The effect of ion irradiation on dephasing of coherent optical phonons in GaP

In the last two decades, the progress of femtosecond (fs) lasers has made time-domain spectroscopy of the coherent lattice vibration in solids possible.^1–31. H. J. Zeiger, J. Vidal, T. K. Cheng, E. P. Ippen, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 45, 768 (1992). https://doi.org/10.1103/physrevb.45.7682. J. Shah, in Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, edited by M. Cardona (Springer Series in Solid-State Sciences, 1999).3. T. Dekorsy, G. C. Cho, and H. Kurz, in Light Scattering in Solids VIII, edited by M. Cardona and G. Güntherodt (Springer-Verlag, Berlin, Heidelberg, 2000), Chap. 4. Coherent phonons are impulsively generated by ultrashort light pulses and lose coherence due to the interaction with their environment, e.g., other lower energy phonon modes.⁴4. M. Hase and M. Kitajima, J. Phys.: Condens. Matter 22, 073201 (2010). https://doi.org/10.1088/0953-8984/22/7/073201 There was active discussion regarding the generation mechanisms of coherent phonons in semimetals,¹1. H. J. Zeiger, J. Vidal, T. K. Cheng, E. P. Ippen, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 45, 768 (1992). https://doi.org/10.1103/physrevb.45.768 transparent materials,⁵5. Y. X. Yan, E. B. Gamble, Jr., and K. A. Nelson, J. Chem. Phys. 83, 5391 (1985). https://doi.org/10.1063/1.449708 semiconductors,^3,63. T. Dekorsy, G. C. Cho, and H. Kurz, in Light Scattering in Solids VIII, edited by M. Cardona and G. Güntherodt (Springer-Verlag, Berlin, Heidelberg, 2000), Chap. 4.6. K. J. Yee, K. G. Lee, E. Oh, D. S. Kim, and Y. S. Lim, Phys. Rev. Lett. 88, 105501 (2002). https://doi.org/10.1103/physrevlett.88.105501 and semiconductor multiple quantum wells.⁷7. K. J. Yee, Y. S. Lim, T. Dekorsy, and D. S. Kim, Phys. Rev. Lett. 86, 1630 (2001). https://doi.org/10.1103/physrevlett.86.1630 Recently, it has been actively reported that driving coherent phonons induces ultrafast structural distortion in ferromagnet,⁸8. M. Först, C. Manzoni, S. Kaiser, Y. Tomioka, Y. Tokura, R. Merlin, and A. Cavalleri, Nat. Phys. 7, 854 (2011). https://doi.org/10.1038/nphys2055 antiferromagnet,⁹9. D. M. Juraschek, M. Fechner, and N. A. Spaldin, Phys. Rev. Lett. 118, 054101 (2017). https://doi.org/10.1103/physrevlett.118.054101 and phase-change materials.¹⁰10. M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, Nat. Commun. 6, 8367 (2015). https://doi.org/10.1038/ncomms9367 However, little is known as to how coherent phonons lose their coherence (dephase) in defective semimetals and semiconductors.

GaP is a III–V semiconductor with an indirect bandgap of ≈2.25 eV at room temperature (RT) and a promising material for device applications such as light emitting diodes.^11,1211. C. H. Henry and P. D. Dapkus, J. Appl. Phys. 47, 4067 (1976). https://doi.org/10.1063/1.32323712. D. R. Wight, J. Phys. D: Appl. Phys. 10, 431 (1977). https://doi.org/10.1088/0022-3727/10/4/010 In addition, GaP has the largest refractive index (n > 3), enabling strong optical confinement and implying a large χ⁽³⁾ nonlinearity. The non-centrosymmetric crystal structure of GaP yields a nonzero piezo-electric effect and large χ⁽²⁾ nonlinearity.¹³13. D. J. Wilson, K. Schneider, S. Hönl, M. Anderson, Y. Baumgartner, L. Czornomaz, T. J. Kippenberg, and P. Seidler, Nat. Photonics 14, 57 (2020). https://doi.org/10.1038/s41566-019-0537-9 The coherent longitudinal optical (LO) phonon in GaP was observed by a transient reflectivity technique.¹⁴14. Y.-M. Chang, Appl. Phys. Lett. 82, 1781 (2003). https://doi.org/10.1063/1.1560874 It has been proposed that under the condition of above bandgap excitation in GaAs, coherent LO phonons are generated by a sudden screening of the surface space-charge field (SCF) by photo-excited carriers.³3. T. Dekorsy, G. C. Cho, and H. Kurz, in Light Scattering in Solids VIII, edited by M. Cardona and G. Güntherodt (Springer-Verlag, Berlin, Heidelberg, 2000), Chap. 4. On the other hand, under the condition of below bandgap excitation, which is the case here, impulsive stimulated Raman scattering (ISRS) will dominate the generation of coherent LO phonons,^5,6,155. Y. X. Yan, E. B. Gamble, Jr., and K. A. Nelson, J. Chem. Phys. 83, 5391 (1985). https://doi.org/10.1063/1.4497086. K. J. Yee, K. G. Lee, E. Oh, D. S. Kim, and Y. S. Lim, Phys. Rev. Lett. 88, 105501 (2002). https://doi.org/10.1103/physrevlett.88.10550115. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 while phonon dephasing by multiphoton-generated carriers is possible.⁶6. K. J. Yee, K. G. Lee, E. Oh, D. S. Kim, and Y. S. Lim, Phys. Rev. Lett. 88, 105501 (2002). https://doi.org/10.1103/physrevlett.88.105501 At a sufficiently low photo-excited carrier density, the dephasing process of the coherent LO phonon in GaP has been accounted for the anharmonic decay due to phonon–phonon interaction,¹⁶16. W. E. Bron, J. Kuhl, and B. K. Rhee, Phys. Rev. B 34, 6961 (1986). https://doi.org/10.1103/physrevb.34.6961 and the dephasing time was obtained as ∼10 ps at room temperature.¹⁶16. W. E. Bron, J. Kuhl, and B. K. Rhee, Phys. Rev. B 34, 6961 (1986). https://doi.org/10.1103/physrevb.34.6961 By increasing the photo-excited carrier density, the dephasing time was decreased to below 1 ps.¹⁵15. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 This suggests that another dephasing process related to electron–phonon interaction is operative at a high carrier density.¹⁷17. G. O. Smith, T. Juhasz, W. E. Bron, and Y. B. Levinson, Phys. Rev. Lett. 68, 2366 (1992). https://doi.org/10.1103/physrevlett.68.2366

Incorporation of a small amount of defects into semiconductors is an intriguing method for manipulating their electrical properties such as carrier lifetime¹⁸18. S. Gupta, J. F. Whitaker, and G. A. Mourou, IEEE J. Quantum Electron. 28, 2464 (1992). https://doi.org/10.1109/3.159553 and carrier mobility.¹⁹19. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors, 2nd ed. (Springer-Verlag, Berlin, Heidelberg, 1999), Chap. 4. Ultrafast carrier dynamics have been examined in low-temperature (LT) grown GaAs, which has been a key material for the generation of THz radiation since the 1990s.²⁰20. M. Tani, S. Matsuura, K. Sakai, and S.-i. Nakashima, Appl. Opt. 36, 7853 (1997). https://doi.org/10.1364/ao.36.007853 The carrier lifetime was decreased to a sub-picosecond time scale due to trapping of carriers by As-precipitates.^18,2118. S. Gupta, J. F. Whitaker, and G. A. Mourou, IEEE J. Quantum Electron. 28, 2464 (1992). https://doi.org/10.1109/3.15955321. S. D. Benjamin, H. S. Loka, A. Othonos, and P. W. E. Smith, Appl. Phys. Lett. 68, 2544 (1996). https://doi.org/10.1063/1.116178 Defects also affect the lattice properties in solids, e.g., the dephasing time and the frequency of phonons.²²22. T. Dekorsy, H. Kurz, X. Q. Zhou, and K. Ploog, Appl. Phys. Lett. 63, 2899 (1993). https://doi.org/10.1063/1.110291 In fact, the dephasing time of the coherent phonons was found to decrease with increasing density of lattice defects, which was explained by phonon-defect scattering.²³23. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, Appl. Phys. Lett. 76, 1258 (2000). https://doi.org/10.1063/1.126002 Introduction of lattice defects can thus be a perturbation of elementary excitations in solids through localized defect potential.⁴4. M. Hase and M. Kitajima, J. Phys.: Condens. Matter 22, 073201 (2010). https://doi.org/10.1088/0953-8984/22/7/073201 Furthermore, introduction of lattice defects can change the nonlinear optical effect through nonlinear susceptibility, e.g., χ⁽²⁾ and χ⁽³⁾.²⁴24. M. Motojima, T. Suzuki, H. Shigekawa, Y. Kainuma, T. An, and M. Hase, Opt. Express 27, 32217 (2019). https://doi.org/10.1364/oe.27.032217

In this paper, the effect of lattice defects on the dephasing of the coherent LO phonon in GaP is investigated. The dephasing time of the coherent LO phonons is found to be dramatically prolonged by the introduction of a small amount of vacancies by means of ion irradiation. The prolongation is not expected by the phonon-defect scattering but is explained in terms of a modification of the decay channel of photo-generated carriers by lattice defects, resulting in the suppression of electron–phonon scattering.

The samples used were non-doped GaP (100) wafers with 300 μm thickness. In order to introduce lattice defects in a controlled manner, the samples were irradiated with 30 keV Ga⁺ ions at various doses from 1.0 ×  10¹³ to 8.0 ×  10¹³  Ga⁺/cm² in a focused ion beam (FIB) system [Fig. 1(a)]. The irradiation of the Ga⁺ beam induces Ga- and P-vacancies.²⁵25. M. J. Legodi, F. D. Auret, and S. A. Goodman, Mater. Sci. Eng.:B 71, 96 (2000). https://doi.org/10.1016/s0921-5107(99)00356-6 The damage profile was calculated by Monte Carlo simulations²⁶26. J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon Press, New York, 1985), Vol. 1. to be a Gaussian function with a peak at ≈12 nm from the surface and a width of ≈16 nm, as shown in Fig. 1(b).

Femtosecond pump-probe measurements were performed at 300 K. The light source used was a mode-locked Ti:sapphire laser with a pulse duration of ≈25 fs, a central wavelength of 830 nm (≈1.49 eV), and a repetition rate of 80 MHz. The average powers of pump- and probe-beams were fixed at 175 mW and 8.7 mW, respectively. Both the pump- and probe-beams were focused via an off-axis mirror to a diameter of ∼20 μm on the sample, and the pump- and probe-fluences were kept at ≈1.19 mJ/cm² and 60 μJ/cm², respectively. The optical penetration depth at 830 nm was estimated from the absorption coefficient to be ≈130 nm.¹⁵15. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 Since the optical penetration is an exponential function, the optical penetration depth overlaps well with that of the vacancy distribution (Fig. 1). Because of much less transition probability across the indirect bandgap at the X-valley, the one-pump and one-probe pulses can excite carriers via two-photon absorption (TPA) near the zone center (Γ point), where the direct gap is ≈2.78 eV at RT.¹⁵15. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 Anisotropic reflectivity change (ΔR_EO/R) was measured by an electro-optic (EO) sampling technique³3. T. Dekorsy, G. C. Cho, and H. Kurz, in Light Scattering in Solids VIII, edited by M. Cardona and G. Güntherodt (Springer-Verlag, Berlin, Heidelberg, 2000), Chap. 4. to detect coherent LO phonons as a function of delay time. The delay between the pump and probe pulses was scanned by using an oscillating retroreflector operated at a frequency of 10.5 Hz up to 30 ps (Ref. 2727. M. Hase, M. Katsuragawa, A. M. Constantinescu, and H. Petek, Nat. Photonics 6, 243 (2012). https://doi.org/10.1038/nphoton.2012.35).

The time derivatives of the ΔR_EO/R signals for non-doped GaP before and after Ga⁺ ion irradiation are shown in Fig. 2. The coherent oscillation due to the LO phonon (12.15 THz) is observed in three different samples, as shown in the Fourier transformed (FT) spectra in Fig. 3.^14,1514. Y.-M. Chang, Appl. Phys. Lett. 82, 1781 (2003). https://doi.org/10.1063/1.156087415. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 The peak frequency of the LO mode implies a significant change from ≈12.2 THz down to ≈12.1 THz, as seen in Fig. 3, which will be discussed in more detail Fig. 4. Note that in Fig. 3, the peak intensity of the LO mode for 2.0 × 10¹³ Ga⁺/cm² is slightly greater and the width is narrower than that of the non-irradiated GaP, implying that the dephasing time of the LO mode becomes longer for 2.0 × 10¹³ Ga⁺/cm² than that before the Ga⁺ ion irradiation.

To further investigate the effect of irradiation on the dephasing of the coherent LO phonon, the time-domain data were analyzed with an exponentially damped harmonic oscillation, as shown in Fig. 2. The dephasing time of the coherent LO phonon thus obtained is plotted in Fig. 4(a) as a function of Ga⁺ dose. The frequency of the LO phonon is also plotted in Fig. 4(b) as a function of Ga⁺ dose. The frequency gradually shifts from ≈12.15 down to ≈12.11 THz at an irradiation of 8.0 × 10¹³  Ga⁺/cm². The decrease in the peak frequency of ∼0.04 THz is possibly governed by strains introduced by the implanted Ga⁺ ions, i.e., the strains resulting from the displacement of the host Ga and P lattice from its normal equilibrium position.²⁸28. C. S. R. Rao, S. Sundaram, R. L. Schmidt, and J. Comas, J. Appl. Phys. 54, 1808 (1983). https://doi.org/10.1063/1.332815 The dephasing time before ion-irradiation was 8.3 ± 0.1 ps, which is comparable but significantly shorter than that obtained using 800 nm light for the n-doped GaP Schottky diode, ∼10 ps (Ref. 1414. Y.-M. Chang, Appl. Phys. Lett. 82, 1781 (2003). https://doi.org/10.1063/1.1560874), and the n-doped GaP wafer, ∼12 ps (Ref. 1515. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203). The shorter dephasing time before the irradiation implies the existence of electron–phonon interaction under the presence of photo-generated carriers, as discussed later in the present study.¹⁵15. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 An irradiation of 8.0 × 10¹³  Ga⁺/cm² increases the dephasing time up to 9.1 ps, being consistent with the peak narrowing observed in the FT spectra (see after irradiation in Fig. 3).

Scattering of the coherent phonon by lattice defects generally promotes its dephasing when the ion dose was typically ≥10¹⁴/cm² (Ref. 2323. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, Appl. Phys. Lett. 76, 1258 (2000). https://doi.org/10.1063/1.126002). However, the increase in the dephasing time for lower ion doses cannot be explained by defect scattering. Dekorsy and co-workers observed a slightly longer dephasing time for the coherent LO phonon in as-grown LT-GaAs (4.0 ps) than in annealed LT-GaAs (3.5 ps), in which better crystal quality serves longer dephasing time. They explained the longer dephasing time in terms of phonon localization,²²22. T. Dekorsy, H. Kurz, X. Q. Zhou, and K. Ploog, Appl. Phys. Lett. 63, 2899 (1993). https://doi.org/10.1063/1.110291 but the mechanism would lead only to a decrease in the dephasing time.²³23. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, Appl. Phys. Lett. 76, 1258 (2000). https://doi.org/10.1063/1.126002 Even if there were structural modifications, it would lead only to a decrease in the dephasing time, corresponding to the broadening of the Raman line in defective GaAs,²⁹29. M. Kitajima, Crit. Rev. Solid State Mater. Sci. 22, 275 (1997). https://doi.org/10.1080/10408439708241263 being contrary to the present results.

The prolonged dephasing time can be explained by considering the (one)electron-LO phonon coupling^30,3130. N. Dharmarasu, B. Sundarakkannan, R. Kesavamoorthy, K. G. M. Nair, and J. Kumar, Nucl. Instrum. Methods Phys. Res., Sect. B 145, 395 (1998). https://doi.org/10.1016/s0168-583x(98)00510-231. M. Hase, K. Ishioka, M. Kitajima, and K. Ushida, Appl. Phys. Lett. 82, 3668 (2003). https://doi.org/10.1063/1.1578179 or plasmon-LO phonon coupling.^32,3332. F. Vallée, F. Ganikhanov, and F. Bogani, Phys. Rev. B 56, 13141 (1997). https://doi.org/10.1103/physrevb.56.1314133. H. Kunugita, K. Hatashita, Y. Ohkubo, T. Okada, and K. Ema, Opt. Express 23, 19705 (2015). https://doi.org/10.1364/oe.23.019705 The decay rate 1/τ of the coherent LO phonon in defective GaP is given by the sum of the intrinsic anharmonic decay rate 1/τ_anharmonic and the elastic scattering rate due to point defects 1/τ_defect. 1/τ_anharmonic is given by the Klemens formula γ₀[1 + n(ω_TA) + n(ω_LO)],^34,3534. P. G. Klemens, Phys. Rev. 148, 845 (1966). https://doi.org/10.1103/physrev.148.84535. F. Vallée and F. Bogani, Phys. Rev. B 43, 12049 (1991); https://doi.org/10.1103/physrevb.43.12049F. Vallée, Phys. Rev. B 49, 2460 (1994). https://doi.org/10.1103/physrevb.49.2460 where γ₀ is an effective anharmonic constant, n(ω) is the phonon distribution function, and ω_TA and ω_LO are the frequencies of the TA and the LO phonons, respectively. As pointed out earlier,²³23. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, Appl. Phys. Lett. 76, 1258 (2000). https://doi.org/10.1063/1.126002 1/τ_defect is expected to increase linearly with increasing concentration of point defects, 1/τ_defect = ${\gamma }_{{\omega }_{LO}}{N}_d$, where ${\gamma }_{{\omega }_{LO}}$ is a phonon-defect scattering constant and N_d is the density of defects. In photo-excited GaP, the scattering by hot carriers (or photo-generated plasma) should also be taken into account; 1/τ_plasma = $C_{LO}{\omega }_P^2$, where ω_P is the plasma frequency, $C_{LO}=({\omega }_{LO}^2-{\omega }_{TO}^2)/2{\omega }_{LO}^4{\tau }_{\infty }$ is a constant, where ω_TO is the TO phonon frequency and τ_∞ is an average carrier momentum scattering time.³²32. F. Vallée, F. Ganikhanov, and F. Bogani, Phys. Rev. B 56, 13141 (1997). https://doi.org/10.1103/physrevb.56.13141 Since ${\omega }_P^2\propto N$, where N is the carrier density, 1/τ_plasma ∝ N.^32,3632. F. Vallée, F. Ganikhanov, and F. Bogani, Phys. Rev. B 56, 13141 (1997). https://doi.org/10.1103/physrevb.56.1314136. M. Hase, S.-i. Nakashima, K. Mizoguchi, H. Harima, and K. Sakai, Phys. Rev. B 60, 16526 (1999). https://doi.org/10.1103/physrevb.60.16526 In total, the effective decay rate 1/τ can thus be given by

$$\frac{1}{\tau }=\frac{1}{{\tau }_{anharmonic}}+\frac{1}{{\tau }_{defect}}+\frac{1}{{\tau }_{plasma}}.$$

(1)

From the literature, we set 1/τ_anharmonic ≈ 0.08 ps⁻¹ (Ref. 1515. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203), and thus, 1/τ_plasma ≈ 0.04 ps⁻¹ is obtained from the total decay rate of 1/τ ≈ 0.12 ps⁻¹ before Ga ion irradiation. Since the longer dephasing time of 9.1 ps corresponds to 1/τ ≈ 0.11 ps⁻¹ [see the inset of Fig. 4(a)], it is expected that the value of 1/τ_plasma decreases by ≈0.01 ps⁻¹, which is obtained by the difference of 1/τ before and after the ion irradiation, i.e., 0.12 ps⁻¹–0.11 ps⁻¹ = 0.01 ps⁻¹. In addition, because the anharmonic decay channel (1/τ_anharmonic) depends mainly on the distribution of lower lying TA phonons and thus on the lattice temperature, the change in 1/τ_anharmonic is negligibly small in the present study. We would argue that the term 1/τ_plasma decreases over the 1/τ_defect term in the case of GaP after the Ga⁺ ion irradiation, i.e., 1/τ_defect ≪ 0.01 ps⁻¹. This means that the concentration of carriers in the conduction band of GaP was reduced by the carrier trapping via defect states in the bandgap.

To test the above-mentioned hypothesis of the dominant contribution for the prolonged dephasing time from 1/τ_plasma, we show the electro-optic response from GaP in Fig. 5. The transient electro-optic response exhibits a surprisingly ultrashort time scale, i.e., a full width at half maximum (FWHM) of ≈45 fs at zero time delay, corresponding to nearly an autocorrelation function of the laser pulse used (≈25 fs), suggesting the transient signal is dominated by degenerate TPA from the one-pump and one-probe photons.³⁷37. E. Z. Chong, T. F. Watson, and F. Festy, Appl. Phys. Lett. 105, 062111 (2014). https://doi.org/10.1063/1.4893423 We found that the peak intensity of the transient electro-optic response shown in Fig. 5 decreases as the Ga⁺ dose increases. This implies either a depletion of TPA by the deep levels associated with Ga⁺ ions or ultrafast trapping of photogenerated carriers by the deep levels. In photoexcited GaP, the photogenerated electrons decays via intervalley scattering from the zone center (Γ point) into the lower-lying X₁, X₂, and L valleys within only ≈30 fs.³⁸38. J. Sjakste, N. Vast, and V. Tyuterev, Phys. Rev. Lett. 99, 236405 (2007). https://doi.org/10.1103/physrevlett.99.236405 Therefore, the ultrafast electro-optic response (≈45 fs) can be explained by the intervalley scattering just after the TPA, rather than the trapping by deep levels, which usually takes more than several hundred femtoseconds. The carrier density excited via TPA with the one-pump and one-probe photons can be expressed by^39,4039. A. J. Sabbah and D. M. Riffe, Phys. Rev. B 66, 165217 (2002). https://doi.org/10.1103/physrevb.66.16521740. D. C. Hutchings and E. W. Van Stryland, J. Opt. Soc. Am. B 9, 2065 (1992). https://doi.org/10.1364/josab.9.002065

$$N_{TPA}=\frac{\beta I_{pump}{I}_{probe}}{2E_p{\tau }_p},$$

(2)

where β = 2.0 cm/GW (for 830 nm) represents the TPA coefficient,⁴¹41. G. Grinblat, M. P. Nielsen, P. Dichtl, Y. Li, R. F. Oulton, and S. A. Maier, Sci. Adv. 5, eaaw3262 (2019). https://doi.org/10.1126/sciadv.aaw3262 I_pump ≈ 1.19 mJ/cm² (I_probe ≈ 60 μJ/cm²) is the laser fluence of the pump (probe) pulse, E_p = 1.49 eV is the photon energy of the laser used, and τ_p = 25 fs is the pulse length. The carrier response measured for various pump fluences by isotropic reflectivity change (ΔR/R ∝ N_TPA)²⁴24. M. Motojima, T. Suzuki, H. Shigekawa, Y. Kainuma, T. An, and M. Hase, Opt. Express 27, 32217 (2019). https://doi.org/10.1364/oe.27.032217 revealed the linear dependence on I_pump, as shown in Fig. 6(a), indicating the relationship given by Eq. (2). By using the linear fit to the fluence dependence in the inset, we found that β decreased by 40% after irradiation. Hence, we may estimate β after irradiation to be 0.8 cm/GW; this is possible since β depends on the refractive index⁴⁰40. D. C. Hutchings and E. W. Van Stryland, J. Opt. Soc. Am. B 9, 2065 (1992). https://doi.org/10.1364/josab.9.002065 and it would be changed after irradiation as revealed by changing the color of the irradiated area [Fig. 1(b) inset]. We thus estimated the maximum photo-generated carrier density via TPA to be N_TPA ≈ 1.2 × 10¹⁶/cm³ before ion irradiation. We note that the slow carrier decay signal, appearing just after the transient TPA in Fig. 6(b), would represent signal from the carrier plasma scattered from the Γ point to the X₁, X₂, and L valleys, the magnitude of which was decreased after ion irradiation (data not shown but also visible in Fig. 5). Note also that the carrier plasma would interact with coherent LO phonons via Frölich coupling,¹⁵15. K. Ishioka, K. Brixius, U. Höfer, A. Rustagi, E. M. Thatcher, C. J. Stanton, and H. Petek, Phys. Rev. B 92, 205203 (2015). https://doi.org/10.1103/physrevb.92.205203 i.e., the effect of excited carriers through one-pump and one-probe photon induced TPA on the dephasing of the coherent LO phonon was examined by probe-power dependence on the phonon dephasing, which exhibited the decrease in the time constant with increasing probe fluence (data not shown). The decrease in the TPA excited carriers will therefore weaken the plasmon-LO phonon coupling after the intervalley scattering, i.e., after ∼30 fs, resulting in the increase in the dephasing time of the coherent LO phonon (Fig. 4).

In the present case, the energy of the pump photon (E_p = 1.49 eV) approaches the defect-induced deep levels as an intermediate-state. In fact, the anti-site defect of P_Ga, where one Ga site is occupied by a P atom, shows a mid-gap energy level of 1.59 eV from the top of the valence band,⁴²42. M. J. Puska, J. Phys.: Condens. Matter 1, 7347 (1989). https://doi.org/10.1088/0953-8984/1/40/010 which will not allow the pump photon to exactly resonant at the P_Ga level but partly contribute to one-photon absorption at the P_Ga bands (see Fig. 7).⁴³43. R. Zallen and W. Paul, Phys. Rev. 134, A1628 (1964). https://doi.org/10.1103/physrev.134.a1628 Thus, we can conclude that the excited carrier plasma density at the zone center (Γ point) can be decreased by depletion of TPA by nearly resonant one-photon absorption at P_Ga states, whose carriers decay into the underlying Ga_P band.

In summary, we observed the prolonged dephasing time of the coherent LO phonon in Ga ion irradiated GaP by use of the fs pump-probe reflectivity technique. The prolongation of the dephasing time of the coherent LO phonon observed for defective GaP is not intuitive since defects generally promote dephasing. However, we present an effective model for suppression of interaction between the photo-generated carrier plasma and coherent LO phonon caused by quenching of the TPA photo-excited carriers by P_Ga deep levels. Our observation of prolonged dephasing time, which may be called phonon cooling by lattice defects, provides a new insight into controlling the electrical properties of semiconductors for the development of device applications. In addition, the results obtained may be useful for investigating a possible generation of micro- or nano-structures of GaP and even other nonlinear materials by the FIB technique, while the lattice properties are unchanged.