Highly Efficient Inverted Light-Emitting Diodes Based on Vertically Aligned CdSe/CdS Nanorod Layers Fabricated by Electrophoretic Deposition

Inverted colloidal-nanocrystal-based LEDs (NC-LEDs) are highly interesting and invaluable for large-scale display technology and flexible electronics. Semiconductor nanorods (NRs), in addition to the tunable wavelengths of the emitted light (achieved, for example, by the variation of the NR diameter or the diameter of core in a core–shell configuration), also exhibit linearly polarized emission, a larger Stokes shift, faster radiative decay, and slower bleaching kinetics than quantum dots (QDs). Despite these advantages, it is difficult to achieve void-free active NR layers using simple spin-coating techniques. Herein, we employ electrophoretic deposition (EPD) to make closely packed, vertically aligned CdSe/CdS core/shell nanorods (NRs) as the emissive layer. Following an inverted architecture, the device fabricated yields an external quantum efficiency (EQE) of 6.3% and a maximum luminance of 4320 cd/m2 at 11 V. This good performance can be attributed to the vertically aligned NR layer, enhancing the charge transport by reducing the resistance of carrier passage, which is supported by our finite element simulations. To the best of our knowledge, this is the first time vertically aligned NR layers made by EPD have been reported for the fabrication of NC-LEDs and the device performance is one of the best for inverted red NR-LEDs. The findings presented in this work bring forth a simple and effective technique for making vertically aligned NRs, and the mechanism behind the NR-LED device with enhanced performance using these NRs is illustrated. This technique may prove useful to the development of a vast class of nanocrystal-based optoelectronics, including solar cells and laser devices.

Please note that the EQE in Device 4 is higher than the spin-coating Device 1 but is lower compared to Device 3. We attribute this to the fine void that might still exist in the macroscale sample.This is supported by the higher current density observed in Device 4 compared to Device 3 at similar voltages.

COMSOL simulations on the 2D model of light emitting diodes
The simulations of the J-V characteristics as well as of the Electron-Hole Concentration plots were conducted by the COMSOL Multiphysics simulation package 6.0 using the semiconductor module.A stationary study was used to calculate the J-V behaviour with and without optical transitions.
Without optical transitions, the semiconductor module in COMSOL 6.0 solves for the drift-diffusion equations of current density Jn(r) (Jp(r)) in the defined region: where n (p) is the electron (hole) density, q is the electron charge, Ec(v) is the conduction (valence) band energy level, μn(p) is the electron (hole) mobility, kb is Boltzmann's constant, T is the lattice temperature and Dn, th(p, th) is the thermal diffusion coefficient for electrons (holes).G is the inverse Fermi-Dirac integral of order 1/2 and Nc(v) is the effective density of states for electrons (holes) in the conduction (valence) band energy level.
With optical transitions, current drain due to spontaneous emission needs to be added: Where Rn(p) is the electron (hole) recombination rate that is equal to spontaneous emission rate Rspon.
For direct bandgap semiconductors, the Rspon is given by: where gred is the reduced density of states and is defined as: where mr is the reduced mass of CdSe/CdS and τspon is the spontaneous emission lifetime.h is Planck's constant, c is the speed of light in a vacuum, E is the photon energy that is equal to ħω and Eg is the bandgap of CdSe/CdS.Eg0 and Eg are the same as no bandgap narrowing was applied to this model.fc(v) is the electron occupancy factors for the conduction (valence) band: where Efn and Efp are the quasi-Fermi levels of the conduction band and the valence band.E2c and E1v are the energy levels of interest where the difference between the two energy levels is equal to the photon energy, ħω.E2c and E1v are described by equations below: where Eg is the bandgap of CdSe/CdS, Ec(v) is the conduction (valence) band, me(h) is the effective electron (hole) mass [1].
The effective density of states for the conduction (valence) band, Nc(v), was determined from the effective electron (hole) mass, me(h).The equation for the effective density of states for the conduction and valence bands can be seen below: S-6 where m0 is the rest mass of the electron.
For the model with the TDPA ligand between three CdSe/CdS nanorods, the WKB tunnelling model for electrons was implemented.The equations for the WKB tunnelling model are as follows: = ( 1 , 2 )  ( 16) is a line integral along the electric field line between the two opposite boundaries 1 and 2 across the potential barrier domain.
For ALD or evaporated ZnO films, the relative permittivity was to 4.17 [2].The bandgap was set to 3.4 eV and the electron affinity was set to 4 eV [3].The electron mobility was set to 25 cm 2 V -1 s -1 and the hole mobility was set to 2.5 cm 2 V -1 s -1 [4].The effective electron mass was set to 0.24 and the effective hole mass was set to 0.59 [5].The donor concentration was set to 1 x 10 23 m -3 and the background doping was set to 1 x 10 18 m -3 .For CdSe/CdS, the relative permittivity was set to 5.8 [6].The bandgap was set to 2.03 eV and the electron affinity was set to 4.27 eV [3].The electron mobility was set to 720 cm 2 V -1 s -1 and the hole mobility was set to 75 cm 2 V -1 s -1 [7].The effective electron mass was set to 0.13 and the effective hole mass was set to 0.45 [8].The spontaneous lifetime of CdSe/CdS was set to 10ns in the optical transitions section [9].The donor concentration was set to 1 x 10 24 m -3 and the background doping was set to 1 x 10 18 m -3 .For PVK, the permittivity was set to 2.82 [10].The bandgap was set to 3.6 eV [11].The electron affinity was set to 2.3 eV [12].The electron mobility was set to 1 x 10 -6 cm 2 V -1 s -1 and the hole mobility was set to 1 x 10 -7 cm 2 V -1 s -1 [13].The effective electron and hole mass were set to 0.55 [14].For TFB, the permittivity was set to 2.72 [15].The bandgap was set to 3.1eV and the electron affinity was set to 2.3eV [16].The electron mobility was set to 2 x 10 -6 cm 2 V -1 s -1 and the hole mobility was set to 2 x 10 -7 cm 2 V -1 s -1 [17].The effective electron and hole mass were set to 1.The acceptor concentration was set to 1 x 10 24 m -3 and the background doping was set to 1 x 10 20 m -3 .The ligand used was TDPA.The relative permittivity was set to 2.14.The bandgap was set to 2.3 eV and the electron affinity was set to 3.6 eV.Both the electron and hole mobility values and the effective electron and hole mass values were set to be the same as the mobility values of CdSe/CdS.The acceptor concentration was set to 1 x 10 24 m -3 and the background doping was set to 1 x 10 20 m -3 .At 2V, the quasi-fermi level for electrons is close to or above the energy level of the conduction band edge in the CdSe/CdS region and the quasi-fermi level for holes is closer to the valence band edge meaning the valence band will be filled with holes.With tunnelling enabled, the potential drop is less notable as both electrons and holes can tunnel through the ligand.Please note that the carriers tunnelling through the TDPA layers is required for the simulation to converge.

Figure S2
Figure S2 The AFM characteristics for the NRs layers made by (a) spin-coating and (b) EPD.

Figure S3
Figure S3 Influence of field strength and deposition time on the thickness of CdSe/CdS NR EPD film.Experimental data points are obtained from EPD of CdSe/CdS NR in Toluene solution with a concentration of 0.5 mg/ml.

Figure S4 A
Figure S4 A histogram of peak EQEs obtained from 23 EPD devices with two layers of NR as the active materials.

Figure
Figure S6 (a)-(d) Current density and luminance versus voltage, and EQE versus luminance characteristics for two more NRs-LEDs by EPD (Device 3: (a) and (b) with deposition time of 60s; Device 4: (c) and (d) with deposition time of 270s).
√max(0, 2(  −   ))  2 1 (19)Where Eb1 and Eb2 are values of Eb, the potential barrier variable, at the two opposite boundaries the potential barrier.The max function is evaluated in the bounds of the potential barrier domain.δnJn is the extra current factor which is determined by a double integration along the electrical field line, dl, as well as along the energy axis, dVx.The integral ∫  2 1

Figure
Figure S7 (a) Energy level diagram of the vertically aligned NR-LED model at 2V.The geometric parameters are the same as used in Figure 4.The black curve corresponds to the conduction band edge, Ec, and the green curve corresponds to the valence band edge, Ev.The red curve represents the quasi-fermi energy level for electrons, Efn, and the blue curve corresponds to the quasi-fermi energy level for holes, Efp.(b) Spontaneous emission recombination rate of the NR-LED in the active region at 2V. (c) Electron-Hole concentration throughout the NR-LED model at 2V.At 2V, the quasi-fermi level for electrons is close to or above the energy level of the conduction band edge in the CdSe/CdS region and the quasi-fermi level for holes is closer to the valence band edge meaning the valence band will be filled with holes.The emission rate is uniform throughout the active μ    + μ     (