## Abstract

A transmission-grating-modulated time-resolved pump-probe absorption spectroscopy is developed and formularized. The spectroscopy combines normal time-resolved pump-probe absorption spectroscopy with a binary transmission grating, is sensitive to the spatiotemporal evolution of photoinjected carriers, and has extensive applicability in the study of diffusion transport dynamics of photoinjected carriers. This spectroscopy has many advantages over reported optical methods to measure diffusion dynamics, such as simple experimental setup and operation, and high detection sensitivity. The measurement of diffusion dynamics is demonstrated on bulk intrinsic GaAs films. A carrier density dependence of carrier diffusion coefficient is obtained and agrees well with reported results.

© 2012 OSA

## 1. Introduction

Nowadays, most of electronic devices work relying on transport of charge carriers. Consequently, an experimental investigation of the transport dynamics of carriers, including diffusion and/or drift dynamics, is an important way to understand response rate of the devices and fundamental transport mechanisms of carriers in semiconductor materials. Then, the development of both simple and high efficient measurement techniques becomes very necessary. Optical measurement techniques reported so far on carrier transport dynamics mainly include the diffraction of transient gratings [1, 2], spatiotemporal scanning of tightly focused pump and probe spots [3, 4] and spatial profiling of luminescence [5, 6]. The first technique, the diffraction of transient grating, requires a pair of time-synchronized pump laser pulses to generate a transient carrier density grating in a sample, while a time-delayed probe laser pulse is employed to detect the decay dynamics of the transient grating by diffraction effect. One primary disadvantage of this method is too weak diffraction signal to be detected, so that optical heterodyne amplification has to be used [7]. However, it adds the complexity of experimental setup and operations because of the addition of “local” light. The second technique, the spatiotemporal scanning of tightly focused pump and probe spots, requires tightly focused pump and probe spots whose size is comparable to diffusion length (usually less than a few micrometers) of carriers, and high-resolution spatial relative scanning of both spots. This technique is mainly restricted to no-ease availability of small focused pump and probe spots and hence not suitable to measure slow diffusion dynamics. The third technique, the spatial profiling of luminescence, has the same spatial resolution restrictions as the second one, such as the size of pump laser spot and spatial resolution of luminescence detection system. Furthermore, it is also restricted to only luminous samples.

In this article, we develop and report a very simple and highly sensitive absorption spectroscopy which is sensitive to spatiotemporal evolution of photoexcited carriers. The developed spectroscopy combines the standard time-resolved pump-probe absorption spectroscopy with a transmission binary grating. The absorption change, instead of the diffraction light intensity change induced by transient gratings, is detected in the spectroscopy so that detection sensitivity is enhanced at least 300 times [8]. It has many advantages, such as simple experimental setup and operation, no requiring a second pump beam as in the first technique, tightly focused pump and probe laser spots and spot scanning as well as the luminescence of samples. Meanwhile, a formula is also developed to describe the absorption change measured experimentally with the spectroscopy. Transient diffusion transport experiment is performed on a bulk intrinsic GaAs film to demonstrate the validation of this spectroscopy in measurements of diffusion dynamics and coefficients since the diffusion coefficient of GaAs has been measured with the diffraction of transient grating [9] and the spatiotemporal scanning of tightly focused pump and probe spots [10], and also calculated theoretically [11, 12], so that abundant reference data are available to compare with our results.

## 2. Principle and model

Figure 1(a) shows the schematic of experimental setup of our spectroscopy. At a glance, it is just the setup of standard time-resolved pump-probe absorption spectroscopy with an optical delay line in probe path. However, at a careful look, one may find a transmission grating is added in front of and as close as possible to the sample to avoid diffraction effect or even contacted with the sample if the contact does not lead to any side effects. A somewhat similar setup was reported previously [13], but there a heterodyne diffraction signal was detected. The transmission grating is one-dimensional binary opaque/transparent, fabricated on a Cr plate by photolithography, and has a transparent slit width comparable to a diffusion length of carriers. It is the grating added that makes the setup sensitive to spatial evolution of carrier distribution or carrier diffusion. The transmission grating modulates Gaussian profile of incident pump and probe spots into transmitted periodic stripe profile. The periodic stripe-profiled (PSP) pump laser excites a transient carrier grating (TCG) in the sample, as shown in Fig. 1(b), while PSP probe laser tracks the spatiotemporal evolution of TCG by absorption saturation change instead of diffraction intensity change. PSP probe, instead of normal large-size-spot

Gaussian profile probe, is a key factor that makes our spectroscopy be able to sense carrier diffusion because PSP probe can sense only the partial carriers in the light area (corresponding to transparent slit area of the transmission grating) of the sample. However, carrier diffusion will lead to a carrier transfer from the light to dark (corresponding to opaque area of the transmission grating) areas in the sample,whereas the transferred carriers cannot be seen by PSP probe and hence are equivalent to being recombined additionally in the light area, so that the transient absorption change of PSP probe decays obviously faster than that of Gaussian profile probe with no transmission grating added. The narrower the transparent slit of the transmission grating is, the faster the transient absorption variation decays, that is to say, the diffusion effect becomes more obvious for a narrower transparent slit. It is similar to the phenomena observed in the diffraction measurement of TCG, where the decay rate of the diffraction light intensity of TCG increased with the decrease of the period of the TCG [1, 2, 9]. Therefore, the transient absorption saturation dynamics reflects the recombination and diffusion dynamics of photoexcited carriers. Their quantitative relation will be modeled as follows.

Pump-excited transient carrier density, *N*(*r*,*t*), will evolve in space and time due to carrier diffusion and recombination, respectively. The evolution is controlled by common diffusion transport equation [3],

*D*

_{a}is an ambipolar diffusion coefficient.

*τ*

_{r}denotes an electron-hole recombination lifetime. For the initial carrier density distribution shown in Fig. 1(b), Eq. (1) has no analytical solution so that it must be numerically solved for

*N*(

*r*,

*t*) under a preset

*D*

_{a}and the known

*τ*

_{r}which may be measured independently by normal time-resolved pump-probe absorption spectroscopy with no grating added. Maybe no analytical solution may be thought of a drawback of our spectroscopy.

For the known transient carrier density given by Eq. (1), *N*(*r*,*t*), corresponding transient absorption may be expressed by [14, 15],

*α*

_{0}is a linear absorption coefficient of the sample with no pump excitation.

*N*

_{s}denotes the density of state of the sample, and is usually much larger than

*N*(

*r*,

*t*).

The transient transmitted intensity of the probe through the grating and sample may be given by,

where*I*

_{0}(

*r*) is the incident intensity profile of the probe.

*T*

_{G}(

*r*) denotes transmittance of the transmission grating and the

*L*the thickness of the sample.

Substituting Eq. (2) into Eq. (3), the transient transmission intensity change of the probe may be given by,

where*C*=

*α*

_{0}

*L exp*(-

*α*

_{0}

*L*)/

*N*

_{s}is a scaling constant.

The transient differential transmission change measured experimentally can be written as,

*D*

_{a}and a scaling constant

*C*. Both

*D*

_{a}and

*C*can be obtained by best fitting transient experiment dynamic data obtained by our spectroscopy with Eq. (5) plus Eq. (1). A numerical optimization program based on Eqs. (1) and (5) has been developed to execute the best fitting.

## 3. Sample and experiment

The sample studied here is a 0.5 μm thick intrinsic bulk GaAs film which was grown by molecular beam epitaxy, and is strain-free mounted on a piece of sapphire substrate. All measurements are performed at room temperature.

Experimental setup is the same as Fig. 1(a) shows. Ti:Sapphire self-mode-locked laser oscillator generates a train of laser pulses with the duration of 60 fs, a repetition rate of 94 MHz and a central wavelength at 850 nm. The pump and probe pulses are focused onto the sample and grating to a same spot of ~50 μm in diameter. The differential transmission change of the probe is detected by a photodiode and measured by a lock-in amplifier referenced at the modulation frequency of an optical chopper which modulated the pump beam at 1.13 kHz. When a grating is added in front of the sample, it is about 15 μm away from the sample. This distance is much smaller than a Talbot distance of the grating used in experiments, and thus diffraction effect is negligible.

## 4. Measurements of diffusion dynamics and its photoexcited carrier concentration dependence

The transient differential transmission trace with no gratings is first measured at a photoexcited carrier concentration, N = ~7.7 × 10^{17} cm^{−3}, and plotted in Fig. 2(a)
by red open squares. As well known, it reflects the dynamics of carrier recombination. Then, a transmission grating with transparent slit width of 2 μm and a period of 6 μm is added in front of the sample. A transient differential transmission trace is taken again under the same excited carrier concentration as afore, and also plotted in Fig. 2(a) by green open circles. Obviously, it decays faster than red trace with no grating added. That is just the effect of carrier diffusion. To further demonstrate the role of the grating in visual enhancement of diffusion effect, another grating with a narrower slit of 1 μm is used. The transient trace is recorded again under a same excited carrier concentration and also plotted in Fig. 2(a) by blue open triangles. Evidently, it decays faster than green trace, again revealing the key role of the grating in the enhancement of diffusion effect.

Two sets of transient transmission traces, respectively with and without the grating added, are taken for multiple different excited carrier concentrations ranged from 0.3x10^{17} to 8.6x10^{17} cm^{−3}. One set of transient traces with no gratings are plotted in Fig. 2(b), while the other ones with the grating added in Fig. 2(c) for the same carrier concentrations as ones used in Fig. 2(b). It is obvious that each transient trace in Fig. 2(c) decays faster than the corresponding one in Fig. 2(b), showing the enhancement of carrier diffusion after the grating added. Furthermore, it looks that the decay rate of transient traces increases with carrier concentration regardless of the grating added.

## 5. Results and discussions

A single exponential decay function is used to fit the transient trace with no gratings to extract a recombination lifetime *τ*_{r} of carriers. A best fitting to the red square trace in Fig. 2(a) gives out a recombination lifetime of *τ*_{r} = 3.06 ± 0.06 ns, and is also plotted by a solid line in Fig. 2(a). Similarly, a best fitting to the green circle and blue triangle traces in Fig. 2(a) with Eq. (5) plus Eq. (1) with a given *τ*_{r} = 3.06 ns gives out a similar diffusion coefficient of *D*_{a} = 13.0 ± 0.3 cm^{2}/s. The best fittings are also plotted in Fig. 2(a) by solid lines. The obtained diffusion coefficient of *D*_{a} = 13.0 cm^{2}/s agrees well with previous reports. Jarasiunas and Lovergine measured the *D*_{a} of bulk GaAs with the diffraction of transient gratings, and found *D*_{a} = 11.0 cm^{2}/s at a low excited carrier concentration and *D*_{a} = 18.0 cm^{2}/s at high excitations [9]. Our excited carrier concentration is 7.7 × 10^{17} cm^{3}, and in a moderate concentration range. Therefore, our measured value of *D*_{a} = 13.0 cm^{2}/s locating between 11.0 cm^{2}/s and 18.0 cm^{2}/s should be reasonable. Ruzicka et al also measured the *D*_{a} of bulk GaAs with the spatiotemporal scanning of tightly focused pump and probe spots, and found *D*_{a} = ~20.0 cm^{2}/s at room temperature [10]. However, their probe wavelength is set at 800 nm, so that high momentum electrons were measured. Therefore, a slightly larger *D*_{a} should be expected.

Best fittings to all transient traces in Fig. 2(b) and Fig. 2(c) as described above give out excited carrier concentration dependences of recombination lifetime *τ*_{r} and diffusion coefficient *D*_{a} of carriers, which are plotted in Fig. 3(a)
. It is interesting to note the non-monotonous variation of *D*_{a} with the increase of N. In the range of low excitations with N < ~1.2 × 10^{17} cm^{3}, *D*_{a} decreases slowly with increasing N. Contrarily, in the range of high excitations with N > ~1.2 × 10^{17} cm^{3}, *D*_{a} increases slowly with N. Such a variation tendency has been well predicted theoretically by Young and van Driel [11]. Our carrier concentration dependence of *D*_{a} agrees very well with the theoretical prediction of Young and van Driel [11]. Therefore, our measured results on *D*_{a} agree well with both previous experimental reports [9, 10] and theoretical calculation [11], proving the validation of our spectroscopy.

Excited carrier concentration dependence of a diffusion length can also be calculated by a formula *L*_{d} = (*D*_{a}*τ*_{r})^{1/2} with the data in Fig. 3(a), and is plotted in Fig. 3(b). It decreases slowly with the increase of N. The diffusion length is less than 2.5 μm. Therefore, the diffusion effect is not apparent and can be ignored in normal pump-probe absorption spectroscopy where pump and probe spots are in order of several tens of micrometers at least, whereas in our spectroscopy it is the transmission grating added that makes diffusion effect visible.

## 5. Conclusion

A time-resolved pump-probe absorption spectroscopy, combining a binary transmission grating with normal time-resolved pump-probe absorption spectroscopy, has been developed. Its feasibility and validation are demonstrated on intrinsic bulk GaAs films. It is found that the diffusion coefficient measured by our spectroscopy decreases slowly first and then increases with the increase of excited carrier concentration, and agrees well with both previous experimental reports and theoretical predictions. This spectroscopy is simple in experimental setup and operation, and highly sensitive in signal detection. It is expected to have extensive applications in studies of carrier diffusion dynamics.

## Acknowledgments

This work is partially supported by National Natural Science Foundation of China under grant Nos. 10874247, 61078027, National Basic Research under grant Nos. 2010CB923200, and Natural Science Foundation of Guangdong Province under grant No. 9151027501000077 as well as doctoral specialized fund of MOE of China under grant No. 20090171110005.

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