A bright future for colloidal quantum dot lasers

Geiregat et al. NPG Asia Materials (2019) 11:41 https://doi.org/10.1038/s41427-019-0141-y NPG Asia Materials PERSPECTIVE Open Access A bright future for colloidal quantum dot lasers 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Pieter Geiregat 1,2 , Dries Van Thourhout2,3 and Zeger Hens1,2 Since they were first synthesized nearly 30 years ago, colloidal quantum dots (QDs) have attracted much attention as an enabling material for solution-processed opto-electronics1,2. QDs offer seamless tunability of the optical bandgap from the UV to the mid-infrared (IR), are fit for substrate-independent and cost-effective processing, and have the prospect of long-term stability inherent to inorganic materials. Given these advantages, QDs quickly took a firm position in the optoelectronic materials community. As of today, QDs find applications in diverse fields such as biolabeling, displays, lighting, sensing, and solar energy conversion3, applications that all rely on the spectrally broad absorption or the highly efficient and spectrally narrow photoluminescence of QDs. Nearly two decades ago, Klimov and coworkers demonstrated net stimulated emission and amplified spontaneous emission by CdSe-based QDs, a result that opened up the exciting prospect of fabricating QD-based lasers3,4. Lasers are ubiquitous in modern society as sources of spatio-temporal coherent and quasimonochromatic light. Lasers find applications in consumer products, telecommunications, healthcare, imaging, and so on and enable fundamental research in increasingly diverse fields. Even so, laser fabrication remains challenging due to the stringent requirements on the active light-amplifying medium, the pump mechanisms and the need for a high-quality feedback structure or optical cavity. Current opto-electronic technology heavily relies on epitaxially grown semiconductors, a materials platform that is, however, limited by its high cost, limited spectral tunability and the need for rigid substrate- mediated growth. Given the current needs for lasers on flexible substrates5 or as disposable, low-cost appliances, such as a lab-on-a-chip6, this creates an opportunity for QDs to revolutionize the field of laser-based opto-electronics, much as these materials currently do for the growing markets of displays and lighting. Lasing action requires that the roundtrip gain through stimulated emission in the cavity exceeds the losses due to re-absorption in the active medium and transmission through the cavity end mirrors, see Fig. 1a. Characterizing a QD by its two band-edge states, this roundtrip gain in a QD-laser is provided by stimulated emission across the band-edge transition. Building on the initial models of Klimov et al.3, one can propose an intuitive mathematical formulation of this 2-level model depicted in Fig. 1a that captures the essence of attaining net optical gain in a colloidal QD ensemble7. We consider a 2-level system with degeneracies (ge, gh) for the electron/hole levels involved in the gain transition and linearly increasing spectral shifts of multi-excitons δN = NδE, where δE is the biexciton-exciton shift and N the number of excitons. This brings us to the following expressions for the absorbance at an energy E of unexcited QDs and QDs excited with Ne electrons and Nh holes: Absorbance of unexcited dots: A0(E) Absorbance of QDs with (Ne, Nh) (electrons, holes): Ne Nh AN ðE Þ ¼ ð1  Þð1  ÞA0 ðE  Nδ E Þ ge gh ● ● ● Stimulated emission of QDs with (Ne, Nh) (electrons, holes): GN ð E Þ ¼ Correspondence: Pieter Geiregat () 1 Physics and Chemistry of Nanostructures Group, Department of Chemistry, Ghent University, 9000 Gent, Belgium 2 Centre for Nano and Bio-photonics, Ghent University, 9000 Gent, Belgium Full list of author information is available at the end of the article. Ne Nh A0 ðE  ðN  1Þδ E Þ ge gh Note that optical excitation usually yields Ne = Nh, but special cases, such as doped QDs or trap-state gain, allow © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Geiregat et al. NPG Asia Materials (2019) 11:41 Page 2 of 8 Fig. 1 Colloidal quantum dots (QDs) as optical gain material. a Typical loss channels for population inversion through bi-exciton Auger recombination, affecting the inversion lifetime τg and photon loss through a finite photon-cavity lifetime (τc). (b) Calculated CW pump threshold as a function of the biexciton Auger lifetime τXX (horizontal axis) and cavity lifetimes varying (colors) from 1 ps to 1 ns, adapted from Park et al. 11 for Ne ≠ Nh. In summary, we can write the absorbance A as: X AðEÞ ¼ Pð0ÞA0 ð E Þ þ PðNÞðAN ð E Þ  GN ð E ÞÞ N1 where P(N) is the Poisson probability to have N excitations in ahN i dotN given an average occupation of hN i: P ð N Þ ¼ e N!hN i 3. For example, one can show that for Cdbased QDs, A turns negative if h N i excitations in a dot given an average exceeds unity, where the exact value depends on the assumed degeneracies of the hole levels involved7,8. Building on this two-state model, net stimulated emission by an ensemble of QDs is typically summarized by three descriptors: The threshold occupation hN  i, which is the minimum number of electron-hole pairs QDs must hold on average to attain net stimulated emission. The inversion lifetime τg, which is the time a state of net stimulated emission is preserved after pulsed photo-excitation. The material gain gi, which is the gain, measured in cm−1, provided by a fictitious ensemble of QDs packed with a QD volume fraction of unity. It can be translated to device scenarios using the volume fraction and optical mode confinement of the QD layer in a laser cavity9. Since the discovery of light amplification by QDs4, it was realized that net stimulated emission requires biexciton states, i.e., QDs containing two electron-hole pairs. Such states suffer from fast, non-radiative Auger recombination (see Fig. 1a), which limits τg to a few tens of ps in the case of bare CdSe QDs4,8. Because the threshold pump power Pth required to achieve lasing action in a lossless cavity under steady-state conditions scales with the ratio hN  i=τ g , suppressing this fast Auger recombination (...truncated)