An elegant route to overcome fundamentally-limited light extraction in AlGaN deep-ultraviolet light-emitting diodes: Preferential outcoupling of strong in-plane emission

While there is an urgent need for semiconductor-based efficient deep ultraviolet (DUV) sources, the efficiency of AlGaN DUV light-emitting diodes (LEDs) remains very low because the extraction of DUV photons is significantly limited by intrinsic material properties of AlGaN. Here, we present an elegant approach based on a DUV LED having multiple mesa stripes whose inclined sidewalls are covered by a MgF2/Al omni-directional mirror to take advantage of the strongly anisotropic transverse-magnetic polarized emission pattern of AlGaN quantum wells. The sidewall-emission-enhanced DUV LED breaks through the fundamental limitations caused by the intrinsic properties of AlGaN, thus shows a remarkable improvement in light extraction as well as operating voltage. Furthermore, an analytic model is developed to understand and precisely estimate the extraction of DUV photons from AlGaN DUV LEDs, and hence to provide promising routes for maximizing the power conversion efficiency.


Supplementary Figure S1. Fabrication processes for SEE DUV LEDs
Supplementary Figure S1 shows the fabrication steps for a SEE DUV LED with inclined and reflective sidewalls of the active mesa. Figure S1a shows the schematic epitaxial structure of an AlGaN-based DUV LED grown on a 4 inch sapphire substrate. First, the active mesa stripes were patterned by a conventional photolithography (Fig. S1b). In order to obtain the active mesa stripes with inclined sidewalls, thermal reflow of photoresist was carried out at 140 °C for 10 minutes to form a rounded shape (Fig. S1c), followed by inductively coupled plasma dry etching to expose the n-AlGaN (Fig. S1d). Then, ohmic contact stripes were patterned on the exposed n-AlGaN between the active mesa stripes, and Ti/Al/Ni/Au (30/120/40/100 nm) were sequentially deposited by using an electron-beam/thermal evaporation, followed by lift-off and annealing at 900 °C for 1 min in N2 ambient to form ohmic contacts. Ni/Au (20/100 nm) ohmic contact stripes were deposited on p-GaN and annealed at 750 °C for 1 min in air (Fig. S1e). Then, Ti/Au (20/100 nm) pad metals were formed on both ohmic contact stripes for n-AlGaN and p-GaN. MgF2/Al (250/150 nm) omni-directional reflectors were formed on the inclined sidewalls of the mesa stripes ( Fig. S1f and Fig. S1g) by using conventional photolithography, electron-beam evaporation, and lift-off. 4

Supplementary Figure S2. SEE DUV LEDs with various numbers of mesa stripes
AlGaN-based SEE DUV LEDs with a 1 × 1 mm 2 chip area and with various numbers of mesa stripes, ranging from 5 to 50, were designed and fabricated. As the number of the stripes increases, the perimeter length of the active mesa increases as summarized in Supplementary Table S1, therefore, the strong TMpolarized sidewall-directed emission can be reflected down to the sapphire substrate by the MgF2/Al omnidirectional mirror that is located on the inclined sidewalls.

Supplementary Figure S3. EL spectra for various injection currents and TE/TM polarization
The electroluminescence (EL) spectra of a SEE DUV LED with the peak wavelength of 275 nm at various drive currents are shown in Supplementary Fig. S3a. As the drive current increases from 20 mA to 100 mA, the EL intensity linearly increases as well. Supplementary Figure S3b shows the EL spectra at 100 mA along with its TE and TM polarized characteristics. Inset Fig. S3b shows the schematic for the EL and polarization measurement setup. Only a small part of the sample is attached to the double-side-polished sapphire support to make a free standing condition so that DUV absorption by the sapphire support can be neglected. The  Table S2.

Supplementary Information. Estimation of the LEE by an analytic model
We develop an analytic model to accurately estimate the LEE of AlGaN-based DUV LEDs by taking into account critical factors affecting the LEE including the TM/TE polarization ratio, the number of stripes, the current crowding effect, and the effect of interface roughening.
At first, the current crowding effect is considered and included in the model as a weighting factor. Due to the lateral carrier transport in the highly resistive AlGaN layers of the DUV LEDs grown on an insulating sapphire substrates, the injection current crowds near the edge of the active mesa stripes, resulting in an exponential decrease in LOP from the edge. Therefore, the current spreading length (Ls), defined as the length where the current density (J) drops to the 1/e value of the current density at the edge, is defined as 3 , ( is the p-type specific contact resistance, is the resistivity of the p-type layer, is the resistivity of the n-type cladding layer). With Ls, the current density as a function of distance from the edge of the active mesa stripe x is given by, In order to apply such a non-uniform current distribution along x into the estimation of the LEE, we introduce a weighting factor (WF) for the intensity of each dipole source. When the injection current is the same for all the devices, the following relation based on the integration by the rectangular method is valid.
where N is the number of dipole sources, Lm is the length of the one stripe, and C is a constant. The equation can be simplified by replacing 1 • +1 by k to obtain, In the rectangular integration method, the area of one rectangle can be used as the weighting factor, WF(n), given as, Next, we discuss the effective critical angle at the interface between two optical media. In our analytic model, there are two interfaces encountered by light travelling toward a bottom direction, the n-AlGaN/sapphire and sapphire/air interfaces. When the interfaces are planar, two critical angles should be considered for optical loss by the total internal reflection. The critical angle at the sapphire/air surface is Similarly, the critical angle at the interface between n-AlGaN and sapphire substrate is Considering the two planar interfaces, the effective critical angle θ * is given as It is well known that by roughening or texturing the interface, one can overcome the total internal loss, thus, increase the effective critical angle of total internal reflection at the interface, and consequently increase the LEE, which we consider in the analytic model. Introducing the surface roughening factor SR, the equation for the effective critical angle can be generalized as The value of SR can be obtained by ray-tracing simulations or reported enhancement values by using roughening or patterning of the sapphire substrate. We assume that conventional surface roughening technique can make about 50% enhancement in LEE based on the references including IEEE Electron Device Letters 30, where  is absorption coefficient of AlGaN, l(n,) is length of light path depending on dipole location, and θ * is the effective critical angle.

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In the second case, we assume that all of light is absorbed in the p-GaN layer, which is reasonable considering the thick p-GaN layer with a large absorption coefficient of GaN at 275 nm. In the third case, we need to consider the reflectance, R, of Al/MgF2 ODR. , , ITM and ITE are described in Fig. 4a. The values for  and  also depend on the dipole location.