Observation of time-dependent luminescence from excited states with a wide range of lifetimes allows students to explore the connection between selection rules and transition rates. It is fairly simple to measure microsecond and longer lifetimes with equipment common to undergraduate programs, because the instrument response time of even modest bandwidth systems is insignificant on microsecond and longer time scales. The measurement of nanosecond lifetimes, however, is more challenging, because the instrument response time is comparable to the lifetimes being measured. In this case, the instrument temporal response must be deconvolved from the observed luminescence signals in order to extract the actual excited state lifetime. We describe a method for measuring nanosecond fluorescence lifetimes in the advanced undergraduate laboratory that uses real-time analog luminescence signals instead of traditional photon counting techniques. The detection electronics of this method are fairly simple, consisting of an oscilloscope monitoring the time-dependent output of an inexpensive silicon photomultiplier. We introduce a simple and transparent method for students to characterize the instrument response and deconvolve it from the observed luminescence signals, yielding measured nanosecond fluorescence lifetimes in good agreement with the corresponding literature values obtained by time-correlated single photon counting. The limitations of silicon photomultipliers for this method of measuring nanosecond lifetimes are discussed in detail. Application of this treatment to decay processes that are not single exponential is also discussed.
REFERENCES
The NIM based components required for generating luminescence decay curves by TCSPC include a NIM bin with power supply, two wideband amplifiers (if detector output pulses require amplification), two constant fraction discriminators, a time-to-amplitude convertor, and a multichannel analyzer. These components can sometimes be found used at affordable prices; however, an anonymous reviewer of this work has indicated that such used legacy components are becoming hard to find.
Prices obtained from four of the largest manufacturers of integrated TCSPC systems indicate that the least expensive units cost about $12,000. These systems integrate the individual components listed in Ref. 8 on a PC plug-in card, necessitating the added expense of installing an appropriate communications bus in the host PC. A smaller manufacturer (Marina Photonics, <www.photoncounting.net>) offers an integrated TCSPC system for less than $4000. We do not know how well any of these systems work with the inexpensive silicon photomultiplier used here, as the manufacturers of these systems only offer discrete avalanche photodiode modules or photomultiplier tubes as detectors. The TCSPC system that was sold by the manufacturer of the silicon photomultiplier used here has been discontinued.
The relationship between rise time τrise and the 3 dB bandwidth BW3 dB that is most often used, τrise = 0.35/BW3 dB, defines τrise as the time it takes the signal to rise from 10% to 90% of its peak value assuming the system can be modeled as a charging RC circuit with equivalent resistance R and equivalent capacitance C.
The absorber concentration c is estimated from the Beer-Lambert relationship, OD = εcL, where OD is the sample optical density, ε is the extinction coefficient of the absorber, and L is the path length through the sample.
Unweighted fits are appropriate when the uncertainties of the individual points on the luminescence curves are not well characterized. However, fit parameter uncertainties reported by unweighted fitting routines can be unreliable precisely because they are estimated without knowledge of the individual point uncertainties.
It can be shown that by a change of variables.
A laboratory class handout (available from the corresponding author) attributed to Montana State University Professor of Chemistry Patrik Callis describes such a numerical convolution method using Excel.
