Micro-LED

1. Theory

• Definition: A micro-LED is an inorganic LED (usually InGaN/GaN or AlGaInP) whose mesa is shrunk to a few micrometres to a few tens of micrometres.
• Sidewall recombination: Etch damage on the mesa sidewall adds non-radiative recombination, and its share grows as $1/D$ ($A_{eff}=A+4S/D$).
• Carrier diffusion: Carriers diffuse tens of micrometres at low density, so even fairly large mesas feel the sidewall.
• Shifted efficiency peak: Higher effective trap rate pushes the peak-efficiency current density upward as the device shrinks.
• Heat spreading: Small sources spread heat well, so temperature rise scales with $JD$.
• Pixel current density: Display luminances need only about $1mA/c{\mathrm{m}}^2$ to $1A/c{\mathrm{m}}^2$, on the low-current side where sidewall losses matter most.

2. Working Principle

• Emission: Same carrier injection and quantum-well recombination as a standard LED.
• Low-current penalty: At display drive levels, sidewall recombination dominates, so smaller pixels are less efficient.
• High-current behaviour: Smaller devices show less droop at high current density, partly because of better current spreading.
• Sidewall passivation: Annealing and dielectric passivation partly recover sidewall damage.
• Self-heating: Single small pixels heat very little, but dense arrays with poor heat paths can still warm up.

3. Applications

• Current status: Early commercial stage; mass transfer, colour conversion and yield remain major challenges.
• AR/VR microdisplays: Very bright, high-pixel-density displays for smart glasses and headsets.
• Wearable and large-format displays: Smartwatch screens and modular video walls needing high brightness and long life without OLED burn-in.
• Visible-light communication (research): Small, fast micro-LEDs for high-speed optical data links.

Name	Formula	Related Formulae	Variables/Constants
Sidewall recombination of a small mesa (uniform carrier density)	$A_{eff}\left(D\right)=A+\frac{4S}{D}$	$n_{peak}\left(D\right)=\sqrt{\frac{A_{eff}}{C}}$ ${\eta }_{rad,max}\left(D\right)=\frac{B}{B+2\sqrt{A_{eff}C}}$	$\begin{array}{r}{A}_{eff}\left(D\right):effectiveShockley-Read-Hall\\ coefficientofacylindricalmesaof\\ diameterD,includingthelossatthe\\ etchedsidewall\end{array}$ $\begin{array}{r}A:bulkShockley-Read-Hallcoefficientof\\ theABCmodelontheLightEmittingDiode\\ page\end{array}$ $\begin{array}{r}S:surfacerecombinationvelocityofthe\\ sidewall\end{array}$ $\begin{array}{r}D:diameterofthemesa(theterm4S/Dis\\ theratioofthesidewallarea\pi Dtofthe\\ activelayerofthicknessttoitsvolume\\ \pi D^{2}t/4,multipliedbyS)\end{array}$ $\begin{array}{r}{n}_{peak}:carrierdensityofthemaximum\\ radiativeefficiency,whichrisesasthe\\ mesagetssmaller\end{array}$ $B,C:radiativeandAugercoefficients$ $\begin{array}{r}{\eta }_{rad,max}:maximumradiativeefficiency,which\\ fallsasthemesagetssmaller\end{array}$ $\begin{array}{r}(theexpressionisvalidwhenthecarriers\\ arespreadevenlyoverthemesa,thatis\\ whenDissmallerthanthediffusion\\ lengthofthenextrow)\end{array}$
Diffusion length and the fraction of the mesa that is close to the sidewall	$L_d=\sqrt{D_a\tau \left(n\right)}$	$\tau \left(n\right)=\frac{1}{A+Bn+C{n}^2}$ $f_{edge}=1-{\left(1-\frac{2L_d}{D}\right)}^2\approx \frac{4L_d}{D}\left(2L_d<D\right)$ ${\eta }_{rad}^{mesa}=\left(1-f_{edge}\right){\eta }_{rad}^{bulk}+f_{edge}{\eta }_{rad}^{edge}$	$\begin{array}{r}{L}_d:diffusionlengthofthecarriersin\\ thequantumwellatthedensityn\end{array}$ $D_a:ambipolardiffusioncoefficient$ $\begin{array}{r}\tau \left(n\right):carrierlifetimeatthedensityn\\ fromtheABCmodel(thediffusionlength\\ islongatalowdensity,wherethetrap\\ termAsetsthelifetime,andshortata\\ highdensity)\end{array}$ $\begin{array}{r}{f}_{edge}:fractionoftheareaofthemesathat\\ lieswithinonediffusionlengthofthe\\ sidewall(thecarrierstherecanreachthe\\ damagededge)\end{array}$ $D:diameterofthemesa$ ${\eta }_{rad}^{mesa}:averageradiativeefficiencyofthemesa$ $\begin{array}{r}{\eta }_{rad}^{bulk},{\eta }_{rad}^{edge}:radiativeefficienciesof\\ theinteriorandoftheedgezone(the\\ secondislowerbecauseofthesidewall\\ defects),withtheapproximationofa\\ sharpboundarybetweenthetwozones\end{array}$
Current density and the current of the peak efficiency	$J=\frac{4I}{\pi D^2}$	$J_{peak}\left(D\right)=\frac{qd}{{\eta }_{inj}}\left[2\frac{A_{eff}^{3/2}}{C^{1/2}}+B\frac{A_{eff}}{C}\right]$ $I_{peak}=\frac{\pi D^2}{4}{J}_{peak}$	$\begin{array}{r}J:currentdensityinthemesaofdiameter\\ DatthecurrentI\end{array}$ $\begin{array}{r}{J}_{peak}\left(D\right):currentdensityatthemaximum\\ efficiency,obtainedbythesteady-state\\ relationoftheLightEmittingDiodepage\\ at{n}_{peak}=\sqrt{A_{eff}/C}(itriseswith{A}_{eff},sothe\\ peakmovestoahigherdensityforthe\\ smallerdevices)\end{array}$ $q:elementarycharge$ $d:thicknessoftheactiveregion$ ${\eta }_{inj}:injectionefficiency$ $A_{eff},B,C:coefficientsofthepreviousrows$ $\begin{array}{r}{I}_{peak}:currentatthepeak(itfallsas{D}^2\\ foragiven{J}_{peak},soasmallpixeloperates\\ ataverysmallcurrent)\end{array}$
Self-heating of a small light source	$\Delta T=R_{th}{P}_{diss}$	$R_{th}=\frac{1}{2{\kappa }_{th}D}$ $P_{diss}=IV-P_{opt}$	$\begin{array}{r}\Delta T:riseofthejunctiontemperature\\ abovetheheatsink\end{array}$ $\begin{array}{r}{R}_{th}:thermalspreadingresistanceofa\\ circularheatsourceofdiameterDona\\ semi-infinitesubstrate,foranisothermal\\ source\end{array}$ $\begin{array}{r}{\kappa }_{th}:thermalconductivityofthesubstrate,\\ about130W/mKforGaNandabout35W/mK\\ forsapphire\end{array}$ $D:diameterofthesource$ $\begin{array}{r}{P}_{diss}:heatpower,theelectricalpowerIV\\ minustheemittedopticalpower{P}_{opt}\end{array}$ $\begin{array}{r}(forafixedcurrentdensity{P}_{diss}is\\ proportionalto{D}^{2}and{R}_{th}to1/D,so\Delta T\\ isproportionaltoJDandfallsforthe\\ smallerdevices;therealstackhaslayers\\ ofdifferentconductivityandafinite\\ thickness,sotheexpressiongivesthe\\ orderofmagnitudeandnotabound)\end{array}$
Drive current density for a target luminance	$J=\frac{\pi L}{{\eta }_{P}V}$	${\eta }_P=683\bar{y}\left(\lambda \right){\eta }_{EQE}\frac{h\nu }{qV}$ $L_{avg}=FF\cdot L$	$\begin{array}{r}J:currentdensityneededforthe\\ luminanceLofaLambertianemittingarea\end{array}$ $L:luminanceoftheemittingarea(cd/m^2)$ ${\eta }_P:powerefficacy(lm/W)ofthepixel$ $V:operatingvoltage$ $\begin{array}{r}\bar{y}\left(\lambda \right):photopicluminousefficiency\\ functionoftheeye,equaltooneat555\\ nm\end{array}$ $\begin{array}{r}{\eta }_{EQE}:externalquantumefficiencyatthat\\ currentdensity\end{array}$ $h\nu :photonenergy$ $L_{avg}:luminanceaveragedoverthepixelpitch$ $\begin{array}{r}FF:fillfactor,theratiooftheemitting\\ areatothepixelarea(amicro-LEDwitha\\ smallfillfactormustbedrivenata\\ higherluminancetoreachagivenaverage\\ luminance)\end{array}$

Important Questions

Ques: Why are smaller micro-LEDs less efficient at a low current but droop less at a high current?

The etching of the mesa damages the sidewall and creates states that recombine the carriers without light, and the ratio of the sidewall to the area grows as 1/D, so the trap term $A_{eff}=A+4S/D$ grows. At a low current density the trap term dominates the recombination, so the small devices have a lower efficiency. At a high current the Auger term dominates, and a report on blue InGaN micro-LEDs attributes the higher efficiency of the smaller devices at a high current density to a better current spreading. The same report found that a longer thermal annealing partly recovers the sidewall defects and the efficiency at a low current. Reference: P. Tian et al., “Size-dependent efficiency and efficiency droop of blue InGaN micro-light emitting diodes,” Appl. Phys. Lett. 101, 231110 (2012).

Ques: How large is the effect of the sidewall for realistic sizes, and does it depend on how far the carriers diffuse?

With an assumed surface recombination velocity of $S=10^3$ cm/s (an illustrative value, not a measured one) and the assumed ABC coefficients of the Light Emitting Diode page, the lumped model gives $A_{eff}=1.04\times 10^7$ s${}^{-1}$ and ${\eta }_{rad,max}=0.756$ for $D=100\mu$m, 1.4$\times 10^7$ and 0.728 for 10 $\mu$m, 2.3$\times 10^7$ and 0.674 for 3 $\mu$m and 5$\times 10^7$ and 0.586 for 1 $\mu$m (computed), and the current density of the peak efficiency, for a 3 nm active layer and ${\eta }_{inj}=1$, rises from 13 A/cm${}^2$ to 18, 33 and 82 A/cm${}^2$. The lumped model assumes a uniform density, which is wrong for a large device. A recent study measured a diffusion length in InGaN quantum wells of about 50 $\mu$m at a low density, falling to less than 1 $\mu$m at a high density, and concluded that the sidewall can reduce the efficiency even of a device 100 $\mu$m wide. With the edge-fraction row, $f_{edge}$ is 4% for $L_d=1\mu$m and $D=100\mu$m, 36% for $L_d=1\mu$m and $D=10\mu$m and 56% for $L_d=17\mu$m and $D=100\mu$m (computed from the formula). Reference: arXiv:2104.07199, “Observation of long-range carrier diffusion in InGaN quantum wells, and implications from fundamentals to devices” (the values of the diffusion length are those of that preprint, measured by photoluminescence on specific samples; the authors were not retrieved).

Ques: How much does a micro-LED heat up?

For a disc source of diameter 10 $\mu$m on GaN (${\kappa }_{th}=130$ W/mK) the spreading resistance is $1/(2{\kappa }_{th}D)=385$ K/W. At 100 A/cm${}^2$ the current is 78.5 $\mu$A, and with 3.2 V and a wall-plug efficiency of 20% the heat power is 0.20 mW, so $\Delta T=0.077$ K; at 1 kA/cm${}^2$ it is 0.77 K, and on sapphire (${\kappa }_{th}=35$ W/mK) the values are 3.7 times higher, 0.29 K and 2.9 K (computed, with assumed conductivities). The rise is proportional to $JD$, so small devices stay cooler than large ones at the same current density, but a pixel array with a poor heat path can still heat up because the sources are close together, which this single-source expression does not include. Reference: The spreading-resistance form $1/(4{\kappa }_{th}a)$ for an isothermal circular source of radius $a$ on a half-space is the classical result (H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford University Press, 1959); the University of Waterloo Microelectronics Heat Transfer Laboratory (mhtlab.uwaterloo.ca) uses the same $4ka$ normalization.

Ques: What current density does a micro-LED display pixel need?

For a green LED at 530 nm (2.34 eV) with an EQE of 20% at 3 V, the power efficacy is $683\times 0.862\times 0.2\times 2.34/3=92$ lm/W (the value 0.862 of the eye sensitivity at 530 nm is recalled), and the current density for a luminance of 1000 cd/m${}^2$ on the emitting area is $J=\pi L/({\eta }_{P}V)=11$ A/m${}^2$, 1.1 mA/cm${}^2$, and for $10^6$ cd/m${}^2$ it is 1.1 A/cm${}^2$ (computed). A pixel with a fill factor of 10% needs a ten times higher luminance on the emitting area for the same average. This is a low current density at which a small device is on the rising part of its efficiency curve (the peak rows), which is why the sidewall damage matters for the display. Reference: the numbers are computed from the relations of the Organic Light Emitting Diode page, with the CIE 1924 photopic value $\bar{y}(530\mathrm{nm})=0.862$.

Related pages in this vault: Light Emitting Diode (Homojunction and Heterojunction LED), Organic Light Emitting Diode (OLED), Quantum Well LED (InGaN-GaN and AlGaInP), Quantum Dot LED (QLED), Ultraviolet LED (AlGaN Deep-UV LED), Vertical-Cavity Surface-Emitting Laser (VCSEL), Light Emitting Diodes (InGaN, AlInGaP, UV and White).