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Abstract
The temperature-dependent optical properties of PECVD deposited amorphous silicon films are determined for radiation wavelengths of 1000 nm up to 2000 nm in a temperature range of up to 1110 K. The measurements are performed at heating rates of over 2300 K/s in order to shift the onset of solid-phase crystallization of the amorphous material to temperatures above 1110 K and to make the optical properties of amorphous silicon accessible for examination. In this work, the laser-based measurement setup, the experimental procedure, the simulation methods, and the resulting material-specific data are shown.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
During solid-phase crystallization using laser radiation in the near-infrared spectrum, the optical properties of hydrogenated amorphous silicon (a-Si:H) undergo a drastic temperature-dependent change. This significantly complicates the specific energy deposition in an amorphous silicon film using laser radiation. Hence, a profound understanding of the temperature-dependent optical properties of the processed material is required. However, the characterization of materials in a metastable state comes along with a major challenge: Amorphous silicon undergoes an irreversible phase change with a temperature-dependent delay and rate, starting when heated up above 773 K to eventually reach a stable crystalline state [1–4]. Consequently, the heating rate must be set accordingly high to enable the investigation of the optical properties of amorphous silicon at elevated temperatures > 773 K without a premature phase change. For crystalline silicon this problem does not apply and numerous publications on the temperature-dependent optical properties for elevated temperatures are available [5 –12]. At the same time, there are very few studies on amorphous silicon, which will be discussed below.
Previous studies on the temperature-dependent optical properties of amorphous silicon using furnaces or hotplates for sample heating are limited to comparably low temperatures of up to 810 K [13,14].
The rather low heating rates of furnaces and hotplates are unsuitable for significantly delaying the onset of crystallization. Further difficulties emerge from thermal background radiation and refractive index fluctuations in the surrounding atmosphere due to thermal convection, both of which accompany the temperature rise. These problems can be minimized using laser radiation for sample heating since very high heating rates of several thousand Kelvins per second can be achieved in a small locally confined area. However, the determination of the actual temperatures in the interaction zone is rather difficult, due to short time frames and small dimensions. That’s why calculations based on complex models [15] are used.
If laser radiation is also used as a probe beam, this is advantagous for the separation from the thermal emission background. On the other hand the investigation is constrained to a single wavelength [14,16] or a narrow wavelength range [13].
This work presents a method to address the drawbacks mentioned above and allows for the determination of the desired material properties over a wide spectral and thermal range with a single measurement.
2. Experimental setup
The sample consists of a 5 µm thick phosphorous doped a-Si:H layer which is deposited on a 750 µm thick crystalline silicon wafer with a 2.5 µm thick thermal oxide layer using PECVD at 673 K. The layer thicknesses were determined by capacitive measurements and scanning electron microscopy. The surface roughness of the a-Si:H layer measured by a profilometer is Ra = 3.6 nm. An illustration of the experimental setup and the layer system of the sample is shown in Fig. 1.
The probe beam is provided by a white light source (A), HL-200-FHSA, Ocean Optics, Florida, USA. The probe beam is first collimated and then directed and focused on the sample surface utilizing parabolic mirrors (B). By applying reflective optics, chromatic aberration is avoided. The probe beam has a diameter of 2 mm on the sample surface and an angle of incidence of 21.7° to the surface normal. The sample (C) is placed on a quartz glass sample holder (D), which provides a low thermal conductivity and a high transmittance for the probe and heat beam. The probe beam, reflected from the sample surface, is then collimated and introduced into a spectrometer (E), NIRQuest-512 2.2, Ocean Optics, Florida, USA, by another pair of parabolic mirrors (F). In the configuration used, the spectrometer covers a spectral range of 900 nm to 2100 nm with a spectral resolution of 5.4 nm FWHM and captures spectra with an integration time of 1 ms and a sample rate of 100 Hz.
During the measurement, the sample (C) is heated by laser radiation which is provided by a beam source (G), DILAS Compact Evolution, DILAS Diodenlaser GmbH, Germany, emitting radiation at a wavelength of 980 nm with a maximum power of 450 W and a top hat shaped intensity distribution. The spot size of the laser beam is 4 × 4 mm2 and centered with the probe beam on the sample surface. The sample temperature is captured by two pyrometers (H). For low temperatures up to 473 K the pyrometer KT19.82 II, Heitronics Infrarotmesstechnik GmbH, Germany, is used. The temperature range from 473 K to 1110 K is covered by the Pyrometer EP60P, Dr. Mergenthaler GmbH & Co. KG, Germany.
3. Results
In preliminary tests, a laser power ramp has been determined to achieve an approximately linear temperature ramp of 2334 K/s in the sample during the measurement. With this setting, a temperature of 1110 K is reached in the a-Si:H layer after 0.35 s without crystallization occuring. Sample heating, temperature and spectra capturing are conducted simultaneously during the measurement.
Examples of the captured data are shown in Fig. 2 for different temperatures and wavelengths. The black line (Fig. 2, left) represents the detected reflectance spectra in the initial state at a temperature of 293 K in the considered wavelength range. Characteristic is the oscillation pattern with smoothly curved maxima and sharp minima, which amplitudes feature an envelope with several nodes. The envelope is due to the superposition of two interference patterns, which are respectively caused by the interaction of the probe beam with the a-Si:H layer and the underlying oxide layer.
With increasing temperature, the envelope constricts due to the increasingly attenuated amplitude of the interference pattern (red line, Fig. 2, left). The dominant peak at 980 nm is due to scattered radiation from the laser used for heating. Simultaneously to the attenuation, the reflectance at discrete wavelengths alternately passes through minima and maxima, decreasing in amplitude with increasing temperature, as shown in Fig. 2, right. In the spectrum (Fig. 2, left), this appears as a shift of the extreme points to higher wavelengths at increasing temperatures, comparable with previous investigations [13].
Both effects are caused independently by changes of the real part n and the imaginary part k of the complex refractive index of the a-Si:H layer
Changes in the refractive index n affect the phase shift and thereby the superposition of probe-beam fractions reflected at the respective interfaces of the layer system by changing the optical path length between them [17]. When the refractive index n increases with temperature increase, this leads to an alternation between constructive and destructive interference, as shown in Fig. 2, right. Thereby, the mean value of the interference pattern corresponds to the probe beam fraction reflected at the first interface between the atmosphere and the a-Si:H layer. The interference amplitude corresponds to the beam fraction reflected at lower-lying interfaces of the layer system. An increase in the extinction coefficient k leads to an attenuation of the interference amplitude due to increasing absorption of the probe beam fraction penetrating and propagating within the layer system. Thus, changes in the refraction index n and the extinction coefficient k of the a-Si:H layer have mutually distinguishable effects on the reflectance spectrum. Consequently, the change in reflectance can be used to infer the change in these variables. Therefore, an optical model of the layer system based on the OJL model [18] is designed using the commercial software SCOUT 3.97, W. Theiss Hard- and Software, Germany.
The OJL model is suitable to simulate the interband transitions in amorphous semiconductors under the assumption of parabolic shaped valence and conduction band with exponentially decaying tail states. Additionally, a dielectric background is applied to cover the spectral regions far away from the bandgap energy. To extract the complex refractive index ń of the a-Si:H layer from the captured data, a spectrum is simulated based on the model and fitted to each spectrum captured at discrete temperatures during heating by adjusting the model parameters.
Measured and simulated reflectance spectra as well as the corresponding thermal emission and the derived dispersion of the refractive index n and the extinction coefficient k of a-Si:H at temperatures of 293 K and 1110 K are shown in Fig. 3.
Fig. 3. Measured and simulated reflectance spectra at a temperature of 293 K (top left) and 1110 K (bottom left) with the corresponding thermal emission and the extracted spectra of n and k of phosphorous doped a-Si:H (right).
Starting from the initial parameters determined at 293 K, the fitting of the model to the subsequently captured spectra at increasing temperature was performed in the same manner and completely achieved by adjusting two parameters of the applied model: the bandgap energy of the OJL model and the imaginary part of the dielectric background. Temperature-dependent changes in the optical properties of the SiO2 layer and the crystalline silicon substrate wafer were taken into account, but had no significant effect on the results and were considered negligible.
According to the used model, the bandgap energy at room temperature is 1.60 eV and decreases linearly at a temperature coefficient of −4×10−4 eV/K with increasing temperature. Both are in agreement with previous investigations of phosphorous doped a-Si:H [19].
The limited resolution due to the spectrometer’s spectral bandwith of about 5.4 nm FWHM is considered for the simulation since it is similar to the period length of the interference pattern to take averaging effects into account. Otherwise, the averaging effect could be misinterpreted as absorption-related attenuation. Nevertheless, there are noticeable deviations between measurement and simulation data: At the initial temperature of 293 K, the minima of the interference pattern are strongly tapered and therefore not fully resolvable due to the limited spectral resolution of the spectrometer. This can be neglected since the amplitude of the interference pattern is the same for both constructive and destructive interference. Thus, no information about the attenuation of the amplitude is lost because this is also contained in the better resolvable maxima of the interference pattern.
An additional effect occurs for high temperatures, as the sample begins to glow and thermally emit increasingly. As the temperature increases, the spectrometer detects not only the reflected fraction of the probe beam, but also an increasing fraction of thermal emission. The thermal emission can be quantified by means of an additional dark measurement, with the probe beam switched off (Fig. 3, left). At temperatures above 1040 K, thermal emission is noticeable and exceeds 1% of the measured signal at wavelengths around 2000 nm. Fom this point onwards, the thermal emission increases significantly with increasing temperature. At a temperature of 1110 K, the thermal emission is 1% at a wavelength around 1700 nm and 3% around 2000 nm.
On the basis of the dark measurements it is assumed that the deviation between measurement data and simulation at a temperature of 1110 K in the wavelength range between 1700 nm and 2000 nm is caused mainly by the mix of the probe beam with the thermal emission of the sample.
The refractive index n and the extinction coefficient k derived from the model are exemplarily shown for the wavelength of 1500 nm in Fig. 4.
Fig. 4. Temperature-dependent refractive index n (left) and extinction coefficient k (right) at a wavelength of 1500 nm
With increasing temperature, the refractive index n of the a-Si:H layer increases linearly and the extinction coefficient k increases exponentially according to
Applied to the data of the full spectrum, the thermo-optical coefficients Cn and Ck are obtained in dependence of the wavelength, as shown in Fig. 5.
Fig. 5. Thermo-optical coefficients Cn and Ck of phosphorous doped a-Si:H for the considered wavelength range of 1000 nm up to 2000nm
The thermo-optical coefficient of the real part of the refractive index Cn(λ) decreases from 3.7×10−3 K−1 to 2.5×10−3 K−1 while the thermo-optical coefficient of the corresponding imaginary part Ck(λ) increases with increasing wavelengths from 2.6×10−3 K−1 to 3.9×10−3 K−1. During evaluation the impact of thermal expansion on the results has been neglected, since the thermal expansion coefficients of a-Si:H with 4.5×10−6 K−1 [20] and SiO2 with 0,5×10−6 K−1 [14] are three orders of magnitude lower compared to the thermo-optical coefficients Cn and Ck.
Compared to the few available data from literature at 808 nm and 820 nm wavelength, which are slightly outside the spectral range considered here, the observed thermo-optical coefficients are of the same order of magnitude [13,15]. In addition, it should be mentioned that the optical properties of a-Si:H not only depend on the wavelength but also on the parameters for layer deposition and doping concentrations [16,19,21].
4. Conclusion
The temperature-dependent optical properties of phosphorus-doped a-Si:H films are determined for elevated temperatures of up to 1110 K for a considerably extended spectral range from 1000 to 2000 nm. The investigation of amorphous silicon in this temperature range is made possible by realizing heating rates of over 2300 K/s, thus preventing premature crystallization during the investigation. This is achieved by combining laser-based sample heating with probe beam guidance and shaping, which enables the analysis of the entire reflected probe beam and, thus, allows for short integration times in the spectrometer.
Acknowledgments
The authors would like to thank Amit Kulkarni and Hans-Joachim Quenzer from the Fraunhofer ISIT for providing us the sample material.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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