In this thesis photonic crystal LEDs have been designed, fabricated and characterized to answer the question if light extraction with photonic crystals yields higher efficiency and/or directionality than state-of-the-art LEDs with surface roughening. The fundamental advantage with photonic crystal light extraction is that light in a guided mode is extracted in a controlled and predictable way (given by Bragg’s law) that can be directional if the photonic crystal has the right lattice constant. Real LEDs have several modes and the first challenge is to design the vertical layer stack so that the majority of the guided modes can be extracted by one and the same photonic crystal in a directional way. The second challenge is to optimize the properties of the photonic crystal for the particular LED. This includes choosing the right lattice constant, lattice type and air filling factor together with a sufficiently large etch depth. Below I will summarize some general design rules for multi-mode PhC-LEDs. Thereafter I will discuss the choice of lattice type and the experimental results for AlGaInP PhC-LEDs and InGaN PhC-LEDs.
Design rules
In Section 4.3 we concluded that the optimal lattice constant and air filling factor varies strongly even for a single mode depending on the absorption strength. A few design rules can however be made that applies for all multi-mode PhC-LEDs.
1. The use of the thin-film technology is very advantageous for photonic crystal light extraction. All emitted light stays in the LED slab confined at the bottom by a metallic mirror until it is extracted by the photonic crystal or absorbed. 2. The active region should be placed as close to the bottom mirror as possible to
induce a modulation of the spontaneous emission. In this way, directional light extraction with a photonic crystal is possible even for LEDs several microns thick. The position of the active region must at the same time give a directional farfield for the directly extracted light. However, the internal quantum efficiency and the direct light extraction must not be negatively affected by the proximity to the mirror.
3. The LED thickness should be as small as possible without affecting the internal efficiency and the lateral current spreading. This reduces the number of guided modes which generally makes beam-shaping with the photonic crystal easier. The extraction length in a thin LED is also shorter due to the stronger coupling
with the photonic crystal. Ideally, there should be only one Fabry Perot resonance in the light extraction cone to enable directional direct light extraction.
4. The etch depth of the photonic crystal should be at least as large as the
attenuation length of guided modes. This typically corresponds to 100nm.
5. Directional light extraction of a single mode (or a single resonant mode range) with a hexagonal lattice can be realized by using the first diffraction order (i.e.
G0 ~ ki) or a combination of the second and third diffraction order
(ki/2 < G0 < ki/√3). The latter yields omnidirectional extraction but requires low absorption in order to be efficient.
6. In the case of a quasi-continuum of guided modes, the most efficient lattice constant is found in the range 1 < G0 < nPhC. A reciprocal lattice constant in this range extracts the modes that couples most strongly with the photonic crystal by first order diffraction.
Hexagonal lattice vs. Archimedean lattice
The hexagonal lattice – the regular 2D crystal with highest symmetry – has been used as the standard lattice throughout my work. Drawbacks with the hexagonal lattice have been identified and alternative lattices have been investigated. The hexagonal lattice has an insufficient number of first order diffraction points to enable omnidirectional diffraction of modes with effective index ki > 2. The Archimedean lattices such as the A7 lattice proposed in literature have enough lattice points. The experimental results in this thesis show that a minor extraction efficiency improvement is obtained for AlGaInP LEDs whereas the performance in InGaN LEDs is similar to hexagonal lattices. The radiant intensity (and directionality) is however reduced. A possible explanation for this experimental result is the lower diffraction strength for the lower diffraction orders in the A7 lattice compared with a hexagonal lattice. The biggest advantage with photonic crystals compared to surface roughening – the ability to shape the farfield – is thus less pronounced when Archimedean lattices are used.
AlGaInP thin-film photonic crystal LEDs
The external quantum efficiency as well as the PhC enhancement factor demonstrated with AlGaInP photonic crystal LEDs are better than for any other AlGaInP PhC-LEDs found in literature. Several important conclusions have been drawn regarding the
potential of thin-film AlGaInP PhC-LEDs. First of all, the range of guided modes present expressed in terms of effective index is much too large for a photonic crystal with one dominating diffraction order. This is a fundamental problem, since the allowed mode range is given by the refractive index of AlGaInP. The quasi-continuum of guided modes found in standard thin-film LEDs results in a dense net of diffraction lines at all emission angles which makes directional light extraction very difficult. One must choose between trying to extract low order modes with much light but very small interaction with the photonic crystal or to extract high order modes that have higher mode overlap but less energy. Experimental results as well as simulations show that the latter alternative is better. To reach the ultimate goal of 100% extraction efficiency, the remaining modes must then be extracted via photon recycling, high order diffraction or multiple diffraction processes. Strong photon recycling requires an internal efficiency close to 100%, which sets high demands on the epitaxial quality as well as on the electrical bandgap engineering. It is however the only way to extract the (type I) modes that are guided between the electrical confinement layers. These modes do hardly experience the extracting surface structure – whether it is a photonic crystal or surface roughness. High order diffraction and multiple diffraction processes are slow processes that require that the mode absorption in the remaining low order modes is low. The direct comparisons made between PhC-LEDs and LEDs with surface roughening have not been clarifying – the quality of the surface roughness for the reference devices can be questioned. It highlights the fact that there is no such thing as “one piece surface roughening” – the topography varies between different processes and material systems. The main objective of my work has been to realize directional LEDs. Efforts to reduce the total thickness of the AlGaInP LED and to form a resonant cavity resulted in directional light extraction and higher PhC enhancement factors than for previous experiments with thicker PhC-LEDs. The thinner LED supported less modes and the farfield of the most directional devices was dominated by only three guided modes. It was thus shown that a sufficiently strong modulation of the spontaneous emission to the guided modes to achieve directional emission is possible. The super-position of the FP- resonance formed by the resonant cavity and the diffraction lines also showed that these two light extraction mechanisms can be combined. This principally important demonstration of directional light extraction from AlGaInP LEDs was however achieved at the cost of lower internal efficiency and the absence of photon recycling.
This reduction of the internal efficiency is not believed to be inevitable. But it shows how sensitive the overall efficiency of AlGaInP LEDs is to changes in layer composition and thicknesses that reduces the internal efficiency. It remains to show that a vertical layer design suited for photonic crystal light extraction can be just as efficient as standard LEDs with thicker epitaxial layers.
InGaN thin-film photonic crystal LEDs
Thin-film InGaN LEDs are better suited for photonic crystal light extraction due to the low refractive index of InGaN. The ideal single-mode PhC-LED was approached with the 850nm thick micro-cavity LED with 400nm deeply etched photonic crystals. It was shown that the farfield radiation pattern can be varied strongly by changing the lattice constant of the PhC in these LEDs that contained only three guided modes. Even higher directionality would have been achieved if the directly emitted light had also been tuned correctly. This part of the vertical layer stack design should not be neglected, since a large fraction of the light is extracted without being diffracted by the photonic crystal. The realization of sub-micron PhC-MCLEDs is however very difficult with current epitaxial growth technology on sapphire substrates. A very precise control of the back- etching of the GaN buffer layer is necessary. Growth thickness fluctuations on the wafer will always result in a variety of final cavity thicknesses. The mode dispersion will change accordingly and fine-tuning of the lattice constant will therefore be impossible. It was however shown that farfield shaping with photonic crystals is also possible in thick InGaN LEDs. The proximity of the active region to the bottom mirror strongly modulates the spontaneous emission into the guided modes. This enables beam-shaping even in devices several microns thick. The weaker diffraction strength in these thick LEDs does however result in unwanted side-emission which reduces the directionality. The light extraction in InGaN PhC-LEDs of standard thin-film thickness is thus not fast enough whereas ultra-thin PhC-MCLEDs are at least not viable for industrial production
today. A practical optimum may exist in between. InGaN LEDs ~2µm thick with a
fairly deeply etched photonic crystal would be easier to fabricate and the current spreading would be sufficiently good to allow lateral current spreading without using an absorbing ITO-contact. The mode overlap with the photonic crystal is enhanced and the extraction length thus shorter.
A direct comparison between InGaN-LEDs with surface roughness and photonic crystals showed that the high directionality achieved with photonic crystals is compensated by lower extraction efficiency – for thick as well as thin LEDs. The absolute enhancement achieved within a certain acceptance angle θ has therefore been positive only for very small angles. Is this the end of story for PhC-LEDs in the InGaN material system – no! The extraction efficiency is simply given by the relation between the extraction strength β and the absorption strength α: η = β/(β +α). Even if the PhC extraction strength remains at a somewhat lower level compared to surface roughening, the efficiency gap will be reduced as the absorption is minimized in future chip concepts. The difference in directionality on the other hand is fundamental: LEDs with surface roughening will keep being Lambertian whereas PhC-LEDs will stay directional also when the absorption is minimized. It is therefore foreseeable that the use of PhC- LEDs will yield higher system efficiency for étendue limited optical systems corresponding to their higher directionality.
Novel concepts
Two new concepts that might help to close the efficiency gap faster were presented in Chapter 6. The dual lattices are alternative photonic crystals that address a weakness of the hexagonal lattice: it can only extract light efficiently in a mode range smaller than the mode range in InGaN and AlGaInP LEDs. Dual lattices – here realized either as a hole-size variation or a superposition of two lattices – distribute the diffraction strength more evenly between two reciprocal lattice vector lengths. It can therefore in principle extract two mode ranges with moderate diffraction strength rather than one mode range with high diffraction strength. It has been shown that this in principle works and the first experimental results are promising. The key issue here is to ensure that the high directionality for PhC-LEDs is maintained while extracting more light from a wider mode range.
A complete different PhC-LED approach was suggested in Section 6.2. The photonic crystal is here etched into a dielectric with lower refractive index than the semiconductor material. The guided modes are confined to a smaller effective index range in this material. This is the ideal case for photonic crystal light extraction and directional emission is thus possible. A scattering mechanism is required to extract the light from the semiconductor material to the low index dielectric. This could be either a
second photonic crystal or a conventional rough surface. 3D FDTD simulations showed that this design works. The extraction efficiency approaches the efficiency of state-of- the-art LEDs with surface roughening whereas the directionality is high like for a PhC- LED. Another advantage with this design is that changes of the epitaxial design to improve the internal efficiency can be made without changing the directional light extraction. Precise control of the layer thickness to design the guided mode distribution is thus not necessary. The dielectric PhC-LED design could bring directional emission for AlGaInP as well as InGaN LEDs.
Finally, strongly coupled PhC-LEDs deserve a comment. This type of PhC-LED was ruled out as a viable alternative in Section 4.2 since etching of the active layer induces non-radiative surface recombination and the active material volume is reduced. Nanorod LEDs [59]-[60] are however also in principle strongly coupled photonic crystal LEDs. Epitaxial grown nano-rods are potentially defect-free and core-shell growth [61] would allow for a large active volume per area unit. Effects typically associated with photonic crystals like the Purcell effect, inhibited spontaneous emission in bandgaps and flat bands could then be used to increase the internal efficiency as well as the extraction efficiency. However, there is a long and challenging way to go before nano-rod LEDs can be grown with a material quality that gives them a performance comparable to state- of-the-art LEDs.