• A method for the measurement of mass and number of graphene oxide sheets in suspension based on non-spherical approximations

      Crica, Livia Elena; orcid: 0000-0002-9665-0862; Dennison, Thomas James; Guerini, Elise Andrea; Kostarelos, Kostas; orcid: 0000-0002-2224-6672; email: kostas.kostarelos@manchester.ac.uk (IOP Publishing, 2021-06-02)
      Abstract: Currently, particle analysis of 2D materials in suspension is commonly restricted to microscopic techniques in the dry state, and thus does not permit an accurate investigation of colloidal suspensions. Colloids in bulk can be assessed by light scattering and diffraction to investigate features such as their hydrodynamic size, charge and concentration. However, the main drawback of such techniques lies in the application of analytical and computational methods based on models assuming particle sphericity which are not representative for 2D materials. Resonance mass measurement (RMM) is a technique which can enable the analysis of 2D materials in suspension without the assumptions of spherical models. Here, we report the application of RMM to measure particle mass and concentration for three types of graphene oxide (GO) aqueous dispersions. Using micro- and nano-suspended resonating sensors, we were able to decipher gravimetric differences between GO and graphitic materials. Our results support the urge for proper definitions and standardisations of graphene based materials, and offer a new method of characterisation for 2D material colloids in liquid suspension.
    • A method for the measurement of mass and number of graphene oxide sheets in suspension based on non-spherical approximations

      Crica, Livia Elena; orcid: 0000-0002-9665-0862; Dennison, Thomas James; Guerini, Elise Andrea; Kostarelos, Kostas; orcid: 0000-0002-2224-6672; email: kostas.kostarelos@manchester.ac.uk (IOP Publishing, 2021-06-02)
      Abstract: Currently, particle analysis of 2D materials in suspension is commonly restricted to microscopic techniques in the dry state, and thus does not permit an accurate investigation of colloidal suspensions. Colloids in bulk can be assessed by light scattering and diffraction to investigate features such as their hydrodynamic size, charge and concentration. However, the main drawback of such techniques lies in the application of analytical and computational methods based on models assuming particle sphericity which are not representative for 2D materials. Resonance mass measurement (RMM) is a technique which can enable the analysis of 2D materials in suspension without the assumptions of spherical models. Here, we report the application of RMM to measure particle mass and concentration for three types of graphene oxide (GO) aqueous dispersions. Using micro- and nano-suspended resonating sensors, we were able to decipher gravimetric differences between GO and graphitic materials. Our results support the urge for proper definitions and standardisations of graphene based materials, and offer a new method of characterisation for 2D material colloids in liquid suspension.
    • Blind map level systematics cleaning: a quadratic estimator approach

      Williams, Joel; email: christopher.williams-4@manchester.ac.uk; McCallum, Nialh; email: nialh.mccallum@manchester.ac.uk; Rotti, Aditya; email: aditya.rotti@manchester.ac.uk; Thomas, Daniel B.; email: daniel.thomas-2@manchester.ac.uk; Battye, Richard; email: richard.battye@manchester.ac.uk; Brown, Michael L.; email: m.l.brown@manchester.ac.uk (IOP Publishing, 2021-07-09)
      Abstract: We present the first detailed case study using quadratic estimators (QE) to diagnose and remove systematics present in observed Cosmic Microwave Background (CMB) maps. In this work we focus on the temperature to polarization leakage. We use an iterative QE analysis to remove systematics, in analogy to de-lensing, recovering the primordial B-mode signal and the systematic maps. We introduce a new Gaussian filtering scheme crucial to stable convergence of the iterative cleaning procedure and validate with comparisons to semi-analytical forecasts. We study the limitations of this method by examining its performance both on idealized simulations and on more realistic, non-ideal simulations, where we assume varying de-lensing efficiencies. Finally, we quantify the systematic cleaning efficiency by presenting a likelihood analysis on the tensor to scalar ratio, r, and demonstrate that the blind cleaning results in an un-biased measurement of r, reducing the systematic induced B-mode power by nearly two orders of magnitude.
    • Blind map level systematics cleaning: a quadratic estimator approach

      Williams, Joel; email: christopher.williams-4@manchester.ac.uk; McCallum, Nialh; email: nialh.mccallum@manchester.ac.uk; Rotti, Aditya; email: aditya.rotti@manchester.ac.uk; Thomas, Daniel B.; email: daniel.thomas-2@manchester.ac.uk; Battye, Richard; email: richard.battye@manchester.ac.uk; Brown, Michael L.; email: m.l.brown@manchester.ac.uk (IOP Publishing, 2021-07-09)
      Abstract: We present the first detailed case study using quadratic estimators (QE) to diagnose and remove systematics present in observed Cosmic Microwave Background (CMB) maps. In this work we focus on the temperature to polarization leakage. We use an iterative QE analysis to remove systematics, in analogy to de-lensing, recovering the primordial B-mode signal and the systematic maps. We introduce a new Gaussian filtering scheme crucial to stable convergence of the iterative cleaning procedure and validate with comparisons to semi-analytical forecasts. We study the limitations of this method by examining its performance both on idealized simulations and on more realistic, non-ideal simulations, where we assume varying de-lensing efficiencies. Finally, we quantify the systematic cleaning efficiency by presenting a likelihood analysis on the tensor to scalar ratio, r, and demonstrate that the blind cleaning results in an un-biased measurement of r, reducing the systematic induced B-mode power by nearly two orders of magnitude.
    • Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum

      Ravenni, Andrea; email: andrea.ravenni@manchester.ac.uk; Rizzato, Matteo; email: rizzato@strw.leidenuniv.nl; Radinović, Slađana; email: sladana.radinovic@astro.uio.no; Liguori, Michele; email: liguori@pd.infn.it; Lacasa, Fabien; email: fabien.lacasa@universite-paris-saclay.fr; Sellentin, Elena; email: sellentin@strw.leidenuniv.nl (IOP Publishing, 2021-06-14)
      Abstract: Non-Gaussian (NG) statistics of the thermal Sunyaev-Zeldovich (tSZ) effect carry significant information which is not contained in the power spectrum. Here, we perform a joint Fisher analysis of the tSZ power spectrum and bispectrum to verify how much the full bispectrum can contribute to improve parameter constraints. We go beyond similar studies of this kind in several respects: first of all, we include the complete power spectrum and bispectrum (auto- and cross-) covariance in the analysis, computing all NG contributions; furthermore we consider a multi-component foreground scenario and model the effects of component separation in the forecasts; finally, we consider an extended set of both cosmological and intra-cluster medium parameters. We show that the tSZ bispectrum is very efficient at breaking parameter degeneracies, making it able to produce even stronger cosmological constraints than the tSZ power spectrum: e.g. the standard deviation on σ8 shrinks from σPS(σ8)=0.35 to σBS(σ8)=0.065 when we consider a multi-parameter analysis. We find that this is mostly due to the different response of separate triangle types (e.g. equilateral and squeezed) to changes in model parameters. While weak, this shape dependence is clearly non-negligible for cosmological parameters, and it is even stronger, as expected, for intra-cluster medium parameters.
    • Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum

      Ravenni, Andrea; email: andrea.ravenni@manchester.ac.uk; Rizzato, Matteo; email: rizzato@strw.leidenuniv.nl; Radinović, Slađana; email: sladana.radinovic@astro.uio.no; Liguori, Michele; email: liguori@pd.infn.it; Lacasa, Fabien; email: fabien.lacasa@universite-paris-saclay.fr; Sellentin, Elena; email: sellentin@strw.leidenuniv.nl (IOP Publishing, 2021-06-14)
      Abstract: Non-Gaussian (NG) statistics of the thermal Sunyaev-Zeldovich (tSZ) effect carry significant information which is not contained in the power spectrum. Here, we perform a joint Fisher analysis of the tSZ power spectrum and bispectrum to verify how much the full bispectrum can contribute to improve parameter constraints. We go beyond similar studies of this kind in several respects: first of all, we include the complete power spectrum and bispectrum (auto- and cross-) covariance in the analysis, computing all NG contributions; furthermore we consider a multi-component foreground scenario and model the effects of component separation in the forecasts; finally, we consider an extended set of both cosmological and intra-cluster medium parameters. We show that the tSZ bispectrum is very efficient at breaking parameter degeneracies, making it able to produce even stronger cosmological constraints than the tSZ power spectrum: e.g. the standard deviation on σ8 shrinks from σPS(σ8)=0.35 to σBS(σ8)=0.065 when we consider a multi-parameter analysis. We find that this is mostly due to the different response of separate triangle types (e.g. equilateral and squeezed) to changes in model parameters. While weak, this shape dependence is clearly non-negligible for cosmological parameters, and it is even stronger, as expected, for intra-cluster medium parameters.
    • Characterization on microstructure of interface and failure analysis of SiC fiber reinforced Ti-17 composites under tension load

      Zhao, Wenxia; Ciuca, Octav.; email: octav.ciuca@manchester.ac.uk; Yang, Xiaoguang; Tao, Chunhu; Zhou, Xiaorong; Liu, Changkui (IOP Publishing, 2021-05)
      Abstract: In this study, the ultimate tensile strength of unidirectional SiC-fiber/Ti-17 composites was measured in the as-produced condition at room temperature. Fracture and interfacial reaction zone was characterized by using laser confocal microscopy, field emission scanning electron microscopy (FE-SEM) and transmission electron microscopy. Elemental distribution maps of the interfacial reaction layer and titanium matrix were quantitatively examined by electron probe micro-analyzer (EPMA). Micromechanical properties of SiC fiber and titanium matrix was inspected by Nano-indentation. The Fracture failure mechanisms was show that the key microstructural parameters which dominate damage initiation, damage growth and fracture behavior of the composites were explained in detail.
    • Characterization on microstructure of interface and failure analysis of SiC fiber reinforced Ti-17 composites under tension load

      Zhao, Wenxia; Ciuca, Octav.; email: octav.ciuca@manchester.ac.uk; Yang, Xiaoguang; Tao, Chunhu; Zhou, Xiaorong; Liu, Changkui (IOP Publishing, 2021-05)
      Abstract: In this study, the ultimate tensile strength of unidirectional SiC-fiber/Ti-17 composites was measured in the as-produced condition at room temperature. Fracture and interfacial reaction zone was characterized by using laser confocal microscopy, field emission scanning electron microscopy (FE-SEM) and transmission electron microscopy. Elemental distribution maps of the interfacial reaction layer and titanium matrix were quantitatively examined by electron probe micro-analyzer (EPMA). Micromechanical properties of SiC fiber and titanium matrix was inspected by Nano-indentation. The Fracture failure mechanisms was show that the key microstructural parameters which dominate damage initiation, damage growth and fracture behavior of the composites were explained in detail.
    • Conformal screen printed graphene 4 × 4 wideband MIMO antenna on flexible substrate for 5G communication and IoT applications

      Zhou, Xinyao; orcid: 0000-0001-5797-439X; Leng, Ting; orcid: 0000-0001-6559-6974; Pan, Kewen; Abdalla, Mahmoud; orcid: 0000-0001-6759-7268; Novoselov, Kostya S; Hu, Zhirun; email: z.hu@manchester.ac.uk (IOP Publishing, 2021-08-20)
      Abstract: Screen-printed graphene is integrated with multiple-input multiple-output (MIMO) technology to conquer the most concerned surge in electronic waste caused by the mass deployment of Internet of things (IoT) applications. A flexible MIMO antenna is implemented with simple fabrication process suitable for large-scale production by screen printing graphene highly conductive ink on paper substrate, ensuring high-speed 5G mass data wireless transmission without damaging the ecological environment. This environmental-friendly, low-cost, flexible and conformal MIMO antenna with orthogonal polarization diversity employs co-planar waveguide feed and planar pattern for achieving high space utilization and better integration in most scenarios, for instance, body centric networks and monitoring systems. Excellent performance has been achieved due to the high conductivity of the graphene: the fabricated antenna exhibits an average sheet resistance of 1.9Ωsq−1 . The bandwidth of the antenna ranges from 2.22 GHz to 3.85 GHz (53.71% fractional bandwidth), covering 4G long term evolution, sub-6 GHz 5G mobile communication networks, 2.5 and 3.5 GHz WiMAX, and 2.4 and 3.6 GHz WLAN. Within this range, the antenna exhibits effective radiation, also its envelope correlation coefficient remains below 0.2×10−6 , manifesting outstanding signal transmission quality in a variety of wireless networks. This work illustrates a novel aggregation of MIMO technology and graphene printing electronics, enabling cheap accessible and green MIMO antennas to be massively integrated in IoT applications.
    • Conformal screen printed graphene 4 × 4 wideband MIMO antenna on flexible substrate for 5G communication and IoT applications

      Zhou, Xinyao; orcid: 0000-0001-5797-439X; Leng, Ting; orcid: 0000-0001-6559-6974; Pan, Kewen; Abdalla, Mahmoud; orcid: 0000-0001-6759-7268; Novoselov, Kostya S; Hu, Zhirun; email: z.hu@manchester.ac.uk (IOP Publishing, 2021-08-20)
      Abstract: Screen-printed graphene is integrated with multiple-input multiple-output (MIMO) technology to conquer the most concerned surge in electronic waste caused by the mass deployment of Internet of things (IoT) applications. A flexible MIMO antenna is implemented with simple fabrication process suitable for large-scale production by screen printing graphene highly conductive ink on paper substrate, ensuring high-speed 5G mass data wireless transmission without damaging the ecological environment. This environmental-friendly, low-cost, flexible and conformal MIMO antenna with orthogonal polarization diversity employs co-planar waveguide feed and planar pattern for achieving high space utilization and better integration in most scenarios, for instance, body centric networks and monitoring systems. Excellent performance has been achieved due to the high conductivity of the graphene: the fabricated antenna exhibits an average sheet resistance of 1.9Ωsq−1 . The bandwidth of the antenna ranges from 2.22 GHz to 3.85 GHz (53.71% fractional bandwidth), covering 4G long term evolution, sub-6 GHz 5G mobile communication networks, 2.5 and 3.5 GHz WiMAX, and 2.4 and 3.6 GHz WLAN. Within this range, the antenna exhibits effective radiation, also its envelope correlation coefficient remains below 0.2×10−6 , manifesting outstanding signal transmission quality in a variety of wireless networks. This work illustrates a novel aggregation of MIMO technology and graphene printing electronics, enabling cheap accessible and green MIMO antennas to be massively integrated in IoT applications.
    • Cosmological gravity on all scales. Part II. Model independent modified gravity N-body simulations

      Srinivasan, Sankarshana; email: sankarshana.srinivasan@postgrad.manchester.ac.uk; Thomas, Daniel B.; email: dan.b.thomas1@gmail.com; Pace, Francesco; email: francesco.pace9@unibo.it; Battye, Richard; email: richard.battye@manchester.ac.uk (IOP Publishing, 2021-06-08)
      Abstract: Model-independent constraints on modified gravity models hitherto exist mainly on linear scales [1]. A recently developed formalism presented a consistent parameterisation that is valid on all scales [2]. Using this approach, we perform model-independent modified gravity N-body simulations on all cosmological scales with a time-dependent μ. We present convergence tests of our simulations, and we examine how well existing fitting functions reproduce the non-linear matter power spectrum of the simulations. We find that although there is a significant variation in the accuracy of all of the fitting functions over the parameter space of our simulations, the ReACT [3] framework delivers the most consistent performance for the matter power spectrum. We comment on how this might be improved to the level required for future surveys such as Euclid and the Vera Rubin Telescope (LSST). We also show how to compute weak-lensing observables consistently from the simulated matter power spectra in our approach, and show that ReACT also performs best when fitting the weak-lensing observables. This paves the way for a full model-independent test of modified gravity using all of the data from such upcoming surveys.
    • Cosmological gravity on all scales. Part II. Model independent modified gravity N-body simulations

      Srinivasan, Sankarshana; email: sankarshana.srinivasan@postgrad.manchester.ac.uk; Thomas, Daniel B.; email: dan.b.thomas1@gmail.com; Pace, Francesco; email: francesco.pace9@unibo.it; Battye, Richard; email: richard.battye@manchester.ac.uk (IOP Publishing, 2021-06-08)
      Abstract: Model-independent constraints on modified gravity models hitherto exist mainly on linear scales [1]. A recently developed formalism presented a consistent parameterisation that is valid on all scales [2]. Using this approach, we perform model-independent modified gravity N-body simulations on all cosmological scales with a time-dependent μ. We present convergence tests of our simulations, and we examine how well existing fitting functions reproduce the non-linear matter power spectrum of the simulations. We find that although there is a significant variation in the accuracy of all of the fitting functions over the parameter space of our simulations, the ReACT [3] framework delivers the most consistent performance for the matter power spectrum. We comment on how this might be improved to the level required for future surveys such as Euclid and the Vera Rubin Telescope (LSST). We also show how to compute weak-lensing observables consistently from the simulated matter power spectra in our approach, and show that ReACT also performs best when fitting the weak-lensing observables. This paves the way for a full model-independent test of modified gravity using all of the data from such upcoming surveys.
    • Creation of electrospray emitters from a flat polytetrafluoroethylene sheet through the use of laser micro-manufacturing

      Maharaj, S; email: sahil.maharaj@manchester.ac.uk; Allegre, O; Smith, KL (IOP Publishing, 2021-05)
      Abstract: Electrospray propulsion is a form of electrostatic propulsion that shows potential for use as a thruster on small satellites. Electrospray emitters traditionally use arrays of capillaries, however, this paper investigates the suitability of manufacturing an emitter by laser drilling holes in sheets of polytetrafluoroethylene (PTFE), also known as Teflon. This is done by examining factors such as the machining time, hole shape and degree of taper in holes drilled through different methods. Experimental work was done to determine the shape of holes drilled in a flat sheet, and a computational model was used to simulate the performance of these drilled holes. These results were used to judge if this would be a valid method to manufacture electrospray thrusters, and how these thrusters would compare to more traditional emitters. Based on these results, it was concluded that a PTFE sheet with a width of 0.81 mm would be sufficient to achieve electrospray at voltages lower than those needed for traditional emitters.
    • Creation of electrospray emitters from a flat polytetrafluoroethylene sheet through the use of laser micro-manufacturing

      Maharaj, S; email: sahil.maharaj@manchester.ac.uk; Allegre, O; Smith, KL (IOP Publishing, 2021-05)
      Abstract: Electrospray propulsion is a form of electrostatic propulsion that shows potential for use as a thruster on small satellites. Electrospray emitters traditionally use arrays of capillaries, however, this paper investigates the suitability of manufacturing an emitter by laser drilling holes in sheets of polytetrafluoroethylene (PTFE), also known as Teflon. This is done by examining factors such as the machining time, hole shape and degree of taper in holes drilled through different methods. Experimental work was done to determine the shape of holes drilled in a flat sheet, and a computational model was used to simulate the performance of these drilled holes. These results were used to judge if this would be a valid method to manufacture electrospray thrusters, and how these thrusters would compare to more traditional emitters. Based on these results, it was concluded that a PTFE sheet with a width of 0.81 mm would be sufficient to achieve electrospray at voltages lower than those needed for traditional emitters.
    • Effect of layered water structures on the anomalous transport through nanoscale graphene channels

      Chen, S; orcid: 0000-0002-8118-5849; Draude, A P; Nie, A X C; Fang, H P; Walet, N R; orcid: 0000-0002-2061-5534; Gao, Shiwu; email: swgao@csrc.ac.cn; Li, J C; email: j.c.li@manchester.ac.uk (IOP Publishing, 2018-08-16)
      Abstract: We analyse the enhanced flow rate of water through nano-fabricated graphene channels that has been recently observed experimentally. Using molecular dynamics simulations in channels of similar lateral dimensions as the experimental ones, our results reveal for the first time a relationship between water structure and the variation of flux in the rectangular graphene channels. The substantial enhancement in the flow rate compared to Poieseuille flow is due to the formation of layered 2D structures in the confined space, which persists up to a channel height of 2.38 nm, corresponding to six graphene layers. The structure of the water shows an intricate crystal of pentagonal and square tiles, which has not been observed before. Beyond six layers we find a sudden drop in flux due to the disordering of the water, which can be understood by classical flow dynamics.
    • Effect of layered water structures on the anomalous transport through nanoscale graphene channels

      Chen, S; orcid: 0000-0002-8118-5849; Draude, A P; Nie, A X C; Fang, H P; Walet, N R; orcid: 0000-0002-2061-5534; Gao, Shiwu; email: swgao@csrc.ac.cn; Li, J C; email: j.c.li@manchester.ac.uk (IOP Publishing, 2018-08-16)
      Abstract: We analyse the enhanced flow rate of water through nano-fabricated graphene channels that has been recently observed experimentally. Using molecular dynamics simulations in channels of similar lateral dimensions as the experimental ones, our results reveal for the first time a relationship between water structure and the variation of flux in the rectangular graphene channels. The substantial enhancement in the flow rate compared to Poieseuille flow is due to the formation of layered 2D structures in the confined space, which persists up to a channel height of 2.38 nm, corresponding to six graphene layers. The structure of the water shows an intricate crystal of pentagonal and square tiles, which has not been observed before. Beyond six layers we find a sudden drop in flux due to the disordering of the water, which can be understood by classical flow dynamics.
    • Effect of Micron-scale Photoluminescence Variation on Droop Measurements in InGaN/GaN Quantum Wells

      Barrett, R M; Ahumada-Lazo, R; Alanis, J A; Parkinson, P; Church, S A; Kappers, M J; Oliver, R A; Binks, D J; email: david.binks@manchester.ac.uk (IOP Publishing, 2021-05)
      Abstract: Micro-photoluminescence maps reveal micron-scale spatial variation in intensity, peak emission energy and bandwidth across InGaN/GaN quantum wells. To investigate the effect of this spatial variation on measurements of the dependence of emission efficiency on carrier density, excitation power-dependent emission was collected from a bright and dark region on each of blue-and green emitting samples. The onset of efficiency droop was found to occur at a greater carrier density in the dark regions than in the bright, by factors of 1.2 and 1.8 in the blue and green-emitting samples, respectively. By spatially integrating the emission from progressively larger areas, it is also shown that collection areas greater than ∼50 μm in diameter are required to reduce the intensity variation to less than 10%.
    • Effect of Micron-scale Photoluminescence Variation on Droop Measurements in InGaN/GaN Quantum Wells

      Barrett, R M; Ahumada-Lazo, R; Alanis, J A; Parkinson, P; Church, S A; Kappers, M J; Oliver, R A; Binks, D J; email: david.binks@manchester.ac.uk (IOP Publishing, 2021-05)
      Abstract: Micro-photoluminescence maps reveal micron-scale spatial variation in intensity, peak emission energy and bandwidth across InGaN/GaN quantum wells. To investigate the effect of this spatial variation on measurements of the dependence of emission efficiency on carrier density, excitation power-dependent emission was collected from a bright and dark region on each of blue-and green emitting samples. The onset of efficiency droop was found to occur at a greater carrier density in the dark regions than in the bright, by factors of 1.2 and 1.8 in the blue and green-emitting samples, respectively. By spatially integrating the emission from progressively larger areas, it is also shown that collection areas greater than ∼50 μm in diameter are required to reduce the intensity variation to less than 10%.
    • Effect of Micron-scale Photoluminescence Variation on Droop Measurements in InGaN/GaN Quantum Wells

      Barrett, R M; Ahumada-Lazo, R; Alanis, J A; Parkinson, P; Church, S A; Kappers, M J; Oliver, R A; Binks, D J; email: david.binks@manchester.ac.uk (IOP Publishing, 2021-05)
      Abstract: Micro-photoluminescence maps reveal micron-scale spatial variation in intensity, peak emission energy and bandwidth across InGaN/GaN quantum wells. To investigate the effect of this spatial variation on measurements of the dependence of emission efficiency on carrier density, excitation power-dependent emission was collected from a bright and dark region on each of blue-and green emitting samples. The onset of efficiency droop was found to occur at a greater carrier density in the dark regions than in the bright, by factors of 1.2 and 1.8 in the blue and green-emitting samples, respectively. By spatially integrating the emission from progressively larger areas, it is also shown that collection areas greater than ∼50 μm in diameter are required to reduce the intensity variation to less than 10%.
    • Effect of Micron-scale Photoluminescence Variation on Droop Measurements in InGaN/GaN Quantum Wells

      Barrett, R M; Ahumada-Lazo, R; Alanis, J A; Parkinson, P; Church, S A; Kappers, M J; Oliver, R A; Binks, D J; email: david.binks@manchester.ac.uk (IOP Publishing, 2021-05)
      Abstract: Micro-photoluminescence maps reveal micron-scale spatial variation in intensity, peak emission energy and bandwidth across InGaN/GaN quantum wells. To investigate the effect of this spatial variation on measurements of the dependence of emission efficiency on carrier density, excitation power-dependent emission was collected from a bright and dark region on each of blue-and green emitting samples. The onset of efficiency droop was found to occur at a greater carrier density in the dark regions than in the bright, by factors of 1.2 and 1.8 in the blue and green-emitting samples, respectively. By spatially integrating the emission from progressively larger areas, it is also shown that collection areas greater than ∼50 μm in diameter are required to reduce the intensity variation to less than 10%.