Open Access
Add to BibSonomyAbstract
We have investigated coherent LO phonon properties in zinc-based II–VI widegap semiconductors, focusing on phonon-plasma coupled modes. By a careful treatment of the time evolution of the signals in ZnS, ZnSe, and ZnTe, we found a frequency upshift as the pump intensity increases. Using a classical coupled oscillator model, we have explained the pump intensity dependence of both the shift and the decay rates by a mixing of highly damped two-photon generated plasma. From the linear dependence between them we can estimate the photo-excited carrier mobilities, leading to a new powerful estimation method to measure the mobility.
© 2015 Optical Society of America
1. Introduction
Advances in ultrashort optical pulse generation technologies over the last few decades have opened new areas for study in physics and material sciences. One of such studies is coherent phonon spectroscopy [1–4]. Irradiation of much shorter optical pulses than the atomic vibration period in solids or molecules makes it possible to create in-phase collective motion of atoms. So far, coherent phonons have been observed in various materials using pump-probe techniques. In such measurements, in contrast to spontaneous Raman studies, the temporal profiles of lattice dynamics can be directly studied.
Since sensitive pump-probe measurements in GaAs were first reported [5], interest in coherent phonons in various semiconductors has grown. Furthermore, the time evolution of phonon-plasma coupled modes in carrier doped semiconductors have been intensively investigated [6–11]. The contribution of photo-generated and chemically-doped carriers to the properties of phonon-plasma coupled modes were discussed [10], and the carrier mobility [7] and its effective mass [9] was determined from the profiles of the phonon-plasma coupled modes. It has been suggested that the bandgap renormalization caused by a dense electron-hole plasma is one of the events triggering the lasing action in semiconductors [12], therefore it is meaningful to explore a new probe tool for photo-generated plasma states in semiconductors.
In this paper, we study coherent LO phonon properties in zinc-based II–VI widegap semiconductors, focusing on phonon-plasma coupled modes. In many widegap semiconductors including II–VI semiconductors, coherent LO phonons have been investigated with photons with energies below the bandgap [13–16]. We performed conventional nonresonant transmission pump-probe measurements for ZnS, ZnSe, and ZnTe single crystals. By a careful treatment of the time evolution of the signals, we have concluded that the observed intensity dependences of the coherent phonon decay are due to the coupling between phonons and a strongly damped plasma (Fig. 1). Through a theoretical analysis using a simple model, we have succeeded in the determination of the mobility of photo- excited carriers from derived damping rates. This determination process can be applied even to materials which are difficult to be doped and is characterized by a non-contact measurement of important carrier properties. The investigation of carrier mobilities in II–VI semiconductors has not been fully conducted because of the difficulty of chemical doping, although II–VI semiconductors have been thought to have a great potential for application such as visible-to-ultraviolet wavelength lasers. Therefore our method is a highly effective approach to developing new materials for electronic devices in addition to its intrinsic attractive scientific interest.
Fig. 1 Excitation and detection of photo-generated coherent LO phonon-plasma coupled modes by a transmission pump-probe measurement. While passing through the transparent medium, the pump pulse generates the coherent LO phonon and the two-photon excited carriers. The delayed probe pulse rides the coupled wave [17] and feels the delay-dependent change of the refractive index since the phase velocity of the coupled mode is equal to the group velocity of the pump and probe pulses.
2. Experimental setup
To obtain pulses with durations sufficiently shorter than the period of lattice vibration, we used a home-built noncollinear optical parametric amplifier (NOPA) pumped by a flash-lamp-excited Ti:Sapphire amplified laser system (Clark-MXR CPA-2001, 1 kHz repetition rate at 775 nm central wavelength and 150 fs pulse duration). The output pulses of the NOPA was compressed to 20–35 fs by a pair of BK7 prisms.
The samples used in this study were 10 × 10 × 1mm3 (100) ZnS, ZnSe, and ZnTe single crystal plates with zincblende structure (supplied by RMT Ltd), which were cooled by a liquid nitrogen optical cryostat for the measurements. As was reported in previous coherent phonon studies in widegap semiconductors [13,15,16], a transmission electro-optic sampling technique was used in this study. To emphasize the probe spectral modulation peculiar to the coherent phonon signal from a transparent medium [4, 18], we used an interference filter to pick up a part of the spectrum of the probe pulse. The filtered signal was divided into components that were parallel and perpendicular to the pump polarization. The intensity difference between these components was lock-in detected as a function of the delay time between pump and probe pulses. For this orientation, the LO mode was allowed [19] while the TO mode was forbidden.
3. Results and discussion
Figure 2 shows typical results of coherent phonon measurements for ZnS, ZnSe, and ZnTe. By subtracting the smoothed signal (non-oscillating signal) from the raw data, we obtained the small oscillating components present beyond the intense peaks close to zero delay (Fig. 2 insets). The frequencies of these oscillations correspond to those of LO phonons in each sample [20].
Fig. 2 Typical results for the coherent phonon signal in ZnS, ZnSe, and ZnTe measured at 77K. (ΔT‖ − ΔT⊥)/T is plotted as a function of delay time. In the case of the ZnS and ZnSe measurements the center wavelength of the pump and probe pulses were 570nm and 530nm, respectively while to avoid a resonant band transition by the spectral tail of the pulse, the center wavelength was set to 600nm in the ZnTe measurements.
Coherent phonon measurements are suitable for the precise detection of frequency change because the frequency accuracy is limited only by the uncertainty of the delay time between pump and probe pulses [21]. In our experiments, only the LO phonon mode contributes to the signal, and we could obtain the frequencies and decay rates for various pump intensities by a nonlinear least squares fitting method using a simple damped oscillating function A = A0 exp [−Γt] sin [ωt + ϕ].
Figure 3 shows the obtained frequency and decay time for ZnS as a function of pump intensity. As was found in studies on other semiconductors, we observed increasing decay rates of the coherent phonon signals as the intensity of the pump pulse increased. This phenomenon has been often attributed to an interaction between the LO phonon and multi-photon-excited carriers. Considering a classical harmonic lattice, however, the oscillation frequency of the signal ( ) should show a downshift if its decay rate increases. Contrary to this expectation, the center frequencies also increase with the pump intensity. Therefore we conclude that the increasing decay rate cannot be explained by the simple harmonic lattice model.
Fig. 3 Decay time and frequency of the observed coherent LO phonon signal in ZnS as a function of pump pulse intensity.
From a careful consideration of the scattering process between a coherently generated LO phonon and two-photon excited incoherent carriers, we can see that the assignment of the increasing decay rates to LO phonon scattering of the excited carriers is unlikely. In transmission type experiments, the phase velocity of a generated phonon is equal to the group velocity of the pump pulse [17]. This means the wavevector of the phonon is in the vicinity of the Γ point. Two-photon excited carriers involved in a coherent phonon generation process decay rapidly to the bottom (top) of the conduction (valence) band for electrons (holes). In that case, their momenta are almost zero if the carrier density is low enough. Therefore considering the dispersion of valence or conduction bands, we can see that the scattering between LO phonon and single carriers is forbidden by energy and momentum conservation [22].
As the origin of the “hardening” in our measurements, we consider photogenerated phonon-plasma coupling. It is known that in highly doped semiconductors, ionic bonding is shielded and the lattice oscillation frequency becomes close to that of a TO phonon. There is a lot of work discussing such coherent phonon-plasma coupled modes, and a recent study shows the possibility of controlling carrier transport [6]. However, to our knowledge, the intrinsic influence of the photo-generated phonon-plasma coupling on the coherent phonon have never been discussed although the decay change of the LO phonon signal in coherent anti-Stokes Raman measurements of semiconductors was attributed to mixing of plasma [23–25]. It was shown in Ref. [24] that the decay time is sensitive to the carrier density even in the low-density (∼ 1016/cm3) regime.
In II–VI semiconductors, the damping of carrier motion is large because of the strong polaron effect. Therefore, contrary to most of the phonon-plasma coupling studies in the Raman or time-domain measurements for other materials, the carrier damping rate should be considered in our study. In the limit of large carrier damping, the upper mode frequency of the coupled mode is insensitive to the carrier density [26]. As shown in Fig. 3, the relative change in the frequency (Δω/ω) was quite small compared to that in the decay time in our results, indicating that large carrier damping was occurring. It should be noted that the lower-branch (plasma-like) signal vanishes in the case of over-damped plasmon with sufficiently low carrier density [26–28].
Hereafter, we concentrate on the relationship between the frequency shift and the change in the decay rate (the inverse of the decay time) of the coherent phonon signals. Although Lindhard-Mermin model is often used for analysis of the coupled modes in Raman studies [29, 30], we used a classical Drude oscillator model. This is because, in contrast to ”backscattering” Raman measurements, the coupled modes observed here were generated by forward impulsive Raman processes, and the phase velocities of the observed modes are much larger than the carrier Fermi velocity.
The electric displacement of the LO phonon and plasma oscillation is zero, since both have a longitudinal polarization. Separating the longitudinal lattice displacement from the transverse part [31], and considering the interaction with the electron-hole plasma through the polarization field [23], coupled equations of motion for both carriers and the lattice system are available.
Here x and W are longitudinal components of the carrier and lattice displacement, respectively. ωp is the plasma frequency and ωLO is the LO phonon frequency. γ and ΓLO are damping rates of carrier and lattice motion. m* is the averaged effective mass of photo-excited carriers (shown below). M and e* are the reduced mass and effective charge of ions, respectively. N and n are the number density of the ions and the carriers. In the above model, we regarded the carrier density as constant because the luminescence lifetime of the same samples measured by a streak camera was a few 100ps which is sufficiently longer than the decay time of the coherent phonon signals.
First, we consider trial functions (x, W ∝ exp[−iωt]). Supposing that the frequencies of both plasma and lattice motion are the same (≈ ωLO) and the time derivative of the amplitude of plasma motion is negligible, we obtained the following relationship between the plasma and lattice displacements from equation (1).
Substituting into equation (2), and using the relationship, gives following equation. where ωTO is the TO phonon frequency. Considering the sinusoidally damped lattice motion W (t) = W0 exp [−Γtotalt] exp [−iω+t] and Γtotal ≪ ω+, we can finally obtainTheoretical frequency and decay rate calculated from these equations (Fig. 4(a) and 4(b)) are in good accordance with the properties of the strongly damped plasmon-LO phonon oscillations [32, 33]. Using the reported two photon absorption coefficients [34, 35] and ignoring the group velocity dispersion of the propagating pump pulse in the media, the maximum carrier density in our experimental condition was estimated to be at most in the mid- 1016/cm3 range. In the limit where the carrier density is low, we can see that the damping rate of the mode is proportional to its frequency (Fig. 4(c)).
Fig. 4 Theoretical frequency (a) and decay rate (b) of the coupled modes as functions of plasma frequency for different carrier damping rate using phonon parameters for ZnS in Ref. [20]. (c) Decay rate versus frequency of the coupled mode for low plasma frequency limit.
As shown in Fig. 5, this linearity was reproduced for ZnS, ZnSe, and ZnTe, and using the frequencies for the weak pump pulse limit, we can deduce the damping rates for both lattice and electron systems in each material as shown in Table 1.
Fig. 5 Decay rates versus frequencies of the coherent phonon signal in Zn-based semiconductors measured for various pump intensities.
Table 1. Damping rates for longitudinal lattice and carrier motion at 77K.
Because of the difficulties of carrier doping, there are few studies on carrier mobilities in ZnS, ZnSe and ZnTe. A possible method for determining the carrier mobilities is estimation from the plasma damping rates using the well-known relation μ = e/m*γ. By conventional Raman measurements and through more complicated analytical processes, the plasma damping rates for highly damped carriers have been determined [27, 28, 32, 36]. The calculated carrier mobilities from these damping rates were reported to be consistent with Hall measurements in various semiconductors such as GaP [27], ZnO [36], SiC [28], and GaAs [32]. Therefore we can estimate the mobilities for ZnS, ZnSe, and ZnTe from the obtained damping rates. In the estimation, we used conductive effective masses [37] and applied the values in Ref. [38],
and obtained values are μZnS = 68cm2/Vs, μZnSe = 210cm2/Vs, μZnTe = 420cm2/Vs.These are in relatively good agreement with each of the reported Hall mobilities at room temperature [39–42]. However, in general, considerably enhanced carrier mobilities are theoretically expected at around 100K where the thermal phonon effects decrease. In fact, the Hall mobility of ZnSe at the same temperature is reported to be 3000–10000 [40] which is one order larger than our result. This discrepancy may come from the fact that we do not consider excitonic effects even though such electron-hole interactions are present in low temperature measurements. A high damping rate especially for ZnS may originate from a shortening of the effective carrier relaxation time as a result of thermal equilibrium between free carriers and excitons. A complete understanding of the temperature dependence of such dynamics will lead to new insights into transition between excitons and free carriers. We believe that the new estimation technique for photo-generated carrier mobility we presented here will become a powerful tool for such investigations. It should be noted that our method for mobility determination does not require an accurate estimation of the carrier density which is usually difficult in transmission pump-probe measurements.
4. Conclusions
In conclusion, we have demonstrated a new method for measuring photo-excited carrier mobility from a transmission pump-probe coherent phonon study using polar zinc-based semiconductors. We elucidated that the origin of the increasing decay rate with increasing pump intensity is phonon-plasma coupling. Using a classical coupled harmonic oscillator model, we have explained the linear dependence of the frequency shift to the change in decay rates.
References and links
1. T. Dekorsy, G. Cho, and H. Kurz, “Coherent phonons in condensed media,” in “Light Scattering in Solids VIII,” vol. 76 of Topics in Applied Physics, M. Cardona and G. Gntherodt, eds. (Springer BerlinHeidelberg, 2000), pp. 169–209. [CrossRef]
2. A. Kuznetsov and C. Stanton, “Theory of coherent phonon oscillations in bulk GaAs,” in Ultrafast Phenomena in Semiconductors, K.-T. Tsen, ed. (SpringerNew York, 2001), pp. 353–403. [CrossRef]
3. L. Dhar, J. A. Rogers, and K. A. Nelson, “Time-resolved vibrational spectroscopy in the impulsive limit,” Chem. Rev. 94, 157–193 (1994). [CrossRef]
4. R. Merlin, “Generating coherent THz phonons with light pulses,” Solid State Commun. 102, 207–220 (1997). [CrossRef]
5. G. Cho, W. Kütt, and H. Kurz, “Subpicosecond time-resolved coherent-phonon oscillations in GaAs,” Phys. Rev. Lett. 65, 764–766 (1990). [CrossRef] [PubMed]
6. M. Hase, D. Hayashi, and J. D. Lee, “Control of carrier transport in GaAs by longitudinal-optical phonon-carrier scattering using a pair of laser pump pulses,” J. Appl. Phys. 109, 073715 (2011). [CrossRef]
7. M. Hase, “Carrier mobility in a polar semiconductor measured by an optical pump-probe technique,” Appl. Phys. Lett. 94, 112111 (2009). [CrossRef]
8. O. V. Misochko and T. N. Fursova, “Coupled phonon-plasmon modes in indium phosphide observed by an ultrafast pump-probe technique,” J. Phys. Condens. Matter 17, 5577–5585 (2005). [CrossRef]
9. Y.-M. Chang, H. W. Chu, C.-H. Shen, H.-Y. Chen, and S. Gwo, “Determination of the electron effective mass of wurtzite InN by coherent upper-branch A1(LO) phonon-plasmon coupling mode,” Appl. Phys. Lett. 90, 072111 (2007). [CrossRef]
10. G. Cho, T. Dekorsy, H. Bakker, R. Hövel, and H. Kurz, “Generation and Relaxation of Coherent Majority Plasmons,” Phys. Rev. Lett. 77, 4062–4065 (1996). [CrossRef] [PubMed]
11. K. Ishioka, A. Basak, and H. Petek, “Allowed and forbidden Raman scattering mechanisms for detection of coherent LO phonon and plasmon-coupled modes in GaAs,” Phys. Rev. B 84, 235202 (2011). [CrossRef]
12. C. Klingshirn, Semiconductor Optics (Springer BerlinHeidelberg, 2007). [CrossRef]
13. Y.-S. Lim, S.-C. Yoon, K.-J. Yee, Y.-H. Ahn, E. Oh, and J.-H. Lee, “Coherent optical phonon oscillations in cubic ZnSe,” Appl. Phys. Lett. 82, 2446 (2003). [CrossRef]
14. I. H. Lee, K. J. Yee, K. G. Lee, E. Oh, D. S. Kim, and Y. S. Lim, “Coherent optical phonon mode oscillations in wurtzite ZnO excited by femtosecond pulses,” J. Appl. Phys. 93, 4939 (2003). [CrossRef]
15. K. Yee, K. Lee, E. Oh, D. Kim, and Y. Lim, “Coherent Optical Phonon Oscillations in Bulk GaN Excited by Far below the Band Gap Photons,” Phys. Rev. Lett. 88, 105501 (2002). [CrossRef] [PubMed]
16. Y.-S. Lim, S.-C. Yoon, K.-J. Yee, J.-H. Lee, D. Kim, and D. Lee, “Coherent phonon oscillations excited by second-order Raman scattering in CdZnTe multiple quantum wells and cubic ZnTe,” Phys. Rev. B 68, 153308 (2003). [CrossRef]
17. Y.-X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391 (1985). [CrossRef]
18. K. Mizoguchi, R. Morishita, and G. Oohata, “Generation of Coherent Phonons in a CdTe Single Crystal Using an Ultrafast Two-Phonon Laser-Excitation Process,” Phys. Rev. Lett. 110, 077402 (2013). [CrossRef] [PubMed]
19. Y. Kasai, D. Suzuki, H. Kunugita, and K. Ema, “Resonantly excited coherent optical phonons in wide-gap semiconductor ZnTe,” J. Lumin. 129, 1820–1823 (2009). [CrossRef]
20. J. Serrano, A. Cantarero, M. Cardona, N. Garro, R. Lauck, R. Tallman, T. Ritter, and B. Weinstein, “Raman scattering in β-ZnS,” Phys. Rev. B 69, 014301 (2004). [CrossRef]
21. C. Aku-Leh, J. Zhao, R. Merlin, J. Menéndez, and M. Cardona, “Long-lived optical phonons in ZnO studied with impulsive stimulated Raman scattering,” Phys. Rev. B 71, 205211 (2005). [CrossRef]
22. N. D. Fatti, F. Ganikhanov, P. Langot, R. Tommasi, and F. Vallée, “Optical Phonon Coherence and Population Decays in III–V Semiconductors,” J. Nonlinear Opt. Phys. Mater. 07, 271–289 (1998). [CrossRef]
23. G. Smith, T. Juhasz, W. Bron, and Y. Levinson, “Interaction of an electron-hole plasma with optical phonons in GaP,” Phys. Rev. Lett. 68, 2366–2369 (1992). [CrossRef] [PubMed]
24. F. Vallée, F. Ganikhanov, and F. Bogani, “Dephasing of LO-phonon-plasmon hybrid modes in n-type GaAs,” Phys. Rev. B 56, 13141–13146 (1997). [CrossRef]
25. W. Bron, S. Mehta, J. Kuhl, and M. Klingenstein, “Interaction of optical phonons with a one-component plasma,” Phys. Rev. B 39, 12642–12648 (1989). [CrossRef]
26. H. Yugami, S. Nakashima, K. Sarai, H. Kojima, M. Hangyo, and A. Mitsuishi, “Raman scattering from plasmon-LO-phonon coupled modes in n-ZnSe,” J. Phys. Soc. Japan 56, 1881–1889 (1987). [CrossRef]
27. G. Irmer, V. V. Toporov, B. H. Bairamov, and J. Monecke, “Determination of the charge carrier concentration and mobility in n-gap by Raman spectroscopy,” Phys. Status Solidi B 119, 595–603 (1983). [CrossRef]
28. S. Nakashima, T. Kitamura, T. Mitani, H. Okumura, M. Katsuno, and N. Ohtani, “Raman scattering study of carrier-transport and phonon properties of 4H-SiC crystals with graded doping,” Phys. Rev. B 76, 245208 (2007). [CrossRef]
29. M. Ramsteiner, J. Wagner, P. Hiesinger, K. Köhler, and U. Rössler, “Raman spectroscopic and Hall effect analysis of the free electron concentration in GaAs with ultrahigh silicon doping,” J. Appl. Phys. 73, 5023 (1993). [CrossRef]
30. L. Artús, R. Cuscó, J. Ibáñez, N. Blanco, and G. González-Díaz, “Raman scattering by LO phonon-plasmon coupled modes in n-type InP,” Phys. Rev. B 60, 5456–5463 (1999). [CrossRef]
31. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1998).
32. G. Irmer, M. Wenzel, and J. Monecke, “Light scattering by a multicomponent plasma coupled with longitudinal-optical phonons: Raman spectra of p-type GaAs:Zn,” Phys. Rev. B 56, 9524–9538 (1997). [CrossRef]
33. Y.-M. Chang, “Interaction of electron and hole plasma with coherent longitudinal optical phonons in GaAs,” Appl. Phys. Lett. 80, 2487 (2002). [CrossRef]
34. M. Yin, H. Li, S. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single z-scan method,” Appl. Phys. B 70, 587–591 (2000). [CrossRef]
35. M. Balu, L. a. Padilha, D. J. Hagan, E. W. Van Stryland, S. Yao, K. Belfield, S. Zheng, S. Barlow, and S. Marder, “Broadband Z-scan characterization using a high-spectral-irradiance, high-quality supercontinuum,” J. Opt. Soc. Am. B 25, 159 (2008). [CrossRef]
36. B. H. Bairamov, a. Heinrich, G. Irmer, V. V. Toporov, and E. Ziegler, “Raman study of the phonon halfwidths and the phonon-plasmon coupling in ZnO,” Phys. Status Solidi (B) 119, 227–234 (1983). [CrossRef]
37. J. Kardontchik and E. Cohen, “Raman Scattering from Plasmons in Photoexcited GaP,” Phys. Rev. Lett. 42, 669–672 (1979). [CrossRef]
38. S. Adachi, Properties of Group-IV, III–V and II–VI Semiconductors, (Wiley, 2005), Chap. 7.
39. S. Adachi, Properties of Group-IV, III–V and II–VI Semiconductors, (Wiley, 2005), Chap. 12, p. 406.
40. M. Aven, “High Electron Mobility in Zinc Selenide Through Low-Temperature Annealing,” J. Appl. Phys. 42, 1204 (1971). [CrossRef]
41. D. Rode, “Electron Mobility in II–VI Semiconductors,” Phys. Rev. B 2, 4036–4044 (1970). [CrossRef]
42. S. Fujita, H. Mimoto, H. Takebe, and T. Noguchi, “Growth of cubic ZnS, ZnSe and ZnSxSe1−x single crystals by iodine transport,” J. Cryst. Growth 47, 326–334 (1979). [CrossRef]
