseconds but much slower than the voltage. For including the correct power evolution into the simulations, exponential functions were chosen to fit the measured laser power as depending on time. In this way the laser power for any arbitrary controlling voltage could be calculated.

4. Results

Staring from a correct temperature simulation one can find a time evolution of the laser power to lead to a constant temperature on a selected point of the sample. This was achieved by trial and error in the simulations. Figure 6
Fig. 6 Power for a constant temperature in the center of the sample surface. The power and temperature scale are normalized.
shows the simulated and measured power function of the diode laser together with the resulting temperature in the middle of the sample surface. The temperature rises very fast within the first 20 ms of the irradiation and remains on the final high level with a variation of 5 K. To achieve this behavior the laser power must be lowered by about 75% in the considered time span since the heat dissipation through heat conduction in the glass is rather small as compared to the initial laser heating. A higher temperature rising slope as that showed in Fig. 6 cannot be achieved due to the laser response time shown in Fig. 4. This limits the temperatures on which useful investigations of SPC can be done. If the temperature is high enough to get a significant crystal fraction in times shorter than the rise time of the laser, a transient analysis of the SPC process becomes necessary with the problems mentioned in section 1.

From the shown curves we can calculate the time evolution of the crystalline silicon fraction for the given temperatures. By evaluating these data and assuming a constant temperature the kinetic parameters for crystallization can be extracted which, however, is not the scope of this work.

7. Conclusion

In this work an experimental setup for the investigation of silicon solid phase crystallization at temperatures above 800°C was introduced. A diode laser with a homogenized top-hat profile was used to heat up the samples within a few milliseconds. The reflectivity of the samples was measured during the crystallization from the backside using a helium neon laser. The silicon was prepared as a thin film on glass substrates. A molybdenum layer on the silicon was used to achieve well-defined laser absorption and heating independent of the crystalline state of the silicon. Intermediate layers of SiO2 were introduced to avoid metal induced crystallization of the silicon and oxidation of the molybdenum. A theoretical model was presented to calculate the temperature evolution during laser irradiation. The calculated irradiation time until melting of the silicon layer agreed very well with the measured one. A time dependent laser power was determined which leads to a constant temperature on an given point on the sample after a short heat-up time of 20 ms. Irradiation of samples using this power function shows clear SPC characteristics in TRR measurements. Depending on the temperature level, the time needed for SPC varies from 5 ms to 500 ms. Based on these results, kinetic parameters of SPC processes in silicon thin films could be extracted in further work.

References and links

1.

D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett. 27(7), 564–566 (2006). [CrossRef]

2.

A. Aberle, “Progress with polycrystalline silicon thin-film solar cells on glass at UNSW,” J. Cryst. Growth 287(2), 386–390 (2006). [CrossRef]

3.

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 74(1-4), 295–303 (2002). [CrossRef]

4.

A. Matsuda, “Microcrystalline silicon. Growth and device application,” J. Non-Cryst. Solids 338-340, 1–12 (2004). [CrossRef]

5.

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C 5(10), 3221–3228 (2008). [CrossRef]

6.

T. Chaki, “Solid-phase-epitaxy – Effects of irradiation, dopant, and pressure,” Phys. Status Solidi A 142(1), 153–166 (1994). [CrossRef]

7.

C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys. 84(10), 5383–5414 (1998). [CrossRef]

8.

U. Köster, “Crystallization of amorphous silicon films,” Phys. Status Solidi A 48(2), 313–321 (1978). [CrossRef]

9.

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys . 110, 063530 (2011).

10.

G. Farhi, M. Aoucher, and T. Mohammed-Brahim, “Study of the solid phase crystallization behavior of amorphous sputtered silicon by X-ray diffraction and electrical measurements,” Sol. Energy Mater. Sol. Cells 72(1-4), 551–558 (2002). [CrossRef]

11.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells 101, 186–192 (2012). [CrossRef]

12.

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films 520(24), 7087–7092 (2012). [CrossRef]

13.

G. Olson and J. Roth, “Kinetics of solid phase crystallization in amorphous silicon,” Mater. Sci. Rep. 3(1), 1–77 (1988). [CrossRef]

14.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett. 97(2), 022107 (2010). [CrossRef]

15.

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films 516(15), 4946–4952 (2008). [CrossRef]

16.

Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran. 40(7), 1591–1600 (1997). [CrossRef]

17.

J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express 20(S6), A856–A863 (2012). [CrossRef]

18.

B. T. Barnes, “Optical constants of Inandescent Refractory Metals,” J. Opt. Soc. Am. 56(11), 1546–1549 (1966). [CrossRef]

19.

E. P. Mikol, “The thermal conductivity of molybdenum over the temperature range 1000-2100°F,” Oak Ridge National Laboratory (1952). http://www.ornl.gov/info/reports/1952/3445603609021.pdf.

20.

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys. 16(5), L97–L100 (1983). [CrossRef]

21.

B. Brixner, “Refractive-Index Interpolation for Fused Silica,” J. Opt. Soc. Am. 57(5), 674–676 (1967). [CrossRef]

22.

Accuratus Corporation, “Fused Silica, SiO2 Glass Properties”. http://accuratus.com/fused.html.

23.

T. A. Redfield and J. H. Hill, “Heat capacity of Molybdenum,” Oak Ridge National Laboratory (1951). http://www.ornl.gov/info/reports/1951/3445603608861.pdf.

24.

International Molybdenum Association, “Molybdenum Properties”. http://www.imoa.info/molybdenum/molybdenum_properties.php.

25.

S. de Unamuno and E. Fogarassy, “A thermal description of the melting of c-silicon and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci. 36(1-4), 1–11 (1989). [CrossRef]

26.

A. Bensberg, Research and Technology Development, Schott AG (personal communication, 2011).

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(310.3840) Thin films : Materials and process characterization
(310.4165) Thin films : Multilayer design
(310.6845) Thin films : Thin film devices and applications

ToC Category:
Thin Films

History
Original Manuscript: May 21, 2013
Manuscript Accepted: June 18, 2013
Published: July 1, 2013

Citation
Thomas Schmidt, Annett Gawlik, Henrik Schneidewind, Andreas Ihring, Gudrun Andrä, and Fritz Falk, "Experimental setup for investigating silicon solid phase crystallization at high temperatures," Opt. Express 21, 16296-16304 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-14-16296


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References

  1. D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett.27(7), 564–566 (2006). [CrossRef]
  2. A. Aberle, “Progress with polycrystalline silicon thin-film solar cells on glass at UNSW,” J. Cryst. Growth287(2), 386–390 (2006). [CrossRef]
  3. N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002). [CrossRef]
  4. A. Matsuda, “Microcrystalline silicon. Growth and device application,” J. Non-Cryst. Solids338-340, 1–12 (2004). [CrossRef]
  5. G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5(10), 3221–3228 (2008). [CrossRef]
  6. T. Chaki, “Solid-phase-epitaxy – Effects of irradiation, dopant, and pressure,” Phys. Status Solidi A142(1), 153–166 (1994). [CrossRef]
  7. C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys.84(10), 5383–5414 (1998). [CrossRef]
  8. U. Köster, “Crystallization of amorphous silicon films,” Phys. Status Solidi A48(2), 313–321 (1978). [CrossRef]
  9. T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).
  10. G. Farhi, M. Aoucher, and T. Mohammed-Brahim, “Study of the solid phase crystallization behavior of amorphous sputtered silicon by X-ray diffraction and electrical measurements,” Sol. Energy Mater. Sol. Cells72(1-4), 551–558 (2002). [CrossRef]
  11. Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012). [CrossRef]
  12. T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012). [CrossRef]
  13. G. Olson and J. Roth, “Kinetics of solid phase crystallization in amorphous silicon,” Mater. Sci. Rep.3(1), 1–77 (1988). [CrossRef]
  14. G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010). [CrossRef]
  15. W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008). [CrossRef]
  16. Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran.40(7), 1591–1600 (1997). [CrossRef]
  17. J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express20(S6), A856–A863 (2012). [CrossRef]
  18. B. T. Barnes, “Optical constants of Inandescent Refractory Metals,” J. Opt. Soc. Am.56(11), 1546–1549 (1966). [CrossRef]
  19. E. P. Mikol, “The thermal conductivity of molybdenum over the temperature range 1000-2100°F,” Oak Ridge National Laboratory (1952). http://www.ornl.gov/info/reports/1952/3445603609021.pdf .
  20. T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys.16(5), L97–L100 (1983). [CrossRef]
  21. B. Brixner, “Refractive-Index Interpolation for Fused Silica,” J. Opt. Soc. Am.57(5), 674–676 (1967). [CrossRef]
  22. Accuratus Corporation, “Fused Silica, SiO2 Glass Properties”. http://accuratus.com/fused.html .
  23. T. A. Redfield and J. H. Hill, “Heat capacity of Molybdenum,” Oak Ridge National Laboratory (1951). http://www.ornl.gov/info/reports/1951/3445603608861.pdf .
  24. International Molybdenum Association, “Molybdenum Properties”. http://www.imoa.info/molybdenum/molybdenum_properties.php .
  25. S. de Unamuno and E. Fogarassy, “A thermal description of the melting of c-silicon and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci.36(1-4), 1–11 (1989). [CrossRef]
  26. A. Bensberg, Research and Technology Development, Schott AG (personal communication, 2011).

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