Abstract

Scattering-type scanning near-field optical microscopy (SNOM) offers the possibility to analyze material properties like strain in crystals at the nanoscale. In this paper we introduce a SNOM setup employing a newly developed tunable broadband laser source with a covered spectral range from 9 µm to 16 µm. This setup allows for the first time optical analyses of the crystal structure of gallium nitride (GaN) at the nanometer scale by excitation of a near-field phonon resonance around 14.5 µm. On the example of an artificially induced stress field within a GaN wafer, we present a method for a 2D visualization of small deviations in the crystal structure, which allows for fast qualitative characterizations. Subsequently, the stress levels at chosen points were quantified by recording complex near-field spectra and correlating them with theoretical model calculations. Applied to the cross-section of a heteroepitaxially grown GaN wafer, we finally demonstrate the capability of our setup to analyze the relaxation of the crystal structure along the growth axis with a nanometer spatial resolution.

© 2014 Optical Society of America

1. Introduction

Near-field microscopy offers the possibility to gain insights into material composition [1–5] and material properties like crystal structures [6] and strain [7,8] as well as free carrier concentrations in semiconductors [9] at the nanoscale. In contrast to aperture-SNOM [1], scattering-SNOM offers a better wavelength-independent lateral resolution [10] especially in the mid-infrared spectral range where many materials show characteristic vibrational bands such as polymers [2,11,12], or optical phonon bands (crystal lattice vibration) like in SiC [6,13,14], AlN and GaN [15]. In far-field spectroscopy, polar crystals like SiC or GaN possess a broad “reststrahlen” band of high reflectivity where the real part ε1 of their dielectric function is below zero. In the near-field response measured with SNOM, however, these materials exhibit a sharp spectral feature, a so-called “phonon resonance” [13,16] for values of ε1 between −1 and −3 (and small imaginary part ε2 for low damping). In the spectral range of the phonon resonance, the near-field amplitude signal of the resonant sample exceeds the one from e.g. gold by an order of magnitude. Typically, the peak in near-field spectra is found close to the longitudinal optical (LO) phonon frequency ωLO within the “reststrahlen” reflectivity band of far-field IR spectra [13]. The phonon resonance is very sensitive to changes in the crystal lattice, e.g. due to stress, defects or different polytypes, and therefore ideally suited to monitor these as was already demonstrated for SiC [6–8,13].

GaN and GaN alloys have a wide application range in high-frequency and high-power electronics, e.g. in high-electron mobility transistors (HEMT). Other examples for applications are LEDs emitting from the UV to visible spectral range. In these devices, there are different nitrides grown heteroepitaxially on top of one another or on substrate materials like SiC or sapphire [17]. This leads to stress in the crystal structures causing defects during growth or on relaxation, changing the polarization and altering properties of the devices at the nanoscale [18–20], e.g. in terms of charge carrier mobilities [18] and light emission of LEDs [19]. Therefore, it is highly desirable to examine the stress levels with nanometer resolution.

With a scattering-type scanning near-field optical microscope, infrared (IR) spectra have first been recorded by repeatedly scanning across the sample area of interest at different wavelengths, when stepwise-tunable narrow-band laser systems like CO- or CO2-lasers are used [2,4,7]. This measurement procedure can be time-consuming and spectra can be easily affected by changing experimental conditions like tip degradation during scanning [4]. For fastly tunable narrow-band lasers like quantum cascade lasers (QCLs) also used for SNOM [21,22], it is possible to circumvent these issues by automatically changing the wavelength while measuring at a single position on the sample [21]. However, the use of QCLs is limited in terms of the accessible spectral range. To overcome this problem, there have also been broadband laser systems [see Fig. 1(a)] employed to record infrared spectra within one single measurement [12,16,23,24] in an expanded spectral range. While thermal sources have a comparably low spectral power density that only allow for examing of resonant samples [24], there are broadband laser sources with spectral widths of up to 700 cm−1 emitting up to 250 µW with a long-range wavelength-limit around 14.3 µm [12,16] that were employed to examine polymers that exhibit a low signal level [12]. SNOM measurements were also performed with a tunable broadband laser with a laser power of 1 mW, a spectral width of 80 cm−1 and a wavelength of up to 11 µm [23].

 figure: Fig. 1

Fig. 1 Broadband SNOM. (a) Spectral range of different laser systems successfully used for SNOM experiments. See literature [12,16,23] for further details; part of the data were taken from the web pages of the companies Edinburgh Instruments, Block Engineering and Daylight Solutions. (b) Calculated SNOM amplitude spectra for various phonon resonant materials normalized on gold. (c) Examples of laser spectra of the ILT broadband laser used in this paper. The central wavelength is continuously tunable between 9 µm and 16 µm, with spectral widths (FWHM) from approx. 40 cm−1 to 130 cm−1. Note that these widths are matched very well to those of the phonon-resonances. (d) Experimental setup of the broadband SNOM.

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Since the application range of IR SNOM is restricted by the limited spectral range of the laser sources available, the investigation of technological relevant GaN samples are not reported up to now. Figure 1(a) shows an overview of some lasers. It is restricted to table-top setups because they are easier accessible than large-scale facilities, so free-electron lasers or synchrotrons also employed for SNOM are not included [25–27]. The new tunable broadband laser [28] employed in the setup and presented in this paper extends the spectral range for SNOM measurements in a table-top setup to higher wavelengths of around 17 µm with laser powers in the milliwatt range and spectral width around 100 cm−1, also including the GaN phonon resonance. Other phonon resonant materials like AlN, SiC, sapphire and SiO2 are also covered. Their calculated near-field spectra, normalized to gold, are presented in Fig. 1(b). The calculations were performed according to the finite dipole model [29,30] and literature values for the dielectric function (SiO2 [16], SiC [30], GaN and AlN [31], sapphire [32]). The broadband laser has a high spectral power density and the spectral width perfectly matches the materials of interest, allowing for 2D imaging by chosing an appropriate mirror position to visualize even small changes in the spectra. This is a time-saving method to record maps of differently stressed areas on a sample compared to recording a full spectrum at every single measurement point.

2. Experimental setup

The SNOM setup consists of a commercial scattering-SNOM and a newly developed IR broadband system.

The laser system used for our SNOM measurements was developed by the Fraunhofer ILT [28]. It consists of a commercially available ps-laser as the pump source and two subsequent nonlinear converter steps to cover the mid-IR range. The peak wavelength is continuously tunable from 9 µm to 16 µm with bandwidths of some tens to more than hundred wavenumbers [see Fig. 1(c)]. A stabilized beam path allows for fast wavelength tuning within milliseconds without loss of the beam alignment. At a repetition rate of 20 MHz and a pulse duration of 10 ps, the system provides an average power of up to 10 mW. Compared to other broadband laser systems already successfully used for SNOM measurements, the average laser power is up to one order of magnitude higher than values stated in literature [12,16,23,24]. The laser parameters allow for the first time near-field analyses of GaN in the mid-IR range with a table-top setup.

The scattering-type scanning near-field optical microscope (NeaSNOM from Neaspec) is based on an atomic force microscope (AFM). The optical setup within the SNOM is designed as a Michelson interferometer [Fig. 1(d)]. The incoming laser light is first split into two equal beams by a ZnSe window. One of these beams is focused on the tip-sample region by an off-axis parabolic mirror. The same parabolic mirror is used to collect the backscattered laser light. The second beam is sent to a reference beam path with a moveable end mirror. Both beams are recombined and detected by a liquid nitrogen cooled MCT (Mercury-Cadmium-Telluride) detector (further details in Appendix 7.1).

For spectral analysis, the position of the sample is kept constant, while the reference mirror is continuously moved to record interferograms. The spectral information is then extracted by complex Fourier transformation. As in conventional FTIR spectroscopy, the spectra are finally normalized to a reference spectrum (e.g. gold) to obtain near-field spectra, independent of the laser beam parameters, optical components and environmental influences. From these spectra, information about optical properties, stress in crystal structures or charge carriers can be deduced [7,8,11–13].

In our setup, the spectral resolution is up to 3.3 cm−1, as given by the full available path length of the end mirror in the reference arm of 1.5 mm, which corresponds to an optical path difference of up to 3 mm between the two interferometer arms. In comparison to FTIR microscopes that are diffraction-limited in lateral resolution, the spatial resolution of the SNOM is wavelength-independent and reaches down to a few 10 nm [10,12], only depending on the AFM tips used. The main advantage of using broadband lasers for SNOM is the possibility to record near-field spectra within a few minutes [12]. For recording 2D images, the AFM tip is scanned across the surface, while the position of the reference mirror is kept constant. Thus, both the sample topography and its optical properties are recorded simultaneously. As the spectral bandwidth of the broadband laser matches the width of the phonon resonances and the laser power is concentrated on the spectral range of interest, even small differences in the optical response of the sample are visible for an appropriate mirror position in the reference arm.

3. Stress in gallium nitride

The broadband SNOM setup is employed to analyze locally induced stress fields in a GaN layer sample. The layer system consists of a sapphire wafer, an intermediate AlN layer of 300 nm thickness and a GaN top layer of 2.5 µm thickness, see Fig. 2(c), grown by MOCVD (metal-organic chemical vapor deposition). The GaN has a wurtzite crystal structure and the c-axis is oriented perpendicularly to the surface. Details about the growth process can be found in Appendix 7.2. To prove the sensitivity of the broadband SNOM to local stress fields, we first induced strong local stress fields by indentations. According to literature, an area of compressively stressed crystal lattice has been found in SNOM images next to the edges of triangular shaped indents in a SiC crystal [7,8]. As both SiC and GaN are anisotropic, polar and phonon-resonant crystals, a similar behavior is expected. To match the phonon resonance of GaN, the laser system is set to a center wavelength of roughly 14.5 µm with a FWHM (full width at half maximum) of about 1.5 µm and an average power output of approx. 300 µW.

 figure: Fig. 2

Fig. 2 Indent in GaN layer. (a) Topography and (b) interferometrically recorded 2D optical near-field image (second harmonic amplitude) of the indent. See text and Fig. 3 for more details about this measurement method. The shape of the indent is clearly visible. It is surrounded by brighter and darker areas denoting different stress levels in the crystal structure. (c) Sketch of the sample. (d) Near-field spectra of GaN, normalized to gold, measured at different positions on the sample: A and B are close to one of the indents as marked in 2(b). Position C is further away from the indent where the sample is expected to be unaffected by the indentation. The spectra are evaluated by a fit which is shown as solid line.

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Figure 2(a) shows the topography of the indent. Its original depth was approx. 500 nm which corresponds to an indentation with around 90 mN. These parameters were chosen arbitrarily to induce stress patters in GaN. The topography is purely flat outside the indent. Figure 2(b) shows the corresponding optical amplitude 2D image. It reveals a hexagonal pattern of brighter and darker areas around the indent that can be explained by different stress levels in the crystal structure. For this 2D imaging technique, the end mirror in the reference arm is slightly offset from the white-light position. By this certain spectral components can be “emphasized” by a reduced or enhanced interferometric amplification depending on the position of the end mirror. For the white-light position where all spectral components can interfere to the maximum, the 2D image shows no contrast and the hexagonal stress pattern remains hidden. Details of this method can be found further below in part 4. Please note that the optical contrast in Fig. 2(b) is a relative one between different areas on GaN and that there is no normalization on a reference material included. To quantify the differences in the crystal structure, spectra are recorded at two positions close to one indent [labeled A and B in Fig. 2(b), 2(d)] and further away from them for comparison [labeled C, outside the area shown in Fig. 2(b)]. Figure 2(d) shows the second harmonic of the optical amplitude of the GaN spectra normalized to spectra taken on gold. The measurement time on GaN was roughly 10 min per spectrum.

To evaluate the GaN spectra, a fit procedure is employed. It is assumed that the spectral shifts solely stem from different stress levels in the crystal structure. The fit procedure is based on the finite dipole model [29] and the following Eq. (1) for the dielectric function.

ε(ω)=ε+ε(ωLO2ωTO2)ωTO2ω2iωΓ+ωp2ω2iωγ

The transversal optical phonon frequency ωTO is set to 560 cm−1 and the high-frequency dielectric constant ε¥ to 5.35 cm−1 [33]. The longitudinal optical phonon frequency ωLO and the phonon resonance damping parameter Γ are determined with the fit. The Drude term contains the damping parameter γ of the plasmon resonance, which is set as 50 cm−1, and the plasma frequency ωp, calculated with ne set to 1017 cm−3 for unintentionally doped GaN [33]. In this range, SNOM spectra are not sensitive to small changes in doping concentration, whereby effects for example by piezoelectric polarization can be neglected in a first approximation. The anisotropy is neglected in the dielectric function and the fit procedure because of the lack of a suited near-field model. We evaluate our results under the assumption that the changes of the fitted parameters (i.e. ωLO and Γ) relative to one another are not significantly changed by this simplification. This assumption is supported by small changes in the LO splitting for biaxial compressive stress, compared with the larger changes of the frequencies of the two LO modes [31].

The fits [solid lines in Fig. 2(d)] match well with the different peak positions and spectral widths of the resonances. The phonon frequencies determined from the fit are 740 cm−1 for position A, 742.5 cm−1 for B and 738.7 cm−1 for C. The spectral shift of ωLO is found to be approx. 2.5 cm−1 (for A and B). It is interpreted as result of different stress levels around the indent. As a rough estimate, the difference in stress levels between these two measurement points (i.e. A and B) is calculated with the conversion factors for the A1(LO) phonon modes of Raman measurements given in literature. For biaxial stress (perpendicular to the c-axis of the crystal) the factor is 0.8 cm−1/GPa [15,34]. This leads to estimated stress levels of about 3.1 GPa. For the measurement positions A and C, the latter one not influenced by the indent, results an even smaller value of approx. 1.6 GPa. Beside the different stress levels at the three measurement positions which are mainly given by the spectral peak position, the spectral shape changes too as it is mainly given by the phonon damping factor Γ in Eq. (1). At position C the damping is comparably low with 11.8 cm−1. It increases to 12.6 cm−1 for A and is highest at B with 14.2 cm−1. As for the spectral shift of ωLO, the difference in Γ from A to C is twice as large as from A to B. While the reason for a spectral shift is clearly related to the crystal structure and can be quantified with a conversion factor well-known from Raman spectroscopy [15,34], the change of the spectral shape can up to now only be interpreted qualitatively. It is known, that even non-resolvable defects lead to a damping of the phonon resonance, which was demonstrated for ion implanted SiC [14]. Based on this, we interpret our data as an effect of different defect densities. For a more in-depth analysis, a direct correlation for example with TEM measurements would be needed. According to literature data [7], a blue shift of the spectra indicates compressive stress in the crystal lattice. This fits to literature parameters for different stress levels in GaN crystals [31]. The fit procedure employed here allows for monitoring and quantifying very small changes in the spectra, even below the spectral resolution of the SNOM of 3.3 cm−1 that would correspond to approx. 4 GPa. This means that the sensitivity to differences in stress in the crystal structure is significantly improved and not restricted by the physical spectral resolution of the SNOM. The limit depends on the quality of the fit which itself depends on the signal-to-noise ratio. So the evaluation procedure for the spectra presented here has the potential to even differentiate smaller changes in the stress levels of the crystal structure.

4. Interferometric 2D imaging with a broadband laser source

Additional to the spectra, the different stress levels can be visualized by an interferometric 2D imaging technique that was already employed in Fig. 2(b). This technique is described in the following, including differences to the use of monochromatic lasers often employed for SNOM measurements.

When using monochromatic lasers, a common technique for near-field imaging is the pseudo-heterodyne interferometric setup [35]. This technique allows for the detection and separation of both amplitude and phase. For broadband laser sources this technique in general is not applicable, because of the wide spectral range covered simultaneously. The broadband laser employed here allows for circumventing this problem because its spectral bandwidth matches well with the spectral width of the phonon resonance under investigation.

For 2D imaging with a broadband source, the reference beam path is either blocked, which means that there is no interferometric enhancement of the signal [23], or kept constant at the white light position (WLP) [12,24]. At this position, the beam path lengths are equal for both signal and reference arm which gives a high signal due to constructive interference. In both cases, the signal is integrated over the whole spectral range. Both methods allow a clear separation between different kinds of materials [12,24] (e.g. silicon and polymer [12]) but no visualization of small spectral changes like stress fields as possible with narrow band lasers. If the local spectral differences are small compared to the spectral width of the broadband laser and the signal strength is similar, no contrasts in 2D images are visible.

To overcome this disadvantage, the position of the reference mirror is set outside the WLP but still within the coherence length of the laser pulse, as illustrated in Fig. 3. Outside the WLP, the magnitude of the interferometric amplification depends on the position of the reference mirror and the local optical properties of the sample. Local changes in the sample signal, for example caused by a small shift of the phonon resonance due to crystal stress, lead to a different signal at the detector and therefore to a visible contrast in the 2D images.

 figure: Fig. 3

Fig. 3 2D imaging of stress in a GaN layer. (a) and (b) show the second harmonic amplitude of the interferograms that correspond to the spectra in Fig. 2(d) and to the positions marked in (c). The interferograms differ from one another which leads to an optical contrast between differently stressed crystal areas as illustrated with the black. (c)-(e) show the optical amplitudes (second harmonic) for different positions of the end mirror in the interferometer arm that are marked in 3(b) (dashed lines). The color scale is the same as in (e) for all three images. In (c) and (e), a hexagonal pattern is visible that reveals the differently strained areas on the sample.

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To illustrate this effect, the raw interferograms of the second harmonic of the amplitude signal recorded at the positions A and B [see Fig. 2] are plotted in Fig. 3(a), 3(b). Because of the small spectral difference induced by strain, the interferograms are slightly different from each other. While recording 2D images, those differences become visible as an optical contrast which is illustrated with the black curve in Fig. 3(a), 3(b). The second harmonic of the amplitude signal is presented in Fig. 3(c)-3(e). Depending on the mirror position chosen for the 2D images [marked in Fig. 3(b)], there is a hexagonal pattern visible in the optical image which allows for differentiating between differently strained areas. This optical contrast can be weakened and also reversed by shifting the end mirror in the reference arm. The area around position B (where the sample exhibits stronger compressive stress) appears brighter, similar or darker compared to the area around position A. The same applies to similarly strained areas on the sample, respectively, as presented in Fig. 3(c)-3(e). The periodicity of this oscillation is equal to the wavelength λ. The contrast is reversed at λ/2. It should be noted, that the mirror position for best optical contrast is not equal to the one for maximum signals at both positions A and B. Therefore, this technique allows for visualization of even small spectral changes, but on the cost of total signal amplitude.

As described previously, this imaging technique using the broadband laser, whose spectral width matches with the width of the phonon-resonances, gives a quick qualitative overview about spectral changes within an area, which can now easily be analyzed in detail by recording spectra at single positions as described previously in part 3. All in all, this 2D imaging measurement technique further enhances the informative value of broadband SNOM.

5. Characterization of cross sections with SNOM

Apart from measuring different stress levels next to indents, the broadband SNOM can also be employed to characterize naturally occurring stress fields as they form in heteroepitaxy. This is demonstrated in the following by examining a cross section of an epitaxially grown layered semiconductor structure like the one imaged before (see Appendix 7.2).

To prepare the second sample, the layered sapphire/AlN/GaN structure, similar to Fig. 2(c), is separated into small pieces. One of them is embedded in between two glass slides and mechanically polished from the side (compared to the indent, the sample is rotated by 90°). The result is a cross section on which all three material systems are accessible with the SNOM tip [see Fig. 4(a) and Fig. 5(a)]. The topography of the cross-section is very flat as shown in Fig. 5(b). The sapphire is on the left hand side of the image, the slightly deeper line next to it is the AlN layer and further to the right the GaN layer. It is grown on top of the 300 nm thick AlN layer and has a thickness of 3 µm. As the lattice parameter a1 of AlN is smaller than that of GaN (a1 = 0.3112 nm for AlN compared to a2 = 0.3189 nm for GaN [36]), GaN is expected to exhibit compressive stress in the first part of the layer [37,38], as sketched in Fig. 4(b). The second harmonic amplitude of the optical image that was recorded simultaneously with the topography is displayed in Fig. 5(c). The average laser power was about 1 mW. The GaN layer is visible as brighter area in the middle of the image. Sapphire and especially AlN appear darker. In this case, the interferometric 2D imaging technique described previously is not employed because the optical contrast due to differences in strain are overlayed by illumination effects at the material boundaries.

 figure: Fig. 4

Fig. 4 (a) Sketch of the second sample. The cross section sample is tilted 90° compared to the indent sample. The spectra are taken on the GaN layer with different distances from the AlN layer. (b) illustrates schematically the lattice mismatch between GaN and AlN that leads to strain in the crystal lattice.

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 figure: Fig. 5

Fig. 5 Cross section of a layered sapphire/AlN/GaN structure. (a) Sketch of the sample structure. (b) Topography of the sample and (c) the corresponding second harmonic optical amplitude signal. The bright area next to GaN is from the covering. Across the GaN layer, several spectra are recorded that are shown in (d). The solid lines are fits to the data. (e) shows the relative differences in stress levels calculated from the shift in the LO phonon frequencies ωLO. Note that the value of 0 GPa at a GaN thickness of 0.6 µm is set arbitrarily. The damping constants Γ are plotted in (f).

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Figure 5(d) shows amplitude spectra recorded on the GaN layer at different distances from the AlN layer. Plotted is the second harmonic of the optical amplitude signal normalized to gold (data points) and a fit (solid line) that was calculated as described before. The spectra change in terms of peak position and amplitude. The spectra recorded within the first 200 nm are blue-shifted indicating stronger compressive stress [7,15]. The different amplitudes are attributed to both differences in the crystal structure and illumination effects on the sample. The latter one is expected to have a large effect as the indirect irradiation of the tip-sample system strongly depends on the reflection of the surrounding materials (the laser focus is diffraction limited and therefore several microns in diameter). For the cross section sample, the fit contains an additional scaling factor in the range of 0.3-0.4 to account for the lower indirect illumination due to the surrounding materials compared to a homogeneous GaN sample. As the GaN layer is only unintentionally doped, effects of free charge carriers are neglected in a first approximation as described before. Therefore, the spectra are interpreted as exclusively stress-dependent. From the calculated shifts of the LO phonon frequencies of the spectra, the relative difference in stress levels across the GaN layer is estimated as plotted in Fig. 5(e). The smallest value for ωLO obtained is set as zero level for relative stress. The shift of the other spectra are converted according to the same calibration factor of 0.8 cm−1/GPa [15,34] as used before. The first part of the GaN, which is closer to AlN, is stronger compressively stressed, whereas the middle part indicates less compressive stress compared to the spectrum recorded furthest away from AlN. The difference in stress found here amounts up to 5 GPa. Our results show comparable stress levels for thicker GaN layers. A more detailed analysis of the slight increase in stress is left for future correlation with TEM measurements. According to literature, the properties of heteroeptaxially grown GaN show a large variability [39–41]. Concerning changes in the stress levels in GaN layers with thicknesses in the micron range, the findings vary from showing saturation effects [37,42] to not showing saturation [38]. Monitoring stress in GaN by broadband SNOM via the phonon resonance is a complementary method to e.g. TEM for thinner samples and diffraction-limited Raman measurements. As SNOM has been successfully applied to monitor stress differences in SiC [7,9] and differences in the crystal structure of SiC [6], we expect our SNOM results to be consistent. SNOM can provide useful insights into the crystal structures of e.g. GaN, allowing for a further improvement in terms of tailoring the properties of the materials. Compared to literature, the differences in stress presented here are quite large. As the stress critically depends on the growth parameters, different GaN samples are expected to exhibit individual relative stress changes for the same GaN layer thickness [37–40,42]. Apart from the different stress levels along the cross section which are mainly given by the spectral peak position, the spectral shape changes as well. It is mainly given by the phonon damping factor Γ in Eq. (1) as described in part 3. The largest value of 9.2 cm−1 was found at the boundary to the AlN buffer layer, the lowest of 5.1 cm−1 near the surface [see Fig. 5(f)]. As already described in part 3, the spectral shift is clearly related to the crystal structure and can be interpreted quantitatively. The change of the spectral shape can up to now only be interpreted qualitatively. According to this, we interpret our data as an effect of different defect densities along the cross section which are highest close to the AlN buffer layer and by trend decreasing towards the surface. To prove this and to provide a quantitative description, a direct correlation for example with TEM measurements would be necessary which will be part of our future work.

All in all, SNOM allows for characterizing the crystal structure of the GaN layer with a lateral resolution of a few 10 nm in terms of stress and defects in the crystal structure at the same time. Commonly, TEM measurements are employed to monitor such defects [43], which includes the need for thin samples with extensive sample preparation not necessary for SNOM measurements. Additionally, SNOM does not require vacuum or a conductive surface and the measurements are non-destructive. Therefore, SNOM is ideally suited to monitor changes in the crystal structure of phonon resonant materials like GaN at the nanoscale. Defect densities and local stress influence the free carrier density and their mobility, so we expect SNOM measurements to provide valuable insights for the characterization and tailoring of material properties and devices.

6. Conclusions

In summary, we have introduced a broadband SNOM setup that for the first time allows for investigating the crystal structure of GaN in the mid-IR spectral range with a lateral resolution of a few 10 nm only. It is shown that different stress levels in GaN can be distinguished in the near-field spectra. The sensitivity to spectral changes is enhanced by employing a fit procedure to determine the LO phonon frequency for the spectra that allows for quantitative monitoring of stress differences, limited by the signal-to-noise ratio and the quality of the resulting fit. The application range of the broadband SNOM is widened by the interferometric 2D imaging that has the potential to show even small spectral shifts as optical contrast. With this measurement technique, the stress pattern surrounding an indent in a GaN layer is quickly mapped with one single 2D overview scan, instead of recording a spectrum at every single point. The 2D imaging opens up the possibility to combine the different advantages of sequential and broadband near-field microscopy with one broadband SNOM setup. Additionally to the stress fields around indents, a cross-section of a layered GaN/AlN/sapphire sample is examined. The sample is heteroepitaxially grown and therefore exhibits stress in the crystal lattice. With SNOM, the naturally occurring different stress levels throughout the GaN layer are determined from the shift of the LO phonon frequency to amount up to 5 GPa. At the same time, the damping of the resonance, which is due to defects in the crystal lattice, is evaluated from the fit of the spectra. Both the compressive stress and the damping are found to be largest within the first 200 nm of the GaN layer. Apart from pure GaN crystal structures it is expected to be feasible to examine GaN alloys like AlGaN, free carrier concentrations in GaN or differently doped sample areas [9]. This widens the application range of the broadband SNOM to the characterization of semiconductor devices like high-electron mobility transistors (HEMTs) or LEDs [3,18,19] as well as to the monitoring of the effects of growth conditions on defects, defect densities and crystal structures that influence the performance of the devices. Additionally, the quality of mesas [19] can be tested. For the future, SNOM even opens up the possibility to characterize buried layers of semiconductor devices. The spectral region covered by the broadband laser is not only interesting for semiconductor devices but also for antenna structures and nanophotonic applications further broadening the application range of the SNOM setup presented in this paper.

Appendix

A. Methods

For the SNOM measurements, standard Au-coated AFM tips (PPP-NCSTAu) from Nanosensors are used which are specified to have a radius of curvature below 50 nm. The tip quality was checked during the measurement series by repeating single scans and comparing the results. The MCT detector employed is a FTIR-16-0.10 detector from InfraRed Associates. For an efficient suppression of the far-field background of the optical signal, the AFM is operated in tapping mode. The tip oscillates with a frequency Ω close to its own resonance frequency leading to a modulation of the backscattered light. While the far-field background scales mostly linear with the tip-sample distance, the near-field signal shows a strong nonlinear dependency. By lock-in detection and demodulation at higher harmonics nΩ, n≥2, the remaining signal contains a nearly pure near-field signal, further details on the background suppression can be found in [35].

B. Sample preparation

Both samples were grown by Ada Wille, group Prof. Vescan, GaN-BET, RWTH Aachen. The samples were grown by metal organic vapor phase epitaxy (MOVPE) on 2” c-plane sapphire. Trimethylaluminium (TMAl), Trimethylgallium (TMGa) and ammonia were used as precursors for AlN and GaN, respectively. Hydrogen was used as carrier gas. The AlN growth was initiated by a low temperature AlN nucleation layer at 764°C, followed by a 300 nm AlN buffer grown at 1270°C. The GaN buffer was grown at 1060°C with a growth rate of approx. 1.6 µm/h. The samples were characterized by high resolution X-ray diffraction, which proves the assumed crystal orientation. The rocking curves of (0002) and (10-15) reflexes featured FWHM values between 241 arcsec and 281 arcsec indicating good crystal quality.

The cross-section was polished with a diamond deposited foil and afterwards with a silica suspension. Then it was cleaned with DI water and dried with nitrogen.

Acknowledgments

The authors are grateful to J. Caldwell (U.S. Naval Research Laboratory), the group of Prof. Dr. A. Vescan (GaN-BET RWTH Aachen), J. M. Hoffmann, B. Hauer (both group of T.T. at RWTH Aachen) and Dr. R. Noll (ILT) for valuable discussions. We thank A. Wille (GaN-BET RWTH Aachen) for the samples and J. Perne (IOT RWTH Aachen) for the indentation of the sample. We thank F. Huth (Neaspec GmbH and CIC nanoGUNE Consolider) for his help with the evaluation of SNOM spectra (script). This work was financially supported by Fraunhofer ATTRACT grant No 692220. The above results were acquired using facilities and devices funded by the Federal State of North-Rhine Westphalia and the European Union within the EFRE-program “Regionale Wettbewerbsfähigkeit und Beschäftigung 2007-2013” under grant number 290047022. T.T. acknowledges funding from the DFG under SFB917.

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2. T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004). [CrossRef]  

3. A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnology 21(23), 235702 (2010). [CrossRef]   [PubMed]  

4. M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006). [CrossRef]   [PubMed]  

5. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007). [CrossRef]   [PubMed]  

6. A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006). [CrossRef]   [PubMed]  

7. A. J. Huber, A. Ziegler, T. Köck, and R. Hillenbrand, “Infrared nanoscopy of strained semiconductors,” Nat. Nanotechnol. 4(3), 153–157 (2009). [CrossRef]   [PubMed]  

8. A. M. Gigler, A. J. Huber, M. Bauer, A. Ziegler, R. Hillenbrand, and R. W. Stark, “Nanoscale residual stress-field mappingaround nanoindents in SiCby IR s-SNOM and confocal Raman microscopy,” Opt. Express 17(25), 22351–22357 (2009). [CrossRef]   [PubMed]  

9. A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007). [CrossRef]  

10. T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003). [CrossRef]   [PubMed]  

11. J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012). [CrossRef]  

12. F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012). [CrossRef]   [PubMed]  

13. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002). [CrossRef]   [PubMed]  

14. N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004). [CrossRef]   [PubMed]  

15. M. Kuball, “Raman spectroscopy of GaN, AlGaN and AlN for process and growth monitoring/control,” Surf. Interface Anal. 31(10), 987–999 (2001). [CrossRef]  

16. S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011). [CrossRef]  

17. I. M. Watson, “Metal organic vapour phase epitaxy of AlN, GaN, InN and their alloys: A key chemical technology for advanced device applications,” Coord. Chem. Rev. 257(13-14), 2120–2141 (2013). [CrossRef]  

18. B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013). [CrossRef]  

19. J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy Jr, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006). [CrossRef]  

20. Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012). [CrossRef]   [PubMed]  

21. I. M. Craig, M. S. Taubman, A. S. Lea, M. C. Phillips, E. E. Josberger, and M. B. Raschke, “Infrared near-field spectroscopy of trace explosives using an external cavity quantum cascade laser,” Opt. Express 21(25), 30401–30414 (2013). [CrossRef]   [PubMed]  

22. Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011). [CrossRef]   [PubMed]  

23. X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012). [CrossRef]  

24. F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011). [CrossRef]   [PubMed]  

25. S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007). [CrossRef]  

26. S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008). [CrossRef]   [PubMed]  

27. P. Hermann, A. Hoehl, P. Patoka, F. Huth, E. Rühl, and G. Ulm, “Near-field imaging and nano-Fourier-transform infrared spectroscopy using broadband synchrotron radiation,” Opt. Express 21(3), 2913–2919 (2013). [CrossRef]   [PubMed]  

28. J. Wueppen, B. Jungbluth, T. Taubner, and P. Loosen, “Ultrafast tunable mid IR source,” in Proceedings of IEEE IRMMW-THz (Houston, TX, 2011).

29. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007). [CrossRef]   [PubMed]  

30. N. Ocelic, “Quantitative near-field phonon-polariton spectroscopy,” Dissertation, TU München, 2007.

31. J. M. Wagner and F. Bechstedt, “Properties of strained wurtzite GaN and AlN: Ab initio studies,” Phys. Rev. B 66(11), 115202 (2002). [CrossRef]  

32. G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004). [CrossRef]  

33. A. S. Barker Jr and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973). [CrossRef]  

34. F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996). [CrossRef]  

35. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006). [CrossRef]  

36. I. Vurgaftman and J. R. Meyer, “Band paramters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003). [CrossRef]  

37. C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996). [CrossRef]  

38. T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995). [CrossRef]  

39. X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010). [CrossRef]  

40. T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001). [CrossRef]  

41. J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010). [CrossRef]  

42. R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999). [CrossRef]  

43. S. Y. Huang and J. R. Yang, “A transmission electron microscopy observation of dislocations in GaN grown on (0001) sapphire by metal organic chemical vapor deposition,” Jpn. J. Appl. Phys. 47(10), 7998–8002 (2008). [CrossRef]  

References

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  1. F. Keilmann and R. Hillenbrand, “Near-field nanoscopy by elastic light scattering from a tip,” in A. Zayats and D. Richards, eds., Nano-Optics and Near-Field Optical Microscopy (Artech House, 2009), Chap. 11, pp. 235–265.
  2. T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
    [Crossref]
  3. A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnology 21(23), 235702 (2010).
    [Crossref] [PubMed]
  4. M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
    [Crossref] [PubMed]
  5. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007).
    [Crossref] [PubMed]
  6. A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006).
    [Crossref] [PubMed]
  7. A. J. Huber, A. Ziegler, T. Köck, and R. Hillenbrand, “Infrared nanoscopy of strained semiconductors,” Nat. Nanotechnol. 4(3), 153–157 (2009).
    [Crossref] [PubMed]
  8. A. M. Gigler, A. J. Huber, M. Bauer, A. Ziegler, R. Hillenbrand, and R. W. Stark, “Nanoscale residual stress-field mappingaround nanoindents in SiCby IR s-SNOM and confocal Raman microscopy,” Opt. Express 17(25), 22351–22357 (2009).
    [Crossref] [PubMed]
  9. A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
    [Crossref]
  10. T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
    [Crossref] [PubMed]
  11. J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012).
    [Crossref]
  12. F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
    [Crossref] [PubMed]
  13. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
    [Crossref] [PubMed]
  14. N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
    [Crossref] [PubMed]
  15. M. Kuball, “Raman spectroscopy of GaN, AlGaN and AlN for process and growth monitoring/control,” Surf. Interface Anal. 31(10), 987–999 (2001).
    [Crossref]
  16. S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
    [Crossref]
  17. I. M. Watson, “Metal organic vapour phase epitaxy of AlN, GaN, InN and their alloys: A key chemical technology for advanced device applications,” Coord. Chem. Rev. 257(13-14), 2120–2141 (2013).
    [Crossref]
  18. B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
    [Crossref]
  19. J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
    [Crossref]
  20. Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
    [Crossref] [PubMed]
  21. I. M. Craig, M. S. Taubman, A. S. Lea, M. C. Phillips, E. E. Josberger, and M. B. Raschke, “Infrared near-field spectroscopy of trace explosives using an external cavity quantum cascade laser,” Opt. Express 21(25), 30401–30414 (2013).
    [Crossref] [PubMed]
  22. Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
    [Crossref] [PubMed]
  23. X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012).
    [Crossref]
  24. F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
    [Crossref] [PubMed]
  25. S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
    [Crossref]
  26. S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
    [Crossref] [PubMed]
  27. P. Hermann, A. Hoehl, P. Patoka, F. Huth, E. Rühl, and G. Ulm, “Near-field imaging and nano-Fourier-transform infrared spectroscopy using broadband synchrotron radiation,” Opt. Express 21(3), 2913–2919 (2013).
    [Crossref] [PubMed]
  28. J. Wueppen, B. Jungbluth, T. Taubner, and P. Loosen, “Ultrafast tunable mid IR source,” in Proceedings of IEEE IRMMW-THz (Houston, TX, 2011).
  29. A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
    [Crossref] [PubMed]
  30. N. Ocelic, “Quantitative near-field phonon-polariton spectroscopy,” Dissertation, TU München, 2007.
  31. J. M. Wagner and F. Bechstedt, “Properties of strained wurtzite GaN and AlN: Ab initio studies,” Phys. Rev. B 66(11), 115202 (2002).
    [Crossref]
  32. G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004).
    [Crossref]
  33. A. S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973).
    [Crossref]
  34. F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
    [Crossref]
  35. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
    [Crossref]
  36. I. Vurgaftman and J. R. Meyer, “Band paramters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
    [Crossref]
  37. C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
    [Crossref]
  38. T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
    [Crossref]
  39. X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
    [Crossref]
  40. T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
    [Crossref]
  41. J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
    [Crossref]
  42. R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
    [Crossref]
  43. S. Y. Huang and J. R. Yang, “A transmission electron microscopy observation of dislocations in GaN grown on (0001) sapphire by metal organic chemical vapor deposition,” Jpn. J. Appl. Phys. 47(10), 7998–8002 (2008).
    [Crossref]

2013 (4)

I. M. Watson, “Metal organic vapour phase epitaxy of AlN, GaN, InN and their alloys: A key chemical technology for advanced device applications,” Coord. Chem. Rev. 257(13-14), 2120–2141 (2013).
[Crossref]

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

I. M. Craig, M. S. Taubman, A. S. Lea, M. C. Phillips, E. E. Josberger, and M. B. Raschke, “Infrared near-field spectroscopy of trace explosives using an external cavity quantum cascade laser,” Opt. Express 21(25), 30401–30414 (2013).
[Crossref] [PubMed]

P. Hermann, A. Hoehl, P. Patoka, F. Huth, E. Rühl, and G. Ulm, “Near-field imaging and nano-Fourier-transform infrared spectroscopy using broadband synchrotron radiation,” Opt. Express 21(3), 2913–2919 (2013).
[Crossref] [PubMed]

2012 (4)

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
[Crossref] [PubMed]

X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012).
[Crossref]

J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012).
[Crossref]

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

2011 (3)

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
[Crossref] [PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

2010 (3)

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnology 21(23), 235702 (2010).
[Crossref] [PubMed]

J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
[Crossref]

2009 (2)

2008 (2)

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

S. Y. Huang and J. R. Yang, “A transmission electron microscopy observation of dislocations in GaN grown on (0001) sapphire by metal organic chemical vapor deposition,” Jpn. J. Appl. Phys. 47(10), 7998–8002 (2008).
[Crossref]

2007 (4)

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
[Crossref] [PubMed]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
[Crossref]

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[Crossref]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007).
[Crossref] [PubMed]

2006 (4)

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006).
[Crossref] [PubMed]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

2004 (3)

G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004).
[Crossref]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[Crossref]

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

2003 (2)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

I. Vurgaftman and J. R. Meyer, “Band paramters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

2002 (2)

J. M. Wagner and F. Bechstedt, “Properties of strained wurtzite GaN and AlN: Ab initio studies,” Phys. Rev. B 66(11), 115202 (2002).
[Crossref]

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
[Crossref] [PubMed]

2001 (2)

M. Kuball, “Raman spectroscopy of GaN, AlGaN and AlN for process and growth monitoring/control,” Surf. Interface Anal. 31(10), 987–999 (2001).
[Crossref]

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

1999 (1)

R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
[Crossref]

1996 (2)

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
[Crossref]

C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
[Crossref]

1995 (1)

T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
[Crossref]

1973 (1)

A. S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973).
[Crossref]

Amarie, S.

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

Andreev, G. O.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Aulombard, R. L.

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
[Crossref]

Bao, W.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Barker, A. S.

A. S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973).
[Crossref]

Basov, D. N.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Bassim, N. D.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Bauer, M.

Bechstedt, F.

J. M. Wagner and F. Bechstedt, “Properties of strained wurtzite GaN and AlN: Ab initio studies,” Phys. Rev. B 66(11), 115202 (2002).
[Crossref]

Böttcher, T.

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Brehm, M.

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

Briot, O.

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
[Crossref]

Caldwell, J. D.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Castro-Neto, A. H.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Cebula, M.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

Chierchia, R.

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Craig, I. M.

I. M. Craig, M. S. Taubman, A. S. Lea, M. C. Phillips, E. E. Josberger, and M. B. Raschke, “Infrared near-field spectroscopy of trace explosives using an external cavity quantum cascade laser,” Opt. Express 21(25), 30401–30414 (2013).
[Crossref] [PubMed]

X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012).
[Crossref]

Cvitkovic, A.

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007).
[Crossref] [PubMed]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
[Crossref] [PubMed]

Demangeot, F.

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
[Crossref]

Di Forte-Poisson, M.

R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
[Crossref]

Ding, Y.

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
[Crossref] [PubMed]

Dominguez, G.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Eddy, C. R.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Einfeldt, S.

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Eng, L. M.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
[Crossref]

Fei, Z.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Figge, S.

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Fogler, M. M.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Frandon, J.

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
[Crossref]

Gigler, A. M.

Gil, B.

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
[Crossref]

Glembocki, O. J.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Govyadinov, A.

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

Grafström, S.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
[Crossref]

Guo, X.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Hahn, H.

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

Hao, Y.

J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
[Crossref]

Härtling, T.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

Hauer, B.

J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012).
[Crossref]

Heinke, H.

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Helm, M.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
[Crossref]

Henry, R. L.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Hermann, P.

Heuken, M.

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

Hillenbrand, R.

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
[Crossref] [PubMed]

A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnology 21(23), 235702 (2010).
[Crossref] [PubMed]

A. J. Huber, A. Ziegler, T. Köck, and R. Hillenbrand, “Infrared nanoscopy of strained semiconductors,” Nat. Nanotechnol. 4(3), 153–157 (2009).
[Crossref] [PubMed]

A. M. Gigler, A. J. Huber, M. Bauer, A. Ziegler, R. Hillenbrand, and R. W. Stark, “Nanoscale residual stress-field mappingaround nanoindents in SiCby IR s-SNOM and confocal Raman microscopy,” Opt. Express 17(25), 22351–22357 (2009).
[Crossref] [PubMed]

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[Crossref]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007).
[Crossref] [PubMed]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
[Crossref] [PubMed]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006).
[Crossref] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[Crossref]

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
[Crossref] [PubMed]

Hobart, K. D.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Hoehl, A.

Hoffmann, J. M.

J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012).
[Crossref]

Holländer, B.

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

Holm, R. T.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Hommel, D.

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Hu, Y.

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Jungbluth, B.

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T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
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A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
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M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
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T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
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T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
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R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
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Ketteniss, N.

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
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Kim, K.

C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
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A. J. Huber, A. Ziegler, T. Köck, and R. Hillenbrand, “Infrared nanoscopy of strained semiconductors,” Nat. Nanotechnol. 4(3), 153–157 (2009).
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T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
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Lea, A. S.

Lin, L.

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
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Lockwood, D. J.

G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004).
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J. Wueppen, B. Jungbluth, T. Taubner, and P. Loosen, “Ultrafast tunable mid IR source,” in Proceedings of IEEE IRMMW-THz (Houston, TX, 2011).

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T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
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J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
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R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
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C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
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T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
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J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
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J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
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Ocelic, N.

F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
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A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007).
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A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
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N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
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A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006).
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N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
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Pereira, E.

R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
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Phillips, M. C.

Powell, J. A.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
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Qiu, Y. X.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
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X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012).
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F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
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B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
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Robinson, I. K.

C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
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Rowell, N. L.

G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004).
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Rühl, E.

S McLeod, A.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
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Schneider, S.

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
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Schnell, M.

F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
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Seidel, J.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
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S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
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Seitz, R.

R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
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Shim, K.

C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
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T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
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Stark, R. W.

Stehr, D.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
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Stewart, M. K.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
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Tauber, M. J.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
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Taubman, M. S.

Taubner, T.

J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012).
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A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006).
[Crossref] [PubMed]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[Crossref]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
[Crossref] [PubMed]

J. Wueppen, B. Jungbluth, T. Taubner, and P. Loosen, “Ultrafast tunable mid IR source,” in Proceedings of IEEE IRMMW-THz (Houston, TX, 2011).

Thiemens, M.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
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Trunek, A. J.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Twigg, M. E.

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

Ulm, G.

Vescan, A.

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

Vurgaftman, I.

I. Vurgaftman and J. R. Meyer, “Band paramters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

Wagner, J. M.

J. M. Wagner and F. Bechstedt, “Properties of strained wurtzite GaN and AlN: Ab initio studies,” Phys. Rev. B 66(11), 115202 (2002).
[Crossref]

Wang, C.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Wang, H.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Wang, Y. T.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Wang, Z. L.

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
[Crossref] [PubMed]

Watson, I. M.

I. M. Watson, “Metal organic vapour phase epitaxy of AlN, GaN, InN and their alloys: A key chemical technology for advanced device applications,” Coord. Chem. Rev. 257(13-14), 2120–2141 (2013).
[Crossref]

Wille, A.

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

Winnerl, S.

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
[Crossref]

Wittborn, J.

F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
[Crossref] [PubMed]

A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnology 21(23), 235702 (2010).
[Crossref] [PubMed]

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[Crossref]

Wueppen, J.

J. Wueppen, B. Jungbluth, T. Taubner, and P. Loosen, “Ultrafast tunable mid IR source,” in Proceedings of IEEE IRMMW-THz (Houston, TX, 2011).

Xu, K.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Xu, X. G.

X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012).
[Crossref]

Xue, J. S.

J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
[Crossref]

Yang, H.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Yang, J. R.

S. Y. Huang and J. R. Yang, “A transmission electron microscopy observation of dislocations in GaN grown on (0001) sapphire by metal organic chemical vapor deposition,” Jpn. J. Appl. Phys. 47(10), 7998–8002 (2008).
[Crossref]

Yoo, M. C.

C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
[Crossref]

Yu, G.

G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004).
[Crossref]

Zhang, J. C.

J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
[Crossref]

Zhang, L. M.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Zhang, S. M.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Zhang, Y.

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
[Crossref] [PubMed]

Zhao, D. G.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Zhao, Z.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Zhu, G.

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
[Crossref] [PubMed]

Zhu, J. J.

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Ziegler, A.

Adv. Mater. (1)

A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007).
[Crossref]

Appl. Phys. Lett. (7)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattering infrared near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[Crossref]

J. M. Hoffmann, B. Hauer, and T. Taubner, “Antenna-enhanced infrared near-field nanospectroscopy of a polymer,” Appl. Phys. Lett. 101(19), 193105 (2012).
[Crossref]

J. D. Caldwell, M. A. Mastro, K. D. Hobart, O. J. Glembocki, C. R. Eddy, N. D. Bassim, R. T. Holm, R. L. Henry, M. E. Twigg, F. Kub, P. G. Neudeck, A. J. Trunek, and J. A. Powell, “Improved ultraviolet emission from reduced defect gallium nitride homojunctions grown on step-free 4H-SiC mesas,” Appl. Phys. Lett. 88(26), 263509 (2006).
[Crossref]

S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90(14), 143101 (2007).
[Crossref]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

C. Kim, I. K. Robinson, J. Myoung, K. Shim, M. C. Yoo, and K. Kim, “Critical thickness of GaN thin films on sapphire (0001),” Appl. Phys. Lett. 69(16), 2358–2360 (1996).
[Crossref]

T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, “The role of high-temperature island coalescence in the development of stresses in GaN films,” Appl. Phys. Lett. 78(14), 1976–1978 (2001).
[Crossref]

Chin. Phys. B (2)

J. S. Xue, Y. Hao, J. C. Zhang, and J. Y. Ni, “Comparative study of different properties of GaN films grown on (0001) sapphire using high and low temperature AlN interlayers,” Chin. Phys. B 19(5), 057203 (2010).
[Crossref]

X. Guo, Y. T. Wang, D. G. Zhao, D. S. Jiang, J. J. Zhu, Z. S. Liu, H. Wang, S. M. Zhang, Y. X. Qiu, K. Xu, and H. Yang, “Microstructure and strain analysis of GaN epitaxial films using in-plane grazing incidence X-ray diffraction,” Chin. Phys. B 19(7), 076804 (2010).
[Crossref]

Coord. Chem. Rev. (1)

I. M. Watson, “Metal organic vapour phase epitaxy of AlN, GaN, InN and their alloys: A key chemical technology for advanced device applications,” Coord. Chem. Rev. 257(13-14), 2120–2141 (2013).
[Crossref]

J. Appl. Phys. (2)

I. Vurgaftman and J. R. Meyer, “Band paramters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

T. Kozawa, T. Kachi, H. Kano, H. Nagase, N. Koide, and K. Manabe, “Thermal stress in GaN epitaxial layers grown on sapphire substrates,” J. Appl. Phys. 77(9), 4389–4392 (1995).
[Crossref]

J. Electron. Mater. (1)

B. Reuters, A. Wille, N. Ketteniss, H. Hahn, B. Holländer, M. Heuken, H. Kalisch, and A. Vescan, “Polarization engineered enhancement-mode high-electron-mobility transistors using quaternary AlInGaN barrier layers,” J. Electron. Mater. 42(5), 826–832 (2013).
[Crossref]

J. Microsc. (1)

T. Taubner, R. Hillenbrand, and F. Keilmann, “Performance of visible and mid-infrared scattering-type near-field optical microscopes,” J. Microsc. 210(3), 311–314 (2003).
[Crossref] [PubMed]

J. Phys. Chem. Lett. (1)

X. G. Xu, M. Rang, I. M. Craig, and M. B. Raschke, “Pushing the sample-size limit of infrared vibrational nanospectroscopy: from monolayer toward single molecule sensitivity,” J. Phys. Chem. Lett. 3(13), 1836–1841 (2012).
[Crossref]

J. Vac. Sci. Technol. A (1)

G. Yu, N. L. Rowell, and D. J. Lockwood, “Anisotropic infrared optical properties of GaN and sapphire,” J. Vac. Sci. Technol. A 22(4), 1110–1114 (2004).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Y. Huang and J. R. Yang, “A transmission electron microscopy observation of dislocations in GaN grown on (0001) sapphire by metal organic chemical vapor deposition,” Jpn. J. Appl. Phys. 47(10), 7998–8002 (2008).
[Crossref]

Nano Lett. (6)

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of Dirac plasmons at the graphene-SiO₂ interface,” Nano Lett. 11(11), 4701–4705 (2011).
[Crossref] [PubMed]

Y. Hu, Y. Zhang, L. Lin, Y. Ding, G. Zhu, and Z. L. Wang, “Piezo-phototronic effect on electroluminescence properties of p-type GaN thin films,” Nano Lett. 12(7), 3851–3856 (2012).
[Crossref] [PubMed]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Material-specific infrared recognition of single sub-10 nm particles by substrate-enhanced scattering-type near-field microscopy,” Nano Lett. 7(10), 3177–3181 (2007).
[Crossref] [PubMed]

A. Huber, N. Ocelic, T. Taubner, and R. Hillenbrand, “Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling,” Nano Lett. 6(4), 774–778 (2006).
[Crossref] [PubMed]

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

Nanotechnology (1)

A. J. Huber, J. Wittborn, and R. Hillenbrand, “Infrared spectroscopic near-field mapping of single nanotransistors,” Nanotechnology 21(23), 235702 (2010).
[Crossref] [PubMed]

Nat. Mater. (2)

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

A. J. Huber, A. Ziegler, T. Köck, and R. Hillenbrand, “Infrared nanoscopy of strained semiconductors,” Nat. Nanotechnol. 4(3), 153–157 (2009).
[Crossref] [PubMed]

Nature (1)

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002).
[Crossref] [PubMed]

Opt. Express (4)

Phys. Rev. B (3)

J. M. Wagner and F. Bechstedt, “Properties of strained wurtzite GaN and AlN: Ab initio studies,” Phys. Rev. B 66(11), 115202 (2002).
[Crossref]

A. S. Barker and M. Ilegems, “Infrared lattice vibrations and free-electron dispersion in GaN,” Phys. Rev. B 7(2), 743–750 (1973).
[Crossref]

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

Phys. Rev. Lett. (1)

S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100(25), 256403 (2008).
[Crossref] [PubMed]

Phys. Status Solidi, A Appl. Res. (1)

R. Seitz, T. Monteiro, E. Pereira, and M. Di Forte-Poisson, “Strain relaxation in GaN films as a function of growth direction and buffer layer measured by Raman spectroscopy,” Phys. Status Solidi, A Appl. Res. 176(1), 661–664 (1999).
[Crossref]

Solid State Commun. (1)

F. Demangeot, J. Frandon, M. A. Renucci, O. Briot, B. Gil, and R. L. Aulombard, “Raman determination of phonon deformation potentials in alpha-GaN,” Solid State Commun. 100(4), 207–210 (1996).
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Surf. Interface Anal. (1)

M. Kuball, “Raman spectroscopy of GaN, AlGaN and AlN for process and growth monitoring/control,” Surf. Interface Anal. 31(10), 987–999 (2001).
[Crossref]

Other (3)

F. Keilmann and R. Hillenbrand, “Near-field nanoscopy by elastic light scattering from a tip,” in A. Zayats and D. Richards, eds., Nano-Optics and Near-Field Optical Microscopy (Artech House, 2009), Chap. 11, pp. 235–265.

N. Ocelic, “Quantitative near-field phonon-polariton spectroscopy,” Dissertation, TU München, 2007.

J. Wueppen, B. Jungbluth, T. Taubner, and P. Loosen, “Ultrafast tunable mid IR source,” in Proceedings of IEEE IRMMW-THz (Houston, TX, 2011).

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Figures (5)

Fig. 1
Fig. 1 Broadband SNOM. (a) Spectral range of different laser systems successfully used for SNOM experiments. See literature [12,16,23] for further details; part of the data were taken from the web pages of the companies Edinburgh Instruments, Block Engineering and Daylight Solutions. (b) Calculated SNOM amplitude spectra for various phonon resonant materials normalized on gold. (c) Examples of laser spectra of the ILT broadband laser used in this paper. The central wavelength is continuously tunable between 9 µm and 16 µm, with spectral widths (FWHM) from approx. 40 cm−1 to 130 cm−1. Note that these widths are matched very well to those of the phonon-resonances. (d) Experimental setup of the broadband SNOM.
Fig. 2
Fig. 2 Indent in GaN layer. (a) Topography and (b) interferometrically recorded 2D optical near-field image (second harmonic amplitude) of the indent. See text and Fig. 3 for more details about this measurement method. The shape of the indent is clearly visible. It is surrounded by brighter and darker areas denoting different stress levels in the crystal structure. (c) Sketch of the sample. (d) Near-field spectra of GaN, normalized to gold, measured at different positions on the sample: A and B are close to one of the indents as marked in 2(b). Position C is further away from the indent where the sample is expected to be unaffected by the indentation. The spectra are evaluated by a fit which is shown as solid line.
Fig. 3
Fig. 3 2D imaging of stress in a GaN layer. (a) and (b) show the second harmonic amplitude of the interferograms that correspond to the spectra in Fig. 2(d) and to the positions marked in (c). The interferograms differ from one another which leads to an optical contrast between differently stressed crystal areas as illustrated with the black. (c)-(e) show the optical amplitudes (second harmonic) for different positions of the end mirror in the interferometer arm that are marked in 3(b) (dashed lines). The color scale is the same as in (e) for all three images. In (c) and (e), a hexagonal pattern is visible that reveals the differently strained areas on the sample.
Fig. 4
Fig. 4 (a) Sketch of the second sample. The cross section sample is tilted 90° compared to the indent sample. The spectra are taken on the GaN layer with different distances from the AlN layer. (b) illustrates schematically the lattice mismatch between GaN and AlN that leads to strain in the crystal lattice.
Fig. 5
Fig. 5 Cross section of a layered sapphire/AlN/GaN structure. (a) Sketch of the sample structure. (b) Topography of the sample and (c) the corresponding second harmonic optical amplitude signal. The bright area next to GaN is from the covering. Across the GaN layer, several spectra are recorded that are shown in (d). The solid lines are fits to the data. (e) shows the relative differences in stress levels calculated from the shift in the LO phonon frequencies ωLO. Note that the value of 0 GPa at a GaN thickness of 0.6 µm is set arbitrarily. The damping constants Γ are plotted in (f).

Equations (1)

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ε ( ω ) = ε + ε ( ω LO 2 ω TO 2 ) ω TO 2 ω 2 i ω Γ + ω p 2 ω 2 i ω γ

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