Two-photon absorption DOI: 10.1002/smll.200600157 The Empirical Correlation Between Size and Two-Photon Absorption Cross Section of CdSe and CdTe Quantum Dots Shih-Chieh Pu, Meng-Ju Yang, Cheng-Chih Hsu, Chih-Wei Lai, Cheng- Chih Hsieh, Sheng Hsien Lin,* Yi-Ming Cheng, and Pi-Tai Chou* The tuning of CdSe quantum dot (QDs) sizes, and consequently their corresponding two-photon absorption (TPA) cross section, has been sys- tematically investigated. As the size (diameter) of the quantum dots increases, the TPA cross section is found to be empirically related via a power-law proportionality of 3.5  0.5 and 5.6  0.7 to the diameters of CdSe and CdTe QDs, respectively. The results are tentatively rationalized via a theoretical model of two-photon excitation properties in a system in- corporating excitons and defects. Keywords: · cadmium · chalcogenides · fluorescence · quantum dots · two-photon absorption 1. Introduction Recent studies regarding the special characteristics of II–VI quantum dots (QDs) using intense two-photon ab- sorption(TPA)haveshownthatthesematerialshaveavari- ety of potential applications, including three-dimensional microfabrication, [1,2] informationtechnology, [3] laser technol- ogy, [4] and biological system imaging. [5] Both theoretical and experimental approaches predicted that a two-photon ab- sorptioncrosssectioncouldbeashighas10 4 GM (Gçppert- Mayer units, 1GM = 10 50 cm 4 sphoton 1 ) upon nanosizing CdSe. [6,7] Nevertheless, despite numerous TPA applications havingbeenreportedoverthelastfewyears, [8–10] fundamen- tal approaches applied to the TPA properties of II-VI QDs are currently rare. Blanton etal. [6,11] have performed TPA experiments for CdSe QDs at 5–20K. In their classical ap- proach, a linear relationship between TPA cross section and volume has been proposed. It is also worth noting that this experiment requires cryogenic temperatures due to the pre- dominant radiationless transition in CdSe QDs. Recently, the TPA cross section has been measured for CdTe of cer- tain sizes. [12] However, the correlation between TPA and QD properties remains unexplored. Owing to the increasing importance of various cutting- edge applications, it is thus urgent to initiate a systematic study of the TPA properties of II-VI QDs. The main obsta- cle of this experiment is believed to be the equally obscure reporting of the one-photon absorption cross section and hence the difficulty in deducing the number of particles, that is, concentration, in solution. Moreover, in order to deduce a reliable TPA cross section, precise size parameters as well as the corresponding pertinent quantum efficiency are also necessary (vide infra), data on which has proven to be very difficult to obtain previously. Recently, thanks to the progress on both the synthesis and characterization of II-VI QDs, [13–15] particularly on the precise correlation be- tween size, type of QD, and several other photophysical properties, [15] the relevant fundamental approach has [*] Dr. S.-C. Pu, M.-J.Yang, C.-C. Hsu, C.-W. Lai, C.-C. Hsieh, Prof. S. H. Lin, Prof. P.-T. Chou Department of Chemistry, National Taiwan University Taipei 106 (Taiwan) Fax: (+ 886)2-2369-5208 E-mail: chop@ntu.edu.tw Prof. S. H. Lin Institute of Atomic and Molecular Sciences, Academia Sinica P.O. Box 23-166, Taipei (Taiwan) E-mail: hcshaw@po.iams.sinica.edu.tw Dr. Y.-M. Cheng Department of Chemistry, National Tsing Hua University Hsinchu 300 (Taiwan) Supporting information for this article is available on the WWW under http://www.small-journal.com or from the author. 1308 # 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim small 2006, 2, No. 11, 1308 – 1313 full papers P.-T. Chou et al.