We report our study of deposited thermal energy in silicon induced by multiple-pulse femtosecond laser irradiation. Using infrared thermography, we quantified through in situ direct measurement of temperature fields that a significant portion of laser power (two-thirds or more) was deposited into the silicon substrate instead of being reflected or carried away with the ablated material. This is believed to be the first reported study of direct in situ measurement of temperature fields as the result of deposited thermal energy from multiple femtosecond laser pulses. Our simulation results support the measured data.
© 2006 Optical Society of America
During the past ten years, the femtosecond (fs) laser has been demonstrated as a high-precision micromachining tool for materials processing mainly because of its advantages of less mechanical and thermal damage in the vicinity of the processed regions (holes, cutting kerfs, or grooves) compared to long-pulsed (nanosecond or longer) counterparts [1–3]. This has important implications in industrial and medical applications. Because of less mechanical and thermal effects when processing with fs laser, it is commonly believed that most of the absorbed laser energy is carried away by the ablated material, leaving negligible amounts of thermal energy dissipated into the bulk of the remaining material. This is in contrast to processing materials with long pulse laser where a substantial amount of thermal energy remains in the bulk materials and causes mechanical and thermal effects on materials. In recent years, however, different experimental studies [4–12] have found the existence of mechanical and thermal effects even with fs laser processing although these effects (i.e., mechanical and thermal) are much less when compared with longer pulse lasers.
Different experimental techniques have been employed to study mechanical and thermal effects on materials irradiated by fs laser pulses. Most of these studies employed high resolution microscopy such as Scanning Electron Microscopy (SEM) [4, 7] or Transmission Electron Microscopy (TEM) [4, 6–8] to observe the microstructure of the Heat-Affected Zone (HAZ) which indirectly indicates the thermal effects caused by the fs laser. The X-Ray diffraction (XRD) technique has also been employed [5, 12] to analyze the microstructure of the HAZ region before and after processing materials with fs laser. The phase change of the microstructure, for example, from crystalline to amorphous after processing also indirectly indicates the influence of the thermal effect. Recently, by employing a calorimetric method, Vorobyev et al. [9, 10] concluded that a substantial amount of thermal energy remained in the materials after irradiating by multiple fs laser pulses. Yokotani et al.  have also recently investigated the thermal effects of single fs laser pulse on silicon by employing time-resolving image analysis. They have found a relationship between the rise time of the image evolution with the thermal conductivities of different materials, indicating heat propagation during processing by the fs laser.
All of the studies described above indeed indicated the presence of thermal energy that dissipated into the bulk of different materials in fs laser processing. To the best of our knowledge, in situ direct measurement and viewing of the temperature fields induced by the deposited thermal energy during fs laser processing has not been reported. Here, we report in situ observation of temperature fields in silicon and quantify the power for heat flow during multiple-pulse fs laser interaction with the silicon substrate. We not only observed in situ the heat flow into the materials but also quantified the power for heat flow into the silicon specimens. Without ambiguity, we found that there was a substantial amount of the incident laser power (two-thirds or more) deposited into the silicon substrate and caused the temperature rise in the area adjacent to the irradiated region. We have also demonstrated that, for a given laser power and frequency, this temperature rise is a function of the time of irradiation and the location of the substrate.
2. Experimental setup
The experimental set-up is shown in Fig. 1. A Ti:sapphire fs laser (Clark-MXR, Inc., CPA- 2001, central wavelength λ=775 nm, at 1 kHz repetition rate, TEM00, and ~240 fs measured at Full Width Half Maximum (FWHM) by an autocorrelator (APE Pulse Check)) irradiated the top of the silicon specimen. The specimen had dimensions of ~1.0 mm by ~0.7 mm (crosssection) by ~12 mm (length) and was cut from a silicon wafer. The fs laser irradiated the specimen through a focusing lens (f=50 mm) but at an out-of-focus position, with an irradiated spot size of ~0.3 mm and ~0.6 mm in diameter. Different spot sizes were chosen to control the fluences (energy/area) at the appropriate levels. The temperature field along the specimen was captured by an infrared camera (AGEMA Thermovision® 900). The spectral response of the infrared camera is in the Long Wavelength (LW) band (8–12 µm) with a temperature measurement range from -30°C to 1500°C. The accuracy of the infrared camera is ± 1°C. The maximum frequency to capture the thermal images is ~16 Hz. The sides of the specimen were painted black to enhance emissivity of the surrounding surfaces. The infrared radiation emitted by the specimen was captured as a function of time. The infrared emission recorded was converted to temperature readings by calibration of the camera with thermocouples on a similar specimen by performing separate heating experiments.
3. Results and discussion
The typical time sequences of thermal images for silicon during fs laser heating for spot sizes of 0.3 mm (incident average laser power ~210 mW) and of 0.6 mm (power ~300 mW) are shown in Fig. 2. From these thermal images, the temperature rise with time and the temperature gradient along the specimen were observed. Note that for the thermal image of silicon at the spot size of 0.6 mm (Fig. 2(b)), we could see clearly the region where the fs laser irradiated the top of the specimen. This is because the dimension of the spot size (~0.6 mm) is nearly the same as that of the cross section of the silicon specimen (~0.7 mm).
The single-pulse fluence (energy/area) was chosen to be below the single-pulse melting threshold, between the single-pulse melting and ablation threshold, and above the single-pulse ablation threshold of silicon. After 60 s to 100 s, depending on the power, a saturated condition (i.e. little temperature change with time) was achieved. At 1 kHz repetition rate, this condition corresponded to about 60,000 to 100,000 pulses. Fig. 3 shows clearly the existence of temperature gradients along the specimen for various incident laser powers and spot sizes. For Fig. 3(a), at a region close to the irradiated spot (spot size 0.3 mm), the temperature distribution was three dimensional and heat loss is by convection and radiation at the surface. Therefore the temperature in the region smaller than 0.35 mm is less than the maximum temperature, which occurs at the position of 0.35 mm. For Fig. 3(b), the laser spot size of 0.6 mm is nearly the same as the cross section of the specimen, the temperature at the regions less than 0.35 mm is very high, which could also be observed clearly in the thermal images in Fig. 2(b). Further away (i.e., greater than ~0.35 mm) uniform temperature over a given cross section could be assumed, thus satisfying the requirements of one dimensional heat conduction. For ease of understanding, and to simplify subsequent calculations, only regions beyond 0.35 mm were analyzed (i.e., right hand side of the dashed line in Fig. 3). This does not have any impact on the conclusions, except an underestimation of the deposited thermal power as heat loss less than 0.35 mm would be neglected.
The temperature gradients along the specimens in Fig. 3 unambiguously indicate the existence of deposited thermal energy along the specimens. From these saturated temperature distributions, we calculated the average of the deposited laser power required to establish the temperature gradients observed. The solid lines in Fig. 3 were obtained by simulating the specimen as a one-dimensional heat conduction problem with a power source at one end (i.e., at about 0.35 mm from the top of the specimen) and a prescribed temperature (as measured by the infrared camera) at the other (far) end of the specimens, taking into consideration of convective and radiative heat losses along the specimen to the environment (air, ~20°C). To achieve accurate results, the thermal properties for the simulation study are taken to be temperature-dependent. At T=300 K, the values of the density ρ, the thermal conductivity k and the specific heat cp are 2328 kg/m3, 148 W/mK, and 710 J/kgK respectively. Depending on the temperature, the total heat loss coefficient (including both convective and radiative coefficients) varied from 17.56 W/m2K to 30.01 W/m2K. The total heat flow deposited into the specimen includes the power for heat conduction deposited into the specimens and the power for heat losses along the specimen to the environment by convection and radiation. From the temperature profiles and the boundary condition, the total power for heat flow is calculated and it is found that the power for heat flow is dominated by the power for conduction deposited into the specimens compared to the heat losses to the environment by convection and radiation. Excellent correlation between predicted and experimental temperature profiles for all cases was achieved, indicating that the deposited thermal energy so determined were reliable.
To validate further that the deposited thermal energy determined from the saturated condition above was reliable and accurate, the same power in the saturated condition was re-employed to predict the transient temperature distributions at various axial locations of the specimen for the same experiment. The transient temperature profiles for the spot size of 0.6 mm are given in Fig. 4. The results of the temperature profiles for a typical location at ~4.05 mm from the top of the specimens are shown in Fig. 4(a) for different incident laser powers. Figure 4(b) shows the temperature profiles at power of 300 mW at different positions along the specimens. The agreements of the transient temperature profiles between experimental and simulation studies indicate that the power so-determined is reliable. Note that the squiggles in Fig. 4 are presented. This is because the time-dependent boundary condition for the temperature at the other far end of the specimen has been employed. Similar agreements were also achieved for the experiments at spot size of 0.3 mm. Thus, we have confidence in the powers determined for depositing thermal energy in the specimen for all the cases.
Table 1 summarizes the percentage of average power of the deposited thermal energy left in silicon at different incident laser powers or fluences. The fluence for the single-pulse melting and ablation thresholds of silicon is ~150 mJcm-2 and ~300 mJcm-2 respectively . Thus, the laser fluence used in our study is below, between, and above the thresholds of the silicon. Our results indicate that a significant amount of the incident laser power (two-thirds or more) was deposited into the bulk silicon substrate instead of being carried away by the ablated materials for all the cases investigated.
Indeed, when a single-pulse fs laser irradiates on the solids, the heating process caused by the fs laser pulse could be described by the following two-temperature heat conduction equation 
where Te and Ti are the electron and ion temperatures respectively, x is the axial distance of the specimen from the irradiated surface, t is time, Ce and Ci are the volume heat capacities for electrons and ions, κe and κi are the thermal conductivities for electrons and ions, A(x, t) is the laser heat source, and G is the electron-lattice coupling coefficient. Because the pulse duration of the fs laser is shorter than the electron relaxation time (which is a few picoseconds), it has been shown that the electron temperature Te could be first heated to a higher temperature as compared to the ion temperature Ti . The electron heating process, however, only take places within about 100 fs (10-13 s) after the laser pulse . After a longer period of time, say a few picoseconds (1 ps=10-12 s), the ion temperature Ti eventually increases over a longer timescale. As such, when multiple-pulse fs laser irradiates the solids, we expect that over a comparatively much longer time period, energy could eventually transfer to the solids as deposited thermal energy and cause thermal effects such as the HAZ or residual thermal energy in solids, which indirectly indicates the existence of thermal conduction. Although our study is on the heat transfer from the laser source to the substrate over a long time scale as compared to the duration of a single laser pulse, the energy of this heat transfer will have to come from the laser source. Our results indicated that the proportion of energy from the laser source ended up as deposited thermal energy in the substrate is significant (two-thirds or more). Another possibility of observing the heat flow into the silicon specimen could be the enhancement of absorption on materials due to the surface roughness when irradiated by multiple femtosecond laser pulses as explained by Vorobyev et al. [9, 10].
In conclusion, we report a simple yet reliable method for direct in situ observation of the temperature fields in silicon induced by multiple fs laser pulses. Our results are significant as the incident laser powers investigated were below and above the various thresholds of silicon. The percentage of the laser power deposited into the solids as thermal energy was substantial, ranging from 66.7% to 87.8%.
The authors thank Thompson C. V. (MIT) for his stimulating discussions, and SIMTech A*STAR Singapore for its technical support. This work was supported by the Singapore-MIT Alliance program.
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