Month: August 2024

Pitfalls when measuring recombination lifetimes in organic solar cells

Six years ago, I came across an interesting publication by David Kiermasch and Kristofer Tvingstedt, [Kiermasch et al 2018], Frosch verlässt Seerose. titled Revisiting lifetimes from transient electrical characterization of thin film solar cells; a capacitive concern evaluated for silicon, organic and perovskite devices. It shows that particular in thin film solar cells, the time constant determined by voltage based techniques – open circuit voltage decay (OCVD), transient photovoltage (TPV), intensity modulated photovoltage spectroscopy (IMVS) – is in many cases not the recombination lifetime, but corresponds to an RC-time from the device itself. While the authors did not find this effect, they showed impressively how most modern solar cells are limited in this respect, and it has to be verified carefully whether or not the experimentally determined time constants do correspond to recombination lifetimes!

I took this publication very seriously. Below I show you a summary slide I made for my group seminar in the year of publication, 2018.

Carstens tuesday note 2018.

The shown equation was actually animated, sorry for making your life harder (but mine easier;). Briefly, the idea of why an RC limitation shows up is the following. The charge in the device Q is changing with time during the measurement – no matter if the method is a large signal (OCVD) or small signal method (TPC, IMVS):

\frac{dQ(t)}{dt} = \underbrace{\frac{dQ(t)}{dt}}_{-\frac{Q(t)}{\tau_\text{rec}}} - \underbrace{\frac{\partial Q}{\partial V}}_{C(V)} \frac{d V(t)}{d t},

where the first term on the right hand side represents the recombination rate – of which we want to measure the recombination lifetime \tau_\text{rec} – and the second term a contribution coming from the response of charge due to the measured signal of the experimental technique: the time variation of the voltage as response to a time dependent light signal (pulsed or modulated). If the latter capacitive term becomes dominant, the recombination lifetime cannot be determined anymore, as is hidden behind the RC time.

As you can see in this slide, based on our data, for P3HT:PCBM (bottom left of the slide) the capacitive (RC) times remain lower than the measured time constants. We can state with some confidence that the RC times do not limit the measured recombination lifetimes. Also, the slopes of \tau vs V_{oc} are different and, in this case, a measure of the recombination order.

In contrast, for the PCDTBT:PC70BM solar cell, for which I took the measured time constants at room temperature from literature, you see that the RC time limits the recombination lifetime, as the measured time constants just correspond to the RC times. This implies that the recombination lifetime is too short to be measured for the given RC limitation.

A nice aspect of the paper by Kiermasch et al. is that it gives a comparatively simple way to estimate the RC times:

\tau_{RC} \approx \frac{C(V_{oc})}{j_\text{gen}(V_{oc})} \frac{nkT}{e}

Here, nkT/e is the recombination ideality factor times the thermal voltage, C is the voltage dependent capacitance, which can be estimated (as lower bound) by the geometric capacitance of the active layer, C_\text{geo} = \epsilon_r\epsilon_0/L, with the dielectric constants (relative and vacuum) and L the active layer thickness (you could also include organic transport layers, but probably not PEDOT:PSS as it has a relative dielectric constant \gg 3). The generation current density can be approximated, in most cases, by the short circuit current density j_{sc} (unless the transport resistance loss is too large:).

Please note, that in this particular RC time where both R and C come from the solar cell itself, the active area cancels out (as both j and C contain it and are in denominator and numerator, respectively). So, in order to reduce the RC time for a given solar cell, the only way seems to either 1. increase the current, by increasing the light intensity, measuring up to higher Voc… if possible, or 2. reduce the (geometric) capacitance by increasing the device thickness… a lot.

All of this came to my mind again when looking at IMVS data that we took on PM6:Y12 solar cell devices (made by Chen, measured by Nino with support from Christopher).
PM6-Y12 IMVS RC time vs IMVS time constant.
On the left, you see the estimation of the RC time \tau_{RC} after Kiermasch 2018, compared to the measured time constants by IMVS, \tau_c. Except for, maybe, low temperatures, the RC times dominate the measured signal at high open circuit voltages, whereas the shunt limits the lifetime determination at lower open V_{oc}. A direct comparison is shown on the right hand side, where everything in the shaded triangle is either shunt or RC-limited.

While quite sad, I think this is important: if you want to determine recombination lifetimes in thin film solar cell devices, check for limitations by RC times and shunt.