Coarse-grained tight-binding models.

Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with energies close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation with errors of less than 1%. We give data for the trade-offs between computing time and loss of accuracy. We also tested calculations of the density of states for a GaAs/AlAs quantum well and find a ten times speedup without much loss in accuracy.

Dislocation-Free and Atomically Flat GaN Hexagonal Microprisms for Device Applications.

III-nitrides are considered the material of choice for light-emitting diodes (LEDs) and lasers in the visible to ultraviolet spectral range. The development is hampered by lattice and thermal mismatch between the nitride layers and the growth substrate leading to high dislocation densities. In order to overcome the issue, efforts have gone into selected area growth of nanowires (NWs), using their small footprint in the substrate to grow virtually dislocation-free material. Their geometry is defined by six tall side-facets and a pointed tip which limits the design of optoelectronic devices. Growth of dislocation-free and atomically smooth 3D hexagonal GaN micro-prisms with a flat, micrometer-sized top-surface is presented. These self-forming structures are suitable for optical devices such as low-loss optical cavities for high-efficiency LEDs. The structures are made by annealing GaN NWs with a thick radial shell, reforming them into hexagonal flat-top prisms with six equivalents either m- or s-facets depending on the initial heights of the top pyramid and m-facets of the NWs. This shape is kinetically controlled and the reformation can be explained with a phenomenological model based on Wulff construction that have been developed. It is expected that the results will inspire further research into micron-sized III-nitride-based devices.

Non-resonant Raman scattering of wurtzite GaAs and InP nanowires.

It is now possible to synthesize the wurtzite crystal phase of most III-V semiconductors in the form of nanowires. This sparks interest for fundamental research and adds extra degrees of freedom for designing novel devices. However, the understanding of many properties, such as phonon dispersion, of these wurtzite semiconductors is not yet complete, despite the extensive number of studies published. The E2L and E2H phonon modes exist in the wurtzite crystal phase only (not in zinc blende) where the E2H mode has been already experimentally observed in Ga and In arsenides and phosphides, while the E2L mode has been observed in GaP, but not in GaAs or InP. In order to determine the energy of E2L in wurtzite GaAs and InP, we performed Raman scattering measurements on wurtzite GaAs and InP nanowires. We found clear evidence of the E2L phonon mode at 64 cm-1 and 54 cm-1, respectively. Polarization-dependent experiments revealed similar selection rules for both the E2L and the E2H phonon modes (as expected) where the intensity peaked with excitation and detection polarization being perpendicular to the [0001] crystallographic direction. We further find that the splitting between the E1(TO) and A1(TO) modes is around 2 cm-1 in wurtzite GaAs and below 1 cm-1 in wurtzite InP. We believe these results will be useful for a better understanding of phonons in wurtzite crystal phase of III-V semiconductors as well as for testing and improving phonon dispersion calculations.

Temperature dependent electronic band structure of wurtzite GaAs nanowires.

It has recently become possible to grow GaAs in the wurtzite crystal phase. This ability allows interesting tests of band-structure theory. Wurtzite GaAs has two closely spaced direct conduction bands as well as three nondegenerate valence bands. The energies of the band edges are not well known, in particular not as a function of temperature. In order to improve the accuracy we have studied the temperature dependence of the conduction band minimum as well as of the second valence band maximum using resonant Raman scattering (of up to 3LO Raman lines). We find that the temperature dependence of the bandgap in wurtzite GaAs is very similar to that in zinc blende GaAs. Our results show that they have the same band gaps not only at 7 K but also at room temperature to within 5 meV. This is in some discrepancy with previous work. We find that the energy difference between the first two Γ9V and Γ7V valence bands is constant, around 100 meV, over the investigated temperature range, 7 K to 300 K. Due to a fortuitous spacing of the energy bands we find a very unexpected and strong quadruple resonance in the resonant Raman scattering.

Optimized efficiency in InP nanowire solar cells with accurate 1D analysis.

Semiconductor nanowire arrays are a promising candidate for next generation solar cells due to enhanced absorption and reduced material consumption. However, to optimize their performance, time consuming three-dimensional (3D) opto-electronics modeling is usually performed. Here, we develop an accurate one-dimensional (1D) modeling method for the analysis. The 1D modeling is about 400 times faster than 3D modeling and allows direct application of concepts from planar pn-junctions on the analysis of nanowire solar cells. We show that the superposition principle can break down in InP nanowires due to strong surface recombination in the depletion region, giving rise to an IV-behavior similar to that with low shunt resistance. Importantly, we find that the open-circuit voltage of nanowire solar cells is typically limited by contact leakage. Therefore, to increase the efficiency, we have investigated the effect of high-bandgap GaP carrier-selective contact segments at the top and bottom of the InP nanowire and we find that GaP contact segments improve the solar cell efficiency. Next, we discuss the merit of p-i-n and p-n junction concepts in nanowire solar cells. With GaP carrier selective top and bottom contact segments in the InP nanowire array, we find that a p-n junction design is superior to a p-i-n junction design. We predict a best efficiency of 25% for a surface recombination velocity of 4500 cm s-1, corresponding to a non-radiative lifetime of 1 ns in p-n junction cells. The developed 1D model can be used for general modeling of axial p-n and p-i-n junctions in semiconductor nanowires. This includes also LED applications and we expect faster progress in device modeling using our method.

Optical analysis of a III-V-nanowire-array-on-Si dual junction solar cell.

A tandem solar cell consisting of a III-V nanowire subcell on top of a planar Si subcell is a promising candidate for next generation photovoltaics due to the potential for high efficiency. However, for success with such applications, the geometry of the system must be optimized for absorption of sunlight. Here, we consider this absorption through optics modeling. Similarly, as for a bulk dual-junction tandem system on a silicon bottom cell, a bandgap of approximately 1.7 eV is optimum for the nanowire top cell. First, we consider a simplified system of bare, uncoated III-V nanowires on the silicon substrate and optimize the absorption in the nanowires. We find that an optimum absorption in 2000 nm long nanowires is reached for a dense array of approximately 15 nanowires per square micrometer. However, when we coat such an array with a conformal indium tin oxide (ITO) top contact layer, a substantial absorption loss occurs in the ITO. This ITO could absorb 37% of the low energy photons intended for the silicon subcell. By moving to a design with a 50 nm thick, planarized ITO top layer, we can reduce this ITO absorption to 5%. However, such a planarized design introduces additional reflection losses. We show that these reflection losses can be reduced with a 100 nm thick SiO2 anti-reflection coating on top of the ITO layer. When we at the same time include a Si3N4 layer with a thickness of 90 nm on the silicon surface between the nanowires, we can reduce the average reflection loss of the silicon cell from 17% to 4%. Finally, we show that different approximate models for the absorption in the silicon substrate can lead to a 15% variation in the estimated photocurrent density in the silicon subcell.

Single-nanowire, low-bandgap hot carrier solar cells with tunable open-circuit voltage.

Compared to traditional pn-junction photovoltaics, hot carrier solar cells offer potentially higher efficiency by extracting work from the kinetic energy of photogenerated 'hot carriers' before they cool to the lattice temperature. Hot carrier solar cells have been demonstrated in high-bandgap ferroelectric insulators and GaAs/AlGaAs heterostructures, but so far not in low-bandgap materials, where the potential efficiency gain is highest. Recently, a high open-circuit voltage was demonstrated in an illuminated wurtzite InAs nanowire with a low bandgap of 0.39 eV, and was interpreted in terms of a photothermoelectric effect. Here, we point out that this device is a hot carrier solar cell and discuss its performance in those terms. In the demonstrated devices, InP heterostructures are used as energy filters in order to thermoelectrically harvest the energy of hot electrons photogenerated in InAs absorber segments. The obtained photovoltage depends on the heterostructure design of the energy filter and is therefore tunable. By using a high-resistance, thermionic barrier, an open-circuit voltage is obtained that is in excess of the Shockley-Queisser limit. These results provide generalizable insight into how to realize high voltage hot carrier solar cells in low-bandgap materials, and therefore are a step towards the demonstration of higher efficiency hot carrier solar cells.

Bipolar Photothermoelectric Effect Across Energy Filters in Single Nanowires.

The photothermoelectric (PTE) effect uses nonuniform absorption of light to produce a voltage via the Seebeck effect and is of interest for optical sensing and solar-to-electric energy conversion. However, the utility of PTE devices reported to date has been limited by the need to use a tightly focused laser spot to achieve the required, nonuniform illumination and by their dependence upon the Seebeck coefficients of the constituent materials, which exhibit limited tunability and, generally, low values. Here, we use InAs/InP heterostructure nanowires to overcome these limitations: first, we use naturally occurring absorption "hot spots" at wave mode maxima within the nanowire to achieve sharp boundaries between heated and unheated subwavelength regions of high and low absorption, allowing us to use global illumination; second, we employ carrier energy-filtering heterostructures to achieve a high Seebeck coefficient that is tunable by heterostructure design. Using these methods, we demonstrate PTE voltages of hundreds of millivolts at room temperature from a globally illuminated nanowire device. Furthermore, we find PTE currents and voltages that change polarity as a function of the wavelength of illumination due to spatial shifting of subwavelength absorption hot spots. These results indicate the feasibility of designing new types of PTE-based photodetectors, photothermoelectrics, and hot-carrier solar cells using nanowires.

Growth of wurtzite Al x Ga1-x P nanowire shells and characterization by Raman spectroscopy.

The phonon energies of AlGaP in wurtzite crystal structure are generally not known, as opposed to their zincblende counterparts, because AlGaP crystallizes in zincblende phase in bulk and thin films structures. However, in nanowires AlGaP can be grown in wurtzite crystal structure. In this work we have grown wurtzite GaP/AlGaP/GaP core-shell nanowires by use of MOVPE. After developing suitable growth conditions, the Al composition was determined by STEM-EDX measurements and the wurtzite AlGaP phonon energies by Raman spectroscopy. Raman measurements show a peak shift with increasing Al composition in the AlGaP shell. We find that the phonon energies for wurtzite AlGaP are slightly lower than for zincblende AlGaP. Our results can be used to determine the Al composition in wurtzite AlGaP by Raman scattering.

Recombination dynamics in aerotaxy-grown Zn-doped GaAs nanowires.

In this paper we have investigated the dynamics of photo-generated charge carriers in a series of aerotaxy-grown GaAs nanowires (NWs) with different levels of Zn doping. Time-resolved photo-induced luminescence and transient absorption have been employed to investigate radiative (band edge transition) and non-radiative charge recombination processes, respectively. We find that the photo-luminescence (PL) lifetime of intrinsic GaAs NWs is significantly increased after growing an AlGaAs shell over them, indicating that an AlGaAs shell can effectively passivate the surface of aerotaxy-grown GaAs NWs. We observe that PL decay time as well as PL intensity decrease with increasing Zn doping, which can be attributed to thermally activated electron trapping with the trap density increased due to the Zn doping level.

Optimization of the short-circuit current in an InP nanowire array solar cell through opto-electronic modeling.

InP nanowire arrays with axial p-i-n junctions are promising devices for next-generation photovoltaics, with a demonstrated efficiency of 13.8%. However, the short-circuit current in such arrays does not match their absorption performance. Here, through combined optical and electrical modeling, we study how the absorption of photons and separation of the resulting photogenerated electron-hole pairs define and limit the short-circuit current in the nanowires. We identify how photogenerated minority carriers in the top n segment (i.e. holes) diffuse to the ohmic top contact where they recombine without contributing to the short-circuit current. In our modeling, such contact recombination can lead to a 60% drop in the short-circuit current. To hinder such hole diffusion, we include a gradient doping profile in the n segment to create a front surface barrier. This approach leads to a modest 5% increase in the short-circuit current, limited by Auger recombination with increased doping. A more efficient approach is to switch the n segment to a material with a higher band gap, like GaP. Then, a much smaller number of holes is photogenerated in the n segment, strongly limiting the amount that can diffuse and disappear into the top contact. For a 500 nm long top segment, the GaP approach leads to a 50% higher short-circuit current than with an InP top segment. Such a long top segment could facilitate the fabrication and contacting of nanowire array solar cells. Such design schemes for managing minority carriers could open the door to higher performance in single- and multi-junction nanowire-based solar cells.

GaAsP Nanowires Grown by Aerotaxy.

We have grown GaAsP nanowires with high optical and structural quality by Aerotaxy, a new continuous gas phase mass production process to grow III-V semiconductor based nanowires. By varying the PH3/AsH3 ratio and growth temperature, size selected GaAs1-xPx nanowires (80 nm diameter) with pure zinc-blende structure and with direct band gap energies ranging from 1.42 to 1.90 eV (at 300 K), (i.e., 0 ≤ x ≤ 0.43) were grown, which is the energy range needed for creating tandem III-V solar cells on silicon. The phosphorus content in the NWs is shown to be controlled by both growth temperature and input gas phase ratio. The distribution of P in the wires is uniform over the length of the wires and among the wires. This proves the feasibility of growing GaAsP nanowires by Aerotaxy and results indicate that it is a generic process that can be applied to the growth of other III-V semiconductor based ternary nanowires.

Design for strong absorption in a nanowire array tandem solar cell.

Semiconductor nanowires are a promising candidate for next-generation solar cells. However, the optical response of nanowires is, due to diffraction effects, complicated to optimize. Here, we optimize through optical modeling the absorption in a dual-junction nanowire-array solar cell in terms of the Shockley-Quessier detailed balance efficiency limit. We identify efficiency maxima that originate from resonant absorption of photons through the HE11 and the HE12 waveguide modes in the top cell. An efficiency limit above 40% is reached in the band gap optimized Al0.10Ga0.90As/In0.34Ga0.66As system when we allow for different diameter for the top and the bottom nanowire subcell. However, for experiments, equal diameter for the top and the bottom cell might be easier to realize. In this case, we find in our modeling a modest 1-2% drop in the efficiency limit. In the Ga0.51In0.49P/InP system, an efficiency limit of η = 37.3% could be reached. These efficiencies, which include reflection losses and sub-optimal absorption, are well above the 31.0% limit of a perfectly-absorbing, idealized single-junction bulk cell, and close to the 42.0% limit of the idealized dual-junction bulk cell. Our results offer guidance in the choice of materials and dimensions for nanowires with potential for high efficiency tandem solar cells.

Sn-seeded GaAs nanowires grown by MOVPE.

It has previously been reported that in situ formed Sn nanoparticles can successfully initiate GaAs nanowire growth with a self-assembled radial p-n junction composed of a Sn-doped n-type core and a C-doped p-type shell. In this paper, we investigate the effect of fundamental growth parameters on the morphology and crystal structure of Sn-seeded GaAs nanowires. We show that growth can be achieved in a broad temperature window by changing the TMGa precursor flow simultaneously with decreasing temperature to prevent nanowire kinking at low temperatures. We find that changes in the supply of both AsH3 and TMGa can lead to nanowire kinking and that the formation of twin planes is closely related to a low V/III ratio. From PL results, we observe an increase of the average luminescence energy induced by heavy doping which shifts the Fermi level into the conduction band. Furthermore, the doping level of Sn and C is dependent on both the temperature and the V/III ratio. These results indicate that using Sn as the seed particle for nanowire growth is quite different from traditionally used Au in for example growth conditions and resulting nanowire properties. Thus, it is very interesting to explore alternative metal seed particles with controllable introduction of other impurities.

Wurtzite GaAs Quantum Wires: One-Dimensional Subband Formation.

It is of contemporary interest to fabricate nanowires having quantum confinement and one-dimensional subband formation. This is due to a host of applications, for example, in optical devices, and in quantum optics. We have here fabricated and optically investigated narrow, down to 10 nm diameter, wurtzite GaAs nanowires which show strong quantum confinement and the formation of one-dimensional subbands. The fabrication was bottom up and in one step using the vapor-liquid-solid growth mechanism. Combining photoluminescence excitation spectroscopy with transmission electron microscopy on the same individual nanowires, we were able to extract the effective masses of the electrons in the two lowest conduction bands as well as the effective masses of the holes in the two highest valence bands. Our results, combined with earlier demonstrations of thin crystal phase nanodots in GaAs, set the stage for the fabrication of crystal phase quantum dots having full three-dimensional confinement.

Optical response of wurtzite and zinc blende GaP nanowire arrays.

We compare the optical response of wurtzite and zinc blende GaP nanowire arrays for varying geometry of the nanowires. We measure reflectance spectra of the arrays and extract from these measurements the absorption in the nanowires. To support our experimental findings and to allow for more detailed investigations of the optical response of the nanowire arrays than possible in experiments, we perform electromagnetic modeling. This modeling highlights the validity of the extraction of the absorptance from reflectance spectra, as well as limitations of the extraction due to anti-reflection properties of the nanowires. In our combined experimental and theoretical study, we find for both zinc blende and wurtzite nanowires an absorption resonance that can be tuned into the ultraviolet by decreasing the diameter of the nanowires. This peak stops blue-shifting with decreasing nanowire diameter at a wavelength of approximately 330 nm for zinc blende GaP. In contrast, for the wurtzite GaP nanowires, the resonance continues blue-shifting at 310 nm for the smallest diameters we succeeded in fabricating. We interpret this as a difference in refractive index between wurtzite and zinc blende GaP in this wavelength region. These results open up for optical applications through resonant absorption in the visible and ultraviolet wavelength regions with both zinc blende and wurtzite GaP nanowire arrays. Notably, zinc blende and wurtzite GaP support resonant absorption deeper into the ultraviolet region than previously found for zinc blende and wurtzite InP and InAs.

Carrier Recombination Dynamics in Sulfur-Doped InP Nanowires.

Measuring lifetime of photogenerated charges in semiconductor nanowires (NW) is important for understanding light-induced processes in these materials and is relevant for their photovoltaic and photodetector applications. In this paper, we investigate the dynamics of photogenerated charge carriers in a series of as-grown InP NW with different levels of sulfur (S) doping. We observe that photoluminescence (PL) decay time as well as integrated PL intensity decreases with increasing S doping. We attribute these observations to hole trapping with the trap density increased due to S-doping level followed by nonradiative recombination of trapped charges. This assignment is proven by observation of the trap saturation in three independent experiments: via excitation power and repetition rate PL lifetime dependencies and by PL pump-probe experiment.

Confinement in thickness-controlled GaAs polytype nanodots.

Polytype nanodots are arguably the simplest nanodots than can be made, but their technological control was, up to now, challenging. We have developed a technique to produce nanowires containing exactly one polytype nanodot in GaAs with thickness control. These nanodots have been investigated by photoluminescence, which has been cross-correlated with transmission electron microscopy. We find that short (4-20 nm) zincblende GaAs segments/dots in wurtzite GaAs confine electrons and that the inverse system confines holes. By varying the thickness of the nanodots we find strong quantum confinement effects which allows us to extract the effective mass of the carriers. The holes at the top of the valence band have an effective mass of approximately 0.45 m0 in wurtzite GaAs. The thinnest wurtzite nanodot corresponds to a twin plane in zincblende GaAs and gives efficient photoluminescence. It binds an exciton with a binding energy of roughly 50 meV, including central cell corrections.

Tunable absorption resonances in the ultraviolet for InP nanowire arrays.

The ability to tune the photon absorptance spectrum is an attracting way of tailoring the response of devices like photodetectors and solar cells. Here, we measure the reflectance spectra of InP substrates patterned with arrays of vertically standing InP nanowires. Using the reflectance spectra, we calculate and analyze the corresponding absorptance spectra of the nanowires. We show that we can tune absorption resonances for the nanowire arrays into the ultraviolet by decreasing the diameter of the nanowires. When we compare our measurements with electromagnetic modeling, we generally find good agreement. Interestingly, the remaining differences between modeled and measured spectra are attributed to a crystal-phase dependence in the refractive index of InP. Specifically, we find indication of significant differences in the refractive index between the modeled zinc-blende InP nanowires and the measured wurtzite InP nanowires in the ultraviolet. We believe that such crystal-phase dependent differences in the refractive index affect the possibility to excite optical resonances in the large wavelength range of 345 < λ < 390 nm. To support this claim, we investigated how resonances in nanostructures can be shifted in wavelength by geometrical tuning. We find that dispersion in the refractive index can dominate over geometrical tuning and stop the possibility for such shifting. Our results open the door for using crystal-phase engineering to optimize the absorption in InP nanowire-based solar cells and photodetectors.

In situ etching for control over axial and radial III-V nanowire growth rates using HBr.

We report on the influence of hydrogen bromide (HBr) in situ etching on the growth of InP, GaP and GaAs nanowires. We find that HBr can be used to impede undesired radial growth during axial growth for all three material systems. The use of HBr opens a window for optimizing the growth parameters with respect to the materials' quality rather than only their morphology. Transmission electron microscopy (TEM) characterization reveals a partial transition from a wurtzite crystal structure to a zincblende upon the use of HBr during growth. For InP, defect-related luminescence due to parasitic radial growth is removed by use of HBr. For GaP, the etching with HBr reduced the defect-related luminescence, but no change in peak emission energy was observed. For GaAs, the HBr etching resulted in a shift to lower photon emission energies due to a shift in the crystal structure, which reduced the wurtzite segments.