Quantification of trap states by thermally stimulated current in thin film solar cells
What are trap states and why should we care about them?
The performance of light-emitting (LEDs) and photovoltaic (PV) devices depends on the quality of the photoactive semiconductor material. The unintentional introduction of defects in the semiconductor material due to material impurities or during the fabrication process causes the deviation from optimal performance.
These defects are referred to as trap states, or in short “traps”, which are energetic states within the bandgap of a semiconductor. In general, traps can occur due to material impurities (in the bulk) or at the interfaces between layers of different materials. In organic semiconductors, the trap states are frequently present due to the natural material disorder. In inorganic and hybrid semiconductors (e.g.: hybrid perovskites, silicon,…) the presence of grain boundaries is a known source for trap states.
As there are various reasons for traps, their effect on devices is also rather manifold. A very common effect of – especially shallow – traps is a reduced effective charge carrier mobility, due to multiple trapping and release events of charge carriers.[Kna12] Traps that are centers of recombination, so-called Shockley-Read-Hall recombination, will typically reduce the efficiency of devices. In solar cells, this mechanism limits the open-circuit voltage. In the case of a light-emitting device, such trap states can form and evolve during device operation causing an increase in the driving voltage.[Die22]
In the following blog post, we will present how to characterize the trap states with the technique called thermally stimulated current (TSC). We also propose a method to reliably interpret the TSC results based on drift-diffusion simulations.
Characterization of trap states
Trap states in a semiconductor device can be described by three parameters: the density of trap states Nt, their energetic position within the bandgap – distance to the HOMO (valence band) or LUMO (conduction band) for holes or electrons, respectively – Et, and the capture rate cp which describes the charge trap-release dynamics. The same dynamic can alternatively be expressed with the attempt-to-escape frequency or the cross-section.
There are a plethora of characterization techniques to get insights into trap states in bare thin films and full devices. The most common techniques for organic and perovskite devices are:
space charge limited current (SCLC) current-voltage (IV) scans
thermal admittance spectroscopy (TAS)
deep level transient spectroscopy (DLTS)
Fig 1. Sketch of trap state for electrons within the bandgap of an organic semiconductor.
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Fig. 2. Sketch of light, temperature, current and voltage transients in a stimulated current measurement. The dashed square marks the interesting part of the experiment which we usually refer to as “TSC signal”.
Every technique has its advantages and disadvantages. For example, the frequently used SCLC-IV is easy to implement but provides only information on the trap density while the energetics and dynamics cannot be assessed. Both TAS and DLTS measure the capacitance of the device, which can be strongly influenced by the other layers of the device stack causing misinterpretation of the results.
Alternative techniques are the thermally stimulated current (TSC) and the thermally stimulated luminescence (TSL). These techniques were developed more than 50 years ago[Gar48][Hae60] and allow for extracting all three trap parameters.
The experimental process is shown in Fig. 2. First, the device is cooled down to temperatures well below 100 K. Subsequently, the trap states are filled with charges generated by a light pulse and/or the application of a forward voltage Vload. After a rest time, the temperature is ramped up linearly and optionally an extraction voltage Vextract is applied. The measured current during the heating ramp (marked with a grey square) contains the information about the trap states.
What is the origin of the extracted current?
At the start of the temperature ramp, the trap states are occupied by electronic charges that are immobile due to the low temperature (see the sketch in Fig. 3, T~100 K). With the increase in temperature during the ramp, the shallow traps released the electrons that are then extracted to the contacts due to the internal field or by the applied bias Vextract (Fig. 3, T~200 K). These electrons are creating the measured external current signal (Fig. 3, bottom, green line). Increasing the temperature further releases also the electrons in the deeper traps until all traps are released and the current drops to zero. In a system without losses (such as SRH or bimolecular recombination, extraction barriers, etc.), the integral of the stimulated current equals the trapped charge density inside the device (orange curve in Fig. 3).
Fig. 3. right: sketch of the band diagram during a TSC ramp at different points in time / temperatures. Left: Current signal during the TSC temperature ramp and the integrated current over time (= extracted charge).
Analysis of TSC curves
We can analyze the TSC signal with a simple model that describes the dynamics of trapped nt and free charges n – for simplicity, we restrict ourselves to electrons, but similar equations apply to holes:
Where N0 is the density of available states in the electron transport level, k is the Boltzmann constant, T the temperature and τ the charge carrier lifetime. Under different assumptions, this 0D system of differential equations can be solved analytically. Haering and Adams[Hae60] assumed that recombination is faster than re-trapping, while for Garlick and Gibson[Gar48] both processes are equally probable. These result in the so-called “slow” and “bimolecular” analytical expressions describing the full TSC signal.[Vae22] As those formulas are still fairly complex and not easily applicable for analysing experimental data, it is possible to simplify the analysis by taking only a certain part of the TSC signal. Most common are the “initial rise” or the “T4max” methods, which only consider the first current increase or the peak position, respectively (Fig. 4).
Fig. 4. While the fit methods “slow” and “bimolecular” use the full TSC signal, the initial rise uses only the low temperature current rise. T4max uses only the temperature at the peak position.
The main question is: will the analytical models reliably determine trap parameters in a full device? To answer this question we analyzed the validity of the models described above, using drift-diffusion simulations in Setfos.
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Simulation of TSC curves and validity checks
The approach is as follows: Material and device parameters reflecting the ones of an organic solar cell are used as input in Setfos (a).[Neu18] Setfos provides us with a typical TSC curve that is used as synthetic experimental data (b+c). Hence, the analytical formulas described above are now applied to this TSC transient which gives us a set of trap parameters (d). Those are now compared with the input (a) which lets us analyze the validity ranges of the analytical expressions. This workflow is automated and repeated for various sets of material (e.g. mobilities), devices (e.g. injection barriers), and experimental parameters (e.g. the temperature ramp rate).
Fig. 5. Approach that is used to test the validity of the analytical formulas to determine trap parameters from TSC signals. The TSC signal of a device with certain parameters (a) is simulated with Setfos (b) which provides us a “synthetic” TSC transient (c). We apply different analytical formulas to this data (d) and compare the determined trap parameters with the input in (a).
Selected results
In the context of this blog post, we will show only a part of the results that arose from the above analysis. If you are interested in the full study you can find it in our publication.[Vae22]
In Fig. 6 the analysis of the trap depth (Et) is presented as a function of individual variations of the three trap parameters which are discussed separately:
The trap depth (Et) is very well predicted by the slow and initial rise models. The T4max formula predicts the trend correctly but gets worse for traps that are deeper in the bandgap. The bimolecular formula is not a good model for this, due to the capture rate in the base case (explained in the next point).
The capture rate (cp) affects the applicability range of analytical formulas and therefore the accuracy in determining the trap depth. For slow capture rates (below ~10E-10 cm3/s), the recombination is faster than re-trapping and hence the slow (and initial rise) method works well. For fast capture rates (above ~10E-10 cm3/s), re-trapping becomes relevant and thus the bimolecular formula provides a correct value while both the initial rise and slow formula deviate.
Here the T4max method should only be used for an approximate trap depth estimation.The trap density (Nt) influences the magnitude of the current but also influences the shape of the signal. The latter explains the deviation of the extracted trap depth from the input one for Nt ~10E18 cm-3 if full fit methods are used. Interestingly, the initial rise method seems to be much more robust.
Fig. 6. Determined trap depth using different analytical models as a function of input trap depth Et (left), capture rate cp (middle) and trap density Nt (right).
Already from the examples above, it is evident that the peak method (T4max) does not provide accurate results. On the other hand, the slow and initial rise methods reliably obtain the trap depth for a large range of material and device parameters. In our publication,[Vae22] we present the validation assessments of the analytical models with many more parameter studies.
Not only the accuracy of the determined trap depth Et but also the trap density Nt has been investigated in the full report. For example, we demonstrated that the accuracy of the trap density can be improved by tuning stack and experimental design. Moreover, a large number of traps will affect the results due to space-charge effects and increased recombination. In this case, it might be advisable to compare the determined Nt from TSC with other measurements. Further data is provided in the full publication.[Vae22]
Conclusions and outlook
We presented the thermally stimulated current (TSC) method to obtain the trap parameters in complete organic and perovskite solar cell devices. The values of the trap parameters were determined with four different analytical formulas. With the simulation software Setfos, we defined a test based on synthetic data to verify the validity range of the analytical formulas. The presented method can easily be extended to investigate the influence of electrical doping, mobile ionic charge carriers, trap-assisted (Shockley-Read-Hall) recombination, interface traps, etc.
