OPTICS
Sub–single-exciton lasing using
charged quantum dots coupled
to a distributed feedback cavity
Oleg V. Kozlov^1 , Young-Shin Park1,2, Jeongkyun Roh^1 , Igor Fedin^1 ,
Tom Nakotte1,3, Victor I. Klimov^1 *
Colloidal semiconductor quantum dots (QDs) are attractive materials for realizing
highly flexible, solution-processable optical gain media, but they are difficult to use in
lasing because of complications associatedwith extremely short optical-gain lifetimes
limited by nonradiative Auger recombination. By combining compositional grading of the
QD’s interior for hindering Auger decay with postsynthetic charging for suppressing
parasitic ground-state absorption, we can reduce the lasing threshold to values below the
single-exciton-per-dot limit. As a favorable departure from traditional multi-exciton–based
lasing schemes, our approach should facilitate the development of solution-processable
lasing devices and thereby help to extend the reach of lasing technologies into areas not
accessible with traditional, epitaxially grown semiconductor materials.
S
olution-processable lasers have been the
subject of vigorous research, with the pri-
mary focus being on organic semicon-
ductors ( 1 ) and, more recently, hybrid
organic-inorganic and all-inorganic perov-
skites ( 2 ). Colloidal quantum dots (QDs) have
also shown considerable promise as solution-
processable lasing media with size-controlled
emission wavelengths ( 3 , 4 ). One challenge in
advancing these laboratory-based demonstra-
tions to technologically viable devices is the
multiexcitonic nature of optical gain, which leads
to high lasing thresholds ( 5 , 6 ). The onset of
optical gain corresponds to the situation of band-
edge transparency, when the emitting transition
is completely bleached by carriers introduced into
an active medium by a pump source. In QDs, this
corresponds to the regime when an average per-
dot excitonic occupancy
Consequently, lasing becomes possible only when
a fraction of the QDs in the sample contains bi-
excitons and other multiexcitonic species. This leads
to a major complication due to fast, nonradiative
multicarrier Auger decay, wherein an electron–
hole recombination energy is transferred to a third
carrier residing in the same dot ( 7 ). This process
limits optical-gain lifetimes to tens of picoseconds,
which greatly complicates realization of lasing,
especially in the case of continuous-wave optical
and direct-current electric pumping ( 5 , 6 , 8 ).
Recent experiments have demonstrated that
charging QDs with extra electrons can bleach
the ground-state absorption and thereby reduce
the optical gain threshold ( 9 ). This approach also
extends optical-gain lifetimes, as Auger decay of a
single exciton charged with one or even two addi-
tional electrons is longer than that of biexcitons
( 9 ), which represent the dominant optical-gain
species in traditional lasing schemes. Previously,
the beneficial effects ofextra electrons on ampli-
fied spontaneous emission (ASE) and gain thresh-
olds were observed by means of electrochemically
charged QD samples ( 10 ) and, more recently, pho-
tochemically reduced QDs ( 9 ).
Here, we demonstrate single-mode lasing with
low thresholds using a charged-QD approach. We
use thick-shell, multilayered QDs with strongly
suppressed Auger recombination combined withoptimized second-order distributed feedback
(DFB) resonators. By charging the sample with
about three extra electrons per dot on average,
we achieve an extremely low, sub–single-exciton
lasing threshold <Nlas>≈0.3, which is a more
than fourfold reduction compared with the neu-
tral QDs. Further, we demonstrate a reversible
tuning of the lasing threshold by controlling the
degree of QD charging.
The multiexcitonic nature of optical gain in
QDs is a consequence of a multifold degeneracy
of band-edge electron and hole levels ( 3 ). In the
model of twofold degenerate states, optical gain
(G)islinkedtothedifference in the probability
of a QD to contain a biexciton (PXX) and that to
remain in the ground state (P 0 ):Gº(PXX−P 0 )
(Fig. 1A, left) ( 6 ). In the case where QD excitonic
occupancy (N)canonlybe0(unoccupieddot,
|0i), 1 (single-exciton state, |Xi), or 2 (biexciton
state, |XXi), an optical-gain threshold (G= 0),
or“optical transparency,”is realized when every
dot in the sample contains a single exciton,
i.e., <Ng>=1(Fig.1B,left)( 6 ).
By charging (doping) a QD with extra elec-
trons, partial or even complete bleaching of the
band-edge absorption can be achieved, which
would reduce the optical-gain threshold ( 9 ). In
particular, when the QD ensemble is uniformly
charged withneelectrons per dot, <Ng>decreases
to 0.5 forne= 1 and to 0 forne= 2 (Fig. 1, A and
B; middle and right panels, respectively). If we
consider a situation of nonuniform charging
and further assume Poisson statistics for both
Nandne, then the gain threshold will change to
<Ng> = 1.15, 0.81, and 0.46 for <ne>=0,1,and2,
respectively (Fig. 1C).
Suppression of Auger recombination for
charged excitonic species is key to successfulRESEARCH
Kozlovet al.,Science 365 , 672–675 (2019) 16 August 2019 1of4
(^1) Chemistry Division, C-PCS, Los Alamos National Laboratory,
Los Alamos, NM 87545, USA.^2 Center for High Technology
Materials, University of New Mexico, Albuquerque, NM 87131,
USA.^3 Department of Chemical and Materials Engineering,
New Mexico State University, Las Cruces, NM 88003, USA.
*Corresponding author. Email: [email protected]
Fig. 1. Optical gain model for neutral and charged QDs.(A) Electronic states and optical
transitions between the ground |0i, single-exciton |Xi, and biexciton |XXistates for neutral (left),
singly charged (middle), and doubly charged (right) QDs. Optical transitions leading to absorption
and stimulated emission are shown with black and red arrows, respectively. The transition rates
are indicated next to the respective transitions;gis the probability per single spin-allowed transition
( 6 ).P 0 ,PX, andPXXdenote the probabilities of the QD to be in the ground, single-exciton, or biexciton
state, respectively. Singly charged and doubly charged states are denoted by superscripts“−”
and“ 2 −”,respectively.PX−andPX 2 −are the probabilities of the QD to be in the singly or doubly charged
exciton state, respectively. (B) The condition of optical gain threshold (G= 0) for neutral (left), singly
charged (middle), and doubly charged (right) QDs is met when the average per-dot number of excitons
(
average per-dot number of permanent electrons
according to Poisson statistics ( 9 ).