Objective　Nano-light　emitting　diodes　(nano-LEDs)　offer　significant　potential　for　ultra-high-resolution　display　applications.　A　key　challenge　in　enhancing　these　displays　is　minimizing　the　emission　angle　of　nano-LEDs　to　reduce　optical　crosstalk　between　adjacent　pixels.　This　study　addresses　this　issue　by　investigating　the　influence　of　various　parameters　on　the　emission　characteristics　of　GaN-based　nano-LEDs.　Specifically,　it　explores　the　influences　of　nano-LED　shape,　the　thickness　of　the　GaN　layer　in　the　quantum　well,　and　the　surrounding　dielectric　layer　on　far-field　radiation　intensity　and　light　emission　angle.　The　objective　is　to　provide　a　comprehensive　simulation-based　analysis　that　can　guide　the　design　and　optimization　of　nano-LEDs　for　improved　performance　in　high-resolution　displays.　Methods　The　study　employs　the　finite　element　method　(FEM)　to　simulate　the　optical　behavior　of　GaN-based　nano-LEDs.　Several　parameters　are　adjusted　to　analyze　their　effects　on　emission　characteristics.　First,　different　nano-LEDs　are　tested　to　determine　their　influence　on　the　emission　angle.　Next,　the　thickness　of　the　GaN　layer　within　the　quantum　well　is　varied.　Finally,　the　influence　of　a　dielectric　layer　encasing　the　nano-LED　is　studied.　Simulations　are　performed　to　evaluate　both　far-field　radiation　intensity　and　the　vertical　emission　angle　under　these　different　configurations.　The　parameters　are　systematically　adjusted　to　identify　the　optimal　configuration　that　minimizes　the　emission　angle　and　enhances　the　far-field　radiation　intensity.　Results　and　Discussions　To　analyze　the　influence　of　nano-LED　shape　on　emission　properties,　we　compare　the　emission　effects　of　nano-LEDs　with　various　top　diameters　(D).　As　shown　in　Figs.　1(d)‒1(f),　an　electric　field　distribution　for　D=0,　400,　and　500　nm　reveals　that　a　top　diameter　of　500　nm　results　in　a　more　focused　electric　field.　The　vertical　emission　angle　of　the　cylindrical　nano-LED,　where　the　top　and　bottom　diameters　are　equal,　is　smaller,　indicating　superior　optical　performance.　Figures　1(g)　‒　1(i)　demonstrate　that　the　far-field　radiation　intensity　is　maximized,　and　the　vertical　emission　angle　minimized　when　D=500　nm.　This　relationship　is　summarized　in　Figs.　1(j)　‒　1(k).　Thus,　a　diameter　of　500　nm　is　chosen　for　further　optimization.　Next,　the　effect　of　GaN　thickness　in　the　quantum　well　on　the　electroluminescence　of　cylindrical　nano-LEDs　with　a　diameter　of　500　nm　is　examined.　As　shown　in　Figs.　2(a)‒2(d),　increasing　GaN　thickness　(T)　enhances　electron-hole　recombination　efficiency,　leading　to　an　expanded　emission　range,　The　electric　field　distribution　for　T=3,　5,　and　7　nm　suggests　that　a　thinner　GaN　layer　(T=3　nm)　maintains　strong　far-field　intensity　while　minimizing　the　emission　angle,　as　shown　in　Fig.　2(e),　which　is　ideal　for　achieving　a　smaller　vertical　emission　angle.　The　addition　of　a　dielectric　layer　around　the　nano-LED　controls　the　effective　emission　area,　focusing　the　light　and　improving　its　directionality.　Figures　3(a)　‒　3(d)　show　the　electric　field　distribution　for　different　dielectric　layer　widths　(W=50,　100,　and　200　nm).　A　dielectric　layer　width　of　200　‒　300　nm　is　found　to　effectively　absorb　side-emitted　light,　reducing　the　emission　angle　and　increasing　far-field　intensity　by　approximately　30%　[Figs.　3(e)‒3(g)].　The　optimal　width　for　minimizing　the　emission　angle　and　maximizing　intensity　is　found　to　be　70　nm.　Further　simulations　investigate　the　effect　of　the　dielectric　layer’s　refractive　index　on　emission　properties.　Figures　4(a)　‒　4(d)　illustrate　the　electric　field　distribution　and　far-field　intensity　for　refractive　indices　ranging　from　n=1.3　to　n=1.8,　with　W=200　nm.　The　optimal　refractive　index　of　n=1.5　provides　the　most　focused　far-field　distribution　and　the　smallest　emission　angle.　A　similar　trend　is　observed　for　W=300　nm　[Figs.　4(e)‒4(h)],　where　n=1.5　provides　the　best　performance.　Ultimately,　cylindrical　nano-LEDs　with　a　dielectric　layer　of　n=1.5　and　W=300　nm　demonstrate　a　significantly　narrower　emission　angle　and　a　40%　increase　in　far-field　radiation　intensity　[Figs.　5(a)　and　5(b)].　This　configuration　effectively　absorbs　side-emitted　light　and　concentrates　the　emission,　highlighting　its　potential　for　high-resolution　display　applications.　Conclusions　We　analyze　the　factors　influencing　the　emission　characteristics　of　GaN-based　nano-LEDs.　Through　FEM　simulation,　it　is　found　that　the　top　diameter,　GaN　layer　thickness,　and　dielectric　layer　properties　significantly　affect　farfield　radiation　intensity　and　emission　angle.　The　optimal　configuration,　which　includes　a　top　diameter　of　500　nm,　a　GaN　layer　thickness　of　3　nm,　a　dielectric　layer　refractive　index　of　1.5,　and　a　dielectric　layer　width　of　300　nm,　results　in　a　40%　increase　in　far-field　radiation　intensity　and　a　significantly　reduced　emission　angle.　These　findings　offer　valuable　insights　for　the　design　of　high-performance　nano-LEDs　in　ultra-high-resolution　display　applications.　©　2024　Chinese　Optical　Society.　All　rights　reserved.