Temperature Rise of Silicon Due to Absorption of Permeable Pulse Laser

Blade dicing is used conventionally for dicing of a semiconductor wafer. Stealth dicing (SD) was developed as an innovative dicing method by Hamamatsu Photonics K.K. (Fukuyo et al., 2005; Fukumitsu et al., 2006; Kumagai et al., 2007). The SD method includes two processes. One is a “laser process” to form a belt-shaped modified-layer (SD layer) into the interior of a silicon wafer for separating it into chips. The other is a “separation process” to divide the wafer into small chips. A schematic illustration of the laser process is shown in Fig. 1.


Introduction
Blade dicing is used conventionally for dicing of a semiconductor wafer. Stealth dicing (SD) was developed as an innovative dicing method by Hamamatsu Photonics K.K. (Fukuyo et al., 2005;Fukumitsu et al., 2006;Kumagai et al., 2007). The SD method includes two processes. One is a "laser process" to form a belt-shaped modified-layer (SD layer) into the interior of a silicon wafer for separating it into chips. The other is a "separation process" to divide the wafer into small chips. A schematic illustration of the laser process is shown in Fig. 1. When a permeable nanosecond laser is focused into the interior of a silicon wafer and scanned in the horizontal direction, a high dislocation density layer and internal cracks are formed in the wafer. Fig. 2 shows the pictures of a wafer after the laser process and small chips divided through the separation process. The internal cracks progress to the surfaces by applying tensile stress due to tape expansion without cutting loss. An example of the photographs of divided face of the SD processed silicon wafer is shown in Fig. 3. www.intechopen.com As the SD is a noncontact processing method, high speed processing is possible. Fig. 4 shows a comparison of edge quality between blade dicing and SD. In the SD, there is no chipping and no cutting loss, so there is no pollution caused by the debris. The advantage of using the SD method is clear. Fig. 5 shows an example of SD application to actual MEMS device. This device has a membrane structure whose thickness is 2 m, but it is not damaged. A complete dry process of dicing technology has been realized and problems due to wet processing have been solved. In this chapter, heat conduction analysis by considering the temperature dependence of the absorption coefficient is performed for the SD method, and the validity of the analytical result is confirmed by experiment.

Analysis method
A 1,064 nm laser is considered here, and the internal temperature rise of Si by single pulse irradiation is analyzed . Considering that a laser beam is axisymmetric, we introduce the cylindrical coordinate system O rz  whose z -axis corresponds to the optical axis of laser beam and r -axis is taken on the surface of Si. The heat conduction equation which should be solved is where T is temperature,  is density, C p is isopiestic specific heat, K is thermal conductivity, and w is internal heat generation per unit time and unit volume. The finite difference method based on the alternating direction implicit (ADI) method was used for numerical calculation of Eq. (1). The temperature dependence of isopiestic specific heat (Japan Society for Mechanical Engineers ed., 1986) and thermal conductivity (Touloukian et al. ed., 1970) is considered.    (Fukuyo et al., 2007;Weakliem & Redfield, 1979) shows temperature dependence of the absorption coefficient of single crystal silicon for a wavelength 1,064 nm. The www.intechopen.com When the Lambert law is applied between a small depth z  from depth The absorption coefficient of molten silicon is 5 7.61 10  cm -1 (Jellison, 1987). Therefore, this value is used for the upper limit of applying Eq. (3). The 2 1 e radius at the depth z of a laser beam which is focused with a lens is expressed by The beam is focused when j  is less than 1, and is diverged when j  is larger than 1. Now, the laser intensity ,

The formation mechanism of the inside modified layer
Concrete analyses are conducted under the irradiation conditions that the pulse energy, p0 E , is 6.5 J, the pulse width (FWHM), p  , is 150 ns and the minimum spot radius, 0 r , is 485 nm. The pulse shape is Gaussian. The pulse center is assumed to occur at 0 t  . The intensity distribution (spatial distribution) of the beam is assumed to be Gaussian. It is supposed that the thickness of single crystal silicon is 100 m and the depth of focal plane 0 z is 60 m. The initial temperature is 293 K.
The analysis region of silicon is a disk such that the radius is 100 m and the thickness is 100 m. In the numerical calculation, the inside radius of 20 m is divided into 400 units at a width 50 nm evenly, and its outside region is divided into 342 units using a logarithmic grid. The thickness is divided into 10,000 units at 10 nm increments evenly in the depth direction. The time step is 20 ps. The boundary condition is assumed to be a thermal radiation boundary. For comparison with the following analysis results, the temperature dependence of the absorption coefficient is ignored at first, and a value of 8.1

 
cm -1 at room temperature is used. In this case, the time variation of the intensity distribution inside the silicon is given by where p E is an effective pulse energy penetrating silicon and   e rz is the spot radius of the Gaussian beam at depth z . The time variation of temperature at various depths along the central axis is shown in Fig. 7. The maximum temperature distribution is shown in Fig. 8. It is understood from Fig. 7 that the temperature becomes the maximum at time 20 ns at depth of 60 m which corresponds to the focal position. In Fig. 8, due to reflecting laser absorption, the temperature of the side that is shallower than the focal point of the laser beam is slightly higher. However, the maximum temperature distribution becomes approximately symmetric with respect to the www.intechopen.com focal plane. At any rate the maximum temperature rise is about 360 K, which is much smaller than the melting point of 1,690 K under atmospheric pressure (Parker, 2004). It is concluded that polycrystallization after melting and solidification does not occur at all, if the absorption coefficient is independent of the temperature and is the value at the room temperature.  When the temperature dependence of absorption coefficient (Eq. (3)) is taken into account, the time variation of temperature distribution is shown in Fig. 9. Figure 10 shows the time variation of the temperature distribution along the central axis in Fig. 9. It can be understood from these figures that laser absorption begins suddenly at a depth of 59 z  m at about 45 t  ns and the temperature rises to about 20,000 K instantaneously. The region where the temperature rises beyond 10,000 K will be instantaneously vaporized and a void is formed. High temperature region of about 2,000 K propagates in the direction of the laser irradiation from the vicinity of the focal point as a thermal shock wave. The region where the thermal shock wave propagates becomes a high dislocation density layer due to the shear stress caused by the very large compressive stress.  Figure 11 shows the maximum temperature distribution and a schematic of SD layer formation. SD layer looks like an exclamation mark "!". As a result, a train of the high dislocation density layer and void is generated as a belt in the laser scanning direction as shown schematically in Fig. 1. When the thermal shock wave caused by the next laser pulse propagates through part of the high dislocation density layer produced by previous laser pulse, a crack whose initiation is a dislocation progresses. Figure 12 shows a schematic of crack generation by the thermal shock wave. Analyses of internal crack propagation in SD were conducted later using stress intensity factor (Ohmura et al., 2009(Ohmura et al., , 2011 Fig. 12. Schematic of crack generation Figure 13 shows an inside modified-layer observed by a confocal scanning infrared laser microscope OLYMPUS OLS3000-IR before division (Ohmura et al., 2009). It is confirmed that a train of the high dislocation density layer and void is generated as a belt as estimated in the previous studies. It also can be understood that the internal cracks have been already generated before division.

Stealth Dicing of ultra thin silicon wafer
Here heat conduction analysis is performed for the SD method when applied to a silicon wafer of 50 m thick, and the difference in the processing result depending on the depth of focus is investigated (Ohmura et al., , 2008. Furthermore, the validity of the analytical result is confirmed by experiment. In the analysis, the pulse energy, p0 E , is 4 J, the pulse width, p  , is 150 ns, and the pulse shape is Gaussian. The intensity distribution of the beam is assumed to be Gaussian. It is supposed that the depth of focal plane 0 z is 30 m, 15 m and 0 m. The initial temperature is 293 K. The analysis region of silicon is a disk such that the radius is 111 m and the thickness is 50 m. In the numerical calculation, the inside radius of 11 m is divided into 440 units at a width 25 nm evenly, and its outside region is divided into 622 units using a logarithmic grid. The thickness is divided into 10,000 units at 5 nm increments evenly in the depth direction. The time step is 10 ps. The boundary condition is assumed to be a thermal radiation boundary.

In the case of focal plane depth 30 µm
The time variation the temperature distribution along the central axis is shown in Fig.14. Figure 14(b) shows the temperature change on a two-dimensional plane of depth and time by contour lines. It can be understood from Fig. 14(a) that laser absorption begins suddenly at a depth of 29 z  m at about 8 t   ns and the temperature rises to about 12,000 K instantaneously. The region where the temperature rises beyond 8,000 K will be instantaneously vaporized and a void is formed. The high temperature area beyond 2,000 K then expands rapidly in the surface direction until 100 t  ns as shown in Fig. 14(b). The contour at the leading edge of this high temperature area is clear in this figure. Also the temperature gradient is steep as shown in Fig. 14(a). Therefore, this high-temperature area is named a thermal shock wave as well. It is calculated that the thermal shock wave travels at a mean speed of about 300 m/s. Propagation of the thermal shock wave is shown in Fig. 15 by a time variation of the twodimensional temperature distribution. The contour of the high-temperature area is comparatively clear until 50 t  ns, because the traveling speed of the thermal shock wave is much higher than the velocity of thermal diffusion. The contour of the high temperature area becomes gradually vague at 100 t  ns when the thermal shock wave propagation is finished. Because the temperature history is similar to the case of thickness 100 m, the inside modified layer such as Fig. 3 is expected to be generated.

In the case of focal plane depth 15 µm
The time variation of the temperature distribution along the central axis in case of focal plane depth 15 m is shown in Fig. 16. It can be understood from Fig. 16(a) that laser absorption begins suddenly at a depth of 14 z  m at about 10 t   ns and the temperature rises to about 12,000 K instantaneously. As well as the case of focal plane depth 30 m, the region where the temperature rises beyond 8,000 K will be instantaneously vaporized and a void is formed. Then the thermal shock wave propagates in the surface direction until about 25 ns. It is understood from Fig. 16(b) that laser absorption suddenly begins at the surface, once the thermal shock wave reaches the surface. Though the laser power already passes the peak, and gradually decreases, the surface temperature rises beyond 20000 K, which is higher than the maximum temperature which is reached at the inside. Although the thermal diffusion velocity is fairly slower than the thermal shock wave velocity, the internal heat is diffused to the surrounding. However, because the heat in the neighborhood of the surface is diffused only in the inside of the lower half, the surface temperature becomes very high and is maintained comparatively for a long time. Ablation occurs of course in such a hightemperature state. As a result, it is expected that not only is an inside modified layer generated, but also the surface is removed by ablation. Figure 17 shows that the surface temperature rises suddenly after the thermal shock wave propagates in the inside of the silicon, and reaches the surface, by the time variation of two dimensional temperature distribution.

In the case of focal plane depth 0 µm
When the laser is focused at the surface, as shown in Fig. 18, laser absorption begins suddenly at the surface at 35 t   ns, and the maximum surface temperature in the calculation reaches 5 61 0  K. It is estimated that violent ablation occurs when such an ultrahigh temperature is reached. Because of the pollution of the device area by the scattering of the debris and thermal effect, the ablation at the surface is quite unfavorable.

Comparison of the maximum temperature distributions and the experimental results
The maximum temperature distributions at the focal plane depths of 30 m, 15 m and 0 m are shown in Fig. 19 in order to compare the previous analysis results at a glance. Because high-temperature area stays in the inside of the wafer when 0 z is 30 m, it was estimated that the inside modified layer as shown in Fig. 3 will be generated. In the case of 0 15 z  m, it was estimated that the surface is ablated although the modified layer is generated inside. In the case of 0 0 z  m, it was estimated that the surface was ablated intensely. It is concluded from the above analysis results that the laser irradiation condition for SD processing should be selected at a suitable focal plane depth so that the thermal shock wave does not reach the surface.
In In the case of 0 30 z  m which is shown in Fig. 20 (a), it can be confirmed that voids are generated at the place that is slightly higher than the focal plane and the high dislocation density layer is generated in those upper parts, which are similar to Fig. 3. In the case of 0 15 z  m which is shown in Fig. 20 (b), it is recognized that voids are generated at the place that is slightly higher than the focal plane and the high dislocation density layer is generated in those upper parts. However, it is observed that the surface is ablated and holes are opened from the photograph of the laser irradiated surface. In the case of 0 0 z  m which is shown in Fig. 20 (c), it is seen that strong ablation occurs and debris is scattered to the surroundings. Voids and the high dislocation density layer are not recognized in the divided face. Only the cross section of the hole caused by ablation is seen. These experimental results agree fairly well with the estimation based on the previous analysis www.intechopen.com result. Therefore, the validity of the analytical model, the analysis method, and the analysis results of this study are proven. The processing results can be estimated to some extent by using the analysis model and the analysis method in the present study. It is useful in optimization of the laser irradiation condition.

Conclusion
In the stealth dicing (SD) method, the laser beam that is permeable for silicon is absorbed locally in the vicinity of the focal point, and an interior modified layer (SD layer), which consists of voids and high dislocation density layer, is formed. In this chapter, it was clarified by our first analysis that the above formation was caused by the temperature dependence of the absorption coefficient and the propagation of a thermal shock wave. Then, the SD processing results of an ultra thin wafer of 50 m in thickness were estimated based on this analytical model and analysis method. Particularly we paid attention to the difference in the results depending on the focal plane depth. Furthermore, in order to compare with the analysis results, laser processing experiments were conducted with the same irradiation condition as the analysis conditions. In the case of focal plane depth 0 30 z  m, the analysis result of temperature history was similar to the case when the wafer thickness is 100 m and the focal plane depth is 60 m. Therefore, it was predicted that a similar inside modified layer will be generated. In the case of 0 15 z  m, it was estimated that not only the inside modified layer is generated, but also the surface is ablated. Because the thermal shock wave reached the surface, remarkable laser absorption occurred at the surface. In the case of 0 0 z  m, it was estimated that the surface is ablated intensely. These estimation results agreed well with experimental results. Therefore, the validity of the analytical model, the analysis method and the analysis results of this study was proven. As conclusion of this chapter, the following points became clear: 1. When the analytical model and the analysis method of the present study are used, the processing mechanism can be understood well, and the processing results can be estimated to some extent. It is useful in optimization of the laser irradiation condition. 2. There is a suitable focal plane depth in the SD processing, and it is necessary to select the laser irradiation condition so that the thermal shock wave does not reach the surface. Heat transfer is involved in numerous industrial technologies. This interdisciplinary book comprises 16 chapters dealing with combined action of heat transfer and concomitant processes. Five chapters of its first section discuss heat effects due to laser, ion and plasma-solid interaction. In eight chapters of the second section engineering applications of heat conduction equations to the curing reaction kinetics in manufacturing process, their combination with mass transport or ohmic and dielectric losses, heat conduction in metallic porous media and power cables are considered. Analysis of the safety of mine hoist under influence of heat produced by mechanical friction, heat transfer in boilers and internal combustion engine chambers, management for ultrahigh strength steel manufacturing are described in this section as well. Three chapters of the last third section are devoted to air cooling of electronic devices.