Quantum Dot LED (QLED)

1. Theory

Definition: A quantum-dot LED (QLED) is a layered diode whose emitter is a film of colloidal semiconductor nanocrystals (usually core/shell dots) between organic or oxide charge-transport layers.
Size-tuned colour: The Brus equation sets the emission energy by dot radius, so one material covers the visible range by size alone.
Narrow linewidth: Each dot emits a narrow line; the ensemble width comes mainly from the size spread (e.g. about 22 nm for an 8% radius spread).
Core/shell structure: A wider-gap shell passivates surface traps and confines carriers, raising photoluminescence yield.
No spin limit: Unlike fluorescent OLEDs, all excitons can emit, so internal efficiency can approach 100%.
Auger quenching: Charged dots (trions) lose excitons to non-radiative Auger recombination.

2. Working Principle

Injection: Holes arrive through an organic hole-transport layer and electrons through a ZnO nanoparticle layer.
Charge imbalance: Electron transport is faster, so excess electrons charge the dots and trigger Auger loss.
Insulating interlayer: A roughly 1 nm insulating layer (e.g. $A l_{2} O_{3}$ or PMMA) between dots and ZnO throttles electron current exponentially to restore balance.
Emission: Excitons in balanced, neutral dots recombine radiatively at the size-set wavelength.
Energy transfer: Förster transfer between neighbouring dots moves excitons toward larger, lower-energy dots.
Outcoupling limit: As in OLEDs, the planar stack lets out only about 20% of light, capping external efficiency near 20%.

3. Applications

Current status: Electroluminescent QLEDs are still in development and not yet in mass-produced displays (commercial “QLED” TVs use quantum dots only as photoluminescent colour converters).
Next-generation displays (target): Self-emissive, wide-colour-gamut, printable display pixels.

Name	Formula	Related Formulae	Variables/Constants
Size-dependent emission energy of a quantum dot (Brus equation)	$E (R) = E_{g} + \frac{ℏ ^{2} π ^{2}}{2 μ R ^{2}} - \frac{1.786 q ^{2}}{4 π ε _{0} ε _{r} R}$	$\frac{1}{μ} = \frac{1}{m _{e}^{}} + \frac{1}{m _{h}^{}}$ $a_{B} = \frac{4 π ε _{0} ε _{r} ℏ ^{2}}{μ q ^{2}}$ $λ = \frac{1239.8}{E ( e V )} nm$	$E (R) : e n er g y o f t h e l o w es t e x c i t o n t r an s i t i o n o f a s p h er i c a l d o t o f r a d i u s R in t h e e f f ec t i v e - ma ss a pp r o x ima t i o n w i t h in f ini t e ba r r i er s$ $E_{g} : ban d g a p o f t h e b u l k se mi co n d u c t or$ $ℏ : r e d u ce d P l an c k co n s t an t$ $μ : r e d u ce d ma ss o f t h e e l ec t r o n - h o l e p ai r$ $m_{e}^{}, m_{h}^{} : e f f ec t i v e ma sses o f t h e e l ec t r o n an d t h e h o l e$ $R : r a d i u s o f t h e d o t$ $q : e l e m e n t a r y c ha r g e$ $ε_{0}, ε_{r} : v a c uu m p er mi tt i v i t y an d r e l a t i v e p er mi tt i v i t y o f t h e se mi co n d u c t or$ $a_{B} : e x c i t o n B o h r r a d i u s (t h e s t r o n g co n f in e m e n t r e g im e o f t h e e q u a t i o n i s f or R s ma l l er t han a_{B})$ $(t h e e q u a t i o n o v er es t ima t es t h e co n f in e m e n t e n er g y o f s ma l l d o t s, b ec a u se t h e ba r r i er o f a r e a l d o t i s f ini t e, t h e n o n - p a r ab o l i c i t y o f t h e ban d s i s i g n or e d an d t h e p o l a r i z a t i o n t er m s a r e l e f t o u t; t h e C o u l o mb coe f f i c i e n t i s o f t e n r o u n d e d t o 1.8; L . E . B r u s, J . C h e m . P h y s . 80, 4403 (1984))$
Emission linewidth from the size distribution	$Δ E_{inh} \approx S_{R} Δ R$	$S_{R} = \frac{d E}{d R} = - \frac{ℏ ^{2} π ^{2}}{μ R ^{3}} + \frac{1.786 q ^{2}}{4 π ε _{0} ε _{r} R ^{2}}$ $Δ λ \approx \frac{λ ^{2} Δ E _{inh}}{h c}$	$Δ E_{inh} : inh o m o g e n eo u s w i d t h o f t h e e n se mb l e e mi ss i o n c a u se d b y t h e s p r e a d o f t h e r a d i u s, t ak e n a s t h e ma g ni t u d e o f t h e p r o d u c t$ $S_{R} : se n s i t i v i t y o f t h e e mi ss i o n e n er g y t o t h e r a d i u s, n e g a t i v e b ec a u se a bi g g er d o t e mi t s a t a l o w er e n er g y$ $Δ R : w i d t h o f t h e d i s t r ib u t i o n o f t h e r a d i u s$ $Δ λ : cor r es p o n d in g w i d t h in w a v e l e n g t h$ $λ : ce n t r a l w a v e l e n g t h$ $h, c : P l an c k co n s t an t an d s p ee d o f l i g h t$ $(t h e h o m o g e n eo u s w i d t h o f a s in g l e d o t, t h e f in e s t r u c t u r e an d t h e co u pl in g t o p h o n o n s w i d e n t h e l in e f u r t h er, an d t h e f i l m e mi ss i o n i s a l so c han g e d b y t h e t r an s f er t o t h e l a r g er d o t s in t h e l a s t r o w)$
Leakage through the shell and the insulating interlayer	$κ = \frac{2 m ^{*} V _{0}}{ℏ}$	$T \approx exp (- 2 κ t)$ $J_{e} (t_{i}) \approx J_{e 0} exp (- 2 κ_{i} t_{i})$ $t_{o pt} = \frac{1}{2 κ _{i}} ln \frac{J _{e 0}}{J _{h}}$	$κ : d ec a y co n s t an t o f t h e w a v e f u n c t i o n in a ba r r i er o f h e i g h t V_{0}$ $m^{*} : e f f ec t i v e ma ss o f t h e c a r r i er in t h e ba r r i er$ $V_{0} : ba r r i er h e i g h t see n b y t h e c a r r i er (t h e co n d u c t i o n ban d o f f se t o f t h e s h e l l f or t h e e l ec t r o n)$ $T : W K B es t ima t e o f t h e p r o babi l i t y d e n s i t y r a t i o o f t h e c a r r i er a t t h e o u t er s u r f a ce o f a s h e l l or an in s u l a t in g l a y er o f t hi c k n ess t t o t ha t a t t h e inn er s i d e$ $J_{e} (t_{i}) : e l ec t r o n c u r r e n t d e n s i t y t h r o ug h an in s u l a t in g in t er l a y er o f t hi c k n ess t_{i} b e tw ee n t h e d o t l a y er an d t h e e l ec t r o n t r an s p or t l a y er$ $J_{e 0} : e l ec t r o n c u r r e n t d e n s i t y w i t h o u t t h e in t er l a y er$ $κ_{i} : d ec a y co n s t an t in t h e in t er l a y er$ $t_{o pt} : in t er l a y er t hi c k n ess a t w hi c h t h e e l ec t r o n c u r r e n t i s e q u a l t o t h e h o l e c u r r e n t J_{h} (a s im pl e t u nn e l l in g m o d e l f or t h e c ha r g e ba l an ce, w r i tt e n f or t hi s p a g e, in w hi c h t h e h o l e c u r r e n t i s n o t c han g e d b y t h e in t er l a y er)$
Radiative yield of neutral and charged dots	$Φ_{X} = \frac{k _{r}}{k _{r} + k _{n r}}$	$Φ_{c ha r g e d} = \frac{g k _{r}}{g k _{r} + k _{n r} + k _{A}}$ $τ_{A} \propto V \propto R^{3}$	$Φ_{X} : p h o t o l u min esce n ce y i e l d o f a n e u t r a l d o t w i t h o n e e x c i t o n$ $k_{r}, k_{n r} : r a d ia t i v e an d n o n - r a d ia t i v e r a t es o f t h e s in g l e e x c i t o n$ $Φ_{c ha r g e d} : y i e l d o f a d o t t ha t c a r r i es o n e e x t r a e l ec t r o n or h o l e (a t r i o n s t a t e)$ $g : r a d ia t i v e e nhan ce m e n t f a c t or o f t h e c ha r g e d s t a t e, ab o u t 2 f or t h e t r i o n i f t h e r a t e sc a l es w i t h t h e n u mb er o f r eco mbina t i o n p a t h w a y s$ $k_{A} : A ug er r a t e, a t w hi c h t h e e n er g y o f t h e r eco mbinin g p ai r i s g i v e n t o t h e e x t r a c a r r i er$ $τ_{A} : A ug er l i f e t im e o f t h e bi e x c i t o n, p r o p or t i o na l t o t h e v o l u m e V o f t h e d o t in t h e u ni v er s a l v o l u m e sc a l in g (w hi c h ha s b ee n r e p or t e d n o t t o h o l d f or a l l cor e / s h e l l d o t s)$ $R : r a d i u s o f t h e d o t$
External quantum efficiency of the quantum-dot LED	$η_{E QE} = γ Φ_{P L} η_{o u t}$	$γ = \frac{J _{r ec}}{J}$ $η_{o u t} \approx \frac{1}{2 n ^{2}} (pl ana r s t a c k)$	$η_{E QE} : e x t er na l q u an t u m e f f i c i e n cy$ $γ : c ha r g e ba l an ce f a c t or, t h e f r a c t i o n o f t h e inj ec t e d c u r r e n t t ha t f or m s e x c i t o n s in t h e d o t s (h o l e an d e l ec t r o n c u r r e n t s t ha t d i f f er l o w er i t, an d t h e e x t r a c a r r i er s a l so c ha r g e t h e d o t s)$ $Φ_{P L} : p h o t o l u min esce n ce y i e l d o f t h e d o t f i l m in t h e d e v i ce (r e d u ce d b y t h e c ha r g in g, b y t h e t r an s f er t o t h e t r an s p or t l a y er s an d b y t h e f i e l d)$ $η_{o u t} : o u t co u pl in g e f f i c i e n cy, t ak e n f r o m t h e pl ana r - s t a c k es t ima t e o f t h e O L E D p a g e w i t h t h e in d e x n o f t h e l a y er s$ $J_{r ec}, J : r eco mbina t i o n c u r r e n t an d t o t a l c u r r e n t d e n s i t y$ $(u n l ik e t h e f l u or esce n t O L E D e mi tt er, t h e f a c t or f or t h e f r a c t i o n o f e x c i t o n s t ha t c an e mi t i s t ak e n a s o n e f or t h e d o t, b ec a u se t h e s p in s t a t es a r e b o t h r a d ia t i v e t h r o ug h t h e e x c i t o n f in e s t r u c t u r e a t r oo m t e m p er a t u r e)$
Energy transfer between dots in a film	$E_{F R E T} = \frac{1}{1 + ( R / R _{0} ) ^{6}}$	$k_{F R E T} = \frac{1}{τ _{D}} (\frac{R _{0}}{R})^{6}$ $R_{0}^{6} = \frac{9 l n 10 κ ^{2} Φ _{D}}{128 π ^{5} N _{A} n ^{4}} J$	$E_{F R E T} : e f f i c i e n cy o f t h e t r an s f er o f an e x c i t o n f r o m a d o n or d o t t o an a cce pt or d o t a t t h e d i s t an ce R$ $R : ce n t r e - t o - ce n t r e d i s t an ce o f t h e tw o d o t s, se t b y t h e d iam e t er an d t h e l i g an d s h e l l$ $R_{0} : F oer s t er r a d i u s o f t h e p ai r (t h e d e f ini t i o n an d t h e sy mb o l s a r e t h ose o f t h e O L E D p a g e)$ $k_{F R E T} : t r an s f er r a t e$ $τ_{D} : l i f e t im e o f t h e d o n or d o t w i t h o u t t h e a cce pt or$ $(in a c l ose - p a c k e d f i l m t h e e x c i t o n s h o p t o w a r d s t h e l a r g er d o t s, w hi c h r e d - s hi f t s an d na r r o w s t h e f i l m e mi ss i o n r e l a t i v e t o t h e so l u t i o n, an d i t b r in g s t h e e x c i t o n s t o t h e d o t s t ha t a r e c ha r g e d or d e f ec t i v e)$

Important Questions

Ques: Why are quantum dots used as the emitter of an LED?

The emission energy of a dot is set by its size (the Brus equation), so the colour is tuned across the visible range by the radius of a single material, and the narrow emission spectrum of the dots gives a saturated colour. As an illustration, with the assumed parameters $E_{g} = 1.74$ eV, $m_{e}^{*} = 0.13 m_{0}$ , $m_{h}^{*} = 0.45 m_{0}$ and $ε_{r} = 10$ (CdSe-like, used only as a working example), the equation gives 2.23 eV (555 nm) at $R = 2.5$ nm, 2.07 eV (599 nm) at $R = 3$ nm and 2.54 eV (488 nm) at $R = 2$ nm, and the exciton Bohr radius is 5.2 nm. The same equation gives 3.23 eV (384 nm) for $R = 1.5$ nm, which is too high, as the equation overestimates the confinement of small dots. The first LED with a semiconductor-nanocrystal emitter and a polymer was reported in 1994 by Colvin, Schlamp and Alivisatos, and core/shell nanocrystals with a higher efficiency followed in 1997. Reference: V.L. Colvin, M.C. Schlamp and A.P. Alivisatos, “Light-emitting diodes made from cadmium selenide nanocrystals and a semiconducting polymer,” Nature 370, 354 (1994); M.C. Schlamp, X. Peng and A.P. Alivisatos, “Improved efficiencies in light emitting diodes made with CdSe(CdS) core/shell type nanocrystals and a semiconducting polymer,” J. Appl. Phys. 82, 5837 (1997).

Ques: How wide is the emission line, and what sets it?

A single dot emits a line that is much narrower than the ensemble. The width of the ensemble is mainly the spread of the radius: the sensitivity $S_{R} = d E / d R$ is $- 0.44$ eV/nm for the example dot at $R = 2.5$ nm (the confinement term gives $- 0.47$ eV/nm and the Coulomb term $+ 0.04$ eV/nm), so a spread of $Δ R = 0.2$ nm (8%) gives an inhomogeneous width of 87 meV, which is 22 nm at 555 nm. A narrower size distribution, or a size-independent emission as in a rod or a platelet, gives a narrower line; the numbers are computed from the Brus equation with the assumed parameters and should be taken as an illustration. Reference: the numbers follow from differentiating the Brus equation of the first row (L.E. Brus, J. Chem. Phys. 80, 4403 (1984)).

Ques: Why does the charge balance matter so much in a QLED, and what does the insulating interlayer do?

The ZnO nanoparticle layer that transports the electrons has a higher mobility than the organic hole-transport layer, so the dots receive more electrons than holes; the extra electrons charge the dots, and a charged dot loses its excitons to Auger recombination (the yield row). A thin insulating layer between the dot layer and the ZnO reduces the electron current exponentially with its thickness, and the simple tunnelling model gives the thickness at which the two currents are equal, $t_{o pt} = ln (J_{e 0} / J_{h}) / (2 κ_{i})$ , which is 0.77 nm for $J_{e 0} / J_{h} = 100$ and an assumed decay constant of $3$ nm $^{- 1}$ . In a study of a QLED a 1.0 nm Al $_{2}$ O $_{3}$ interlayer brought the electron-only current close to the hole-only current, and raised the maximum EQE from 10.9% to 12.2% and the half lifetime from 2030 s to 7070 s. In the 2014 report of Dai et al. an insulating layer between the dots and the oxide electron transport layer gave an EQE of up to 20.5% and a lifetime of more than 100,000 hours at 100 cd/m $^{2}$ (as quoted by a trade-press summary; the abstract of the paper itself does not give the numbers). Reference: X. Dai et al., “Solution-processed, high-performance light-emitting diodes based on quantum dots,” Nature 515, 96 (2014); H. Jin, H. Moon, W. Lee, H. Hwangbo, S.H. Yong, H.K. Chung and H. Chae, “Charge balance control of quantum dot light emitting diodes with atomic layer deposited aluminum oxide interlayers,” RSC Adv. 9, 11634 (2019); trade-press summary “Chinese team report best solution-processed red LED,” Compound Semiconductor, article 95512.

Ques: How does the Auger recombination scale with the size of the dot, and does it hold for core/shell dots?

For bare dots the biexciton Auger lifetime has been reported to scale with the volume of the dot, $τ_{A} \propto V \propto R^{3}$ (the universal volume scaling), so a larger dot has a lower Auger rate. A recent study of core/shell dots notes that several reports find that this law does not apply to core/shell dots: it finds that the biexciton Auger lifetime of quasi-type-II CdSe/CdS increases with the total volume, and that of type-I CdSe/ZnS does not depend on the shell thickness. The factor $g$ of the charged-dot yield (2 for a trion, 4 for a biexciton if the radiative rate scales with the number of pathways) is a statistical-counting argument and was not checked. Reference: I. Robel, R. Gresback, U. Kortshagen, R.D. Schaller and V.I. Klimov, “Universal size-dependent trend in Auger recombination in direct-gap and indirect-gap semiconductor nanocrystals,” Phys. Rev. Lett. 102, 177404 (2009), for the volume scaling; arXiv:2005.03111, “Auger recombination lifetime scaling for type-I and quasi-type-II core/shell quantum dots,” for the core/shell results.

Ques: What limits the external quantum efficiency of a QLED to about 20%?

The external efficiency is $γ Φ_{P L} η_{o u t}$ , and the dots are efficient emitters with no restriction of the emitting fraction by the spin (the factor of 0.25 of a fluorescent OLED emitter does not appear), so the internal efficiency can approach unity when the charges are balanced. The remaining limit is the outcoupling of the planar stack, about 20% for an index of 1.7 to 1.8 (the OLED page), so an EQE of 20% would need an internal efficiency near unity (the value of the internal efficiency of the reported devices was not checked). The outcoupling structures of the OLED, such as microlenses or low-index grids, apply in the same way. Reference: See the references of the Organic Light Emitting Diode page; X. Dai et al., Nature 515, 96 (2014).

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