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
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  or for crystalline silicon thin film solar cells [2, 3]. Silicon with crystals of sub-micrometer scale can be directly deposited by plasma enhanced chemical vapor deposition . To get larger grains, amorphous silicon (a-Si) deposition followed by crystallization is necessary . 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, 7]. For temperatures below 700°C kinetic parameters of SPC were studied intensively by various groups [8–11]. 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 . Some measurements of SPC at temperatures of about 800°C by cw laser heating in the millisecond range were performed by Olson et al. . 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 .
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.
Figure 1 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 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  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, 17], 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  and high heat conductivity , 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, 21].
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
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
The spatial intensity distribution of the diode laser was measured with a beam profiler camera (Fig. 3) 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 refractionof 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, 21]. 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 . All parameters used in the simulation are given in Table 1.
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 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.
Figure 5 shows a TRR signal with the related calculated surface temperature in the center of the sample. The film stack was irradiated with 28 W for 35 ms. When the laser power starts to rise (at 4 ms) the reflectivity rises too, which is due to the temperature dependence of the refractive index of a-Si. The sudden drop in reflectivity represents the solid phase crystallization of the silicon, which can be easily proven by stopping the laser pulse after the drop and investigating the irradiated area with an optical microscope after removing the molybdenum. The crystallized area looks much more transparent than the surrounding material. After the drop, the temperature rises further until the crystalline silicon melts at the temperature, which can be observed by the rapid increase in the TRR signal at the time. This effect results from liquid silicon having a much higher index of refraction of liquid as compared to solid silicon. The perfect accordance between calculated and measured time until melting is an indicator for the accuracy of the simulation, which is about 5 K. The experiments were repeated up to ten times and a good reproducibility was observed. In the case shown in Fig. 5 the time until melting varied within 1.5 ms whereas the time at which the SPC starts varied within 0.5 ms.
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 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.
For first experiments the power function shown in Fig. 6 was extended up to irradiation times of 1.5 seconds. By linearly increasing the laser power we were able to achieve constant temperatures in the center of the sample surface between 1150 K and 1290 K. The appropriate TRR signals resulting from different maximum powers corresponding to different temperature plateaus are shown in Fig. 7. Induced by the heating the reflectivity rises fast when the laser pulse starts. Depending on the reached temperature the TRR plateaus have different durations which are related to the time lag of crystallization for SPC following from classical nucleation theory . Especially in the TRR signal for the highest laser power this plateau cannot be seen clearly which means that the crystallization starts within the heating-up time. In this particular case an evaluation of the crystallization process with respect to a constant temperature is critical. After the plateau crystallization starts which leads to a decreasing TRR signal due to the lower index of refraction of c-Si as compared to a-Si. For the highest power the crystallization time is only about 5 ms whereas for the lowest power 500 ms are needed. At 1.5 s the laser pulse was stopped and the films and substrates cooled down to room temperature which results in the strong changes in the reflectivity. The constant TRR signal between heating-up and SPC and also after full crystallization of the silicon implies that the temperature was on a constant level within the corresponding time span.
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.
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.
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