Engineering light absorption in semiconductor nanowires devices

Engineering light absorption in semiconductor nanowires devices

(Parte 1 de 2)

Engineering light absorption in semiconductor nanowire devices

Linyou Cao1, Justin S. White1, Joon-Shik Park1,2, Jon A. Schuller1, Bruce M. Clemens1 and Mark L. Brongersma1*

The use of quantum and photon confinement has enabled a true revolution in the development of high-performance semiconductor materials and devices1–3. Harnessing these powerful physical effects relies on an ability to design and fashion structures at length scales comparable to the wavelength of electrons (∼1nm) or photons (∼1µm). Unfortunately, many practical optoelectronic devices exhibit intermediate sizes4,5 where resonant enhancement effects seem to be insignificant. Here, we show that leaky-mode resonances, which can gently confine light within subwavelength, high-refractive-index semiconductor nanostructures, are ideally suited to enhance and spectrally engineer light absorption in this important size regime. This is illustrated with a series of individual germanium nanowire photodetectors. This notion, together with the ever-increasing control over nanostructure synthesis opens up tremendous opportunities for the realization of a wide range of high-performance,nanowire-basedoptoelectronicdevices,including solar cells6–8, photodetectors9–13, optical modulators14 and light sources14,15.

Whereas dielectric and metallic cavities both offer strong light confinement, their distinct materials properties translate into markedly different behaviour and applications. Metallic nanostructures have recently gained significant attention owing to their unparalleled ability to concentrate light into deep-subwavelength volumes16,17. This property is derived from the unique optical behaviour of metals that enables collective electron excitations, known as surface plasmons18. Many exciting plasmonics concepts have emerged, but their application is limited in extent owing to the lossy nature of metals; heat is always generated when light is manipulated by them. In contrast, high-confinement dielectric resonators offer low optical losses but their size is limited to wavelength-scale or larger dimensions by the fundamental laws of diffraction. Interestingly, strong optical resonance effects have been observed in the elastic scattering19, extinction20, light emission21 and Raman22 measurementsondeep-subwavelengthdielectricspheresandnanowires near natural frequencies of oscillation. These experiments have primarily been far-field measurements, in which the illumination source and detector are located at a substantial distance from the object under study. Here, we point out the possibility to engineer resonant field enhancements inside semiconductor nanowires to tune their spectral absorption features for device applications. We also use the framework of leaky-mode resonances (LMRs) that was originally developed for micrometre-scale resonators to provide an intuitive vantage point from which to understand and engineer these resonant effects in nanoscale structures. To illustrate these concepts and their importance, we directly probe the field enhancements in a set of individual germanium nanowires through

1Geballe Laboratory of Advanced Materials, Stanford University, California 94305, USA, 2Nanomechatronics Research Center, Korea Electronics Technology Institute, Gyeonggi, 463-816, Republic of Korea. *e-mail:brongersma@stanford.edu.

1 µm

Wavelength (nm)

Wavelength (nm) Absorption efficiency (a.u.)

Absorption coefficient (cm c ab

Figure 1 | Measurement of light absorption in individual germanium nanowire devices. a, Schematic illustration of the germanium nanowire device used for photocurrent measurements. b, Scanning electron microscopy image of a 25-nm-radius germanium nanowire device.

c, Measured spectra of absorption efficiency Qabs for unpolarized light taken from individual germanium nanowires with radii of 10nm (black),

25nm (blue) and 110nm (red). The spectra are normalized to their maximum absorption efficiency to highlight the tuneability of the nanowire absorption properties. Inset: Absorption coefficient of bulk germanium as a function of wavelength obtained from ref. 29.

a measurement of their photocurrent response. Such nanowires can be viewed as ultimately scaled-down versions of microcylinder resonators that can trap light in circulating orbits by multiple total internal reflections from the periphery. Owing to their small size, the resonant modes in nanowires become leaky and interact more effectively with the outside world, carrying out a valuable antenna function. The concept of using LMRs of semiconductor structures is extremely general and can be taken advantage of in the design

LETTERS NATUREMATERIALSDOI:10.1038/NMAT2477 of a wide range of nanoscale semiconductor materials and devices, including metamaterials20, nanowire-based light emitters23,24, photovoltaic cells6–8, photodetectors9–13 and even lasers15.

The description of highly confined modes in optical fibres and microscale dielectric resonators is based on classical waveguide theory. By solving Maxwell’s equations with the appropriate boundary conditions25, it follows that excitation of leaky modes occurs in an infinitely long dielectric cylinder of radius a when the following condition is satisfied:

γHm(γa) where γ(κ) and n0(n) are the transverse wave vector and refractive index outside (inside) the cylinder, β and k0 are the wave vectors along the cylindrical axis and in free space, Jm and Hm are the mth-order Bessel function of the first kind and Hankel function

of the first kind and the prime denotes differentiation with respect to related arguments. For normal-incidence illumination

(β = 0) of a cylinder in vacuum (n0 = 1), equation (1) can be split into conditions for purely transverse-magnetic modes with the magnetic fields in the plane normal to the nanowire axis

that nanowires tend to support a limited number of transverseelectric and transverse-magnetic LMRs, which increase in number as their radius is increased. In the following experiments, we will investigate the optical excitation of these modes in individual semiconductornanowiresundervariousexperimentalconditions.

For this study, Ge nanowires of various diameters were grown using a Au-catalysed chemical vapour deposition process with no intentional doping26. These wires were dispersed onto a 300-nm-thick thermally grown oxide on a Si substrate. Approximately 200-nm-thick Ti/Al electrical contacts were patterned by electron-beam lithography and lift-off, as shown in Fig. 1a,b. Spectral photocurrent measurements were carried out with a whitelight supercontinuum source coupled to a monochromator. To compare the photoresponse spectra with theory and simulations, they are plotted in terms of the absorption efficiency, Qabs, defined as the ratio of the absorption cross-section and the physical cross- section of the wire27. Experimentally, this quantity is obtained from the ratio of the external, ηE, and internal quantum efficiencies, ηI. In our data analysis, it was assumed that ηI is wavelength independent, making Qabs directly proportional to the extracted photocurrent; this is a commonly used assumption for photodetectors28 in which the thermalization of photoexcited carriers is much faster than the relevant carrier recombination times. Figure 1c shows spectral measurements of Qabs for three different nanowire radii of 10nm (black), 25nm (blue) and 110nm (red) taken under randomly polarized, normal-incidence illumination. In stark contrast to the relatively featureless spectrum of the absorption efficiency of bulk Ge (Fig. 1c, inset), the nanowire spectra show a number of distinct peaks29. It is clear that the choice of nanowire diameter greatly affectsthespectrumandthelargeabsorptionenhancementsatsome wavelengths are suggestive of resonant behaviour. To investigate whether the peaks could be arising from the excitation of LMRs, we have taken Qabs spectra from a 110-nmradius wire under transverse-electric (red curve) and transverse- magnetic (blue curve) illumination and correlated the observed absorption peak locations to the occurrence of specific LMRs (Fig. 2). Both spectra exhibit peaks in the same locations, although

Absorption efficiency

Ek H k

Figure 2 | Correlation of the absorption peaks in germanium nanowires with LMR. a, Absorption efficiency, Qabs, spectra of a 110-nm-radius germanium nanowire taken using linearly polarized transverse-electric

(TE; red) or transverse-magnetic (TM; blue) light. The spectra are norma- lized to an internal quantum efficiency ηI of 4 assumed to get the best fit between the calculated and experimental results (see Fig. 3). The inset illustrates the illumination geometry for the transverse-electric (electric field of the light polarized perpendicular to the axis of the wire) and transverse-magnetic (electric field of the light polarized parallel to the axis of the wire) polarizations. The red/blue lines at the top indicate locations of all of the LMRs of the 110-nm-radius germanium nanowire in this spectral region. Only some of the modes are labelled for visualization convenience, and the detailed mode labelling is given in Supplementary Table S1. b, The configuration of the electric field intensity for typical transverse-magnetic leaky modes. The blue circle refers to the nanowire/air interface.

substantial quantitative differences between the spectra occur on the long-wavelength side of the spectrum. All LMR wavelengths were calculated numerically using the real part of the refractive index of germanium29. Each mode can be characterized by an azimuthal mode number, m, which indicates an effective number of wavelengths around the wire circumference and a radial order number, l, describing the number of radial field maxima within the cylinder. The modes can thus be termed as TMml or TEml. To assist the reader in visualizing these modes, the field configurations for the lowest-order transverse-magnetic modes are shown in Fig. 2b. (The transverse-electric modes are essentially identical with the electric and magnetic fields interchanged.) Although the index of refraction of nanowires tends to be high, the relevant mode numbers are small owing to the subwavelength size of the wires. The locations of the different resonances are indicated with ticks at the top of Fig. 2a. It is clear that resonance peaks show up near the ticks, whereas the dips in the spectrum occur near regions withoutticks.Alargenumberofexact(forexample,TE01 andTM11) and approximate degeneracies (for example, TE11 and TM21) are observed, explaining the similarity of the transverse-electric and transverse-magnetic spectra. The quantitative difference between the spectra near 1,250nm can largely be attributed to the two-fold degeneracy of the TM11 mode versus a non-degenerate TE01 mode (see Supplementary Fig. S2).

To further confirm the critical importance of LMRs to the photocurrent spectra, we show a quantitative comparison

NATUREMATERIALSDOI:10.1038/NMAT2477 LETTERS

Wavelength (nm)

Calculated Experimental

Wavelength (nm)

Qabs

Radius (nm)

Absorption efficiency 0.5

Figure 3 | Graphs illustrating the tuneability of the absorption efficiency, Qabs, in germanium nanowires. a, Experimental and calculated Qabs spectra for nanowire radii of (1) 110nm, (2) 25nm and (3) 10nm. The blueshift in the peak near 1,250nm in the experimental result for the 110-nm-radius nanowire can be ascribed to substrate effects, as shown in numerical simulations provided in the Supplementary Information. The internal quantum efficiency ηI assumed to get the best fit between the calculated and experimental results for these nanowires is 15 (10nm), 8 (25nm) and 4 (110nm). The internal quantum efficiency being bigger than unity may be ascribed to internal photocurrent gain as reported in ref. 12. b, Two-dimensional plot of calculated absorption efficiency Qabs as a function of wavelength and radius of the nanowire. The dashed grey lines represent the calculated results shown in a.

between experimental and calculated Qabs spectra for three different nanowire diameters illuminated with randomly polarized light (Fig. 3a,b). The calculations were carried out using the well-established Lorenz–Mie theory for light scattering27, which quantifies the coupling strength of free-space light waves to LMRs. Very good qualitative agreement between the spectra is found for all wire sizes. Numerical simulations show that the blueshifted experimental peak near 1,250nm for the 110-nm-radius nanowire can be ascribed to substrate effects (see Supplementary Information). Substrate effects are more noticeable in this peak as it is related to lower-order resonant modes (TM11 and TE01) that extend further outofthenanowiresandintotheunderlyingsubstrate(seeFig. 2b).

Figure 3b shows the extensive wavelength tuneability of the nanowire absorption in two-dimensional colour maps of Qabs as a function of the illumination wavelength and nanowire radius.

For larger radii, an increasing number of peaks are observed in the Qabs spectra. The absorption maxima tend to shift linearly with increasing radius as the resonances depend on the size parameters ka or nka (see equation (1)). It is worth noting that the experimentally observed peak at 600nm in the 10-nm-radius nanowire can be shifted substantially to about 800nm for the 25-nm-radius nanowire. It also clearly shows that the resonant peaks at similar wavelengths in different nanowires may originate from completely different resonances. The peaks near 800nm in the spectra for the 25nm and 110nm wires provide an excellent example of this. Nanotechnology has provided us with an ever-increasing control over nanostructure dimensions and this control can now be used to engineer desired absorption spectra for specific applications.

The concept of LMRs provides valuable intuition for a number of design parameters for semiconductor nanowire-based photonic devices. For example, in many devices it will be important to understand the dependence of the absorption spectra on the polarization24,29 and illumination angle30. From the point of view of LMRs, one would predict that wires of a sufficiently small radius are able to support only the fundamental TM01 LMR (nka ∼ 0.8, for 633nm light, a ∼ 14nm). These wires are thus expected to show very strong polarization dependence. Owing to the heavy transverse-magnetic/transverse-electric degeneracy in larger wires, the polarization dependence sharply drops with increasing size. Measurements and calculation of the absorption ratio for transverse-magnetic and transverse-electric illumination fordifferentdiameternanowiresindeedconfirmthis(Fig. 4).

The general LMRs equation (equation (1)) suggests that a change in the illumination angle, θ, can cause a change in the absorption spectrum as the relevant wave vectors are angle for oblique incidence, hybrid HE and EH leaky modes will be excited instead of pure transverse-electric or transverse-magnetic modes. In other words, the change of the incident angle should carefully be considered in engineering desired absorption features for a device. Simple design rules can readily be derived from equation (1). For example, it can be shown that the size parameter for the fundamental TM01 mode resonance approximately scales with illumination angle as 1/sinθ (see Supplementary Information for a detailed derivation). This can be used to enable marked shifts in the absorption spectrum. Alternatively, device designs that do not take angle-dependent effects into account can result in serious device underperformance. Figure 5 shows the expected large angle dependence for a 25-nm-radius wire that supports only the TM01 LMR. We also see that the absorption sharply drops when the incident angle changes to 20◦, where the wire is effectively too small

LETTERS NATUREMATERIALSDOI:10.1038/NMAT2477

Radius (nm)

TM/TE absorption ratio Angle (°)

Normalized photocurrent

Figure 4 | Polarization dependence of the absorption efficiency, Qabs, and its dependence on nanowire diameter. Theoretical calculations (black solid line) and experimental measurements (red symbols; dashed line serves as a guide to the eye) on the ratio of the absorption efficiencies for transverse-magnetic- and transverse-electric-polarized 633nm light. Inset: Photocurrent of a 25-nm-radius nanowire for 633nm light (red dots) as a function of the angle θ between the electric field polarization and the nanowire axis; the data are normalized to the measurement for transverse-electric-polarized incidence.

Wavelength (nm) Absorption efficiency

Figure 5 | Dependence of the absorption efficiency, Qabs, on incident angle. Measured absorption efficiency spectra taken from the

25-nm-radius Ge nanowire using randomly polarized light with an incident angle of 90◦ (red), 40◦ (pink) and 20◦ (blue). The internal quantum efficiency ηI assumed is 5, identical to what is used in Fig. 3a.

resonant excitation of the TM01 LMR. We have demonstrated the use of LMR-induced field enha- ncements inside nanostructures to spectrally tune and enhance fundamental absorption properties. This work shows that light absorption in nanowire devices is not just a function of the intrinsic optical materials properties, but also can be engineered through control over the size, geometry and orientation of the nanostructure. The concept of using LMRs of semiconductor structures is extremely general and can be applied to engineer absorption spectra for a wide variety of semiconductor materials and object geometries. Key applications that can directly benefit from the observed absorption enhancements are nanowire-based solar cells and photodetectors. Whereas individual and multi-wire solar cells have recently been shown to be capable of efficiently harvesting solar radiation energy6–8, it remains a formidable challenge to attain high energy conversion efficiencies. The LMR framework provides guidance with respect to the desired size and orientation of the nanowires to enhance and better match absorption features to the solar spectrum. The reverse process of controlling fundamental emission properties in subwavelength optical cavities is also rapidly gaining importance out of a desire to generate single-mode nanolasers23. LMRs may enable new ways to engineer and realize such cavities11. For this reason, LMRs provide an exciting new pathway and general guidance towards the realization of novel high-performance nanostructured devices, including solar cells, photodetectors, sensors, modulators, resonators, light sources and lasers.

Methods

Germanium nanowires were grown using a gold-catalysed chemical vapour deposition process without any intentional doping. In a typical preparation, Au colloids with specified diameters as in the text (Ted Pella) were cast on poly-l-lysine-functionalized Si(100) substrates with native oxide and were exposed to flowing precursor of 10% GeH in Ar, 50s.c.c.m., at a temperature of 280 C under 30torr for 15min. The nanowires were then transferred from the substrate into an isopropanol solution by means of sonication and finally dispersed onto Si substrates with 300-nm-thick thermally grown silicon oxides. The nanowires were electrically contacted by Ti/Al (50nm/150nm) contacts fabricated using standard electron-beam lithography, metal deposition and lift-off techniques. Room-temperature photocurrent measurements were carried out at different wavelengths using a supercontinuum white-light source (Fianium) coupled to a 0.25metre monochromator (Spectra Physics) with an average passband of around 1nm. Uniform illumination was carried out by generating a spot on the sample in excess of >5mm in area. The photocurrent measurements on the nanowires were carried out at different bias voltages and illumination powers to ensure operation in a linear regime. To obtain high-signal-to-noise ratio measurements, the illumination source was chopped and the photocurrent signal was measured using a source meter (Keithley) coupled to a lock-in amplifier (Stanford Research Systems).

(Parte 1 de 2)

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