(496f) Quantifying the Accuracy and Uncertainty in Back Focal Plane Imaging for Nanostructured Materials and Optoelectronics

Abstract Summary: To both understand the photophysics of new nanomaterials and design high efficiency optoelectronic devices, it is crucial to accurately and precisely quantify the orientation of the transition dipole moment. This is done by fitting the measured angular emission pattern from back focal plane (or Fourier) imaging, but there is often no discussion on the inherent uncertainty of this measurement despite the fact that small changes in dipole angle (order of degrees) lead to extreme changes in device efficiency. In this presentation, we quantify the accuracy and uncertainty of these measurements by simulating 1000s of BFP images, showing orders of magnitude error difference depending on dipole angle and sample refractive index. Most significantly, we show how the CCD camera noise and emitter refractive index can cause an overestimation of the dipole angle as high as 10 – 20 degrees. Finally, we offer recommendations for improving the accuracy of the fitting.

Background and Significance: Back focal plane (BFP) imaging has emerged as a crucial tool for determining the excitonic and photophysical properties of nanomaterials [1]. As shown by Figure 1A, this technique directly images the 2D projection of the angular emission pattern of a sample. In these measurements, the transition dipole moment (TDM) can be determined by fitting the angular emission profile to a series of dipole angles [2]–[4]. Accurate measurement of the TDM is crucial: while the angular emission patterns between a perovskite nanocrystal film with average dipole angle of 29° and another with an angle of 14° appear very similar, the maximum potential efficiency of an LED made from these structures would correspond to 25.8% and 31.7%, respectively [4]. Since small changes in angular emission correspond to significant changes in device performance, it’s important to accurately quantify the TDM.

Methodology and Analysis: In this work, we determined the inherent accuracy and uncertainty of determining the transition dipole moment (TDM) through back focal plane (BFP) imaging. We simulated 1000s of BFP plane images with varying dipole angle, emitter refractive index, emitter thickness, and number of camera pixels. We fit these generated data sets and show how the accuracy and uncertainty of the fitted TDM strongly depend on these parameters. Notably, our representative of a 2D transition dichalcogenide film (thickness = 5 nm, refractive index = 3, TDM = 0°) had an inherent uncertainty of greater than 20°, owing to the similarity in angular emission patterns for TDMs close to parallel with the substrate.

Additionally, we varied the random noise and blur of the dataset, representing the thermal noise of the CCD camera and aberration of the microscope observed in real data. Comparing these to actual datasets, we surprisingly showed that the uncertainty decreases by up to an order of magnitude. However, the accuracy suffers, as shown in Figure 1(B). Depending on the type of sample measured (films of nanocrystals or solid, high refractive index semiconductors), the fitted angle can be overestimated by 3 - 20°.

Because understanding the fundamental photophysical behavior of these materials depends on accurate characterization of the transition dipole moment, it is imperative that we understand how these measurement parameters affect the characterization and how we can improve this metrology. Therefore, we recommend lower refractive index samples, such as organic emitters, and specific data processing to prevent misinterpretation.

Figure 1. (A) Schematic of the back focal plane (BFP) imaging setup. A luminescent sample will have a certain angular emission pattern (light blue) as determined by the transition dipole moment (TDM) angle and local optical environment. By using a bertrand lens, this angular emission pattern is imaged on the CCD camera (bottom). (B) Accuracy of simulated BFP data as a function of sample type and TDM angle. Higher refractive index films and samples with small TDM angles show an incredibly inaccurate fitted angle, making understanding materials for LEDs incredibly difficult.