Session L28: Electricity-to-Light Conversion: Solid State Lighting

Auger recombination in gallium arsenide from first principles

GaAs and its alloys are technologically important materials for solid-state optoelectronic devices such as LEDs and lasers. The internal quantum efficiency of these devices, defined as the fraction of electron-hole pairs converted to photons, is limited by loss mechanisms. Of particular importance at high carrier densities is Auger recombination, a non-radiative process where the energy and momentum of the recombining electron-hole pair is transferred to a third carrier. Here we use density functional theory to study Auger recombination in GaAs from first principles. When considering Auger recombination due to Coulomb interaction only, the calculated rate is too small and cannot account for the experimental observations. However, once additional electron-phonon interactions are included, the theoretical recombination rate increases towards the experimental value. Our work provides insight into the microscopic origins of the loss in III-V LEDs at high injected-carrier densities, and in the mechanisms governing Auger recombination rates in general.   

Surface Energies and Cracking in GaN

Cracking is one of the biggest limitations to growing thick GaN single crystals and films, caused by the buildup and release of strain energy. Cracking occurs along preferential crystallographic planes in the GaN wurtzite structure, and depends on the tensile stress on the given plane and the energetic balance between the strain energy released from the crack formation versus the cleaved surface area created. It is also well known that the equilibrium shape of a crystal is largely determined by its surface free energy. Therefore, to correctly predict the stresses under which certain planes will crack and aid in understanding crystal growth, knowledge of the absolute surface energy is required. We use first-principles calculations based on density functional theory and a hybrid functional to determine the surface energy for the nonpolar \{11-20\} {\it a}- and \{10-10\} {\it m}-planes, as well to as explore approximations to the surface energies of the polar \{0001\}/\{000-1\} {\it c}-planes in GaN. The effects of structure relaxations and reconstructions are fully taken into account, and the results are discussed in the light of available experimental observations.   

Crystalline Fe films grown on non-polar GaN: theory and experiment

We report an unexpected mechanism by which single crystals of Fe grow epitaxially on $M$-plane GaN substrates despite having a different crystal structure and strongly mismatched lattice constant. A simple model is proposed in which one material tilts out of the interface plane to create a coincidence-site lattice that balances two competing geometrical criteria---low residual strain and short coincidence-lattice period. We apply this model, along with complementary first-principles total energy calculations, to the interface formed by molecular-beam epitaxy of cubic Fe on hexagonal GaN and find excellent agreement between theory and experiment. The success of this model also suggests a strategy for growing non-polar GaN films on a substrate material with a suitably chosen Miller index. One very promising material is Si, which is already in widespread use as a flat substrate for GaN/Si epitaxy despite high dislocation densities. The next talk will present our predictions of the most promising Si(\textit{hhk}) substrates for growing non-polar GaN with high crystalline quality.   

Crystalline non-polar GaN films grown on vicinal Si: theoretical predictions

The ability to grow highly crystalline non-polar GaN films on silicon substrates would be an important advance in optoelectronic device fabrication. We propose a simple strategy to achieve this goal: tilting the Si substrate out of interface plane to provide a good lattice match between the film and substrate. We consider epitaxial interfaces between $M$-plane GaN and arbitrary Si(\textit{hhk}) substrates. Using the model introduced in the previous talk, we downselect these substrates using two geometric criteria---low residual strain and short coincidence-lattice period. We then use density-functional theory to compute the interface formation energies of these selected candidates, which include Si(001), (112), (113), (114), and (223). We find that $M$-plane GaN films have the lowest interface formation energy when grown on the (113) and (112) surfaces. The formation energies are significantly lower than on Si(001) or (111), the substrates most often used for growing GaN. On this basis we predict that Si(113) and (112) substrates will enable growth of non-polar GaN films of higher crystalline quality than can be attained on Si(001) or (111).   

Hybrid functional studies of stability and diffusion of hydrogen in Mg-doped GaN

Nitride semiconductors are known to suffer from low p-type doping efficiency due to the high activation energy of Mg acceptors and the compensation of hole carriers. To enhance hole carrier concentration, the hydrogen co-doping method is widely used, in which hydrogen is intentionally doped with Mg dopants and removed by subsequent thermal annealing. In this work, we perform first-principles density functional calculations to study the stability and diffusion of hydrogen in Mg-doped GaN. For the exchange-correlation potential, we employ both the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof and the hybrid density functional of Heyd, Scuseria, and Ernzerhof. We examine the diffusion pathways and dissociation barriers of H from the Mg-H complex using the nudged elastic band and dimer methods. We compare the results of the GGA and hybrid density functional calculations for the stability of various H interstitial configurations and the migration barriers for H diffusion. Finally, using the calculated migration barriers as inputs, we perform kinetic Monte Carlo simulations for the dissociation of the Mg-H complex and find that the Mg acceptors are activated by thermal annealing up to 700-800 $^{\circ}$C, in good agreement with experiments.   

Electroluminescent Schottky Diodes Fabricated Using Plasma Ion Implantation

Carbon-implanted silicon light-emitting Schottky diodes were produced by Plasma Ion Implantation (PII) in an RF ICP plasma chamber using methane feedstock gas. The electroluminescence spectrum of the devices was fitted with a set of Gaussian peaks corresponding to known emission centers including disordered silicon (broad white background), buried porous silicon and hydrogenated carbon-rich silicon. Some of the emission peaks exhibit a peak intensity at a drive current density of several A/cm$^2$, followed by a drop in emission intensity at higher drive current densities. In this presentation we discuss a possible model for this observed drop in electroluminescent intensity.   

Sub-250nm room-temperature optical gain from AlGaN/AlN multiple quantum dot structures

There are many pressing but yet unrealized applications for optoelectronic materials and devices that can function well into the deep-UV. Group-III nitrides, in particular AlGaN, are particularly suited to cover UV spectral ranges. An intense research effort is targeting the investigation and demonstration of deep-UV lasing from these materials. We developed AlGaN/AlN MQWs by Molecular Beam Epitaxy under a novel growth mode that introduces band structure potential fluctuations and high-density of nanocluster-like features within the AlGaN wells. A characterization of this material will be presented. The Variable-Stripe Length technique, a well-established methodology for measuring optical gain coefficient, is applied for a detailed quantification of the gain properties and polarization. We demonstrate optical gain in AlGaN nanostructures down to 230 nm at room temperature with a maximum net modal gain value of 118 $\pm$ 9 cm-1 at the highest excitation fluence of 15 $\mu$J/cm2. The optical gain threshold was measured to be 5 $\pm$ 1 $\mu$J/cm2 from which we estimate the density of optically excited carriers at the threshold to be 1.4 x 10$^{17}$ cm-3, which is two orders of magnitude lower than what currently achieved by quantum well structures. Moreover, we demonstrate that gain is TE-polarized.   

Room temperature low threshold stimulated emission of electron beam-pumped AlGaN-based deep UV laser structures emitting below 250 nm

The development of semiconductor lasers, operating in the deep UV, will find a number of applications such as identification of biological and chemical agents, non-line-off -sight free space communications and point of site medical diagnostics. In this paper we report the growth of QW laser structures in the configuration 6H-SiC / AlN / AlGaN - AlN MQWs /AlN by PAMBE. A novel growth mode was developed in which arriving active nitrogen species and aluminum atoms dissolve in the excess liquid Ga covering the surface of the growing film and incorporate into the AlGaN film from the liquid phase. This liquid phase epitaxy (LPE) growth was found to introduce band structure potential fluctuations and high-density of nanocluster-like features within the AlGaN wells. The structure and microstructure of these devices were investigated by AFM, XRD and TEM and their emission properties were investigated by electron beam pumping at room temperature. The investigated laser structures were found to emit in the 235-250 nm range and stimulated emission was observed at a threshold power of 20-40 KW / cm$^{2}$. This low threshold value is attributed to nanoclusters-like features in the wells.   

Electronic transport through InGaN heterojunctions

InGaN nanowires have recently sparked great interest for their high tunability and potential in applications like solid-state lighting (LEDs) and concentrated photovoltaics. Determination of device characteristics from first principles modeling is of great importance. In order to treat quantum transport properties of nanoelectronic devices with atomistic disorder, a non-equilibrium vertex correction (NVC) theory was recently developed and implemented into the Keldysh non-equilibrium Green's function (NEGF) -based density functional theory (DFT). NEGF-DFT-NVC enables the representation of disordered structures such as the InGaN heterojunction under non-equilibrium conditions. Electronic and transport properties of a InGaN heterojunction are investigated using this accurate ab initio method.   

Effects of Internal Fields on the Optical Emission in Nanostructured III-N LEDs

Nanostructured optical emitters can accommodate a broader range of lattice mismatch, be used in full-solar-spectrum light emitting diodes, and provide higher temperature stability of the threshold current and the luminescence. However, strong quantum confinement and certain symmetry-lowering mechanisms (caused by various internal fields) lead to pronounced optical polarization anisotropy and strong suppression of interband transitions in these structures. The objective of this work is to study the competing effects of various internal fields on the electronic structure and optical properties of nanostructured III-N LEDs. A multiscale approach has been employed where: 1) the NEMO 3-D tool is used to calculate the atomistic strain distribution and one-particle electronic states within a sp3s*d5 tight-binding framework, and 2) the outputs from NEMO 3-D are then coupled to the Synopsys TCAD tool to determine the terminal electrical and optical properties of the device.   

Accurate first-principles calculation of the rare earth crystal field

Rare earth (RE) doped wide band-gap semiconductors play an important role in solid state lighting. Many aspects of the performance of these materials are characterized and determined by the $f$-electron crystal field (CF). However, CF effects are usually rather small for $f$ electron: the CF splitting is at the order of 0.1 eV, compared to several eV for d-electrons. Therefore accurate theoretical description of RE crystal field is challenging. We present a first-principles method of CF calculation based on an improved LDA+U method. By careful cancellation of errors, the method can reach relatively high accuracy for the CF parameters. As a demonstration we calculate the experimentally well-characterized RE:LaF$_3$ system, which has low point-group symmetry and a large number of CF parameters, representing a stringent test of theory. The predicted CF excitation energies of Ce:LaF3 agree within about 10 meV with experiment, and within several meV if the errors in the free-ion parameters are excluded. Work is underway to apply the method to other materials for solid-state lighting and laser applications.   

The role of extended defects in Nitride Semiconductors on the performance of optoelectronic devices

The question is why nitride semiconductors, which are plagued by high concentration of extended defects, produce efficient minority carrier optoelectronic devices. The equilibrium phase of these materials is the wurtzite and the metastable phase is the zinc blende. However, since the enthalpy of formation of these two structures differ by only a few meV, the conversion from one to the other can occur easily by the creation of stacking faults on the close packed planes. Thus, stacking faults are one of the most abundant defects in these materials even when they are grown homoepitaxially. Since the basal plane stacking fault is the equivalent of a monolayer of a cubic domain and since the energy band gaps of the wurtzite and their cubic counterparts differ by about 0. 2 eV, one expects that stacking faults introduce band structure potential fluctuations. Such fluctuations are beneficial to the performance of lasers and LEDs since they lead to exciton localization and efficient radiative recombination. Other types of abundant defects in heteroepitaxially grown materials are threading dislocations. The insensitivity of the performance of LEDs and lasers to such defects is due to the strong ionicity of these materials as well as to the deep band structure potential fluctuations in the InGaN and AlGaN alloys. Due to the strong ionicity the surface states at free surfaces and dangling bonds in edge dislocations have moved towards the band edges and act as traps rather non-radiative recombination centers.   

Surface scattering from ceramic phosphors

Scattering from phosphor converters and epitaxial surfaces is critical for solid state lighting device performance. Volume and surface scattering in solid state lighting devices can play a critical role in efficiency/efficacy, color points, and color angular consistency. Surface scattering in particular has not been well characterized in solid state lighting devices and can be complex to model. Because large angle scattering is important in lighting applications, surface scattering models generally require vector electromagnetic theory to avoid ambiguities often associated with scalar theory at these angles. Furthermore, surface features are often on the order of a few wavelengths, bringing ray tracing approaches into question. In this work, experimental angular scattering measurements are made on ceramic phosphor components where surface scattering dominates. The surface ceramic grain structure is responsible for the scattering. The results are compared to approximate statistical vector theory predictions that use the height autocorrelation functions as input. The autocorrelation measurements were derived from atomic-force microscopy topography measurements. Resulting predictions are in fairly good agreement with measurements.   

Light emission from electrically stressed ZnO nanorods

Zinc oxide (ZnO) nanorods were grown on various substrates by a chemical growth process based on a ZnO seed solution, and starting from Zinc acetate (ZnAc) material. The nanorods were grown on insulating silicon (low doped) and oxidized silicon substrates, and also over patterned conducting (highly-doped) nanocrystalline silicon microwires. When high voltage is applied directly to the ZnO film using tungsten needles ($\sim $ 50-60 V across $\sim $ 5-10 $\mu $m), high intensity blue and white light emission is observed, both in air and under high vacuum (10$^{-4}$ - 10$^{-5}$ Torr). Blue light appears as broad bright flashes covering a large area whereas white light is more localized and appears to come from individual nanostructures. The results suggest a combination of electroluminescence and photoluminescence processes that take place after an electrical breakdown (possibly across individual ZnO nanorods) that is observed as an exponential increase in current. Percolative conduction and light paths are also observed during the measurements. Measurements of the ZnO films of rods on conducting silicon substrate give more repeatable results, likely due to the higher probability of conducting paths between the two probes. The electrical stress results in significant self-heating and modification of the ZnO nanostructures and the contacts.\\[4pt] [1] Greene L. E. et al. Solution-Grown Zinc oxide nanowires. Innorganic Chemistry. Vol 45. 7535-7543. (2006)   

A First-Principles Analysis of the Crystal Structure, Band Gap Energy, Polarization, and Piezoelectric Properties of ZnO-BeO Solid Solutions

The electrical properties, the spontaneous polarization, and the piezoelectric response of ZnO can be tailored by alloying ZnO with BeO for various optoelectronics applications. We present here the results of a study that employs density functional theory to analyze the crystal structure, the band structure, elastic constants, spontaneous polarization, and piezoelectric properties of Zn$_{1-x}$Be$_{x}$O solid solutions. Our findings indicate that Zn$_{1-x}$Be$_{x}$O alloys may have a different crystal structure than the end components ZnO and BeO that crystallize in the prototypical wurtzite structure (P6$_{3}$mc). It is shown that orthorhombic lattices with Pmn2$_{1}$, Pna2$_{1}$, or P2$_{1}$ structures may have lower formation energies than the wurtzite lattice at a given Be composition. The band gap energies of Zn$_{1-x}$Be$_{x}$O in the wurtzite and the orthorhombic structures are nearly identical and the bowing of the band gap energy increases with increasing Be concentration. The spontaneous polarization of Zn$_{1-x}$Be$_{x}$O in the orthorhombic lattice is markedly larger compared to the wurtzite structure while the piezoelectric polarization in the wurtzite and orthorhombic structures varies linearly with the Be concentration.