Chirped-pulse manipulated carrier dynamics in low-temperature
molecular-beam-epitaxy grown GaAs
Chao-Kuei Lee, Yuan-Yao Lin, Sung-Hui Lin, Gong-Ru Lin, and Ci-Ling Pan
Citation: Applied Physics Letters 104, 172105 (2014); doi: 10.1063/1.4875027 View online: http://dx.doi.org/10.1063/1.4875027
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/17?ver=pdfcov Published by the AIP Publishing
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Chirped-pulse manipulated carrier dynamics in low-temperature
molecular-beam-epitaxy grown GaAs
Chao-Kuei Lee,1,a)Yuan-Yao Lin,2Sung-Hui Lin,3Gong-Ru Lin,4and Ci-Ling Pan3,5
1
Department of Photonics, National Sun-Yat-Sen University, Kaohsiung 80400, Taiwan 2
Department of Electrical Engineering, Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30010, Taiwan
3
Department of Photonics, National Chiao Tung University, Hsinchu 30010, Taiwan 4
Department of Electrical Engineering, Graduate Institute of Photonics and Optoelectronics, National Taiwan University, No. 1, Roosevelt Road, Sec. 4, Taipei 10617, Taiwan
5
Department of Physics, National Tsing Hwa University, Hsinchu 30010, Taiwan
(Received 24 March 2014; accepted 22 April 2014; published online 1 May 2014)
Chirped pulse controlled carrier dynamics in low-temperature molecular-beam-epitaxy grown GaAs are investigated by degenerate pump-probe technique. Varying the chirped condition of excited pulse from negative to positive increases the carrier relaxation time so as to modify the dispersion and reshape current pulse in time domain. The spectral dependence of carrier dynamics is analytically derived and explained by Shockley-Read Hall model. This observation enables the new feasibility of controlling carrier dynamics in ultrafast optical devices via the chirped pulse excitations.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4875027]
Selective carrier population transfer using chirped pulses has been extensively studied based on their potential applica-tions in various areas, such as optical quantum control,1–8 spectroscopy,9and Bose-Einstein condensates.10The chirped pulse control of carriers in direct band-gap semiconductors was discussed11to enable the optimization ultrafast optoelec-tronic devices under chirped pulse illumination. In 1980s, Ippenet al. reported the chirp dependent relaxation dynamics pumped by either positively chirped or negatively chirped pulses.12Yet, no clear discussion on the mechanisms related to carrier dynamics excited and controlled by chirped optical pulses is addressed. Among the ultrafast optoelectronic mate-rials to be studied, either the low-temperature molecular-beam-epitaxy (MBE) grown GaAs (LT-GaAs)13 or the ar-senic-ion-implanted GaAs (GaAs:Asþ)14–16is potentiate for
ultrafast photonic devices because of its high mobility, short carrier lifetime, and high breakdown voltage. In the late 1990s, several groups have developed rate equation sets for LT-GaAs, which accurately predicted the carrier dynamics through a wide scanning on intensities and wavelengths of excitation pulse.17–19
In this Letter, we present a systematic investigation of the carrier dynamics controlled by pulse excitation with varying chirp. The change on lifetime of excited carriers under pulse excitation with different chirps, the simplified rate equation model based on the band diagram of LT-GaAs, and the phenomenal explanation on the spectrally dependent carrier dynamics are addressed. The modified rate equation considers the absorption due to population in valance band via single and two photon processes and the contribution of mid-gap states. We present the model in a semi-classical
pic-Figure1shows the band diagram of LT-GaAs used in this paper. In principle, when LT-GaAs is excited by femtosecond optical pulses with photon energies above the band gap, elec-trons are mostly excited to the upper state (excited state) of the conduction band with high thermal energy. The free car-riers in the conduction band can either be trapped by the mid-gap state or relax to the bottom of the conduction band. The free carriers in the bottom of the conduction band also can be trapped by mid-gap states. The two-photon absorption process and mid-gap state absorption process are neglected here due to the selection of excitation photon energy.
The carrier dynamics for LT-GaAs can be described by the following equations:
dn dt ¼ Ia h n s1 n s2 ; (1) dN dt ¼ n s2 N s3 ; (2)
where n is the population of carriers at the upper state of the conduction band, N is the population of carriers at the
bottom of the conduction band, I is the intensity of the exci-tation pulse, a is the band to band absorption coefficient, h is the photon energies, s1is the carrier trapping time from
the upper state of the conduction band to the mid-gap state, s2is the carrier cooling time in the conduction band, and s3
is the carrier trapping time from the bottom of the conduc-tion band to the mid-gap state.
Since the refractive index change in the semiconductor material is proportional to the carrier density in the conduc-tion band, the carrier dynamics in LT-GaAs can be recorded by a time resolved pump-probe reflectivity measurement. A Ti:sapphire oscillator operating at 800 nm with central pho-ton energy of 1.55 eV. The FWHM bandwidth of the laser pulse is 10 nm and the associated transform-limited pulse du-ration is around 90 fs in FWHM. The pulse dudu-ration of the pump beam was tailored by a zero dispersion pulse compres-sor consisting of a pair of gratings 600 g/mm, two parabolic reflectors with a focal length 37.5 cm, and a liquid crystal spatial light modulator (CRI, SLM-128 phase mode). The pump beam was focused down to 100 lm or 20 lm with two different objective lenses and the incident angle was 25 off normal. The probe beam had 1 mW average power and the incident angle was 55. The transient reflectivity, indicating
the population of free carriers in the conduction band, was recorded as a function of the time delay between two pulses and the carrier relaxation times were retrieved by fitting the signal with Eqs. (1) and(2). The experimental setup of the femtosecond pump-probe system with excitation chirp con-trolled pump beam is schematically shown in Fig.2.
Results for the LT-GaAs sample at low pump fluence of 5 103MW/cm2are presented in Fig. 3. The two chirped excitation conditions, 68000 fs2 at rising regions exhibit equivalent pulsewidth; however, the falling region under pos-itive chirped excitation is larger than the negative one. The carrier relaxation times s1, s2, and s3, are retrieved from
ex-perimental data with a de-convolution procedure via Eqs.(1)
and(2). Apparently, the trend of experimental data (see green lines in Fig.3) reveals that all three relaxation times increase as the quantity of excitation chirp increase from negative to positive, as shown in Figs.3(b)–3(d). We attribute this behav-ior to the spectrally dependent carrier dynamics in LT-GaAs, and similar discussions were mentioned by Ippenet al. previ-ously.12,22The bandgap dependent carrier trapping time was correlated with the gross effect of possible scattering chan-nels depending on the photon energy. Horng et al. also observed shorter carrier cooling time in GaAs under excita-tions at low central wavelength.21–23The consistent observa-tions from two different groups result from the fact that the photo-excited carriers with sufficient excess kinetic energy is able to induce the optical phonon vibration. Especially, when the hot carriers are excited to upper state of conduction band by absorbing high-energy photons, jumping to above bandgap with an excess kinetic energy of smaller than 300 meV is mandatory to screen out the split-off band transition and also to reduce the probability of inter-valley scattering.
Despite the chirp dependent absorption due to intra-pulse pump-dump process and bandgap renormalization,24 we propose a model to explain the carrier relaxation time FIG. 2. The experimental setup of excitation chirp controlled pump probe
system.
FIG. 3. (a) Normalized transient reflec-tivity signals with pump fluence 5 103MW/cm2
and chirped condi-tions 68000 fs2. (b)–(d) Carrier life-times s1, s2, and s3 as a function of
excitation chirp with green lines indi-cating the increasing trend.
increment as a function of the excitation chirp (when increas-ing from negative to positive). Under a positively chirped ex-citation, the photo-excited carriers with low excess kinetic energy are generated first, which exhibit long carrier cooling time corresponding to low thermal velocities. These elec-trons eventually leads to a weak carrier diffusion based on the Shockley-Read-Hall (SRH) model.25The subsequent car-riers with higher thermal velocities will diffuse faster to spa-tially overlap the former excited carriers. This results in a local increase of photo-carrier density in LT-GaAs and long carrier trapping time s1, as a consequence of band filling and
the reduction of the rate of trapping occupancy inferred by SRH model.26 With a negatively chirped excitation, the photo-excited carriers lagged behind the peak excitation have lower thermal velocities than the former and free car-ries spreading out in space. At last stage, these interactions decrease photo-excited carrier density and cause shorter car-rier trapping time s1. Therefore, the carrier trapping times s1
increase with enlarging excitation chirp from negative to positive. Following the same chirping dependent local den-sity variation, the carrier trapping time s3for the population
in the bottom of conduction band also lengthens with enlarg-ing chirp of excitation.
To reinforce, the illustration on the carrier dynamics in the LT-GaAs under the transient excitation by femtosecond laser pulses with varying signs of chirp is shown in Fig.4. In principle, the hot carrier cooling time can be reduced when increasing the pumping photon energy to slightly above band-gap. For a positive chirped excitation, carriers with long cooling time are generated first. At this moment, only few op-tical phonons are excited. Although the subsequently excited carriers exhibit short cooling time with a stronger
carrier-phonon interaction,20carriers are obstructed during period of relaxation. This eventually lengthens the carrier cooling time s2. On the contrary, when excited by negatively chirped
opti-cal pulse, the leading carriers induce large optiopti-cal phonon population that is able to scatter the subsequent carriers and results in short cooling time s2. In our experiment, even the
inter-valley scatterings from C to L still occurs even with an excessive photon energy of only 0.12 eV, but these scatter-ings fail to favor lengthen hot carrier cooling time. The result clearly elucidates that the carrier dynamics can be manipu-lated with chirped excitation, indicating the feasibility of con-trolling carriers in samples by chirped pulses.
In addition, the dynamic responses under various excita-tion intensities are also investigated, since the chirp depend-ence can be attributed to spatial photo-carrier density variation. By varying pump power and focus length, the chirp dependent carrier trapping time (s1) at various pump fluence is obtained,
as shown in Fig.5. The carrier trapping time boosts as the ex-citation fluence increases, and the chirped dependency become significant at high pump fluence. From the modified SRH model, the trapping ability of defects goes down such that car-rier trapping time increases at high excitation density. Therefore, the carrier trapping times s1boost as the excitation
fluence increases. This eventually results in the coupling strength between carriers enhanced at high excitation density. Therefore, the rising chirped dependency is straightforward.
In conclusion, the excitation chirp dependent carrier relaxation time variation is observed, which lengthens the carrier relaxation process by detuning the chirp of excitation from negative to positive. The chirped pulse excitation pump-probe analysis elucidates the spectral dependence of carrier dynamics in LT-GaAs, which discloses the feasibility of controlling carrier dynamics in ultrafast semiconductor with chirped pulses. The introduction of chirping excitation directly re-arranges the photon energy distribution in time domain and creates an environment to be in favor of some specific interactions. This approach should be applicable in FIG. 4. The schematic illustration of the carrier dynamics in LT-GaAs under the excitation by femtosecond laser pulses with varying sign of chirp.
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