Optical Pump Terahertz Probe (OPTP) and Time Resolved Terahertz Spectroscopy (TRTS) of emerging solar materials Open Access

The development of novel solar devices is driven by the discovery and understanding of emerging materials with superior solar performance.^1–5 Design, synthesis, and detailed characterization in collaboration with theory are crucial in driving this interdisciplinary field forward.⁶ Most material scientists expertly utilize x-ray diffraction, diffuse reflectance, and sometimes transient absorption, but conductivity and photoconductivity measurements are often limited to direct current (DC) measurements.

DC conductivity measurements can provide excellent insight into the performance of assembled cells. However, this involves tedious and time-consuming assembling of cells. In addition, even more challenging is the fact that cell-conductivity is influenced not only by the properties of the novel material but also by contact resistance, interface effects, and all the other components of the cell acting together. This hinders a detailed insight into the properties of the novel material itself and makes targeted optimization challenging. Hence, it is common to study the emerging material as-is using DC techniques, which presents a novel set of challenges and draw backs.^7–9 

Two probe DC measurements are strongly influenced by the contact resistance between the electrical pads and the material under study.¹⁰ Furthermore, the measured conductivity is long range, defined by the distance between the contact pads. However, many synthesized novel materials are in powder form, and the measured DC conductivity is as much determined by the air/powder mixture and the resulting percolation as the (to be measured) conductivity of the material itself.^8,9 As such, it is challenging to understand whether DC conductance measured for different synthesis conditions is caused directly by the material conductivity or the properties/grain sizes of the powder.¹¹ Some of these shortcomings can be overcome with four probe techniques, in particular van der Pauw geometry. However, this technique is limited to sufficiently large crystals that can be contacted at four points.

Photoconductivity is even more crucial for the performance of novel solar materials than static ground-state conductivity. The most intuitive approach to measure photoconductivity is to combine the aforementioned DC techniques with a continuous wave (cw) light source, i.e., a solar simulator. This is a good approximation of actual operation conditions; however, it suffers from the same shortcomings as the static DC measurements. Furthermore, cw light sources do not provide any time resolution and, therefore, cannot achieve detailed insight into the underlying photophysics. In other words, DC-cw measurements can shed light on the total performance of a new solar cell but are of very limited help in understanding why a material performs as it does and how its performance can be improved. All these shortcomings can be overcome with contact free conductivity measurements.

Terahertz Time Domain Spectroscopy (TDS) utilizes electromagnetic waves in the 0.1–10 THz range. Corresponding to free space wavelengths between 3000 and 30 μm and photon energies of 0.4–40 meV.^12–15 These waves interact with free electrons, and the THz transmission of a material is an excellent probe of its complex conductivity without the need for any contacts. The high frequency of the conductivity measurement makes THz radiation particularly sensitive to short range conductance, eliminating the aforementioned restrictions on sample/grain sizes. Additionally, THz conductivity measurements can be combined with femtosecond light excitation to yield Optical Pump THz Probe (OPTP) dynamics. The ultrafast temporal resolution provides detailed insight into the life of an electron.¹⁶ Scattering, trapping, recombination, as well as polariton formations take place on these timescales and significantly influence the solar properties of emerging materials.^16–21 OPTP measurements can be supplemented with spectral information gained from Time Resolved THZ Spectroscopy (TRTS). Contact free, sub-ps conductivity measurements are extraordinarily useful to understand the physical limitations of solar materials, the first crucial step to optimizing them.²²  Figure 1 shows a simplified TDS/OPTP/TRTS spectrometer. We would like to point out that the names OPTP and TRTS are sometimes used differently in the literature; some authors use OPTP for time and frequency resolved measurements and some other authors use TRTS for dynamics measurements as well. Additionally, OPTP and TRTS can be referred to as 1D and 2D measurements, respectively, a nomenclature that ought to be avoided as it is easily confused with 2D-THz-spectroscopy, a different technique.²³ However, in this tutorial, we will use the original nomenclature. The TDS/OPTP/TRTS spectrometer utilizes a laser amplifier that emits intense femtosecond pulses. These pulse traces are split into three branches; about half the power is used for THz generation and the other half for the optical pump pulse. The third pulse is a very weak gating pulse used to detect THz radiation. Furthermore, lock-in detection is used for low noise detection of THz radiation. The individual components are discussed in detail in the following chapters.

In this tutorial, we will present terahertz spectroscopy, a contact free ultrafast technique to measure the conductivity and photoconductivity of as-synthesized materials. These measurements follow the workflow depicted in Fig. 2. First, a THz time-domain trace is measured to determine the ground state properties of the material (Sec. II). From these measurements, the timing of the peak THz amplitude is determined. The TDS time-delay is then fixed at this time-point, and the chopper moves into the pump beam. The OPTP dynamics show the on-off difference amplitude transmission for different pump delay times, as illustrated in Fig. 2(b) (Sec. III). OPTP traces measure carrier density/mobility with ps-resolution and provide a detailed insight into carrier lifetime. The OPTP trace is then used to determine pump-probe delays of interest at which the complex difference THz spectrum is collected, called TRTS. A typical TRTS trace is illustrated in Fig. 2(c) (Sec. IV). These spectra are then processed to yield the complex photoconductivity [Fig. 2(d)]. After discussion of this workflow in general, we will provide practical hints for THz spectroscopy in laboratories and discuss the difference between sample parameters and independent material parameters (Sec. V). This tutorial concludes with a perspective on novel OPTP techniques, including in operando measurements and long time delay OPTP (Sec. VI).

Terahertz pulses are broadband, sub-ps pulses spanning from roughly 100 GHz to 10 THz. Direct electrical detection and circuits usually have rise and fall times in the pico- to nanosecond range and are not capable of achieving high enough time resolutions. On the other hand, the corresponding photon energies of just a few milli-electron volts and the large wavelength of 100 μm render usual optical detection techniques (spectrometers) unfeasible. In order to detect THz radiation, a novel concept needed to be developed in which the electrical field is directly measured in the time domain and then the spectral information is gained using a Fourier transformation.²⁴ 

Terahertz time domain spectroscopy (THz-TDS), illustrated in  Fig. 3, leverages the femtosecond length of ultrashort laser pulses in combination with non-linear optics to directly detect the sub-ps THz electrical fields. This detection is sign resolved, meaning that the Fourier transformation provides amplitude and phase directly.

A detailed TDS tutorial is beyond the scope of this tutorial, and the reader is kindly referred to excellent text books,^25,26 review articles,^27–31 and a tutorial by the author on this topic.¹² We will here focus on the aspects of TDS that are most important for optical pump THz probe spectroscopy.

A femtosecond laser pulse, commonly provided by a laser amplifier, is split into two beams. One beam is used for THz pulse generation, while the second pulse is routed over a mechanical delay line and used for THz detection, Fig. 3. THz generation leverages non-linear interactions. An overview of common techniques is given in Table I. Broadly speaking, we can separate the emission mechanism into non-linear effects [different frequency generation (DFG)^48,49 and optical rectification (OR)^33,37] and ultrafast currents (Austin-switch,⁵⁰ photo-Dember effect,⁴³ and spintronic emitter⁴⁷). In both cases, the femtosecond laser pulse is transformed into a sub-picosecond electromagnetic pulse. Based on the Fourier theorem, the spectral bandwidth of such a short pulse spans the THz range, and the time pulse carries the same information as the complex spectra. Hence, we can rightfully refer to this pulse as a THz pulse. The generated THz pulse is then routed through the sample and focused onto a detector, as illustrated in cyan in Fig. 1. This beam path is commonly purged with dry air or nitrogen, as water vapor absorbs THz.⁵¹ 

The detector again leverages either non-linear effects [Pockels effect in Electro Optical Sampling (EOS)^52,53] or ultrafast currents driven by the THz electrical field (Austin Switch, ABCD detection⁵⁴). In both cases, the detector is gated by the second optical pulse. Meaning that only when a THz pulse and optical gate pulse arrive at the same time in the detector is a signal measured. In the ideal case of an instantaneous response, the gate pulse activates the detector for a short time frame defined by its time envelope, commonly 10–100 fs. This snapshot then includes the THz field information at a given time. Changing the timing between THz and the gating pulse is used to scan over the THz pulse and collect the full time-domain information. These time scans are achieved by leveraging the known speed of light and changing the travel length of one of the two beams relative to the other. Changing the travel length is achieved with a computer controlled micro-positioning stage. Such stages allow for sub-μm manipulations, which in turn enable femtosecond changes in the THz-gate beam timing.

TDS traces commonly span about 10–100 ps in “THz time” and can be collected within seconds to minutes of real time.⁵⁵ These time traces are then Fourier transformed to provide the spectral information of the THz pulse. Contrary to most optical techniques, which solely report on the intensity of the pulse, THz spectra include complex spectral information. This means that, in addition to the amplitude, the phase of the electromagnetic wave is also measured. Depending on the spectrometer used, these measurements have frequency resolutions of a few GHz, corresponding to an energy resolution of μ eV (≈0.003 cm⁻¹).

It is important to note that most THz spectrometers are not self-referencing, contrary to commercial UV Vis, which uses a beam splitter to measure and compensate for fluctuations in the probe light. The lack of self-referencing means that in addition to measuring the sample, an (empty) reference measurement needs to be collected. Furthermore, for compound materials—for example, a film grown on a known substrate—a blank substrate reference should also be collected. The measured THz field is then referenced to the empty measurement, which yields the experimental transfer function of the sample.^18,56

For a solar cell to work, the carriers need sufficient time to reach the collection electrode. This makes carrier lifetime a crucially important parameter to judge any emerging material for its potential in solar applications. Carrier lifetime can be influenced by interfaces and contacts, which then camouflage the real material’s photoconductive potential. THz is a contact free probe that allows us to directly explore these material parameters without any electrical contacts. Additionally, by providing a more material-intrinsic value, optical-pump THz probe (OPTP) measurements also avoid the sometimes tedious step of contact fabrication. Novel materials can be measured much faster, and even more intriguingly, the measurement can easily be combined with external means of manipulation, for example, in operando bias conditions⁵⁷ or cryogenic temperature.¹¹ 

Photoconductivity obviously needs light absorption within the sample material. Hence, before any OPTP measurements are undertaken, the UV–visible transmission and/or reflection spectrum should be measured. Based on this spectrum and potentially in collaboration with DFT band calculations, the experimentalist can identify the most suitable wavelengths for photoexcitation. It is important to be aware that the absorption length for photoexcitation commonly depends on the wavelength. This means that charges generated at different wavelengths will have different lateral distributions, as illustrated in Figs. 4(b) and 4(c). However, the underlying physical mechanisms of the absorption will also be different for different wavelengths. Hence, we need to take great care when comparing results for different wavelengths to decipher if the difference in carrier lifetime is related to more pronounced surface recombination or if electrons with more excess energy above the bandgap might trap/recombine following different physical mechanisms.⁵⁸ To illustrate this difference, consider the well known band structure of silicon [shown in Fig. 4(a)] with the direct bandgap of 3.4 eV (λ = 365 nm) and the energetically lower indirect transition at 1.12 eV (λ = 1100 nm). When photoexcited at room temperature, 1100 nm photons will drive solely the indirect transition, while short wavelengths will drive mixtures of indirect and direct transitions, populating different energies in the bands. The lateral carrier gradient will be different, as so will the relative influence of surface recombination compared to bulk recombination.⁵⁹ However, the electron energy and mobility will also depend on the position in the conduction band, making a direct comparison between these two excitation wavelengths challenging, especially if only the lifetime is considered.

The UV–visible absorption is used to identify excitation wavelengths for potential photoconductivity measurements. However, as experimentalists, we are also limited by what wavelengths are available or easily accessible in our laboratory. Commonly, most OPTP experiments are driven by a titanium:sapphire laser with an emission wavelength of 800 nm. This fundamental wavelength has limited interest for solar applications, which should be more optimized toward the solar spectrum maxima at 500 nm. An easy way to transform the fundamental 800 nm pulses into a better proxy for solar light is based on the second harmonic generation in BBO or LBO.⁶⁰ Furthermore, third order harmonic generation is feasible and provides 266 nm, at the higher energy edge of the solar spectrum. More advanced non-linear interactions can span the full spectral range in a tunable fashion. This can be achieved by leveraging optical parametric amplification in either a co-linear or non-co-linear fashion.⁶¹ While this is the most desirable source for optical excitation, the significantly cheaper SHG approach already provides excellent results and insight into novel materials.

OPTP is very sensitive to mobile/conductive charges. A complementary perspective can be achieved with visible techniques. Optical pump optical probe, transient absorption (OTA) measurements can be performed on the same time scale as OPTP, and even with the same excitation wavelengths.⁶² OTA is sensitive to bound electrons or the absence of them.⁷ The injection dynamics of OTA provide insight into the average time a photoexcited electron needs to leave the excited system. A comparison of these time scales and the appearance of photoconductivity, measured with OPTP, provides crucial information about the intermediate steps the electron undergoes before reaching the conduction band.²⁰ This is particularly valuable for dye sensitized nanoparticles in which electrons might not be directly injected into the conduction band but undergo internal conversion or hopping steps first.^63–65 

OTA can also monitor the total time needed for the system to return to equilibrium. This total time is caused by recombination and is commonly much longer than the decay time of photoconductivity. The difference in these timescales can provide insight into charge demobilization mechanisms, e.g., trapping, that reduce photoconductivity but are not directly related to recombination.

Recombination can be measured directly with ultrafast photoluminescence (PL).⁶⁶ PL measures the photon emitted by the recombination of an excited electron with a vacant electron position/hole. This recombination is another direct measure of recombination dynamics and can be compared to trapping dynamics.¹⁶ 

THz TDS scans provide the full complex conductivity information of a sample; however, to achieve a decent signal-to-noise ratio, several minutes per measurement are commonly needed (with a few exceptions).^15,67,68 Therefore, measuring full traces for each pump-probe delay time point of interest is very time consuming.⁶⁹ The time demand is not only tedious but could also result in laser induced damage to the sample. Faster measurements are achieved by leveraging the Fourier theorem again.

The peak point in the time domain is the constructive interference of all frequency components. In other words, the height of the THz peak is directly related to the frequency integrated transmission of the sample. If our main interest is the overall carrier density with respect to the pump time, it is therefore possible to solely monitor the peak transmission for different pump-probe delay times. A single THz TDS scan is performed, from which the THz-time position of the peak is determined. This time position is then fixed so that the THz time frame “sits on the peak” [see frame (b) in Fig. 2].

The THz peak amplitude under photoexcitation commonly changes by a few percent or less.²⁰ These small changes are commonly less than the long time variation of the total THz signal caused by thermal drift and other laboratory conditions. Consecutive measurements with and without excitation cannot reach the stability needed to measure such small signals. Instead, the difference signal is measured directly. For this purpose, an optical chopper is moved into the pump beam, and a lock-in amplification selectively amplifies the THz change at the known chopper frequency. Leveraging the noise suppression in lock-in amplification and sufficient integration time, changes as small as 0.001% can be measured accurately.^16,70

With the chopper moved into the pump beam, the differential THz peak transmission is now measured for each pump-time point of interest. For these measurements, it is furthermore important to ensure that solely the pump pulse is delayed with respect to the THz and probe pulse combination. If the delay between the gate and both THz generation and pump is scanned, artifacts on the pulse length time scale (picoseconds) are introduced. OPTP traces directly monitor the photoinduced conductivity in the sample. The onset of conductivity is directly related to the time needed to form the most mobile carrier. This time can be influenced by several experimental and material properties and can shed light on the underlying physics of charge injection or the generation of mobile charges in the medium in general. However, before these injection dynamics can be accurately described, it is important to consider the fundamental limitation of the temporal resolution of the spectrometer used.

An instantaneous effect will not appear instantaneous when measured with a limited temporal resolution. The time envelope of the pump laser beam presents a fundamental limit for the shortest processes that can be resolved. Additionally, the travel length of the pulses will not be exactly the same for successive measurements; air fluctuations and temperature changes can cause jitter. Additionally, the integration constant of the lock-in detection can smear the measured dynamics out if scanned too fast. Even with all these laboratory effects minimized, the pump and probe beam will experience different dispersion in the medium. If the pump and probe beams overlap in time on the surface of the sample, the pump-pulse might be behind the probe beam in the sample (or the opposite). The pump-time, however, is solely attributed to the delay line position; hence, both real times in the sample are lumped into the same values. All these effects are commonly lumped together in the instrument response function (IRF) of the used spectrometer. For easier mathematical handling, the actual function is approximated by a Gaussian function, and the results are either deconvoluted with the function or, more commonly, the fit function is convoluted with the IRF [see Eq. (1)]. This is illustrated in Fig. 5, where a 1 ps injection (black) is smeared out by a 1 ps IRF, resulting in the cyan signal.

The IRF can be approximated from a well understood sample (GaAs, Si, etc.). This reference measurement must be performed for the same alignment of the system as the actual measurement and should be verified frequently. With an accurate IRF, the onset of conductivity dynamics can now be described. The onset could be instantaneous, as for direct semiconductors excited at the bandedge, or it could be delayed. This delay can be caused by several physical effects. First, it is possible that the photogenerated state is not a conductive, free electron. This is commonly observed for charge injection from dye molecules into large bandgap semiconductors.^19,71 In this case, the injection dynamics can help us understand the intermediate steps in the charge injection process. This is particularly valuable when combined with ultrafast transient absorption, which might be able to monitor these intermediate states directly.^64,65 A comparison of these times can help understand intermittent steps, which need to be optimized for the fastest and most efficient injection.

In the absence of dye molecules, it is still possible that the initial photoexcitation creates immobile electrons. These electrons might be trapped in surface states or localized on surfaces that exhibit low mobility bands. In this case, studying different passivation layers could separate bulk from surface electrons and provide a better understanding of the dynamics of injection.

Second, photogeneration can create a mobile electron, but it is not yet the most mobile charge carrier possible. This could mean that the initial hot electron exhibits a larger effective mass than an electron in the conduction band minimum.⁷² In this case, the delayed onset is related to the mobility increase due to cooling, not the appearance of new electrons. Furthermore, electrons are not the only charge carriers in semiconductors. It is possible that polarons are formed. Polaron-formation requires the interaction of phonons and electrons, which can take picoseconds. If the polarons exhibit a larger mobility than the electron alone, the maximum conductivity will not be reached instantaneously but after this formation time.⁶⁹ 

The complex conductivity of free charges results in a change in the real and imaginary parts of the refractive index. The change in the real part will create an additional delay for the THz pulse, which in turn moves the time position of the peak. This move can be substantial for strong photoconductivity. In this case, the peak amplitude is compared to the amplitude at the shoulder of the pulse, resulting in an overestimation of the photoconductivity. Similarly, if the timing was not accurately placed on the peak, it is possible that the delay moves the peak to the measured time spot. In this case, a negative signal would be measured.

In some cases, it is possible that a sample exhibits a non-linear interaction between THz and an optical pulse. These ultrashort-lived processes would occur only during pump times within the IRF and could explain confusing OPTP traces. The best way to explore this is to measure TRTS at the same delay time to understand the spectrum related to this OPTP feature.

For an accurate interpretation of OPTP traces, it is crucial that we always keep in mind that OPTP monitors the product of mobility and charge density. This means that a reduction in OPTP can be caused by recombination or, more commonly, by trapping. An electron is described as trapped if it scatters into a significantly less mobile state. These states could either be localized at defects and surfaces or delocalized. A delocalized effect would be similar to the aforementioned cooling of the photo-electron. In this case, the cooler electron would exhibit lower conductivity than the hot one, and hence the OPTP signal would be decreased.

Localized traps are the more common final fate of mobile electrons. Surface states commonly exhibit a lower mobility than bulk states. If these states are energetically more favorable, the charges will trap in these. Trapped charges do not contribute to the total conductivity. Furthermore, defects in the lattice and potentially guest molecules could demobilize electrons.

Recombination, on the other hand, refers solely to an electron finding its hole. This process concludes the life-cycle of an electron and commonly occurs on much longer time scales than trapping. OPTP cannot distinguish between trapping and recombination, and additional techniques that monitor the original states are needed (see Sec. III B).

This model does not provide any detailed insight into the character of the charges, nor does it need to separate mobility from carrier density. The lifetimes extracted are solely the photoconductivity lifetimes.

The previous insight can be improved when the same sample material is measured under different photon flux conditions. Generation and several of the previously discussed trapping and recombination mechanisms scale with carrier density, and the magnitude of the signal might not scale linearly with the used flux. It is prudent to always check if the OPTP magnitude and the lifetime depend on pump flux to gain a deeper understanding of the physics of the material.⁵⁸ 

The saturation effect can occur at higher pump-flux. The total magnitude of the OPTP signal can increase non-linearly. This can be caused by the bleaching of surface states that absorb light without contributing high-mobility bulk electrons to the system. When all these states are bleached in the intense laser pulse, the remaining photons of the pulse will be absorbed deeper into the sample, where they generate charges with longer lifetimes. The power dependence of the OPTP signal could also be sub-linear. This could be caused by the surface states actually being the more mobile states in a specific material. Furthermore, two-photon processes could absorb photons without yielding mobile charges or generating hotter electrons. In this scenario, the power-dependent-OPTP is caused by lower mobility at a linearly scaling carrier density.

Even if the magnitude scales linearly, it is still possible that the carrier lifetime is pump fluence dependent. As for the magnitude, this could be related to surface vs bulk state competition. Additionally, for bulk electrons, there are still multiple mechanisms that could give rise to a flux dependent lifetime. An increased lifetime could be caused by trap saturation. Localized traps, caused by defects and impurities, have a finite density based on the number of impurities within the sample volume. If significantly more photo-electrons than traps are generated, the traps will fill up. Filled traps, of course, cannot trap additional electrons, and the influence of this recombination process will decrease with increasing flux.¹⁹ A decrease in lifetime can be caused by multi-electron processes, such as Auger recombination.^73,74

Finally, it is important to be aware that a larger photon flux will also deposit more energy into the sample. This energy will generate phonons and heat the sample, which in turn will promote phonon–electron scattering that limits mobility and can promote phonon-assisted trapping and recombination.

These equations can provide a detailed understanding of physics related to recombination and trapping. However, it is important to stress that the core assumption is that the OPTP signal solely depends on the carrier density. The aforementioned effects that could alter the mobility are not described by rate equations. Therefore, we caution the reader to consider that electron–electron scattering, for example, will also change mobility and, of course, also scale with electron density.

OPTP is an excellent way to measure photoconductivity in a contact free manner. The time resolution is commonly in the sub-ps range. However, OPTP solely measures conductivity, not carrier density and mobility separately. It is possible to approximate the carrier density usin the known photon flux. This approximation, however, needs to assume a value for the photon-to-mobile electron quantum efficiency. Furthermore, OPTP cannot distinguish between electrons, holes or other charge carriers. Therefore, OPTP needs to be combined with in operando biases, or other techniques to separate these effects.⁷⁵ The insight gained from OPTP can be enhanced when we combine this technique with other spectroscopy techniques performed on the same sample. Microwave Photoconductivity measurements can provide conductivity values at time scales not accessible for most OPTP systems.²² OTA and fs-PL can provide insight into electronic energy levels and timescales.^62,66 A comparison between these measurements and OPTP can more accurately track an electron following photoexcitation.¹⁶ 

For OPTP the peak amplitude of the transmitted THz pulse was measured for varying delay times. These fast measurements provide insight into carrier lifetimes. TRTS, on the other hand, can be used to determine the complex photoconductivity spectrum. The broadband spectrum informs us about carrier scattering mechanisms in the material.

TRTS is a hybrid of TDS and OPTP. Based on the OPTP measurement, time points are identified that are representative of the dynamic in the material; commonly, the point with the strongest signal is chosen. Additionally, any points at which a change in dynamics is observed can merit further investigation via TRTS. For example, if the material clearly exhibits two-component injection or trapping dynamics, it can be interesting to measure points representing the two different dynamics, as they might correspond to different charge carrier species. The earlier time point would be dominated by the shorter living or fast injecting carriers; the later points would be more representative of the longer living or later injecting charges.

For TRTS measurements, the pump delay is adjusted to sit on the pump-time of injection. The difference transmission time traces for on-off are measured directly. This is achieved in the same manner as for the OPTP by modulating the excitation pulse and lock-in amplification of the measured difference. TRTS traces commonly have a signal strength of fractions of 1% of the original TDS signal. This is an intrinsic property of photoexcitation, as we should always utilize a small enough pump flux to avoid non-linear changes and permanent damage to the material. As such, the number of injected or photogenerated carriers is much smaller than the ground-state electron density. Hence, the measured signal is weak compared to the ground-state signal. Full TRTS traces can demand hours or even days of integration, depending on the signal strength and the desired signal-to-noise ratio. As a result, TRTS spectrometers should be built with long-time stability in mind. Any known noise source should be eliminated; temperature changes must be minimized; and any potential source of time jitter should be minimized. Potential sources for this change can be local temperature changes or even air flow that impacts the pump-probe-THz timing. Only if the timing between photo-excitation, THz generation, and the THz probe is stable over the full measurement time can a good signal-to-noise ratio be achieved.

TRTS measures the frequency resolved transfer function, which can be used to extract the complex photoconductivity. This extraction is often performed using the thin-film formula.^13,76 However, several publications showed that thin might be a more rigorous criteria than initially assumed. For example, a 3 μm film (which corresponds to λ/100) is not thin in the sense of the approximation.¹⁸ Additionally, phonon modes in the ground state of the crystal can locally break the thinness of the film.⁷⁷ Furthermore, THz measurements cover a broad spectral range, and a sample might be thin at 500 μm wavelength but not at 50 μm. Based on these findings, the reader is strongly advised not to use the thin-film approximation for an emerging, unknown material, and a transfer function evaluation should be carried out.

To calculate the conductivity, first the photoinduced change in the refractive index is calculated. The refractive index is calculated based on the geometry of the sample and the reference measurement. In TRTS, the reference is commonly the non-excited material. This material can be mounted on a non-photoabsorbing substrate like quartz. The geometry for this example is sketched in Fig. 6(a). The mathematical description of the reflection, transmission, and propagation of electromagnetic waves is based on the Fresnel coefficient. The reflection between medium i (with a complex refractive index n_i) and j is described as $rji=ni−njni+nj$⁠. The transmission is then described by t_ij = 1 + r_ij. The phase change and absorption experienced by the wave propagating in medium i for a distance d_i are described as $Pi=e−idinik0$⁠, where k₀ is the free space wavevector.^12,18,78

These equations look fairly scary and might explain why many TRTS-users are tempted to apply the thin-film approximation. However, they can be solved numerically.^79–81 If the reader does not want to spend time writing their own code based on the great work of these colleagues,^79–81 I kindly refer them to Nelly.⁵⁶ This open-source software package implements numerical solutions for TDS and TRTS geometries and should help the reader withstand the temptation of the thin-film approximation.

For most semiconductors, this is a good approximation. However, phonon (and other) resonances need to be considered. Free charges can screen the EM–phonon interaction and therefore alter the phononic spectrum (Δɛ_lattice) of a material under photoexcitation.^69,82 Additionally, ultrafast heating could also change the phonon occupation numbers and, therefore, the resonance frequency and strength. Therefore, it is paramount to critically evaluate the calculated conductivity spectrum for such resonances that cannot be explained by free electrons alone.

The Drude model describes free electron gas in semiconductors. It ignores most surface interactions and averages over all local effects. Single crystalline semiconductors like GaAs, Si, etc., are accurately described by it.^83,84

Monte-Carlo simulations can be utilized to avoid the phenomenological DS model. These simulations mimic the diffusion of charges within nanoparticles and are an excellent approach to separate bulk and interface effects.^89–91 

As a final word of caution, TRTS measures the photoinduced difference in conductivity. The reader should not confuse this with conductivity in general, i.e., ground-state conductivity measured via TDS. To illustrate this, consider a metallic sample. A photoexcitation of this sample will change the conductivity minimally (or even negatively) compared to the large ground-state conductivity.^58,72,92 In contrast, a semiconductor will have a significantly larger on-off contrast and a higher Δσ signal.⁵⁸ It is, therefore, paramount to measure TDS and TRTS whenever possible.

The previous sections gave a general overview of TDS, OPTP, and TRTS. This section will focus on the real lab challenges that a user needs to be aware of to extract accurate results from their measurements. These challenges are separated into sample-related and instrumentation-related categories.

The best sample is a crystal of known size or a homogeneous film with a known thickness on a well-known substrate. In these cases, the measurements and data processing are rather straightforward, and the sample should be measured as is. However, many newly synthesized materials, especially nanoparticles, are powders. Powder samples need to be somehow processed before being placed into the spectrometer. However, each processing step can alter the sample properties and obscure the actual material properties.

OPTP dynamics are commonly not influenced by the amount of sample material used in the measurement. In addition, if the same sample is exposed to different photon fluxes, the power induced changes are also rather independent of the sample itself. Therefore, the best way to explore the dynamics of a material is by just measuring it as powder. Powder samples are the least invasive way to prepare a sample. The simplest approach is to place the powder between two pieces of tape. A slightly more advanced approach uses a tape-cell formed by a spacer of known thickness and two pieces of tape.⁷⁰ 

Tape cells avoid any alteration of the material but also provide limited reproducibility with regard to the sample amount. The sample amount and thickness, however, need to be known for accurate TRTS data processing. If the thickness is not known, a sample parameter like sheet conductance can still be determined from TRTS. However, if the goal of the experiment is to report material conductivity, a more advanced sample preparation is merited. In this case, powder samples are mixed with materials that are transparent for THz radiation and for the optical pump beam. These mixtures are then prepared into films. The films can be prepared either from Nafion,⁹³ PVB, or by doctor blading.⁹⁴ 

Nafion films can be made by mixing the material in ethanol with a Nafion solution.⁹⁵ The solution is then drop casted or spin coated onto a substrate. The sample is heated to 60 °C, and the solvent is evaporated. Nafion films are moderately reproducible and adsorb water, which reduces the total THz transmission, especially for very thick films.⁹³ However, OPTP measurements are solely sensitive to photo-induced changes, which are not noticeably influenced by water content.⁹⁵ Nafion films have the great benefit of using only benign solvents and low temperatures.

Screen printed paste films of nanoparticles (doctor blading) involve harsher processing steps, including ultrasonication, and a final baking step at about 400 °C.⁵⁷ These process steps are intended to alter the material and create a solid film in which the nanoparticles are in close contact. This film is closer to potential solar cell applications; however, the measured photoconductivity will be influenced by the heat treatment and not be representative of the pure material. This is not a bad thing in general; however, the experimentalist needs to consider what insight is sought in the experiment.

Reporting accurate photon flux and consecutive carrier densities—demands well-characterized photoexcitation. The core task that should be performed after each alignment is to measure the optical and THz spot sizes and confirm that they overlap in space.

A first initial alignment of the overlap can be done with a well behaved, simple sample, i.e., silicon. The silicon wafer is mounted, and OPTP is measured. Then the pump time is chosen to be well after the injection timing. Now the magnitude of the OPTP signal can be monitored while the optical beam is moved over the sample. The best optical and THz overlap will result in the strongest OPTP magnitude.

Spot sizes are frequently reported as crude approximations using the iris or other fixed apertures.^21,22 A more rigorous characterization can improve our understanding of photon flux-induced effects and provide a better base for inter-lab comparison.²² 

Spot sizes can be measured with cameras (optical and THz) or with less expensive methods. Adjustable irises can be used, but they are prone to misalignment. A better approach is a linear aperture. This aperture can be easily made in the laboratory by mounting a metal plate with a sharp and flat edge (knife edge, razor blade) on a mechanical micropositioning stage.⁹⁶ This beam blocker is placed outside of the spot and then moved into the spot in measured steps. For each step position, the optical intensity is noted, as illustrated in Fig. 8(a). This measurement should be performed as close to the sample position as possible, as this is the location at which the overlap needs to be achieved.

This function assumes a Gaussian intensity distribution, and it is important to inspect the agreement between fit and data to ensure that the optical profile is actually well described with the simple 1D Gaussian distribution. If a noticeable disagreement, for example, between shoulders, is observed, it is prudent to identify the origin of this. Commonly, dust on optics or damaged optics can result in a non-Gaussian spot. A non-Gaussian spot will not only complicate data interpretation but is also usually linked to reduced performance.

The same knife-edge measurement should then be performed for the THz beam profile. This can either be done by sitting on the TDS peak in THz time—shown in cyan in Fig. 8—or by scanning the full TDS trace. The latter is more time consuming but also presents spectral–spatial information, shown as red and green traces in Fig. 8. Only if the system is well aligned will all frequency components of the THz beam be focused at the same location. Hence, a spectrally resolved knife-edge measurement is an excellent way to check the alignment of the THz beam path.

With spot sizes determined and overlap verified, the remaining question is: what are the correct spot sizes? Let’s assume the intuitive approach of having the same size for optical and THz spots. In this geometry, the carrier generation follows a Gaussian profile with the same size as the two spots, generating carriers in the THz spot. However, the generated carriers are not fixed in their positions. In a conductive medium, carriers are mobile and will diffuse. This diffusion will broaden the original distribution over time. The carriers will diffuse out of the THz beam, and the measured total OPTP signal will decrease due to this diffusion on top of the trapping/recombination taking place.⁹⁷ This diffusion will significantly complicate the data processing, and the reader should double check if this configuration is desirable for the specific experiment. An easier-to-interpret configuration uses a larger pump spot compared to the THz spot.

With a pump spot larger than the THz spot, the effective photon flux can be determined by the overlap integral of the two spots. Basically, the optical power that overlaps with the Gaussian shaped THz beam is considered for the photon flux, while the edges that do not overlap with the THz beam are discarded.

The presented workflow was limited to one dimension. In general, optics and alignment issues can result in egg shaped beams, and for the highest accuracy, it is necessary to repeat all measurements in the second direction and even for different propagation distances.

OPTP was first demonstrated in 1987.⁹⁸ The technique matured quickly moving away from simple semiconductors to nanoparticles,⁹⁹ adaptive metamaterials,^59,100 2D materials,¹⁰¹ and even MOFs.⁷⁵ Over the decades, several improvements have been achieved. The first improvements focused on better generation and detection techniques, improving the signal-to-noise ratio, and allowing the measurement of very small signals below 0.001%.⁷⁰ In recent years, OPTP was combined with microscopy and in operando bias conditions, and the maximum delay time was significantly boosted. Concluding this tutorial, we want to highlight some of these improvements and give a perspective on what the future of OPTP may bring.

Commonly, TDS and TRTS are measured in two consecutive measurements. The actual photo-transfer function is then formed by adding the two contributions. This works great for well behaved samples that do not change in the course of the measurement. However, if the sample changes over time, the original TDS measurement was collected on a “different” sample than the TRTS measurement. Furthermore, two consecutive measurements also mean twice the measurement time. This can be overcome by a double modulation technique.^102,103

Double modulation uses two optical choppers and two lock-in amplifiers. So instead of only measuring the modulation in the THz signal caused by the pump beam, the double modulation also detects the modulation of the THz signal itself, which is used to detect the TDS signal.¹⁰⁴ This double modulation technique can have huge benefits if the conductivity of the sample changes due to laser heating.

Heat induced changes take place on a seconds and longer time scale. OPTP and TRTS measure the difference between on and off on a 1 ms time scale. Therefore, heating that causes a slow overall drift of the conductivity is not detected with regular OPTP. However, static TDS, which is sensitive to the ground state, can measure such slow changes. Double modulation can, therefore, measure the slower drift caused by heat and the on-off contrast on the ultrafast time scale. Additionally, it can provide a better signal-to-noise ratio.

THz radiation has a wavelength of 300 μ m, significantly limiting its usefulness for classical optical microscopy. However, in the last decade, several groups have overcome the Abbe limit. Some of the first approaches used the fact that the optical gate pulse can be focused to spot sizes determined by the Abbe limit for optical beams.^55,105,106

In these experiments, the detection was localized to a few micrometers, and only the local THz field was read out. More advanced techniques use scattering effects in which nanometer sized tips locally scatter the THz field from the sample.^107,108 The field is then measured either in the farfield or directly by an Austin switch on the tip.¹⁰⁹ All of these techniques have been combined with optical excitation to provide OPTP/TRTS nanoscopy. In general, the core challenge of these techniques is to ensure that the optical pump pulse does not interfere with the THz detection.¹⁰⁹ 

Solar cells are commonly biased in operando. This bias might influence the material under study. A detailed understanding of the bias induced changes can help us identify their physical origin. For example, during the OPTP discussion, we mentioned that trap states can be filled by electrons. This filling can happen under stronger light excitation by simply providing more photoelectrons than traps. However, it is also possible to fill these traps electrically. Trap filling then provides a measure of trap density, their energy relative to the Fermi level of the material, and their influence on the carrier lifetime. All these measures can help us understand the origin of these traps and guide us toward eliminating them.^57,110

Adjusting the Fermi level in a material during THz measurements requires electrical contacts to the material. Electrical contacts, however, are conductive and therefore THz opaque. This paradox can be overcome by using smaller DC contacts instead of full plate contacts. Furthermore, we can leverage the fact that THz beams are linearly polarized EM-waves. Linearly polarized waves can propagate through linear wire strips unhindered, a technique commonly used for wire grid polarizers.

Wire grid polarizers can be fabricated directly on the sample. These polarizers can be fabricated out of optical transparent conductors to allow access for the pump beam to the sample materials.¹¹⁰ This fabrication technique can then be used to assemble a three-electrode cell in which the Fermi level of the material can be adjusted while TDS, OPTP, and TRTS measurements are performed.⁵⁷ 

Large scale solar devices need carrier lifetimes sufficient to extract the charges. Charge extraction on commercial length scales can take microseconds and longer. Measuring such lifetimes presents a challenge for OPTP. OPTP uses a mechanical delay line to achieve an accurate temporal delay between the optical pump and the THz probe beam. The time delay is the travel distance divided by the speed of light. Meaning that for a 1 ns delay, a mechanical delay of 30 cm is needed; for a 100 μs delay, 30 km is needed. While a 30 km delay might be an interesting project for an inter-laboratory collaboration, it remains unfeasible, not only because of the space demand but also because of the massive demand for accurate alignment to maintain sub-millimeter spot accuracy over kilometerdelays.

Microsecond and longer delays cannot be achieved with mechanical delays but with electrical delays. This technique was first adapted to THz measurements by the author and Marco Rahm in 2010.⁹⁷ Recently, the group of Lloyd-Hughes (2022) significantly improved upon the original work, as illustrated in Fig. 9(b).¹¹¹ In both configurations, the pump pulse is not provided by the same laser as the THz pulse but by a second laser synchronized to the THz generation/detection. This synchronization allows for electrical delays ranging from hundreds of picoseconds to tens of milliseconds.¹¹¹ These unmatched time ranges are ideally suited to study materials for solar applications.

Terahertz Time Domain Spectroscopy (TDS) is an excellent technique to measure the ground-state properties of emerging materials. These measurements provide complex conductivity values that can be fitted with models to understand carrier scattering in materials. TDS can be combined with low temperature conditions and electrical biases to adjust the phonon contribution and Fermi level, respectively. These measurements can be utilized to measure novel conductors and semiconductors. They can shed light on the contribution of trap states and scattering mechanisms and the activation energies of dopants and hopping mechanisms in emerging materials.

Combining TDS with photoexcitation allows us to understand photogenerated charge lifetimes and dynamics. Optical Pump THz Probe (OPTP) monitors the frequency integrated transmission for different pump-probe delay times. The onset of conductivity following photoexcitation provides information about charge injection and even the formation of quasiparticles, like Polarons. The decay of photoconductivity provides crucial insight into the trapping and recombination effects happening in the material. A detailed understanding of these trapping channels can guide material scientists toward a better understanding of the underlying mechanisms of these traps. Understanding why photoconductivity decays is the crucial first step toward eliminating these mechanisms and designing superior photoconductors.

The measured OPTP traces are then used to identify interesting delay time points for more detailed Time Resolved THz Spectroscopy (TRTS) measurements. TRTS measurements are used to calculate the complex photoconductivity spectrum. This spectrum can then be fitted to known empirical or mechanistic models to yield insight into carrier scattering, effective mass, and localization. The combination of TDS, OPTP, and TRTS provides a detailed insight into an emerging material as synthesized. No electrical contacts are needed, and no complicated sample preparations are involved, which could alter the material properties.

We would like to acknowledge James Lloyd-Hughes and his graduate student Edward Butler-Caddle for providing the data for Fig. 9(b). Furthermore, thanks go to Kendra Hamilton for proof-reading this manuscript. A posthumous thanks to Charles A. Schmuttenmaer for the privilege of working with him and the time he spent teaching myself and many of my colleagues OPTP and TRTS. Thanks to the University of North Texas for not renovating my labs yet; research would have distracted me from writing this tutorial.

The authors have no conflicts to disclose.

Jens Neu: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Project administration (lead); Resources (lead); Software (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.