What is a Continuous Range of a Single Feature Such as Wavelength

Wavelength Range

Advances in Semiconductor Lasers

Eric Tournié , Alexei N. Baranov , in Semiconductors and Semimetals, 2012

Abstract

The mid-infrared (MIR) wavelength range of the electromagnetic spectrum offers a number of applications of growing importance such as photonic sensors for environment, industry or health monitoring, or defense and homeland security. This has driven over the last couple of decades the development of MIR semiconductor lasers at a rapid pace. This chapter aims at reviewing the progress in this field. Although II–VI or IV–VI compound semiconductors exhibit bandgaps in the MIR, other properties limit their use in semiconductor lasers. In contrast, the so-called antimonides, that is, III–V compound semiconductors based on GaSb, InAs, AlSb, InSb, and their alloys, appear to be well suited for developing a variety of lasers covering the whole MIR range. Laser diodes operating under continuous wave at room temperature have been demonstrated in the spectral range from 2 up to 3.5  μm. On the other hand, quantum cascade lasers emitting from 15 down to 2.6   μm have also been realized. Although further progress is possible for antimonide devices, they undoubtedly open the way to exploit the whole MIR wavelength range.

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Including Actinides

Philippe F. Smet , ... Dirk Poelman , in Handbook on the Physics and Chemistry of Rare Earths, 2015

6.2 CIE Model for Mesopic Luminance Measurements

The combined effect of the difference in wavelength range and sensitivity between photopic and scotopic vision and the gradual shift between the two during twilight has been subject of research for a long time. Notably, the nineteenth century Czech anatomist Jan Evangelista Purkyně gave his name to the Purkinje effect, which describes the phenomenon qualitatively: when flowers look bright red compared to their relatively dull green leaves in bright sunlight, this contrast changes at dusk, when the green leaves look much brighter than the red flowers.

Since it is important to take these effects into account for photometric measurements during twilight or during the night, especially for road markings and road lighting, several models have been developed to describe vision in the mesopic regime. An important contribution to this subject was delivered by the European project MOVE (Mesopic Optimisation of Visual Efficiency), which proposed a set of equations for describing luminance in the mesopic region, using a weighted average eye sensitivity in between the sensitivity curves for photopic and scotopic vision (Eloholma and Halonen, 2006). Stated otherwise, they used a sensitivity function which, referring to Fig. 11, gradually shifted from one graph to the other. Rea published an overview of the existing models for mesopic vision, including the one from MOVE, and proposed a slightly different model (Poelman et al., 2009; Rea et al., 2004). Finally, in 2010 and after decades of meetings and preliminary documents, the CIE published a "Recommended system for visual performance based mesopic photometry" in technical report CIE191:2010 (TC-1-58, 2010). The system yields results which are very close to, for example, the MOVE project or the model by Rea. However, it has the advantage that now an internationally recognized organization has provided the scientific community with a standard that can be used as reference. We will not go into all details of this report, but only briefly describe the main results.

Just like the older models, the new CIE model relies on a "mesopic" sensitivity function which is a linear combination of the photopic and scotopic functions:

$M\left(m\right)\cdot V_{\mathrm{m}\mathrm{e}\mathrm{s}}\left(\lambda \right)=m\cdot V\left(\lambda \right)+\left(1-m\right)\cdot V^{\prime }\left(\lambda \right)$

and the resulting mesopic luminance is

$L_{\mathrm{m}\mathrm{e}\mathrm{s}}=\frac{683}{V_{\mathrm{m}\mathrm{e}\mathrm{s}}\left({\lambda }_0\right)}{\displaystyle \int V_{\mathrm{m}\mathrm{e}\mathrm{s}}\left(\lambda \right)L_{\mathrm{e}}\left(\lambda \right)\mathrm{d}\lambda }$

where M(m) is a normalizing function such that V _mes has a maximum value of 1 and L _e(λ) is the spectral radiance in W/m²/sr/nm. V _mes(λ ₀) is the value of V _mes at 555   nm. When L _mes  ≥   5.0   cd/m² then m  =   1 and if L _mes  ≤   0.005   cd/m² then m  =   0. In these cases, the mesopic luminance reduces to the photopic and scotopic luminance, respectively.

Both the coefficient m and the mesopic luminance are calculated using an iterative procedure as follows:

$\begin{array}{l}{m}_0=0.5\hfill \\ L_{\mathrm{m}\mathrm{e}\mathrm{s},0}=\frac{1699\cdot m_{n-1}\cdot P+683\cdot \left(1-m_{n-1}\right)\cdot S}{1699\cdot m_{n-1}+683\cdot \left(1-m_{n-1}\right)}\hfill \\ m_n=0.767+0.333{log}_{10}\left(L_{\mathrm{m}\mathrm{e}\mathrm{s},n}\right)\mathrm{f}\mathrm{o}\mathrm{r}0\le m_n\le 1\hfill \end{array}$

where P and S are the photopic and scotopic luminance, respectively. 683/1699 is the value of the scotopic spectral sensitivity function V′(λ) at 555   nm. It is easily seen that this last equation can be written in terms of P, the photopic luminance, and S/P, the ratio of scotopic to photopic luminance. It is the latter ratio S/P, which is typically used to quantify the appropriateness of a certain light source for low light level illumination applications, since high S/P values lead to higher mesopic luminance under near-scotopic conditions.

This effect is seen in Table 5, where the photopic and mesopic luminance of the different benchmark phosphors are shown at different times after excitation. The violet and blue emitters, having a high S/P ratio (see also Table 3), show a mesopic luminance that is considerably higher than their photopic counterpart, while the red-emitting phosphor, with S/P  =   0.37, performs considerably worse in the mesopic region. The unified luminance as a function of time according to the model of Rea and the mesopic luminance according to the CIE recommended system are shown for the benchmark phosphors in Figs. 12 and 13, respectively. Even though the unified luminance model makes some approximations compared to the CIE model, it is seen that even for quite extreme S/P ratios, such as the benchmark phosphors, the differences remain quite small.

Table 5. Measured Photopic Luminance/Calculated Mesopic Luminance of the Benchmark Phosphors at Different Times (in mcd/m²)

Phosphor	2   min	10   min	30   min	60   min	340   min
Violet	33.6/166	9.54/64.2	3.51/29.9	1.75/17.6	0.275/4.15
Blue	216/470	56.6/164	19.2/70.3	9.03/38.8	1.48/11.5
Green	298/376	68.2/99.7	22.5/37.4	10.7/19.6	1.16/2.71
Red	64.1/46.6	9.41/3.78	1.90/0.765	0.649/0.261	0.042/0.0169

Figure 12. Unified luminance of the benchmark phosphors (Table 3) as a function of time.

Figure 13. Mesopic luminance, following CIE191:2010, of the benchmark phosphors (Table 3) as a function of time.

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Lasers, Optical Fiber

Graham E. Town , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

II.B.1 Linear Properties of Optical Fiber Waveguides

Optical fibers are highly transparent over specific wavelength ranges in the near infrared, a property which makes them attractive for applications such as telecommunication. The linear losses are typically in the range 0.2–1  dB/km, i.e., insignificant compared to losses incurred in coupling to and from fibers, or the gain that can be provided by optical amplifiers, hence the losses in passive optical fibers may usually be ignored in determining the performance of fiber lasers.

Optical fibers used in lasers are usually designed to guide a single mode. Step index fibers are single mode if the normalized frequency parameter satisfies the following constraint,

$\text{V}=2\pi \frac{\rho }{\lambda }\sqrt{({\text{n}}_{\text{c}\text{o}}^2-{\text{n}}_{\text{c}\text{l}}^2)}\le 2.405$

in which ρ is the core radius, n _co and n _cl the core and cladding refractive indices, respectively. The intensity distribution of the fundamental guided mode is approximately Gaussian, with an RMS width or spot size which depends on wavelength. At short wavelengths (i.e., close to V  =   2.4), the intensity distribution is well confined within the core, and consequently the effective index of the guided mode is close to the core refractive index. At long wavelengths the guided mode is only weakly bound to the core, with the intensity distribution extending well into the cladding, and the effective index is then close to the cladding refractive index. The spot size, or mode field radius, w _s , for 1.2   < V  <   3 is well approximated by

${\text{w}}_{\text{s}}\sim \rho \left(0.65+1.619{\text{V}}^{-3/2}+2.879{\text{V}}^{-6}\right).$

The choice of parameters made in designing an optical fiber affects more than the number of propagating modes; trade-offs between dispersion and losses due to bends and splices are also involved. The bend losses in optical fibers with V  >   1 are usually negligible over short lengths, hence in the following we concentrate on dispersion.

The dependence of spot size and effective refractive index of the guided mode on wavelength results in wave guide dispersion, i.e., different guided wavelengths travel at different velocities within the fiber. The total dispersion experienced by light guided in an optical fiber is determined by the sum of material and waveguide dispersion, and is dominated by material dispersion except at wavelengths where the latter is small. Dispersion causes temporal broadening of an optical pulse during propagation, and the development of a "chirp" in the optical carrier frequency across the pulse. The chirp may be positive or negative, depending on the sign of the dispersion, and is often an important factor in the performance of pulsed fiber lasers. The dispersion length, i.e., a characteristic length over which dispersive effects become significant for pulse evolution, may be defined as ${\text{L}}_{\text{D}}={\tau }_{\text{o}}^2/\left|{\beta }_2\right|$ , in which τ _o is the initial RMS pulse width in intensity, and β₂ the group velocity dispersion.

In standard step index fibers the material and waveguide dispersions cancel at about 1.3   μm. At longer wavelengths the total dispersion is usually negative, and referred to as anomalous, (i.e., if β₂  <   0, shorter wavelength components in an optical signal travel faster than longer wavelengths). At shorter wavelengths the total dispersion is of opposite sign, and referred to as normal. Typical values of dispersion in commonly available step index fibers are β₂(1   μm)   =   + 25   ps²/km, and β₂(1.55   μm)   =   − 20   ps²/km. Specially designed fibers can have significantly modified dispersion characteristics. For example, dispersion-shifted fiber may have a zero-dispersion wavelength of 1.55   μm, and dispersion-flattened fiber typically has small dispersion over a wide range of wavelengths, e.g., from 1.3 to 1.55   μm.

Birefringence is another linear property of optical fiber waveguides that often plays an important role in fiber laser performance. Birefringence may be defined as the dependence of the propagation constant of a guided mode on its state of polarization. The magnitude of birefringence may be characterized by the beatlength between orthogonal polarization states, or the period over which the state of polarization evolves, i.e., L _B   =   λ/B, where for linear birefringence B  =   ∣n _x   − n _y ∣. Birefringence may be caused by noncircular symmetry of the fiber core (i.e., form birefringence), and/or an asymmetrical stress across the fiber (through the stress-optic effect). The latter type of birefringence may be induced by squeezing or bending an optical fiber. Bending a silica fiber on radius R typically causes birefringence B  =   −0.093(ρ/R)². For example, bending a 125-μm diameter fiber on a radius of 2.5   cm induces a birefringence with beatlength L _B   ∼   2.5   m. Highly birefringent fibers (e.g., with L _B   <   5   mm) are often referred to as polarization maintaining (PM) fibers, because bends have little effect on their birefringence or the polarization of light propagating through the fiber. Fiber lasers constructed from highly birefringent fibers are less sensitive to bending and other stress-inducing perturbations in their environment.

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Roadmap for photon-magnon coupling and its applications

Biswanath Bhoi , Sang-Koog Kim , in Solid State Physics, 2020

4.5 PMC-based metamaterials

Materials of positive refractive index in a visible wavelength range are ubiquitous in nature, but their counterpart materials of negative refractive index (NRI) (also known as metamaterials) have been artificially fabricated owing to the potential applications for perfect lens [169], invisibility cloaks [170] and sensitive signal detection and processing with superior antenna properties [171]. Coherent coupling between two resonators has been utilized for development of metamaterials, leading to, for example, the demonstration of classical analogs of electromagnetically induced transparency in metamaterials [172]. Such a classical analogue usually applies when the dissipative loss of the radiative resonator is much smaller than the coupling strength. However, in light of physics of metamaterials [173], one may consider their design as a realization of both negative permittivity (ɛ) and negative permeability (μ) in a common frequency. Since a variety of PMCs share both the photonic and magnonic properties due to their strong coupling, an opportunity for control of the permittivity ɛ and the permeability μ of PMC and consequent realization of the novel property of the NRI is provided.

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Advances in Photodetectors and Optical Receivers

Andreas Beling , Joe C. Campbell , in Optical Fiber Telecommunications (Sixth Edition), 2013

3.5.1 SACM APDs

First generation optical fiber communication systems operated in the wavelength range 800–900  nm. The optical receivers utilized Si p-i-n photodiodes or Si APDs [187]. In subsequent generations the operating wavelengths migrated to 1300   nm and 1550   nm, which resulted in the development of "long-wavelength" photodetectors. The most straightforward approach would have been to develop In_0.53Ga_0.47As homojunction APDs [188,189] but this was prevented by excessive dark current caused by tunneling at the electric fields required for impact ionization [204]. To circumvent this limitation, separate absorption and multiplication (SAM) APD structures similar to Si reach-through APDs [190,191] were investigated [192]. In these APDs the p-n junction and thus the high-field multiplication region is located in a wide-bandgap semiconductor such as InP where tunneling is insignificant and absorption occurs in an adjacent InGaAs layer. By properly controlling the charge density in the multiplication layer, it is possible to maintain a high enough electric field to achieve good avalanche gain while keeping the field low enough to minimize tunneling and impact ionization in the InGaAs absorber. However, the frequency response of the InP/InGaAs SAM APDs, as originally implemented, was very poor owing to accumulation of photogenerated holes at the absorption/multiplication heterojunction interface [193]. Several methods to eliminate the slow release of trapped holes were reported; however, the approach that has been most widely adopted utilizes a transition region consisting of one or more intermediate-bandgap In _x Ga_{1− x} As_{1− y} P _y layers [209,194,195]. A second modification to the original SAM APD structure has been the inclusion of a high-low doping profile in the multiplication region [196–198]. In this structure the wide-bandgap multiplication region consists of a lightly doped (usually unintentionally doped) layer where the field is high and an adjacent, doped charge layer or field control region. This type of APD, which is frequently referred to as the SACM structure with the "C" representing the charge layer, decouples the thickness of the multiplication region from the charge density constraint in the SAM APD. At present, most commercial SACM APDs are planar, as opposed to mesa structures, with lateral guard rings to suppress edge breakdown. Figure 3.19 shows a schematic cross-section of an InP/InGaAsP/InGaAs SACM APD with a double-diffused floating guard ring [199]. The adjacent graph shows the electric field profiles normal to the surface through the active and the guard ring regions and illustrates how the charge layer is used to tailor the relative fields in the multiplication and absorption layers.

Figure 3.19. Schematic cross-section of InP/InGaAsP/InGaAs SACM APD with double-diffused floating guard ring configuration. The adjacent graph shows electric field profiles normal to the surface through the active and the guard regions [199].

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Advances in Infrared Photodetectors

S.D. Gunapala , ... D.Z. Ting , in Semiconductors and Semimetals, 2011

Publisher Summary

Intrinsic infrared detectors in the mid-wavelength and long-wavelength ranges are based on interband transition, which promotes an electron across the band gap (E _g) from the valence band to the conduction band. This chapter describes the use of multi-quantum-wells (MQWs)-based intersubband transition for infrared detection. The spectral response of the detectors can be tuned by controlling the E_g of the photosensitive material. The MQW structures to detect infrared radiation can be explained by using the basic principles of quantum mechanics. The quantum well is equivalent to the well-known "particle in a box" problem in quantum mechanics, which can be solved by the time-independent Schrodinger equation. The solutions to this problem are the Eigen values that describe energy levels inside the quantum well in which the particle is allowed to exist. The positions of the energy levels are primarily determined by the quantum-well dimensions. The quantum-well infrared photodetectors (QWIPs) discussed in the chapter use the photo-excitation of the electron between the ground state and the first excited state in the conduction band (valance band) quantum well. The quantum-well structure is designed so that these photoexcited carriers can escape from the quantum well and get collected as photocurrent.

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Fluorescence Microscopy

JOHAN S. PLOEM , in Fluorescent and Luminescent Probes for Biological Activity (Second Edition), 1999

1.5.2 Barrier filters

Barrier filters are used to block the unwanted excitation light in the wavelength range of the fluorescence emission. Mostly colour glasses are used with a high transmission for the longer wavelengths (90% or higher) and a very effective blocking of shorter wavelengths. Colour glass barrier filters absorbing short wavelength excitation light may fluoresce which may lead to a decrease in the image contrast. Barrier filters for some applications requiring an extremely dark background are therefore coated with an interference filter layer that will reflect most excitation light and prevent autofluorescence of the barrier filter.

In some applications not all the fluorescence light longer than a certain wavelength is wanted for observation, but only the fluorescence in a limited wavelength range (e.g. the narrow emission peak of FITC). This is achieved by adding an extra band or a short-pass interference filter to the barrier filter or by coating the colour glass barrier filter with an interference coating, selecting a narrow wavelength band. Such filter combinations can be defined as fluorescence selection filters.

Recently, barrier filters of the interference type have been manufactured which permit the observation of 2 or 3 fluorescence colours simultaneously (Fig. 1.7). Such filters have a complex transmittance curve with several wavelength bands of high transmission for fluorescence and several wavelength regions for strong blocking of unwanted excitation light. Such filters must be used in combination with special excitation interference filters, exactly matching the transmission of the barrier filter.

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Infrared Astronomy

Rodger I. Thompson , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

VI.D Infrared Space Observatory

The ISO was launched in November 1995. Its various instruments operated over the wavelength range between 2.5 and 240  μm. With a primary mirror diameter of 60   cm, it was similar in size to IRAS but carried improved detectors and a more versatile instrument complement. ISO differed in its mission from IRAS. Instead of surveys as its main mission, ISO was designed primarily for pointed observations of objects of interest. Like COBE and IRAS, ISO was cooled by cryogens in order to operate in the mid- and far infrared bands. The liquid helium cryogens lasted until April 1998, providing an observing period of about 2 $\frac{1}{2}$ years. ISO was put into a highly elliptical orbit that provided significant observing time at large distances from the earth with data transmission to two ground stations. ISO was the first infrared space mission to offer observing opportunities to the entire community. The four instruments on the ISO mission were a combination of cameras and spectrometers described below. This mission also provided important information about the performance of some classes of infrared detectors in high radiation environments. In spite of the problems with some of the detectors, ISO was a highly successful mission whose database is an important tool in astrophysics. Its spectrometers demonstrated the richness of the mid- and far infrared spectral region. We will discuss below the ISO instruments.

VI.D.1 ISOPHOT

This instrument provided photometric, polarimetric, and spectrophotometry over the entire wavelength range of ISO. Small arrays of Si:Ga, Si:B, and Ge:Ga detectors also provided limited imaging capabilities. The main role of ISOPHOT was to provide accurate photometry of sources. It included an internal chopper and several calibration sources.

VI.D.2 ISOCAM

ISOCAM provided the main imaging capability for the mission. It was split into two channels. The short wavelength channel was sensitive between 2.5 and 5.5   μm, and the long wavelength channel between 4 and 18   μm. These cameras provided imaging capability in several spectral regions that are inaccessible from the ground. The detector arrays were 32×32 pixels of In:Sb and Si:Ga. The short wavelength In:Sb array was operated in a charge-integrating mode, which has since been superseded by multiplexed readouts for much larger arrays. The long wavelength Si:Ga array was operated as a photoconductor. ISOCAM provided diffraction-limited optical performance with several filter options.

VI.D.3 Short Wavelength Spectrometer

The short wavelength spectrometer (SWS) covered the spectral range between 2.38 and 42.5 μm, with a spectral resolution ranging from 1000 to 2000. It also carried a Fabry-Perot etalon to enhance the spectral resolution in the 11.4 to 44.5-μm region. Fabry-Perot etalons pass radiation in a narrow wavelength range that is altered by changing the spacing between the optical components. A combination of In:Sb, Si:Ga, Si:As, Si:Sb, and Ge:Be linear arrays provided the detectors for the large wavelength range covered by the instrument. Most of the arrays were 1×12 pixels, but the Si:Sb and Ge:Be arrays were 1×2. The SWS detector arrays were found to be very sensitive to the radiation environment encountered in space missions.

VI.D.4 Long Wavelength Spectrometer

The long wavelength spectrometer (LWS) operates between 43.0 and 196.9   μm. Coupled with the SWS it provides continuous spectral coverage from 2.4 to 196.9   μm. This has been a great advantage in studying the emission of objects such as active galactic nuclei and starburst galaxies. The detector array is linear and consists of one Ge:Be, five unstressed Ge:Ga, and four stressed Ge:Ga photoconductive detectors. Like SWS, LWS also carried a Fabry-Perot etalon to increase the spectroscopic resolution of the instrument.

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Radio Astronomy, Planetary

Samuel Gulkis , Imke de Pater , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

IV.E Saturn

Radio emission from Saturn has been observed from the Earth over a wavelength range from 1  mm to approximately 70   cm. The emission is thermal throughout this band, arising in both the atmosphere and the rings. The atmospheric emission is similar to that observed from Jupiter. Model studies indicate that Saturn, like Jupiter, has a deep convective atmosphere. Hydrogen and helium form the bulk of the atmosphere, whereas ammonia in trace amounts provides most of the microwave opacity. High-resolution radio images of Saturn also give information on the latitudinal distribution of NH₃ gas. Figure 15 shows a VLA image at 6-cm wavelength: the resolution is 1.5 arc sec and the disk diameter is 16.8 arc sec. A bright band can be distinguished at midlatitudes, indicative of an average lack of NH₃ gas over the altitude region probed at this wavelength. The region at midlatitudes is likely a region of subsiding gas, just like the bright belts seen on Jupiter. In the 1990s the zonal patterns on Saturn changed drastically compared to what was seen in the 1980s, indicative of strong dynamical interactions.

FIGURE 15. Radio photograph of Saturn at a wavelength of 6.14   cm obtained with the VLA. Resolution is 1.5 arc sec. Equatorial diameter of Saturn is 16.83 arc sec. [After de Pater, I., and Dickel, J. R. (1991). Icarus 94, 474–492.]

As shown in Figs. 15 and 16, interferometer observations of Saturn also detect the thermal emission from the ring particles. Most of the radio emission is due to scattering of Saturn's emission off the ring particles. In front of the planet, the rings are visible as an absorption feature; they block out Saturn's radio emission. The scattering characteristics of the rings contain information on the ring particle sizes and composition.

FIGURE 16. Radio photograph of Saturn at a wavelength of 2.0   cm obtained with the VLA. Resolution is 1.5 arc sec. Equatorial diameter of Saturn is 16.83 arc sec. [After de Pater, I., and Dickel, J. R. (1991). Icarus 94, 474–492.]

Interferometer observations of Saturn at centimeter and millimeter wavelengths have detected thermal emission from the ring particles. The rings have a low brightness temperature, approximately 10   K. The presence of ring particle sizes larger than a few centimeters is suggested by the radio observations. The observations are consistent with the bulk properties of the ring particles being those of water ice.

The Voyager spacecraft detected two distinct classes of nonthermal emissions from Saturn at frequencies below 1   MHz. These emissions are not observable from the Earth because of the opaqueness of the Earth's ionosphere at frequencies below a few megacycles. The first class, called Saturn kilometric radiation, is a relatively narrow band polarized emission. The second class is a broadband, impulsive emission called the Saturn electrostatic discharge.

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Ultrawide Bandgap Semiconductors

Yuanpeng Wu , ... Zetian Mi , in Semiconductors and Semimetals, 2021

4.1.3 AlN nanowire LEDs

Studies have shown that far-UV-C light, in the wavelength range of 207–222  nm, is faster and far more effective than traditional UV-C light (~   265   nm) in preventing the transmission of microbial diseases, while causing virtually no harm since it does not pass through the outer barrier layer of mammalian skin or eye, due to the much shorter wavelengths (Welch et al., 2018). To date, however, such UV-C light can only be generated by toxic, large size, and inefficient excimer lamps, preventing its wide utilization. AlN and BN, with energy bandgap in the range of ~   6   eV, have emerged as the materials of choice for far-UV-C LEDs. The first demonstration of AlN nanowire LEDs emitting at 210   nm was reported by Zhao et al. in 2015 (Zhao et al., 2015a). Following work further confirmed that the dominant light emission direction is from the nanowire top surface, e.g., along the c-axis, due to the strong light scattering effect (Zhao et al., 2015c). Such an efficient surface emitting device was not previously possible using conventional c-plane AlN planar structures wherein the TM polarized light emission is largely confined within the epilayer. Most recently, with optimized p-type AlN growth conditions, AlN nanowire-based p-i-n LED was further grown and fabricated. The measured I-V characteristics have a turn-on voltage ~   5   V with negligible reverse leakage current, shown in Fig. 14A . The obtained minimum ideality factor, extracted by $n=\frac{\mathit{kT}}{q}\left[\frac{\mathit{dV}}{d\left(\mathit{lnI}\right)}\right]$ , is 4.6 $\mathrm{n}=\frac{\mathrm{kT}}{\mathrm{q}}\left[\frac{\mathrm{dV}}{\mathrm{d}\left(\mathrm{lnI}\right)}\right]$ . Fig. 14B shows strong electroluminescence emission at ~   210   nm measured at room temperature. Fig. 14C shows temperature-independent slopes of (logI)-vs-V plots with increasing temperature, which could be attributed to the involvement of charge carrier tunneling. The total forward current J consists of the diffusion component J _D and the tunneling current J _T ,

Fig. 14. (A) I-V characteristics of AlN nanowire LEDs measured at room temperature. (B) Room-temperature EL spectrum measured under 30   mA current injection from as-fabricated AlN LEDs. (C) Temperature-dependent I-V characteristics of AlN nanowire LEDs measured in the temperature range of 20–200   °C. (D) Illustration of the Mg acceptor energy levels under relatively low (left) and high (right) doping concentrations. The dispersion of Mg acceptor energy levels under very high concentrations leads to significantly reduced activation energy.

From Wu, Y., Laleyan, D.A., Deng, Z., Ahn, C., Aiello, A., Pandey, A., Liu, X., Wang, P., Sun, K., Ahmadi, E., Sun, Y., Kira, M., Bhattacharya, P., Kioupakis, E., Mi, Z. 2020. Adv. Electron. Mater. 6, 2000337.

(1) $J=J_{D0}\left[exp\left(\frac{q{V}_A}{\mathit{kT}}\right)-1\right]+J_{T0}\left[exp\left(\frac{q{V}_A}{E_T}\right)-1\right]\mathrm{J}={\mathrm{J}}_{\mathrm{D}0}\left[exp\left(\frac{\mathrm{q}{\mathrm{V}}_{\mathrm{A}}}{\mathrm{kT}}\right)-1\right]+{\mathrm{J}}_{\mathrm{T}0}\left[exp\left(\frac{\mathrm{q}{\mathrm{V}}_{\mathrm{A}}}{{\mathrm{E}}_{\mathrm{T}}}\right)-1\right]\mathrm{J}={\mathrm{J}}_{\mathrm{D}0}\left[exp\left(\frac{\mathrm{q}{\mathrm{V}}_{\mathrm{A}}}{\mathrm{kT}}\right)-1\right]+{\mathrm{J}}_{\mathrm{T}0}\left[exp\left(\frac{\mathrm{q}{\mathrm{V}}_{\mathrm{A}}}{{\mathrm{E}}_{\mathrm{T}}}\right)-1\right]\mathrm{J}={\mathrm{J}}_{\mathrm{D}0}\left[exp\left(\frac{\mathrm{q}{\mathrm{V}}_{\mathrm{A}}}{\mathrm{kT}}\right)-1\right]+{\mathrm{J}}_{\mathrm{T}0}[exp\left(\frac{\mathrm{q}{\mathrm{V}}_{\mathrm{A}}}{{\mathrm{E}}_{\mathrm{T}}}\right)-1$

where V _A is the voltage applied through the AlN p-i-n diode, and E _T is the characteristic tunneling energy (Lee et al., 2010, 2018b). Further detailed study shows that increasing Mg doping concentration from 1   ×   10¹⁹ to 6   ×   10¹⁹  cm^{−   3} leads to drastically reduced activation energy for a portion of Mg dopants, evidenced by reduction of E _T from 364 to 67   meV. As schematically illustrated in Fig. 14D, very high Mg impurity concentrations in AlN can result in the formation of an impurity band, in instead of localized impurity levels due to impurity-impurity interactions, leading to significantly reduced Mg activation energy and enhanced hole carrier concentration.

Recently, hBN has drawn considerable interest for application in deep-UV LED structures (Attaccalite et al., 2011; Dahal et al., 2011). Intentionally incorporated Mg dopants, or unintentionally formed B vacancies can give rise to p-type conductivity for hBN. Notably, theoretical calculations predicted that the energy level of B vacancies is located ~   150   meV above the valence band, with an ionization energy only quarter of that of Mg dopants in AlN (Attaccalite et al., 2011). In 2017, we have demonstrated, for the first time, AlN/hBN based Mg-dopant free far-UV-C LEDs by using hBN as the hole injection layer and p-type contact layer, schematically shown in Fig. 15A (Laleyan et al., 2017). Highly efficient p-type conduction has been achieved in hBN grown at a relatively low temperature (400–800   °C) with N-rich conditions. The as-fabricated 300   ×   300   μm² devices exhibit an excellent rectification characteristic, with a turn on voltage as low as ~   5.5   V, shown in Fig. 15B. A strong emission at ~   210   nm was measured at room-temperature from the AlN/hBN nanowire LEDs (Fig. 15C). The output power (50   nW at 60   A/cm²) is more than one order of magnitude higher than that of the similar AlN nanowire p-i-n LEDs and can be drastically improved by optimize the fabrication process and light extraction.

Fig. 15. (A) Schematic of AlN/hBN far-UV-C LEDs. (B) I-V curve of a 300   ×   300   μm² LED device at room temperature, with a photograph of the device as the inset. (C) Electroluminescence properties, showing strong light emission in the wavelength range of 207–222   nm.

Adapted from Laleyan, D.A., Mengle, K., Zhao, S., Wang, Y., Kioupakis, E., Mi, Z. 2018. Opt. Express 26, 23031.

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