Time-resolved terahertz spectroscopy

 

The transient nature of a THz pulse, combined with the perfect synchronization with a femtosecond optical pulse makes it ideal to use in optical pump – THz probe experiments. The technique, dubbed time-resolved terahertz spectroscopy or TRTS for short, enables one to examine the dynamic properties of a material in the THz region following optical excitation with sub-picosecond resolution. This is an extremely powerful technique for examining charge carrier dynamics in photoactive materials such as semiconductors and their nano-structures.

There are two modes of operation in TRTS, labeled by the number of time-axes required for data aquisition.

  1. 1-D scans (differential transmission of the THz pulse at a single point in time on the THz waveform, for example the peak.)
  2. 2-D scans (full frequency resolved scans recording the entire THz waveform, at variable pump-probe delay.

2-D scans

In 2-D TRTS, the goal is to obtain the time evolution of the frequency dependent amplitude and phase change of the THz pulse due to photoexcitation of the sample with a femtosecond optical pulse. This provides the maximum amount of information obtainable from a TRTS experiment. A reference THz pulse, ( Eref ) is measured in the absence of the pump pulse. The delay lines are then set so the pump pulse arrives at the sample by a known time τ before the THz pulse, exciting the sample into a non-equilibrium state. The transmitted THz pulse Epump(τ) then undergoes an amplitude and phase change containing a signature of the motion of charges in the material at that instant in time. The change in THz pulse transmission, -ΔE(τ) = Eref (τ) – Epump(τ), is what is recorded in practice. At each pump-probe delay time τ, -ΔE(τ) and Eref scans are recorded, and a 2-D map is built in the time domain as is shown in Fig. 1.

GaAsLayout

Figure 1: (a) 3-D surface plot of the modulation of the THz pulse for various pump-probe delays. (b) Surface projection of -ΔE(τ) with one-dimensional cuts indicated. (c) Cut A is a 1-D projection showing the evolution of the transmission of the peak-ΔE(τ), illustrating the dynamics of the photoexcitation and (d) Cut B is a 1-D projection showing the modulation -ΔE(τ=2.8 ps), or 2.8 ps after excitation.

To obtain the frequency dependent complex conductivity, one takes a horizontal cut along Fig. 1b as well as a reference scan, shown in Fig. 2, providing the complex transmission function at a single pump-probe delay time. Fourier transformation of the THz waveforms gives the complex transmission function FFT{Epump}/FFT{Eref}= T(ω,τ) = ¦T(ω,τ)¦ exp{iφ(ω,τ)} which in turn can be related to the complex conductivity σ(ω,τ) of the photoexcited region, shown in Fig. 3.

GaAsExampleTD

Figure 2: Time domain data at a single pump-probe delay time.

GaAsSigma

Figure 3: Extracted complex conductivity for a thin layer of photoexcited GaAs. The data are fit by a simple Drude model.

Thus the ultrafast evolution of transport parameters such as the mobility and carrier density, two fit parameters in the Drude model, can be determined with unparalleled resolution following photoexcitation.

1-D scans

While 2-D scans contain the most information, it takes a long time to acquire the data. An alternative is to take 1-D scans  to provide information on the dynamics (Cut A, Fig. 1(c)). Fig. 4 shows a 1-D vertical cut giving the dynamics of the differential transmission of the THz peak for two different excitation wavelengths. The difference in risetimes is due to intervalley scattering, which is  energetically possible for 400 nm excitation, but not 800 nm excitation. It takes several ps for excited electrons to scatter back to the high mobility gamma valley, leading to a longer buildup of the maximum sample conductivity for the 400 nm excitation. Thus these scans provide valuable information on the dynamics of charge carriers, from creation to relaxation, in a photoexcited medium with sub-picosecond resolution and in a totally non-contact manner.

GaAsRisetimeWavelengths

Figure 4: Differential THz transmission of GaAs after 400 and 800 nm excitation.

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