Experimental Common Tools: (3) Transient Response Analysis

Editor : Sapien

I’ve travelled every country, I’ve travelled in my mind
It seems we’re on a journey, a trip through space and time
And somewhere lies the answer to all the questions why
What really makes the difference between all dead and living things
The will to stay alive.

-From “Move On”, sung by Abba

 ”Transient” is a process of transition before the system reaches a steady-state condition due to external stimulation. The transient itself does not mean nonlinearity because it is a kind of general phenomena even in linear systems such as overshooting, underdamping, and phase shift upon periodic stimulation. In linear systems the transient can be characterized in terms of time constant τ, which represents the time scale of transient response in corresponding process. The nonlinearity in transient phenomena arises mostly from multiplicity of different processes, therefore proper modeling and decomposition of multiple time constants are key issues in transient response analysis (TRA).

 The transient response analysis works generally on external stimulation of the form of step function and by measurement of response as a function of time. In the electrical system, regarding to the stimulation of current step or voltage step, the transient response is used to be voltage or current measurement, respectively. For photovoltaic devices, turning on a light would be a stimulation and either output voltage or current can be the transient response. For light-emitting devices, on the contrary, switching on driving power can be the stimulation and then emitting light becomes the output response.

 The transient measurement requires fast measurement in order to resolve response data at the right time scale corresponding to the process of interest. It is critically important for a step stimulation to have a rise time short enough comparing to the measurement time interval, and also to be properly triggered for the synchronization to data sampling of response signal.

 Although the measurement technique and analytic methodology of the frequency response analysis (FRA) and TRA are quite different, the objective processes are identical and the results are similar. In the frequency domain analysis, the measurement of phase provides additional information on system dynamics, and the modeling of nonlinear process as well as the determination of time constant are relatively straightforward and convenient. The time domain analysis, on the other hand, is more practical for experimental hardware setups and data management.

 For the characterization of rechargeable batteries, the time domain analysis has an advantage in measurements of both the variation of internal resistance due to relatively fast electrochemical processes as well as the variation of amount of charge due to relatively slow charge-discharge process.

 In the study of charge transport in organic semiconductors, TRA experiments for photo-excited charge carriers under electric field, such as the time of flight (TOF) measurement and the charge extraction by linearly increasing voltage (CELIV) measurement, provide the charge carrier mobility. And in the characterization of organic photovoltaic devices, transient measurements such as transient photocurrent (TPC) and transient photovoltage (TPV), provide various device parameters. Furthermore in the characterization of electroluminescence devices like OLED, the TRA techniques can be applied not only for electrical transient analysis, but also for the time-resolved spectroscopy, which measures the change of luminescence spectrum at the transient state.