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The optical breakdown thresholds (OBTs) of typical dielectric and semiconductor materials are measured using double 40-fs laser pulses. By measuring the OBTs with different laser energy and different time delays between the two pulses, we found that the total energy of breakdown decrease for silica and increase for silicon with the increase of the first pulse energy.
©2005 Optical Society of America
1. Introduction
In recent years, the interaction between ultrashort laser pulses and solid materials has attracted extensive attention [1–11], especially due to the promising applications of femtosecond laser pulses in micromachining [5, 6, 9–11]. When femtosecond laser pulses irradiate the solid target, the laser energy is quickly absorbed by electrons, and then transferred to the lattices. The ultra-fast interaction nature restrains the thermal conduction effect and makes cold machining possible, and as a result the precision of laser machining can be considerably improved. The ablation mechanism of dielectric and semiconductor by femtosecond laser pulses is one of the fundamental issues in the interaction between laser and materials. Most investigations attributed the laser-induced breakdown in dielectric and semiconductor to the presence of the conduction band electrons (CBEs). The process of ablation and damage can be described in terms of three major processes related with CBEs: firstly, multiphoton ionization (MPI) and/or tunneling ionization cause the excitation of CBEs, then, electron-electron collision ionization (avalanche process) causes further generation of CBEs, and finally CBEs energy transfer to the lattice [12, 13]. Moreover, ablation process is affected by photoemission, surface charging, electron drift, trapping, recombination, and diffusion, where CBEs play an important role.
More recently the laser machining with temporally shaped femtosecond laser pulses has been proposed [5], in which double- or multi-peak laser pulses are adopted to lower OBTs and to optimize the machining profile. In the ablation with shaped laser pulses, the relaxation of CBEs generated by the leading edge of the pulse or the first pulse is crucial to the whole ablation process, and hence the investigation on the relationship between the parameters of temporally shaped femtosecond laser and the relaxation of CBEs become a subject of great importance. Though many studies have been carried out concerning the generation of CBEs, the behaviors and the mechanism of relaxation of CBEs have not been well understood. Moreover the effect of CBEs on the band gap and the decay of CBEs have rarely been investigated.
In this paper, we use pump-probe method to investigate the effect of the CBEs on the optical breakdown and the decay of CBEs by measuring OBT of fused silica and silicon irradiated by laser pulses at the wavelength of 800 nm and with the pulse duration of 40 fs. By measuring the breakdown threshold of the second pulse with different laser energy in the first pulse and different time delay between two pulses, we found that the CBEs decay is an ultrafast process and there is an obvious difference in the variation of the total thresholds for silica and silicon samples. The total threshold decreases for fused silica, but increases for silicon with the increase of the first pulse energy.
2. Experiment and theory
The experimental setup is shown in Fig. 1. The parameters of the Ti: sapphire laser used in the experiments are 40 fs (FWHM pulse length), 0.6 mJ (laser energy in a pulse), 800 nm (wavelength), and 1 kHz (repetition rate). Horizontally linearly polarized laser pulses are directed to a beam-splitter (BS), where each single pulse is split into two temporally identical pulses with variable delay from 0 to1 ps. The time delay is precisely set from 0 to 1 ps monitored by a single shot autocorrelator (SSA). The collinearity of the two beams sent to the focusing lens is achieved by adjusting their interference pattern at zero time delay. The energies of the two pulses can be individually adjusted by the half wave plates and the polarizers. The collinear beams are focused onto the front surface of the samples in normal incidence. The diameter of the focal spot on samples is measured to be about 45µm. With a long-working-distance microscope and a charge-coupled device (CCD) camera, a magnified image of the target surface is obtained. The experiments are performed on samples of fused silica (FS, 0.5 mm in thickness) and silicon (Si, 0.5 mm in thickness), which have been optically polished.
First, we measure the single pulse OBT. The OBT is measured to be 2.0 J/cm2 for fused silica and 0.2 J/cm2 for silicon with an error of approximately 8%. Here we use the same method of measuring OBT as that of Ref. [2]. Strong plasma radiation features the existence of optical breakdown. Thus, one can measure the OBT through the detecting of plasma radiation. In the double pulse OBT measurements, the pulse energies of both laser pulses are set lower than the single pulse breakdown threshold.
Figure 2(a) shows the breakdown threshold of the second pulse versus the time delay between the two pulses with different laser energy in the first pulses for fused silica. The breakdown threshold of the second pulse rises quickly for the time delay range of 100–125 fs when the first pulse energy is relatively low, and rises more slowly for the time delay range of 100–180 fs with higher energy in the first pulse. The higher the first pulse energy is, the lower is the saturation value, these saturation values are all lower than the single pulse OBT while approaching the single pulse OBT as the single pulse fluence is reduced. In the case of silicon sample (as shown in Fig. 2(b)), the phenomenon is different. The breakdown threshold of the second pulse keeps rising in the time delay range of 100–400 fs, but the slopes are less steep than that in the case of silica sample. Again, beyond 400fs, the OBT saturation are all lower than the single pulse OBT while approaching the single pulse OBT as the single pulse fluence is reduced. It is noted that a systematic dip appears in the second pulse OBT measurement for delays between 200–300fs for silica while less discernible for silicon. For silica, the electrons may absorb the energy of the second laser pulse more efficiently under this specific condition of electron temperature and density for delays between 200–300fs. However, the mechanism is not fully understood.
The OBT is associated with a threshold density of CBEs: nth=ωm/4πe 2, where ω is the laser frequency, m is the electron mass, and e is the electron charge, respectively. nth is chosen to be 1.7×1021 cm-3, which is near the plasma critical density for the laser wavelength at 800 nm [1–3]. The typical equation to calculate the density of CBEs in dielectrics is given by [1, 2, 14]:
where I(t) is the laser intensity pulse, α is the avalanche coefficient, σk is the k -photon absorption cross section, with the smallest k satisfying kħω≥Eg, Eg is the band gap.
Fig. 2. The second pulse OBT vs. the time delay between two pulses for silica and silicon. (a) Silica. The fluence of the first pulse is 1.0J/cm2, 1.2J/cm2, 1.4J/cm2, 1.5J/cm2, and 1.6J/cm2, respectively. (b) Silicon. The fluence of the first pulse is 0.06J/cm2, 0.09J/cm2, 0.12J/cm2, 0.14J/cm2, and 0.16J/cm2, respectively.
And the typical equation to calculate the density of CBEs in silicon is given by [15]:
where z denotes the spatial coordinate perpendicular to the surface, α 0 and β describe linear and two-photon interband absorption, and intraband free-carrier absorption is included via a space- and time-dependent coefficient αfca.
In double-pulse experiment, CBEs excited by the first pulse will relax back to the valence band during the time interval between the two pulses. The relaxation times of CBEs for silica and silicon are about 200 fs and 400 fs, respectively. When the time delay exceeds 200 fs for the silica sample and 400 fs for the silicon sample, the energy is mostly transferred to the crystal lattice by the electrons. Then the conduction band electrons almost relax to the defect state and may recombine with the holes with phonon emission. Therefore, when the time delay is less than 200 fs for silica, some electrons excited by the first pulse are still in the conduction band, which leads to the enhancement of the absorption rate of laser energy by the material through cascade ionization, hence, the decrease in ablation threshold for the second pulse. This conclusion is similar to the result in Ref. [2].
Considering the loss of conduction band electrons generated by the first pulse, as shown in Eq. (3), Ming Li et al. introduced another term to Eq. (1) to explain the experiment result of the fused silica [4],
where τ refers to the decay time constant and in their calculation it was chosen to be about 60 fs.
For the first time we measure the breakdown threshold of the second pulse with different first pulse energy and time delays specified, and the results for fused silica are shown in Fig. 3. We find that the total thresholds (the total thresholds are the sum of the first pulse and the second pulse’s fluences) decreased with the increase of the first pulse energy and this phenomena have not been reported in former literature to our knowledge. And the simulation results of fused silica are also presented in Fig. 3 and compared with the experimental ones.
Fig. 3. Total OBT and the second pulse OBT vs. the fluence of the first pulses for fused silica along with their rescaled theoretical fits based on the modified rate equation [Eq. (3)] with α=4±0.6cm2J and σ6=6×108±0.9 cm-3 ps-1cm2TW6, and τ=60 fs. [4] (a) Time delay is 100fs. (b) Time delay is 300 fs.
As the modificatory equation of silica, another term can be introduced to Eq. (2) to explain the experiment results of silicon. The modificatory equation of silicon is:
Fig. 4. Total OBT and the second pulse OBT vs. fluence of the first pulses for silicon. (a) Time delay is 150fs. (b) Time delay is 300fs.
For silicon, the breakdown thresholds of the second pulse with different first pulse energy and time delays specified are given in Fig. 4. The total threshold increases with the increase of the first pulse energy.
The phenomena can be explained in the light of the different breakdown mechanisms for silica and silicon. For the case of silicon, the bandgap is 1.14 eV, electrons are mainly ionized through one-photon ionization and two-photon ionization. So the remaining ionized electrons after the first pulse will not act as seed electrons for the ionization of the second pulse. Thus, when the decay rate of the electron is constant, as the energy of the first pulse increased the electron produced by the first pulse will decay much more, which results in the corresponding increase of the total threshold energy. As to silica, for which the bandgap is about 8eV, electrons are mainly ionized through multiphoton ionization and avalanche ionization. The remaining electrons, that is, CBEs, will play as seed electrons for the breakdown of the second pulse. Though the number of these electrons is not large, it induces the main ionization mechanism of the second pulse to be avalanche ionization. So the total threshold energy of the two pulses will decrease as the energy of the first pulse increases.
3. Conclusion
In conclusion, we reported the results of double femtosecond laser pulses ablation in silica and silicon. In the experiment, we found that the change of the total breakdown threshold is different in silica and silicon when the energy of the first pulse changes. This work is helpful for investigating the breakdown process, as well as for understanding the damage and micromachining by temporally shaped femtosecond laser pulses, and for optimizing the laser parameters for machining of different materials.
Acknowledgments
The authors thank Prof. Ya Cheng and Prof. Zhinan Zeng for their theoretical assistances. This work is supported by the National Natural Science Foundation of China (No. 69925513, 19974058); Chinese National Major Basic Research Project (G1999075204).
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