How understanding ‘hopping’ could improve solar cells

Energy transfer in light-sensitive materials such as quantum dots is of interest for better solar cells, LEDs, and other devices. MIT chemistry graduate student A. Jolene Mork examines how fast energy transfers from one quantum dot to another, a phenomenon known as hopping.

Mork is lead author of a Journal of Physical Chemistry paper that analyzed energy transfer in colloidal quantum dots. “It’s not looking at how far can an exciton go within a film; it is how fast does it transfer from one quantum dot to another,” she says. Mork is a fifth-year MIT graduate student in the lab of William A. Tisdale, the Charles and Hilda Roddey Career Development Professor in Chemical Engineering at MIT.

A standard formula for calculating the rate of energy transfer for molecules, Förster theory, may be inadequate to explain excitons moving from one quantum dot to another, Mork’s study reveals. “The standard assumption is that it’s center-to-center distance that matters. So we think the edge-to-edge distance may also matter,” Mork says.

Tightly bound

When a quantum dot absorbs a photon of light — from a laser, for example — it converts the light energy to an excited state in the form an exciton, which is a paired electron and hole that are attracted to each other by their opposite charges. In contrast to a material such as silicon, which allows an electron and a hole to separate, in excitons created by quantum dots, because they are so small, the electron and hole can’t move apart very far and are tightly bound together.

“At some point, the quantum dot will want to relax to its ground state because that’s the overall lowest energy, and the way that it relaxes is either by transferring energy to another quantum dot, and the quantum dot that transferred the energy away from itself relaxes back to its ground state, or the quantum dot emits a photon and then also relaxes back down,” Mork explains. “So each quantum dot is trying to achieve its lowest energy, and it can achieve that in a couple of different ways.”

Each quantum dot has an emission spectrum or absorption spectrum that determines what wavelength of light energy it can emit or absorb. “Förster theory describes the rate of energy transfer between these two from the donor to acceptor, and that rate is determined by this spectral overlap and by the distance between the two,” Mork says.

Under standard assumptions, an exciton is modeled as a tiny dipole in the center of the quantum dot, Mork adds. “This works for molecules because molecules are very small, but quantum dots are thousands of atoms, and they are much larger than molecules. Modeling just as a dipole in the center of the quantum dot may not be an appropriate assumption in these cases,” she explains. Measured energy-transfer rates in the study were more than 10 times larger than values expected from Förster theory, the study reports.

For Mork’s study, Tisdale notes that Mork’s lab colleague Mark Weidman traveled to the National Synchrotron Light Source at Brookhaven National Laboratory on Long Island, New York, to perform grazing-incidence small-angle X-ray scattering (GISAXS) and wide-angle X-ray scattering (WAXS) studies of quantum-dot films.

Measuring diffusion

Mork was a co-author of a collaborative study among professors Tisdale, Vladimir Bulovic, and Adam Willard of diffusion in quantum-dot solids, which measured exciton lifetimes and modeled exciton-diffusion lengths. Mork assisted in sample preparation and in spectrally-resolved and time-correlated spectroscopy measurements.

“We’re looking at exciton-diffusion length,” Mork explains. “Once one quantum dot absorbs a photon, it can do energy transfer, which is a non-radiative process, so it doesn’t emit a photon. Then another quantum dot absorbs, it just transfers the energy directly to another quantum dot, so it does energy transfer to some other number of quantum dots, and then where that photon is emitted relative to where it absorbed, is the exciton-diffusion length.”

In a related energy transfer study, Tisdale’s group showed that a system coupling inorganic quantum dots to a molybdenum-disulfide semiconductor could be designed to emit different colors of light by changing the size of quantum dots. “It’s a near-field, dipole-to-dipole coupling between the donor and the acceptor,” Tisdale explains. “This exciton, you can think about it quantum mechanically as an electron-hole pair, an electron and a hole, but you can think about it classically as an oscillating dipole, and that oscillating dipole can induce a polarization in its surroundings at the same frequency, and then if there is resonant frequency in a neighboring material, such as molybdenum disulfide, then it can absorb that energy; that energy can be transferred from the quantum dot to the molybdenum disulfide (MoS2). So you could think about it as an exciton hopping over, you could think about it as this dipole that has some energy here that transfers its energy to another dipole over here. They’re physically equivalent, but different pictures, different ways of describing it.”

Tisdale says one takeaway from Mork’s work is that if you use the properties of quantum dots measured in solution, you’ll predict the wrong distance of, or characteristic distance for, this type of exciton hopping that can happen in thin films, because there are some other effects that happen in thin films that affect the magnitude of the Förster radius.

A typical quantum dot consists of a core of one material, a shell of another material and an attached organic molecule, or ligand. Quantum dots also are affected by the size of ligands attached to their shells, which is a contributing factor to their particle-to-particle spacing. “In quantum-dot LEDs, they use quantum dots with long ligands, and in quantum-dot solar cells, they use quantum dots with short ligands in order to tune the exciton diffusion length,” Mork says.

“We’re trying to use changing the shell thickness to change the interparticle spacing rather than ligands, and the reason that would be interesting is it changes some of the dielectric properties of the film. It changes the index of refraction, which is one of the constants that’s in the Förster rate equation,” Mork says. She is also studying energy transfer by vibrational energy. “For all of my vibrational work, I’ve made my own quantum dots and done any kind of ligand exchange chemistry and I do the spectroscopy on them,” she says. The work could lead to applications in thermoelectrics for materials with high electrical conductivity but low thermal conductivity. “You may be able to tune those independently, whereas for a lot of thermoelectric materials [these two properties] vary in the same way,” she says.

Because energy usually transfers from a quantum dot emitting a higher energy photon to a lower energy photon, over many transfer events, the photon emitted gets redder and redder, Mork says. “That means if you are trying to make a specific color of LED, for instance, out of quantum dots, the reddest dots in your film are going to be more important for dictating the color of light that you get out than you would think from just the whole ensemble emission,” she explains.

Mork, 26, a native of Shoreline, Washington, a suburb of Seattle, graduated from Carleton College in Northfield, Minnesota. She earned a master’s in organic chemistry at MIT, working in the lab of John D. MacArthur Professor Timothy M. Swager. She expects to earn her doctorate at MIT in 2016.

This article is published in collaboration with MIT News. Publication does not imply endorsement of views by the World Economic Forum.

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Author: Denis Paiste is a contributing author for MIT News.

Image: A woman is silhouetted next to a solar panel display by solar module supplier Upsolar at the fourth International Photovoltaic Power Generation (PV) Expo in Tokyo March 2, 2011. REUTERS.