The invention of the blue LED based on the GaN platform has started a revolution in lighting and display applications [1]. By combining these blue LEDs with already available red and green diodes, it is possible to fabricate full-color displays [2]. There is a growing demand for increasing the resolution of displays. In particular, for wearable optical devices, improved micro-displays are required; however, when the dimensions of LEDs decrease, problems arise due to smaller feature sizes in terms of the emission efficiency. In reducing the size of LEDs based on InGaN multiple quantum well (MQW) structures, they start showing a reduction in internal quantum efficiency (IQE) [3], but an increase in light extraction efficiency (LEE) [4]. Furthermore, due to the relatively long free carrier lifetime in GaN quantum wells, the occurrence of non-radiative recombination at the sidewalls of the micro-LED structures increases for smaller devices, lowering the IQE [5,6]. Solutions to this problem have been sought in softer etching techniques [7], and chemical treatment and passivation to reduce etching-induced sidewall defects [8]. The improved LEE can be explained for geometrical reasons, as the sidewall-surface-to-volume ratio improves for smaller devices [9,10]. Red micro-LEDs, which are typically based on AlGaInP, strongly suffer from size-dependent efficiencies due to their high surface recombination velocities (SRV) and carrier diffusion lengths [6,11], and sidewall passivation shows only limited improvements [12]. Also, it is speculated that InGaN-based LEDs could have better size-dependent characteristics because of its strongly limited SRV resulting from carrier localization due to alloy disorder for increasing indium content [13]. However, efficient stable red InGaN-based LEDs remain to be realized.

We have demonstrated efficient red LEDs based on Eu-doped GaN (GaN:Eu), where the red emission originates from intra-${{4f}}$ transitions in the Eu ions [14]. GaN:Eu has a reduced carrier mobility and shorter carrier lifetime as a result of carrier trapping by Eu-related traps [15], when compared to that of InGaN quantum wells. This results in much smaller carrier diffusion lengths in Gan:Eu LEDs than in conventional MQW-based GaN LEDs, thus reducing the influence of non-radiative side-wall defects, which is desirable for micro LEDs.

In this work, we study the photoluminescence (PL) QE of the red emission from GaN:Eu as a function of structure size in order to quantify the side-wall related effects for this material. GaN:Eu samples with a patterned surface consisting of an array of squares with sizes ranging from ${{3}}\;{\times}\;{{3}}\;\unicode{x00B5} {{\rm{m}}^2}$ to ${{192}}\;{\times}\;{{192}}\;\unicode{x00B5} {{\rm{m}}^2}$ were prepared. The PL QE after a pulsed optical excitation of the GaN host material is determined. The influence of the mesa (flat-topped elevation) size on the LEE and the absorption of emitted light within the layer is investigated by finite-difference time-domain (FDTD) simulations in order to explain the results.

The samples in this work were grown by organometallic vapor phase epitaxy (OMVPE) on a sapphire substrate, where trimethylgallium (TMGa) and ammonia (${{\rm{NH}}_3}$) were used as the gallium and nitrogen sources, respectively. The reactor pressure was maintained at 100 kPa during growth. For the GaN:Eu layers, ${\rm{EuCp}}_2^{\rm pm}$ was used as the Eu source. The Eu concentration was approximately ${1.0} \times {{1}}{{{0}}^{20}}\;{\rm{c}}{{\rm{m}}^{- 3}}$ as determined from secondary ion mass spectroscopy. The growth temperature of the optical active layer was 960°C, which is the optimal growth temperature for GaN:Eu [16,17]. The growth sequence was initiated with the growth of a 1.5 µm thick undoped GaN buffer layer, followed by the growth of a 300 nm thick GaN:Eu layer. After growth, a photoresist was applied, which was exposed to the desired pattern using a maskless lithography system (NanoSystem Solutions DL-1000). After development of the photoresist, the sample was etched using ${\rm{C}}{{\rm{l}}_2}$ inductively coupled plasma (ICP) etching. The etch depth, as confirmed using a laser scanning microscope, was 450 nm, which is deep enough to remove the Eu-doped layer. After etching, the resist was removed using a combination of hydrogen peroxide (${{\rm{H}}_2}{{{0}}_2}$) and sulfuric acid (${{\rm{H}}_2}{{\rm{SO}}_4}$). The pattern consisted of square mesas ranging in size from 3 to 192 µm. The width of the channels was chosen in such a way that the relative un-etched area was identical (56 %) for all structures.

Figure 1(a) shows a height map of the ${{9}}\;{\times}\;{{9}}\;{\rm{\unicode{x00B5}{\rm m}}}$ structures taken using a laser scanning microscope, clearly showing the pattern consisting of 450 nm high square mesas. Figure 1(b) depicts a luminescence image from the same structures, which was taken by exciting a large area on the sample and collecting the emitted light through an objective while filtering out the laser light. The image shows that there is emission only from the mesa structures; furthermore, the sides are much brighter, which is due to waveguided light being scattered out on the sides of the structures.

 

Fig. 1. (a) Height map obtained by laser microscope and (b) image of Eu-related luminescence upon excitation with a 350 nm laser of the ${{9}} \times {{9}}\;{{\unicode{x00B5}}\rm m}$ structures.

Download Full Size | PDF

An integrating sphere setup was constructed to determine the PL QE. The samples were excited using a Pharos (Light conversion, Vilnius, Lithuania) operating at 1 kHz with an approximately 200 fs pulse width and 0.2 mJ pulse energy at an output wavelength of 1030 nm, which was used to pump an Orpheus-HP (Light conversion, Vilnius, Lithuania), an optical parametric amplifier (OPA), which generated 350 nm wavelength excitation pulses. The excitation laser was guided through a band-pass filter and a circular pinhole to obtain a homogeneous intensity and small spot size. The sample was placed in an integrating sphere (10 cm, Labsphere, North Sutton, USA) and the signal was recorded using a SpectraPro HRS-300 spectrometer (Acton Research Corporation, Acton, USA) and detected using a CCD, Pixis 256 (Princeton Instruments, Trenton, USA). The determination of the PL QE was based on the integrating sphere methodology originally developed by De Mello et al. [18]. The integrated PL signal in the Eu-emission region is compared with the integrated decrease of the laser signal upon introduction of the sample in the integrating sphere. The sample is placed at the sphere surface with the Eu-doped side facing outwards, so that unabsorbed laser light cannot be reabsorbed by the back side. The laser wavelength has a penetration depth of ${\sim}{{100}}\;{\rm{nm}}$; hence, nearly all absorption takes place in the Eu-doped layer. Due to the transparency of the material for red light, emission in all directions is taken into account. The spectral sensitivity of the system has been carefully calibrated for the wavelength regimes of interest by a light source with known intensity.

 

Fig. 2. (a) PL QE of GaN:Eu, normalized for partial coverage of the active area, as a function of the width of the structures. (b) PL spectrum for the 3, 24, and 192 µm mesas for a pump fluence of ${{21}}\;{{\unicode{x00B5} \rm J}}\;{\rm{c}}{{\rm{m}}^{- 2}}$. (c) SEM picture of a 6 µm structure where the red square indicates a unit cell.

Download Full Size | PDF

Figure 2(a) shows the size dependence of the PL QE. The PL spectrum of the Eu-related luminescence is shown in Fig. 2(b). Approximately 90% of the emission originates from the peak around 630 nm with small contributions at slightly shorter and longer wavelengths originating from different transitions of the ${\rm{E}}{{\rm{u}}^{3 +}}$ ion. The PL spectrum is very similar for different mesa sizes, as is usual for intra-${{4f}}$ transitions [14], and not sensitive to, for example, strain relaxation. This is in stark contrast with InGaN devices, which commonly show a blue shift for smaller sizes [19]. The values of the PL QE of the Eu-related luminescence are normalized for the partial areal coverage of the active regions, and they are shown as a function of mesa size in Fig. 2(c). The relative active region has been determined from scanning electron microscope (SEM) images as the ratio of the average active region and the unit cell size. It can be seen in Fig. 2(c) that due to the resolution of the maskless lithography system, the sidewalls of the etched areas have a roughness on the order of a few 100 nm, which gives smaller values of the partial coverage than the design value of 0.56. This sidewall roughness has an increasing influence on the value of the active area of the smaller mesas due to the larger sidewall-to-area ratio, and also introduces larger uncertainties. The PL QE has been measured for three different pump fluences: 14, 21, and ${{25}}\;{{\unicode{x00B5} \rm J}}\;{\rm{c}}{{\rm{m}}^{- 2}}$, which are all in the region where a thin film of GaN:Eu has its maximum PL QE [20]. The error bars are based on the standard deviation of the measured PL QE and the uncertainty of the coverage of the active region. All values lie above the reference PL QE of a sample without any structures as depicted by the horizontal line in the figure. It can be seen that the PL QE rises when decreasing the structures, to level off at 24 µm: The LEE improves due to the increasing sidewall-surface-to-volume ratio. Conversely, the PL QE does not increase further for smaller sizes, while it is likely that the LEE does. This is probably a result of the increasing contribution of non-radiative recombination of free carriers at sidewalls canceling out the improved LEE. The reduction of the PL QE for larger structures can be understood as a combination of absorption within the material and a reduced LEE.

The absorption coefficient of light in the GaN layer was experimentally determined by measuring the loss of waveguided modes. A small ${\sim}{{10}}\;{{\unicode{x00B5}{\rm m}}}$ excitation spot was moved over an unpatterned sample, and emission was collected from the side of the sample with an optical fiber approximately 1 mm away. The intensity of the light emitted from the side of the sample was determined by the same CCD camera used for the PL QE measurements. The value was obtained from a single exponential fit of the distance dependence of the intensity as $\alpha = {16.9}\;{\rm{c}}{{\rm{m}}^{- 1}}$, which is in line with values in literature for GaN [21,22]. We do note that this value is not truly the absorption coefficient, but rather the effective loss of light in waveguided modes. However, since negligible losses are expected at the interfaces of the epitaxial layers, and mirror-like GaN–air interface, we consider it to be close to the actual value.

 

Fig. 3. (a) Schematic representation of the simulation structure for determination of the light extraction efficiency for 9 µm sized squares. The red dots show the locations of the dipoles of the different simulations over which have been averaged. Periodic boundaries are used on the sides and PML on the top and bottom. The top and bottom gray lines indicate where the total output power has been determined. For determination of the light confined in the sapphire, the sides are set to PML, while the power is determined on the gray lines on the sides. (b) LEE as function of width of the structures, as determined by FDTD simulation averaged over three different simulations with the dipoles at different locations. The reference line corresponds to an unpatterned structure.

Download Full Size | PDF

In order to determine the contribution of the LEE to the measured PL QE, we modeled our system using FDTD simulations with a commercially available software, Lumerical Inc. Since the scale of the structures is too large for a full 3D treatment, we used a 2D representation in terms of a vertical cross section. A schematic of the simulation region can be seen in Fig. 3(a). It is 48 µm wide for all structures in order to keep the computational time reasonable. The structures consist of a bottom layer of sapphire with a refractive index ${n_{\rm Sapphire}} = {1.76}$ and ${k_{\rm Sapphire}} = {{0}}$ and a height of 2.8 µm. On top of this layer, there is a GaN layer of 1.35 µm with ${n_{\rm GaN}} = {\rm of}\; 2.4$ and ${k_{\rm GaN}} = {8.4}\;{{\times}}\;{{1}}{{{0}}^{- 4}}$, which was calculated from the experimentally determined absorption coefficient, $\alpha$, using the relation $k = \frac{{\alpha \lambda}}{{4\pi}}$ with $\lambda$, the wavelength of the emitted light; for GaN and GaN:Eu, the same values are assumed. The structures are represented by rectangles ranging from 3–36 µm with a height of 450 nm based on the same material, and channel widths ranging from 1–12 µm, where the area occupied by these structures is equal for all sizes. The ${\rm{E}}{{\rm{u}}^{3+}}$ ions are represented by a dipole source with an emission spectrum similar to that of the doped ions. They are placed 150 nm from the top of the structure, the center of the Eu-doped layer in the samples. The dipole is placed in the middle, at $2/3$ and at $3/4$ of the rectangles [23]. The top and bottom boundaries are perfectly matched layers (PMLs), which prevent unwanted reflections. Meanwhile the side boundaries are periodic to imitate a semi-infinite structure, thus leaving the mesa-size as the single variable in our simulations. The total power emitted from the top and bottom of the sample was determined at the edges of the simulation region. In general, light confined in modes in the GaN layer will be absorbed in the end if not scattered out at a sidewall, while modes confined in the sapphire were assumed to leave the sample in the end (about 6% of the total power in all structures) and were thus added to the total output power. The contribution from light confined in the sapphire layer was determined in a separate simulation (see caption of Fig. 3). We define the LEE as the total fraction of light that was leaving the sample. The calculated LEE against structure size is shown in Fig. 3(b), where the reference indicates the value of an unpatterned structure. The graph depicts the average and standard deviation determined from three different simulations where the light source is depicted by a dipole at alternated locations.

 

Fig. 4. Normalized internal efficiency (PL QE/LEE) as a function of structure size. The dark red line shows the fit for ${(w - 2d)^2}/{w^2}$, while the light red lines show the plots for the same function but different values of $d$. The black line shows the function for a value of $d = {{100}}\;{\rm{nm}}$.

Download Full Size | PDF

The measured PL QE in the used methodology considers an external efficiency, i.e., photons in and photons out, which is dependent on the LEE. We estimated the internal efficiency by dividing the measured PL QE by the calculated size dependence of the LEE. The result hereof is shown in Fig. 4; for sizes down to 24 µm, it is relatively constant, while for the smaller sizes, it gradually goes down. The decrease in internal efficiency for smaller structures can be attributed to a relative increase in non-radiative recombination at the sidewalls. As a simple estimation of the extent of the influence of the sidewalls, we can determine an effective active area of a mesa by defining an edge thickness $d$ that does not contribute to the emission. The area of the active region is given by ${(w - 2d)^2}$ with $w$ the width of the mesa. The internal efficiency as a function of size is thus proportional to ${(w - 2d)^2}/{w^2}$. We have fitted this formula to the data in Fig. 4 to get a value for $d$, of which the result is depicted by the red line in Fig. 4. It is found that there is a good agreement for a value of approximately 300 nm; the function is also plotted for $d = {{200}}$ and 400 nm. $d$ represents an effective distance from the sidewalls that does not contribute to emission and is thus related to the free carrier diffusion length and sidewall roughness of the samples. In general, the carrier diffusion length, $L$, for a semiconductor is given by

To conclude, we found that the PL QE of Eu-related emission has a considerable dependence on the size of square structures for sizes ranging from 3 to 192 µm. It improves for sizes decreasing down to 24 µm, while for smaller structures, it is fairly constant. From FDTD simulations, which take into account the experimentally determined optical absorption, we conclude that the LEE is responsible for the apparent decrease in PL QE for larger structures. By using the determined size dependence of the LEE, we were able to estimate the internal efficiency of the structures. It is constant for structures larger than 24 µm, while it continuously decreases for smaller sizes. This size dependence can be explained by assuming that the outer edge of 300 nm is effectively not contributing to the PL. Due to the limited carrier diffusion length, we consider that undulations of the sidewall introduced by the used exposure technique are behind this value. By improving the etching procedure, the decrease in internal efficiency can be reduced without the need for any post-etching treatment of the sidewalls, which would give an estimated decrease of only ${\sim}{{10}}\%$ for the smallest size of 3 µm. These results are strongly encouraging the use of GaN:Eu as the active material in red micro-LEDs.