Low-Perturbation Optoelectronic Measuring Techniques. What are they and what are they good for? Antonio Jesús Riquelme Expósito Abstract— In the Nanostructured Solar Cells Group at UPO we like to experiment with solar cells. We always treat them with care and delicacy, as we always use a small perturbation to analyze their response. This small perturbation can be an optical blink, of different colours or electrical, at either at a pleasant room temperature or at freezing cold conditions, in either total darkness or under extreme light soaking. Normally, all cells behave well, although perovskites ones do not appear to stand well our treatments. In any case, they always provide us with tasty information, in the form of resistances and capacitances, or kinetic constants, of different sorts. In addition, we like to run simulations and devise models of reference, to better understand their complex behavior. We do not know if we do it well or badly, but we always do it with frequency and intensity. Key Words— Characterization, EIS, IMPS, IMVS, Spectroscopy. ——————————  —————————— 1. INTRODUCTION lucidating the behavior of the electrons inside our de- vices is a titanic juggling act. However, luckily for us, we have a great mix of tools at our disposal. This arti- cle will focus on low-perturbation optoelectronic measur- ing techniques, due to their current relevance on the field. These techniques work by subjecting the device we want to characterize to a small electrical or optical stimu- lus, modulated in frequency, while keeping known condi- tions of voltage or steady light intensity. It is needed to bear in mind that inside a solar device in operation many different processes take place, at different time scales and loading conditions. The idea behind small- perturbations is to separate these processes and to simplify the kinetics by assuming that small perturbation implies first order kinetics. In first order kinetics, the time evolu- tion is described by equation 1. () =  0  − 1  (1) where n is the electron density and k1 is a first-order kinetic or rate constant. There are three kinds of techniques under the low-per- turbation optoelectronic measuring concept. These are Im- pedance Spectroscopy (EIS), Photocurrent Spectroscopy (IMPS) and Photovoltage Spectroscopy (IMVS). 2. SMALL-PERTURBATION TECHNIQUES The three small-perturbation optoelectronic measuring techniques can be described by a universal equation (2). () = () () (2) Where P represents the Perturbation, S means the signal recorded and Z is the so-called transfer function. All of them are angular frequency (ω) dependent. As we will see later, the most operative way of defining a transfer func- tion is a complex number. The origin of the perturbation and the signal received indicated in equation (2) can vary. The full range of combinations is shown in Table 1. TABLE 1 TRANSFER FUNCTIONS DEPENDING ON PERTURBA- TION AND RESPONSE 2.1. Electrical Impedance (EIS) This technique measures the “hindrance” (resistance) pre- sented by a circuit to a current when a voltage is applied. This useful tool allows us to understand the internal be- havior of a solar device, elucidating the processes that take place inside of it. This technique consists in applying a small perturbation of the voltage that is applied by a sinusoidal perturbation of low amplitude. The current response is also sinusoidal that depends on the frequency of the modulation. Both, re- sponse and perturbation show the same frequency in their sinusoidal behavior. However, as shown in Figure 1, the response can have a phase shift due (φ) to internal electric process that are taking place in the material that we are studying [1]. E ———————————————— Antonio Jesús Riquelme Expósito. Facultad de Ciencias Experimentales, Uni- versidad Pablo de Olavide. ajriqexp@upo.es. Transfer Function Perturbation Response What we expect to find EIS Voltage Current Transport and Re- combination IMPS Light (optical) Short-circuit Current Transport and Trans- fer IMVS Light (optical) Open-circuit Voltage Recombination