Infrared Reflectance Analysis of Epitaxial n-Type Doped GaN Layers Grown on Sapphire

Infrared Reflectance Analysis of Epitaxial n-Type Doped GaN Layers Grown on Sapphire + + Infrared (IR) reflectance spectroscopy is applied to study Si-doped multilayer n /n /n -GaN structure grown on GaN buffer with GaN-template/sapphire substrate. Analysis of the investigated structure by photo-etching, SEM, and SIMS methods showed the existence of the additional layer with the drastic difference in Si and O doping levels and located between the epitaxial GaN buffer and template. Simulation of the experimental reflectivity spectra was performed in a wide frequency range. It is shown that the modeling of IR reflectance spectrum using 2 × 2 transfer matrix method and including into analysis the additional layer make it possible to obtain the best fitting of the experimental spectrum, which follows in the evaluation of GaN layer thicknesses which are in good agreement with the SEM and SIMS data. Spectral dependence of plasmon-LO-phonon coupled modes for each GaN layer is obtained from the spectral dependence of dielectric of Si doping impurity, which is attributed to compensation effects by the acceptor states. Keywords: Gallium nitride, Heterostructure, IR reflectance, Transfer matrix method, Carrier concentration, Mobility, Photo-etching, SIMS Background phonon vibrations but also for characterizing the carrier In recent years, there has been high interest in III-nitride properties [7]. However, the known problem of confocal materials, in particular to GaN [1, 2]. Due to the break- micro-Ramanspectroscopyisadeteriorationindepth through in the growth techniques, epitaxial GaN films spatial resolution due to the refraction of light [8]. It was have found wide application in optoelectronic devices showninref.[6] that at depth scanning of multilayer GaN such as blue and ultraviolet light emitting diodes (LEDs) structure with an excitation wavelength of 488.0 nm, the [3], lasers [4], and microelectronic devices, e. g., high- depth resolution makes only about 1.8 μm while the lateral power and high-frequency field effect transistors [5, 6]. resolution is about 210 nm. IR spectroscopy overcomes this Concentration and mobility of free carriers are the key pa- problem due to high sensitivity to layer thickness due to rameters which determine the performance of the device interference effects and impact of the dispersion of refract- in applications. Hall measurement of concentration and iveindex in awidespectralrange. mobility of free carriers in multilayer GaN-based device IR reflectance spectra of thin GaN films were investi- structures is not trivial and time-consuming technological gated as far back as in 1973 by A.S. Baker [9], but spatial task which needs ohmic contacts attached to each meas- inhomogeneity and overall low structural quality of such uring layer and dedicated measuring procedures. films significantly limited the practical application of the Fourier transform infrared (IR) reflectance spectroscopy obtained results. Nevertheless, a possibility to determine and Raman spectroscopy are contactless and non- parameters of optical phonons and free carriers’ absorp- destructive methods which allow for studying not only the tion in thin films of GaN was demonstrated. The detailed studies of longitudinal optical phonon–plasmon coupled (LOPC) modes in bulk GaN were performed by Perlin et * Correspondence: btsykaniuk@gmail.com V. Lashkaryov Institute of Semiconductor Physics, National Academy of al. [10] using Raman spectroscopy and by Shubert et al. Sciences of Ukraine, Pr. Nauky 41, Kiev 03680, Ukraine [11] using IR ellipsometry. Effect of different substrates on Full list of author information is available at the end of the article © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 2 of 9 the optical properties of cubic and wurtzite GaN films also has been studied in details [12, 13]. Considering the lack of native GaN substrates, it was shown that using sapphire substrates for epitaxial growth of GaN film is optimal for exploiting in devices which operate at high temperatures. IR reflection spectroscopy studies of hexagonal sapphire [14] showed a complex spectrum, the shape of which strongly depends on the polarization and the angle of incidence. This greatly complicates measurements and determination of the spectral characteristics of phonon modes and properties of free carriers in thin GaN film grown on sapphire substrates. Thus, proper selection of spectral analysis algorithm and the form of dielectric function are of great importance for the analysis of the IR reflectance spectra of multilayer GaN-on-sapphire structures [15–17]. This paper shows a possibility of application of IR reflectance spectroscopy and 2 × 2 transfer matrix method for the analysis of planar GaN-based multilayer structures with non-uniform depth and doping profiles, which in practice can be different + + Fig. 1 Schematic of the investigated n /n /n -GaN structure grown type of semiconductor III-nitride-based device structures on GaN-template/(0001) sapphire substrate with vertical design, such as light-emitting and rectifying diodes, Gunn diodes, high electron mobility transistors (HEMTs), etc. impurities concentration. The size of the raster was Methods about 50 × 50 μm , and the secondary ions were col- Experimental lected from a central region of 30 μm in a diameter. For + + The investigated n /n /n -GaN structures were grown on H, C, O, and Si, the concentrations were derived from MOCVD GaN templates on Al O (0001) substrates at a H–,O–,C–,Si– species, respectively, and the matrix 2 3 temperature of 800 °C by plasma-assisted molecular-beam signal Ga– was taken as the reference. epitaxy using an N flow rate of 0.5 sccm and an RF The infrared reflectance spectroscopy measurements in −1 plasma power of 350 W (Fig. 1). This results in a growth the spectral range of 300–4000 cm with the spectral −1 −1 rate of ∼ 0.27 ML s . First, a 0.3-μm-thick GaN buffer resolution of 1 cm were performed at room temperature was grown on MOCVD GaN template. A 0.8-μm-thick using Bruker Vertex 70 V FTIR spectrometer equipped Si-doped GaN layer was followed by a 1.75-μm-thick with Globar source and a deuterated triglycine sulfate undoped GaN layer and a 0.4-μm-thick Si-doped GaN (DLaTGS) detector with polyethylene window. The angle layer (Fig. 1). The nominal Si doping concentration of the of incidence was 11°. S-polarized spectra were measured + 19 −3 n -GaN layers was ∼ 10 cm . using KRS-5 polarizer. The reflectance spectrum of a gold In order to examine the areas of different carrier mirror was used as a reference. concentration, the cleaved edge of the investigated structure was examined by the photo-etching method in an electroless configuration using K S O –KOH Description of the Optical Analysis Model 2 2 8 The reflectance of layers/substrate system was calculated aqueous solution (KSO-D etching system) [18]. This using the 2 × 2 transfer matrix method [17, 21] in which method allows revealing the areas of different carrier concentration and visualizing the relative carrier con- an arbitrary number of layers can be included and interference effects within the films are automatically centration differences by measuring the etch rate using considered. 2 × 2 transfer matrix method for isotropic surface profiling [19, 20]. Cross-section of the investi- gated sample was photo-etched for 3 min. Afterwards, layered systems allows for an independent calculation of s-and p-polarized reflection and transmittance spectra samples were examined by scanning electron micros- in the case of layered systems consisting of homoge- copy (SEM). Secondary ion mass spectroscopy (SIMS) studies of neous biaxial or uniaxial isotropic slabs having their c- axis aligned with the z-axis of laboratory coordinates. In samples were performed on a CAMECA IMS6F system this case, 2 × 2 layered system transfer matrix can be using a cesium (Cs ) primary beam, with the current kept at 400 nA in order to find the profile of the represented in the following view [21]: Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 3 of 9 s=p N þ Y ′ 2 1 1 −r T E  s=p  21 s=p E 1;0 0 Nþ1 ¼ T R ¼ r ¼ : − s=p s=p l=ðÞ lþ1 ′ 0;Nþ1 s=p E E 0 r 1 11 s=p t Nþ1 1;0 l¼1 s=p 0;1 T T 11 12 E Nþ1 ¼ : T T 21 22 IR Dielectric Function Model s=p Nþ1 s=p Refractive index depends on the complex dielectric func- ð1Þ tion ε(ω), which can be written as: Asterisks in the top indexes of field amplitude in the lat fc εωðÞ¼ ε ðÞ ω þ ε ðÞ ω : ð5Þ exit medium are used in Eq. (1) to account for the values of electric field components just at the right side of the The first term corresponds to contribution from lattice N/N + 1 interface. mode dispersion, and the second one to free carrier s=p The 2  2 T transfer-matrix accounts for the l;ðÞ lþ1 excitations. propagation of plane waves from the l-th layer, multiple The contribution of lattice modes to the IR response lat reflections within this layer, and influence of l/(l + 1) ε (ω) at phonon energy ℏω can be described using a interface. Such matrix can be determined as [17]: factorized model with Lorentzian broadening [22]: 2 2 1 ω −ω −iωγ LOk s=p s=p s=p s=p lat LOk T ¼ exp iδ −r exp iδ ε ðÞ ω ¼ ε ð6Þ l=ðÞ lþ1 l lþ1;l l 2 2 s=p ω −ω −iωγ ; TOk t TOk ! k¼1 l=ðÞ lþ1 s=p r s=p s=p l;lþ1 exp −iδ exp −iδ ; l l where M is the number of infrared-active polar phonon modes for s-or p-polarizations to the c-axis; ω and LOk −1 ð2Þ ω are the frequency (cm ) of the k-th LO and TO TOk −1 phonon; γ and γ are their damping constants (cm ). s=p s=p LOk TOk where r and t denote partial reflection and trans- l;lþ1 l;lþ1 For GaN the parameters ω and ω account for LOk TOk mission coefficients for l/(l + 1) interface, δ s=p is the the E (LO), A (LO) and E (TO), and A (TO) vibra- 1 1 1 1 phase shift, imposed to light after propagation by the l- tional modes [23]. th layer for s- and p-polarized light. fc The contribution of the free carrier species ε (ω)to Phase shift for s- and p-polarized light after passing the dielectric function can be described using classical through the l-th layer can be determined as [17]: Drude approximation [15]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2πd 2πd 1 ω l l s=p fc δ ¼ n cosθ ¼ n 1− sinθ ; l l;s=p l;s=p l ε ðÞ ω ¼ −ε  ; ð7Þ λ λ n l;s=p ωω þ iγ ð3Þ with where n is the complex refractive index for the l-th 1=2 layer, d is the thickness of the l-th layer, and θ is the l 2 Ne ω ¼ ð8Þ angle of incidence. p ε ε m ∞ 0 Partial reflection and transmission coefficients for the s- and p-polarizations can be calculated using Fresnel e γ ¼ ð9Þ equations. For example, partial reflection and transmis- m μ sion coefficients for the s-polarization have the following The screened plasma frequencies ω (Eq. (8)) depend form [21]: on the free carrier concentration N, high-frequency n cosθ −n cosθ ls ls dielectric permittivity ε , and the effective mass m of ðÞ lþ1 s ðÞ lþ1 s ∞ r ¼ l;lþ1 the free carriers (ε is the vacuum permittivity and e is n cosθ −n cosθ 0 ls ls ðÞ lþ1 s ðÞ lþ1 s the electrical unity charge). The plasmon damping 2n cosθ ls ls s ¼ parameter γ depends on the optical carrier mobility μ t p n cosθ þ n cosθ l;lþ1 ls ls ðÞ lþ1 s ðÞ lþ1 s (Eq. (9)) [24]. ð4Þ Parameters of ω and LOPC modes can be determined LO The complex reflectance ratios of the multilayer stack from the imaginary part of the energy loss function—Im can be thus obtained by substituting the partial reflection − [7], where ε(ω) is the complex dielectric function, and transmission coefficients for the N+1 interface (Eqs. εωðÞ (4)) in Eq. (1) and phase shifts of all the N layers (Eq. (3)): obtained from Eq. (5). Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 4 of 9 Results and Discussion SEM image (Fig. 2) shows the photo-etched cross sec- + + tion of n /n /n -GaN structure grown on GaN-buffer/ GaN-template/sapphire substrate, where six distinct layers are clearly visible, which are five GaN layers with different carrier concentration and sapphire substrate. It should be noted that the overall thickness of the investi- gated GaN structure as measured by SEM agrees with the technological one, and observed GaN layers accord- ing to Fig. 1 can be tentatively attributed to nominal top Si-doped n region (layer 1), undoped n region (layer 2), bottom Si-doped n region (layer 3), undoped GaN buffer (layer 4), and GaN template. Further, in order to have the deeper insight on the impur- ity/doping level of the investigated samples, SIMS measure- ments were performed. The obtained SIMS profiles (Fig. 3) are in good correlation with the nominal thickness of GaN layers and the overall thickness of the studied multilayer structure. All examined elements (H, C, O, Si) were above 16 3 the detection limit (3 to 5 × 10 at/cm )of SIMS + + technique. Fig. 3 Impurity elements profiles of the investigated n /n /n -GaN structure measured by SIMS from the sample surface Profile of intentional Si doping, in general, agrees with the nominal doping profile with the concentration of 19 −3 + about 2.8 × 10 cm in the doped top and bottom n 17 −3 regions and of about 2.3 × 10 cm in the undoped n region. However, as can be seen from SIMS data, there contains higher concentrations of unintentional oxygen 19 −3 is also thin (<50 nm)-delta layer with Si concentration of and carbon impurities of 2.4 × 10 cm and 1.4 × 18 −3 19 −3 1.1 × 10 cm between the GaN buffer and GaN tem- 10 cm , correspondingly. This delta layer is related plate. It should be noted that Si-doped delta layer also with homoepitaxial regrowth interface, which typically arises from the GaN template contamination with O, Si, and C impurities, absorbed from the atmosphere in the technological process of loading or at the beginning of the regrowth [25, 26]. As discussed above, SEM cross-section and SIMS ana- lysis give the structure of GaN layers, which differs from the nominal parameters by exciting of the additional GaN region, but with the overall thickness in agreement with the nominal one. In order to clarify the influence of additional GaN delta-layer found above on the IR reflectance spectrum of the investigated structure, the simulation of the experimental spectrum was performed by constructing models consisting of six layers, which correspond to nominal technological parameters, SEM images (Fig. 1), and seven layers according to SIMS. The calculated spectra based on the described above models are given in Fig. 4. As can be seen from Fig. 4, based on SIMS profile seven-layer model gives the best approximation of the + + experimental IR reflectance spectrum. Thus, further sim- Fig. 2 SEM image of cross-section of the investigated n /n /n -GaN ulations and analysis are performed using this model structure. The irregular pattern of vertical lines was formed during cleaving (i.e., before photo-etching) and is characteristic for the non- having modified parameters, as compared to nominal polished cleavages of Al O /GaN hetero-structures. Rough pyramidal 2 3 technological ones (Fig. 1), and which accounts for the layer (pinholes) at the sapphire/GaN template indicated by the arrow additional layer between the technological GaN buffer was revealed by photo-etching layer and GaN template (Fig. 5). Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 5 of 9 Fig. 5 The 7-layer model used to simulate the IR reflectance spectra of + + the investigated n /n /n -GaN structure. An additional layer (green)is thin interface layer between GaN template and the investigated GaN layers is a two-step process [27]. First, the fringes in the transparent region above the reststrahlen bands (ω > −1 1200 cm )are duetointerferenceeffects on thelayers of the multi-layer structure. In this way, the overall Fig. 4 Simulations of the IR reflectance spectra with different number thickness of the investigated structure, which is a sum + + of layers. The experimental spectrum of the investigated n /n /n -GaN of all layers, can be estimated. structure is shown by solid line. a Reststrahlen region. b The enlarged Once the stack thickness is known, the individual −1 spectra in the range above 750 cm thicknesses of each layer can be determined by fitting the calculated spectra to interference effects in the rest- Figure 6 shows experimental and fitted theoretical s-po- strahlen region of the spectrum. Layer thicknesses were larized reflectance spectra of the investigated structure at varied by taking into account the previously determined the 11° angle of incidence. The calculated spectrum is overall thickness. Under this constraint, the reflectance −1 based on the model described above (Fig. 5). Dispersion of above 1200 cm does not change significantly. The complex refractive index for the GaN layers and the interference effects in the reststrahlen region can be sapphire substrate was determined using Eq. (5). The distinguished from other features such as TO and LO sapphire substrate was considered as semi-infinite, that vibrational modes based on the fact that the interference allowed neglecting the internal reflections within the sub- fringes shift in position as the layer thicknesses are strate and from the non-polished backside. The compli- varied [28]. cated structure observed in the reststrahlen region of the During the approximation of the experimental spectrum spectrum is due to a combination of the overlapping GaN in the reststrahlen region, the following model parameters and Al O reststrahlen bands along with interference were varied: damping parameters γ and γ for E (LO) 2 3 LO TO 1 effects. Comparison of these data to the calculated spectra and E (TO) phonon modes; plasma frequency ω ;plasmon 1 p not only can provide thickness information on the various damping parameter γ ; and layer thicknesses. It should be layers of the samples, but can also help to interpret the noted, that only E symmetry phonons are IR active in s- complicated structure of the reststrahlen region in terms polarization [9]. Initial frequencies of E (LO) and E (TO) 1 1 of the contributions of the various materials. phonons for GaN and sapphire substrate were taken from The determination of layer thicknesses from the com- the IR reflectance [29] and Raman scattering [6, 14] experi- parison of the reflectance data to the calculated spectrum ments. Typical values of GaN phonon frequency are ω = TO Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 6 of 9 the IR reflectance spectra of bulk GaN and 6.78-μm- thick GaN layer on sapphire, with the thickness of GaN corresponding to the overall thickness of the investigated structure, were simulated in the reststrahlen band region (Fig. 7). As can be seen from Fig. 7, the reflectance spec- tra of 6.78-thick GaN layer on sapphire and bulk GaN in −1 the range of 500–740 cm are similar to the experimen- −1 tal spectrum. The small feature at ~511 cm is associ- ated with the sapphire substrate. It should be mentioned −1 that at ~736 cm , there is a weak dip that corresponds to A (LO) mode of GaN template. According to the se- lection rules, A (LO) mode is forbidden in s-polarized IR spectra [9]. The possible reason for the registration of this forbidden mode could be a polarization leakage due to the aperture of the reflectance accessory as well as microinhomogeneities of GaN crystal structure. Specific- ally, this can be caused by inclination of the c-axis of the column-like wurtzite structure of GaN from the direc- tion perpendicular to the film’s growth plane. This mode was not taken into account in our modeling because of its weak impact on the resulting spectrum. The features −1 in the range of 750–1200 cm are due to overlapping GaN:Si and sapphire reststrahlen bands and interface ef- −1 fects. The drop at ~775 cm is related to interface effect on the edge of the reststrahlen band of GaN layers and −1 sapphire. The broad dip at ~825 cm is associated with overlapping of the high-frequency branch of the + + plasmon-LO-phonon coupled mode (LPP ) of the n layers. Figure 8 shows the calculated imaginary parts of the Fig. 6 Experimental (solid line) and best-fit calculated (dash-dot line) + + IR reflectance spectra of the n /n /n -GaN structure grown on GaN- energy loss function for each layer according to oscillator template/Al O . a Reststrahlen region. b Interference region 2 3 parameters given in Table 1 for estimation of E -LOPC modes. As can be seen, the high-frequency branch of the −1 −1 + 560 cm and ω =740 cm . The phonon frequencies for LOPC modes (LPP ) at carrier concentrations lower than LO 17 −3 each layer were refined in the fitting process. Obtained 10 cm (n layer and template) almost coincide with best-fit parameters with the error bars are given in Table 1. E (LO) phonon mode. The increase in carrier concentra- 17 18 −3 It should be noted that obtainedinthe fittingprocess layer tion in the range of 2 × 10 –3×10 cm (Fig. 5) leads to thicknesses are in good agreement with the SEM data. significant high-frequency shift and broadening of the LPP −1 Referring to Fig. 6a, the reflectance peak at ~450 cm branch, which indicates the increase in interaction between can be attributed to the sapphire substrate. The features LO phonon and plasmon and the decrease in mobility of −1 + observed in the range of 500–740 cm are due to a charge carriers. This behavior of LPP branch agrees well combination of overlapping features from GaN layers with the experimental data on IR reflectance of Si-doped and sapphire reststrahlen bands. For the deeper analysis, GaN films grown on sapphire by Z.F. Li et al. [30], and Table 1 Best fit oscillator parameters for GaN layers of the investigated structure (layers are numbered from top to bottom) -1 −1 −1 −1 −1 −1 Layer no. ω (cm ) γ (cm ) ω (cm ) γ (cm ) ω (cm ) γ (cm )d (μm) d (μm) ε LO LO TO TO p p IR Nominal ∞ 1 740.2 (±0.5) 10.7 (±1.1) 561.1 (±0.8) 15.7 (±0.9) 507.8 (±1.2) 350.5 (±1.0) 0.47 (±0.02) 0.401 5.25 (±0.07) 2 740.7 (±0.8) 12.8 (±0.9) 560.8 (±0.2) 14.4 (±0.5) 55.7 (±0.5) 155.7 (±0.5) 1.73 (±0.06) 1.752 5.01 (±0.03) 3 740.4 (±0.3) 11.4 (±1.0) 562.3 (±0.4) 6.83 (±0.5) 537.1 (±0.9) 390 (±0.7) 0.8 (±0.02) 0.82 5.35 (±0.08) 4 740.1 (±0.7) 6.22 (±0.7) 560.7 (±0.1) 17.8 (±0.5) 132.3 (±0.5) 249.1 (±0.5) 0.27 (±0.03) 0.31 5.35 (±0.1) 5 742.1 (±0.2) 8.68 (±0.8) 560.4 (±0.7) 18.4 (±0.5) 436.1 (±0.7) 383.3 (±0.5) 0.01 (±0.001) - 5.3 (±0.09) Template 741.5 (±1.0) 13.14 (±1.3) 560.2 (±0.3) 7.16 (±0.1) 51.39 (±0.8) 180 (±0.9) 3.48 (±0.05) 3.51 4.99 (±0.07) Thickness of interface layer was not determined from SEM data Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 7 of 9 Table 2 Optically determined values of carrier concentration and mobility for each analyzed GaN layer of the investigated + + n /n /n -GaN structure 17 −1 2 −1 −1 Layer no. N ×10 (cm ) μ (cm V s ) 1 28.8 (±0.13) 133.3 (±1.20) 2 0.37 (±0.01) 300.0 (±0.90) 3 34.4 (±0.12) 119.7 (±0.75) 4 2.04 (±0.03) 187.4 (±0.67) 5 22.20 (±0.07) 121.9 (±0.52) Template 0.31 (±0.01) 259.4 (±1.27) lowers with increasing n-type doping [34]. It should be mentioned, that carrier concentration for the n layers in 18 −3 the order of ~10 cm is in good agreement with the re- sults of our Raman studies of similar GaN structures based Fig. 7 Experimental (solid line) IR reflectance spectra of the + + on analysis of LOPC modes [6]. Obtained decrease of investigated n /n /n -GaN structure and calculated reflectance spectra of 6.78-μm-thick GaN layer on sapphire (dash-dot line) and carrier mobility μ with carrier concentration is also in good bulk GaN (dash line) agreement with Hall experiments in GaN [35] and theoret- ical modeling [36]. Raman measurement in bulk GaN [10] and epitaxial layers The values of high-frequency dielectric permittivity ε [31]. It should be noted that the low-frequency LPP were found to be in the range of 4.99–5.35 (Table 1). branch of the LOPC cannot be reliably defined in our case, The increase in ε for the doped n layers as compared as s-polarized IR reflectance spectra were not measured in to n layers can be related to the red shift of the α-GaN −1 low-frequency range below 300 cm . band gap [37]. It should be noted that values of ε can Values of carrier concentration and mobility listed in be determined with relatively small error only for low- Table 2 were calculated using Eqs. (8) and (9) with electron conductive films. Accuracy in the determination of ε effective mass m* of 0.2 m [32]. It can be seen, that calcu- decrease with carrier concentration, which is related to lated carrier concentration profile is similar to the Si impur- the fact that the ε parameter accounts for “the high- ity concentration profile obtained by SIMS measurements frequency” limit when the dielectric model function is (Fig. 3), but with the order of magnitude lower carrier con- extrapolated to shorter wavenumbers than those studied −1 centrations as compared to concentration Si impurity. Such here [11]. The wide spectral range of 300–4000 cm discrepancy in concentrations of carriers and doping im- was analyzed in order to decrease the error in the deter- purities was observed earlier by M. Bockowski et al. [33], mination of ε and other parameters involved in model- and was related to compensation effects by acceptor states ing the IR reflectance spectra of n layers. (likely by gallium vacancies), formation energy of which Conclusions IR reflectance spectra of the multilayer structure consist- ing of GaN layers grown on a sapphire substrate and doped with different concentrations of Si impurity were measured and analyzed in details. Analysis of the investi- gated structure by SEM of photo-etched cross-section showed good correlation with the technological parame- ters of the GaN layers. SIMS analysis also revealed the presence of thin delta layer near the GaN buffer/GaN- template interface with higher content of Si and O impur- ities, which is related to homoepitaxial regrowth interface. Modeling of IR reflectance spectrum of the studied multi- layer structure by including into analysis the additional layer made it possible to obtain the best fitting of the experimental spectrum. Obtained thicknesses of GaN layers are in good agreement with the SEM and SIMS Fig. 8 Calculated imaginary part of dielectric function obtained for data. 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Everall NJ (2009) Confocal Raman microscopy: performance, pitfalls, and analysis of epitaxial multilayer GaN structures with non- best practice. Appl Spectrosc. doi:10.1366/000370209789379196 uniform doping profiles, and allow for the determination 9. Barker AS, Ilegems M (1973) Infrared lattice vibrations and free-electron dispersion in GaN. Phys Rev B 7:743–750 of the fundamental electron and phonon parameters of 10. Perlin P, Camassel J, Knap W, Taliercio T, Chervin JC, Suski T, Grzegory I, each GaN layer. Porowski S (1995) Investigation of longitudinal-optical phonon-plasmon coupled modes in highly conducting bulk GaN. Appl Phys Lett 67:2524–2526 Abbreviations 11. Kasic A, Schubert M, Einfeldt S, Hommel D, Tiwald TE (2000) Free-carrier and IR: Infrared; FTIR: Fourier transform infrared spectroscopy; SEM: Scanning electron phonon properties of n- and p-type hexagonal GaN films measured by microscopy; SIMS: Secondary ion mass spectrometry; LOPC: Longitudinal optical infrared ellipsometry. Phys Rev B 62:7365–7377 phonon–plasmon coupled 12. Mirjalili G, Parker TJ, Shayesteh SF, Bulbul MM, Smith SRP, Cheng TS, Foxon CT (1998) Far-infrared and Raman analysis of phonons and phonon interface Acknowledgements modes in GaN epilayers on GaAs and GaP substrates. Phys Rev B 57:4656–4663 This work was supported by NATO SfP Grant 984735 and by the US National 13. Dumelow T, Parker TJ, Smith SRP, Tilley DR (1993) Far-infrared spectroscopy Science Foundation Engineering Research Center for Power Optimization of of phonons semiconductor superlattices and plasrnons in semiconductor Electro Thermal Systems (POETS) with cooperative agreement EEC-1449548. The superlattices. Surf Sci Rep 17:153–212 authors are thankful to Ivan Karbovnyk for critical reading of the manuscript. 14. Lee SC, Ng SS, Abu Hassan H, Hassan Z, Dumelow T (2014) Crystal orientation dependence of polarized infrared reflectance response of Authors’ Contributions hexagonal sapphire crystal. Opt Mater (Amst) 37:773–779 BTs was responsible for IR reflectance measurements, analysis of obtained 15. Kroon RE (2007) The classical oscillator model and dielectric constants extracted results, modeling of spectra, participated in discussion of results, and was from infrared reflectivity measurements. Infrared Phys Technol 51:31–43 involved in the drafting of the manuscript. AN performed formulation of the 16. Mitsas CL, Siapkas DI (1995) Generalized matrix method for analysis of research problem, participated in discussion of results, was involved in the coherent and incoherent reflectance and transmittance of multilayer structures drafting of the manuscript. VS was involved in the discussion of the manuscript with rough surfaces, interfaces, and finite substrates. Appl Opt 34:1678–1683 and gave final approval of the version to be published. VN assisted in IR 17. Katsidis CC, Siapkas DI (2002) General transfer-matrix method for optical reflectance measurements. YM, MW, and EADC were responsible for the growth multilayer systems with coherent, partially coherent, and incoherent of the studied structures. BS and JLW performed photo-etching and SEM analysis. interference. Appl Opt 41:3978–3987 RJ performed SIMS analysis. GS and AB were involved in the discussion of the 18. Weyher JL, Tichelaar FD, Van Dorp DH, Kelly JJ, Khachapuridze A (2010) The manuscript and gave final approval of the version to be published. All authors K2S2O8KOH photoetching system for GaN. J Cryst Growth 312:2607–2610 read and approved the final manuscript. 19. Lewandowska R, Weyher JL, Kelly JJ, Konczewicz L, Lucznik B (2007) The influence of free-carrier concentration on the PEC etching of GaN: a calibration with Raman spectroscopy. J Cryst Growth 307:298–301 Competing Interests 20. Weyher JL, Van Dorp DH, Kelly JJ (2015) Principles of electroless The authors declare that they have no competing interests. photoetching of non-uniformly doped GaN: kinetics and defect revealing. J Cryst Growth 430:21–27 Publisher’sNote 21. Katsidis CC, Ajagunna AO, Georgakilas A (2013) Optical characterization of Springer Nature remains neutral with regard to jurisdictional claims in free electron concentration in heteroepitaxial InN layers using Fourier published maps and institutional affiliations. transform infrared spectroscopy and a 2 × 2 transfer-matrix algebra. J Appl Phys 113:1–12 Author details 22. Gervais F, Piriou B (1974) Anharmonicity in several-polar-mode crystals: V. Lashkaryov Institute of Semiconductor Physics, National Academy of adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit Sciences of Ukraine, Pr. Nauky 41, Kiev 03680, Ukraine. Institute for infrared reflectivity. J Phys C Solid State Phys 7:2374 Nanoscience and Engineering, University of Arkansas, West Dickson 731, 23. Harima H (2002) Properties of GaN and related compounds studied by Fayetteville, AR 72701, USA. Institute of High Pressure Physics, Polish means of Raman scattering. J Phys: Condens Matter 14:R967–R993 Academy of Sciences, Sokolowska str. 29/37, 01-142 Warsaw, Poland. 24. Yu P, Cardona M (2010) Fundamentals of semiconductors. Physics and Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, materials properties, 4th edn. Springer-Verlag, Berlin PL-02-668 Warsaw, Poland. 25. Koblmuller G, Chu RM, Raman A, Mishra UK, Speck JS (2010) High-temperature molecular beam epitaxial growth of AlGaN/GaN on GaN templates with Received: 30 December 2016 Accepted: 30 May 2017 reduced interface impurity levels. J Appl Phys 107:43527-1–43527-9 26. Liu JP, Ryou JH, Yoo D et al (2008) III-nitride heterostructure field-effect transistors grown on semi-insulating GaN substrate without regrowth References interface charge. Appl Phys Lett 92:90–93 1. Manasreh MO, Weaver BD (2001) Local vibrational modes of carbon- 27. MacMillan MF, Devaty RP, Choyke WJ, Khan MA, Kuznia J (1996) Infrared hydrogen complexes in proton irradiated AlGaN. Mater Res 692:403–409 reflectance of AlN-GaN short period superlattice films. J Appl Phys 80:2372–2377 2. Sun WH, Chen KM, Yang ZJ, Li J, Tong YZ, Jin SX, Zhang GY, Zhang QL, Qin 28. Feng ZC, Yang TR, Hou YT (2002) Infrared reflectance analysis of GaN GG (1999) Using Fourier transform infrared grazing incidence reflectivity to epitaxial layers grown on sapphire and silicon substrates. Mater Sci study local vibrational modes in GaN. J Appl Phys 85:6430–6433 Semicond Process 4:571–576 Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 9 of 9 29. Yu G, Rowell NL, Lockwood DJ (2004) Anisotropic infrared optical properties of GaN and sapphire. J Vac Sci Technol, A 22:1110–1114 30. Li ZF, Lu W, Ye HJ, Chen ZH, Yuan XZ, Dou HF, Shen SC, Li G, Chua SJ (1999) Carrier concentration and mobility in GaN epilayers on sapphire substrate studied by infrared reflection spectroscopy. J Appl Phys 86:2691–2695 31. Harima H, Sakashita H, Nakashima S (1998) Raman microprobe measurement of under-damped LO-phonon-plasmon coupled mode in n-type GaN. Mater Sci Forum 264–268:1363–1366 32. Suzuki M, Uenoyama T, Yanase A (1995) First-principles calculations of effective-mass parameters of AlN and GaN. Phys Rev B 52:8132–8139 33. Bockowski M, Iwinska M, Amilusik M, Fijalkowski M, Lucznik B, Sochacki T (2016) Challenges and future perspectives in HVPE-GaN growth on ammonothermal GaN seeds. Semicond Sci Technol 31:1–25 34. Limpijumnong S, Van de Walle C (2004) Diffusivity of native defects in GaN. Phys Rev B 69:1–11 35. Huang D, Yun F, Reshchikov MA et al (2001) Hall mobility and carrier concentration in free-standing high quality GaN templates grown by hydride vapor phase epitaxy. Solid State Electron 45:711–715 36. Mnatsakanov TT, Levinshtein ME, Pomortseva LI, Yurkov SN, Simin GS, Khan MA (2003) Carrier mobility model for GaN. Solid State Electron 47:111–115 37. Cremades A, Görgens L, Ambacher O, Stutzmann M, Scholz F (2000) Structural and optical properties of Si-doped GaN. 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Abstract

+ + Infrared (IR) reflectance spectroscopy is applied to study Si-doped multilayer n /n /n -GaN structure grown on GaN buffer with GaN-template/sapphire substrate. Analysis of the investigated structure by photo-etching, SEM, and SIMS methods showed the existence of the additional layer with the drastic difference in Si and O doping levels and located between the epitaxial GaN buffer and template. Simulation of the experimental reflectivity spectra was performed in a wide frequency range. It is shown that the modeling of IR reflectance spectrum using 2 × 2 transfer matrix method and including into analysis the additional layer make it possible to obtain the best fitting of the experimental spectrum, which follows in the evaluation of GaN layer thicknesses which are in good agreement with the SEM and SIMS data. Spectral dependence of plasmon-LO-phonon coupled modes for each GaN layer is obtained from the spectral dependence of dielectric of Si doping impurity, which is attributed to compensation effects by the acceptor states. Keywords: Gallium nitride, Heterostructure, IR reflectance, Transfer matrix method, Carrier concentration, Mobility, Photo-etching, SIMS Background phonon vibrations but also for characterizing the carrier In recent years, there has been high interest in III-nitride properties [7]. However, the known problem of confocal materials, in particular to GaN [1, 2]. Due to the break- micro-Ramanspectroscopyisadeteriorationindepth through in the growth techniques, epitaxial GaN films spatial resolution due to the refraction of light [8]. It was have found wide application in optoelectronic devices showninref.[6] that at depth scanning of multilayer GaN such as blue and ultraviolet light emitting diodes (LEDs) structure with an excitation wavelength of 488.0 nm, the [3], lasers [4], and microelectronic devices, e. g., high- depth resolution makes only about 1.8 μm while the lateral power and high-frequency field effect transistors [5, 6]. resolution is about 210 nm. IR spectroscopy overcomes this Concentration and mobility of free carriers are the key pa- problem due to high sensitivity to layer thickness due to rameters which determine the performance of the device interference effects and impact of the dispersion of refract- in applications. Hall measurement of concentration and iveindex in awidespectralrange. mobility of free carriers in multilayer GaN-based device IR reflectance spectra of thin GaN films were investi- structures is not trivial and time-consuming technological gated as far back as in 1973 by A.S. Baker [9], but spatial task which needs ohmic contacts attached to each meas- inhomogeneity and overall low structural quality of such uring layer and dedicated measuring procedures. films significantly limited the practical application of the Fourier transform infrared (IR) reflectance spectroscopy obtained results. Nevertheless, a possibility to determine and Raman spectroscopy are contactless and non- parameters of optical phonons and free carriers’ absorp- destructive methods which allow for studying not only the tion in thin films of GaN was demonstrated. The detailed studies of longitudinal optical phonon–plasmon coupled (LOPC) modes in bulk GaN were performed by Perlin et * Correspondence: btsykaniuk@gmail.com V. Lashkaryov Institute of Semiconductor Physics, National Academy of al. [10] using Raman spectroscopy and by Shubert et al. Sciences of Ukraine, Pr. Nauky 41, Kiev 03680, Ukraine [11] using IR ellipsometry. Effect of different substrates on Full list of author information is available at the end of the article © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 2 of 9 the optical properties of cubic and wurtzite GaN films also has been studied in details [12, 13]. Considering the lack of native GaN substrates, it was shown that using sapphire substrates for epitaxial growth of GaN film is optimal for exploiting in devices which operate at high temperatures. IR reflection spectroscopy studies of hexagonal sapphire [14] showed a complex spectrum, the shape of which strongly depends on the polarization and the angle of incidence. This greatly complicates measurements and determination of the spectral characteristics of phonon modes and properties of free carriers in thin GaN film grown on sapphire substrates. Thus, proper selection of spectral analysis algorithm and the form of dielectric function are of great importance for the analysis of the IR reflectance spectra of multilayer GaN-on-sapphire structures [15–17]. This paper shows a possibility of application of IR reflectance spectroscopy and 2 × 2 transfer matrix method for the analysis of planar GaN-based multilayer structures with non-uniform depth and doping profiles, which in practice can be different + + Fig. 1 Schematic of the investigated n /n /n -GaN structure grown type of semiconductor III-nitride-based device structures on GaN-template/(0001) sapphire substrate with vertical design, such as light-emitting and rectifying diodes, Gunn diodes, high electron mobility transistors (HEMTs), etc. impurities concentration. The size of the raster was Methods about 50 × 50 μm , and the secondary ions were col- Experimental lected from a central region of 30 μm in a diameter. For + + The investigated n /n /n -GaN structures were grown on H, C, O, and Si, the concentrations were derived from MOCVD GaN templates on Al O (0001) substrates at a H–,O–,C–,Si– species, respectively, and the matrix 2 3 temperature of 800 °C by plasma-assisted molecular-beam signal Ga– was taken as the reference. epitaxy using an N flow rate of 0.5 sccm and an RF The infrared reflectance spectroscopy measurements in −1 plasma power of 350 W (Fig. 1). This results in a growth the spectral range of 300–4000 cm with the spectral −1 −1 rate of ∼ 0.27 ML s . First, a 0.3-μm-thick GaN buffer resolution of 1 cm were performed at room temperature was grown on MOCVD GaN template. A 0.8-μm-thick using Bruker Vertex 70 V FTIR spectrometer equipped Si-doped GaN layer was followed by a 1.75-μm-thick with Globar source and a deuterated triglycine sulfate undoped GaN layer and a 0.4-μm-thick Si-doped GaN (DLaTGS) detector with polyethylene window. The angle layer (Fig. 1). The nominal Si doping concentration of the of incidence was 11°. S-polarized spectra were measured + 19 −3 n -GaN layers was ∼ 10 cm . using KRS-5 polarizer. The reflectance spectrum of a gold In order to examine the areas of different carrier mirror was used as a reference. concentration, the cleaved edge of the investigated structure was examined by the photo-etching method in an electroless configuration using K S O –KOH Description of the Optical Analysis Model 2 2 8 The reflectance of layers/substrate system was calculated aqueous solution (KSO-D etching system) [18]. This using the 2 × 2 transfer matrix method [17, 21] in which method allows revealing the areas of different carrier concentration and visualizing the relative carrier con- an arbitrary number of layers can be included and interference effects within the films are automatically centration differences by measuring the etch rate using considered. 2 × 2 transfer matrix method for isotropic surface profiling [19, 20]. Cross-section of the investi- gated sample was photo-etched for 3 min. Afterwards, layered systems allows for an independent calculation of s-and p-polarized reflection and transmittance spectra samples were examined by scanning electron micros- in the case of layered systems consisting of homoge- copy (SEM). Secondary ion mass spectroscopy (SIMS) studies of neous biaxial or uniaxial isotropic slabs having their c- axis aligned with the z-axis of laboratory coordinates. In samples were performed on a CAMECA IMS6F system this case, 2 × 2 layered system transfer matrix can be using a cesium (Cs ) primary beam, with the current kept at 400 nA in order to find the profile of the represented in the following view [21]: Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 3 of 9 s=p N þ Y ′ 2 1 1 −r T E  s=p  21 s=p E 1;0 0 Nþ1 ¼ T R ¼ r ¼ : − s=p s=p l=ðÞ lþ1 ′ 0;Nþ1 s=p E E 0 r 1 11 s=p t Nþ1 1;0 l¼1 s=p 0;1 T T 11 12 E Nþ1 ¼ : T T 21 22 IR Dielectric Function Model s=p Nþ1 s=p Refractive index depends on the complex dielectric func- ð1Þ tion ε(ω), which can be written as: Asterisks in the top indexes of field amplitude in the lat fc εωðÞ¼ ε ðÞ ω þ ε ðÞ ω : ð5Þ exit medium are used in Eq. (1) to account for the values of electric field components just at the right side of the The first term corresponds to contribution from lattice N/N + 1 interface. mode dispersion, and the second one to free carrier s=p The 2  2 T transfer-matrix accounts for the l;ðÞ lþ1 excitations. propagation of plane waves from the l-th layer, multiple The contribution of lattice modes to the IR response lat reflections within this layer, and influence of l/(l + 1) ε (ω) at phonon energy ℏω can be described using a interface. Such matrix can be determined as [17]: factorized model with Lorentzian broadening [22]: 2 2 1 ω −ω −iωγ LOk s=p s=p s=p s=p lat LOk T ¼ exp iδ −r exp iδ ε ðÞ ω ¼ ε ð6Þ l=ðÞ lþ1 l lþ1;l l 2 2 s=p ω −ω −iωγ ; TOk t TOk ! k¼1 l=ðÞ lþ1 s=p r s=p s=p l;lþ1 exp −iδ exp −iδ ; l l where M is the number of infrared-active polar phonon modes for s-or p-polarizations to the c-axis; ω and LOk −1 ð2Þ ω are the frequency (cm ) of the k-th LO and TO TOk −1 phonon; γ and γ are their damping constants (cm ). s=p s=p LOk TOk where r and t denote partial reflection and trans- l;lþ1 l;lþ1 For GaN the parameters ω and ω account for LOk TOk mission coefficients for l/(l + 1) interface, δ s=p is the the E (LO), A (LO) and E (TO), and A (TO) vibra- 1 1 1 1 phase shift, imposed to light after propagation by the l- tional modes [23]. th layer for s- and p-polarized light. fc The contribution of the free carrier species ε (ω)to Phase shift for s- and p-polarized light after passing the dielectric function can be described using classical through the l-th layer can be determined as [17]: Drude approximation [15]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2πd 2πd 1 ω l l s=p fc δ ¼ n cosθ ¼ n 1− sinθ ; l l;s=p l;s=p l ε ðÞ ω ¼ −ε  ; ð7Þ λ λ n l;s=p ωω þ iγ ð3Þ with where n is the complex refractive index for the l-th 1=2 layer, d is the thickness of the l-th layer, and θ is the l 2 Ne ω ¼ ð8Þ angle of incidence. p ε ε m ∞ 0 Partial reflection and transmission coefficients for the s- and p-polarizations can be calculated using Fresnel e γ ¼ ð9Þ equations. For example, partial reflection and transmis- m μ sion coefficients for the s-polarization have the following The screened plasma frequencies ω (Eq. (8)) depend form [21]: on the free carrier concentration N, high-frequency n cosθ −n cosθ ls ls dielectric permittivity ε , and the effective mass m of ðÞ lþ1 s ðÞ lþ1 s ∞ r ¼ l;lþ1 the free carriers (ε is the vacuum permittivity and e is n cosθ −n cosθ 0 ls ls ðÞ lþ1 s ðÞ lþ1 s the electrical unity charge). The plasmon damping 2n cosθ ls ls s ¼ parameter γ depends on the optical carrier mobility μ t p n cosθ þ n cosθ l;lþ1 ls ls ðÞ lþ1 s ðÞ lþ1 s (Eq. (9)) [24]. ð4Þ Parameters of ω and LOPC modes can be determined LO The complex reflectance ratios of the multilayer stack from the imaginary part of the energy loss function—Im can be thus obtained by substituting the partial reflection − [7], where ε(ω) is the complex dielectric function, and transmission coefficients for the N+1 interface (Eqs. εωðÞ (4)) in Eq. (1) and phase shifts of all the N layers (Eq. (3)): obtained from Eq. (5). Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 4 of 9 Results and Discussion SEM image (Fig. 2) shows the photo-etched cross sec- + + tion of n /n /n -GaN structure grown on GaN-buffer/ GaN-template/sapphire substrate, where six distinct layers are clearly visible, which are five GaN layers with different carrier concentration and sapphire substrate. It should be noted that the overall thickness of the investi- gated GaN structure as measured by SEM agrees with the technological one, and observed GaN layers accord- ing to Fig. 1 can be tentatively attributed to nominal top Si-doped n region (layer 1), undoped n region (layer 2), bottom Si-doped n region (layer 3), undoped GaN buffer (layer 4), and GaN template. Further, in order to have the deeper insight on the impur- ity/doping level of the investigated samples, SIMS measure- ments were performed. The obtained SIMS profiles (Fig. 3) are in good correlation with the nominal thickness of GaN layers and the overall thickness of the studied multilayer structure. All examined elements (H, C, O, Si) were above 16 3 the detection limit (3 to 5 × 10 at/cm )of SIMS + + technique. Fig. 3 Impurity elements profiles of the investigated n /n /n -GaN structure measured by SIMS from the sample surface Profile of intentional Si doping, in general, agrees with the nominal doping profile with the concentration of 19 −3 + about 2.8 × 10 cm in the doped top and bottom n 17 −3 regions and of about 2.3 × 10 cm in the undoped n region. However, as can be seen from SIMS data, there contains higher concentrations of unintentional oxygen 19 −3 is also thin (<50 nm)-delta layer with Si concentration of and carbon impurities of 2.4 × 10 cm and 1.4 × 18 −3 19 −3 1.1 × 10 cm between the GaN buffer and GaN tem- 10 cm , correspondingly. This delta layer is related plate. It should be noted that Si-doped delta layer also with homoepitaxial regrowth interface, which typically arises from the GaN template contamination with O, Si, and C impurities, absorbed from the atmosphere in the technological process of loading or at the beginning of the regrowth [25, 26]. As discussed above, SEM cross-section and SIMS ana- lysis give the structure of GaN layers, which differs from the nominal parameters by exciting of the additional GaN region, but with the overall thickness in agreement with the nominal one. In order to clarify the influence of additional GaN delta-layer found above on the IR reflectance spectrum of the investigated structure, the simulation of the experimental spectrum was performed by constructing models consisting of six layers, which correspond to nominal technological parameters, SEM images (Fig. 1), and seven layers according to SIMS. The calculated spectra based on the described above models are given in Fig. 4. As can be seen from Fig. 4, based on SIMS profile seven-layer model gives the best approximation of the + + experimental IR reflectance spectrum. Thus, further sim- Fig. 2 SEM image of cross-section of the investigated n /n /n -GaN ulations and analysis are performed using this model structure. The irregular pattern of vertical lines was formed during cleaving (i.e., before photo-etching) and is characteristic for the non- having modified parameters, as compared to nominal polished cleavages of Al O /GaN hetero-structures. Rough pyramidal 2 3 technological ones (Fig. 1), and which accounts for the layer (pinholes) at the sapphire/GaN template indicated by the arrow additional layer between the technological GaN buffer was revealed by photo-etching layer and GaN template (Fig. 5). Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 5 of 9 Fig. 5 The 7-layer model used to simulate the IR reflectance spectra of + + the investigated n /n /n -GaN structure. An additional layer (green)is thin interface layer between GaN template and the investigated GaN layers is a two-step process [27]. First, the fringes in the transparent region above the reststrahlen bands (ω > −1 1200 cm )are duetointerferenceeffects on thelayers of the multi-layer structure. In this way, the overall Fig. 4 Simulations of the IR reflectance spectra with different number thickness of the investigated structure, which is a sum + + of layers. The experimental spectrum of the investigated n /n /n -GaN of all layers, can be estimated. structure is shown by solid line. a Reststrahlen region. b The enlarged Once the stack thickness is known, the individual −1 spectra in the range above 750 cm thicknesses of each layer can be determined by fitting the calculated spectra to interference effects in the rest- Figure 6 shows experimental and fitted theoretical s-po- strahlen region of the spectrum. Layer thicknesses were larized reflectance spectra of the investigated structure at varied by taking into account the previously determined the 11° angle of incidence. The calculated spectrum is overall thickness. Under this constraint, the reflectance −1 based on the model described above (Fig. 5). Dispersion of above 1200 cm does not change significantly. The complex refractive index for the GaN layers and the interference effects in the reststrahlen region can be sapphire substrate was determined using Eq. (5). The distinguished from other features such as TO and LO sapphire substrate was considered as semi-infinite, that vibrational modes based on the fact that the interference allowed neglecting the internal reflections within the sub- fringes shift in position as the layer thicknesses are strate and from the non-polished backside. The compli- varied [28]. cated structure observed in the reststrahlen region of the During the approximation of the experimental spectrum spectrum is due to a combination of the overlapping GaN in the reststrahlen region, the following model parameters and Al O reststrahlen bands along with interference were varied: damping parameters γ and γ for E (LO) 2 3 LO TO 1 effects. Comparison of these data to the calculated spectra and E (TO) phonon modes; plasma frequency ω ;plasmon 1 p not only can provide thickness information on the various damping parameter γ ; and layer thicknesses. It should be layers of the samples, but can also help to interpret the noted, that only E symmetry phonons are IR active in s- complicated structure of the reststrahlen region in terms polarization [9]. Initial frequencies of E (LO) and E (TO) 1 1 of the contributions of the various materials. phonons for GaN and sapphire substrate were taken from The determination of layer thicknesses from the com- the IR reflectance [29] and Raman scattering [6, 14] experi- parison of the reflectance data to the calculated spectrum ments. Typical values of GaN phonon frequency are ω = TO Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 6 of 9 the IR reflectance spectra of bulk GaN and 6.78-μm- thick GaN layer on sapphire, with the thickness of GaN corresponding to the overall thickness of the investigated structure, were simulated in the reststrahlen band region (Fig. 7). As can be seen from Fig. 7, the reflectance spec- tra of 6.78-thick GaN layer on sapphire and bulk GaN in −1 the range of 500–740 cm are similar to the experimen- −1 tal spectrum. The small feature at ~511 cm is associ- ated with the sapphire substrate. It should be mentioned −1 that at ~736 cm , there is a weak dip that corresponds to A (LO) mode of GaN template. According to the se- lection rules, A (LO) mode is forbidden in s-polarized IR spectra [9]. The possible reason for the registration of this forbidden mode could be a polarization leakage due to the aperture of the reflectance accessory as well as microinhomogeneities of GaN crystal structure. Specific- ally, this can be caused by inclination of the c-axis of the column-like wurtzite structure of GaN from the direc- tion perpendicular to the film’s growth plane. This mode was not taken into account in our modeling because of its weak impact on the resulting spectrum. The features −1 in the range of 750–1200 cm are due to overlapping GaN:Si and sapphire reststrahlen bands and interface ef- −1 fects. The drop at ~775 cm is related to interface effect on the edge of the reststrahlen band of GaN layers and −1 sapphire. The broad dip at ~825 cm is associated with overlapping of the high-frequency branch of the + + plasmon-LO-phonon coupled mode (LPP ) of the n layers. Figure 8 shows the calculated imaginary parts of the Fig. 6 Experimental (solid line) and best-fit calculated (dash-dot line) + + IR reflectance spectra of the n /n /n -GaN structure grown on GaN- energy loss function for each layer according to oscillator template/Al O . a Reststrahlen region. b Interference region 2 3 parameters given in Table 1 for estimation of E -LOPC modes. As can be seen, the high-frequency branch of the −1 −1 + 560 cm and ω =740 cm . The phonon frequencies for LOPC modes (LPP ) at carrier concentrations lower than LO 17 −3 each layer were refined in the fitting process. Obtained 10 cm (n layer and template) almost coincide with best-fit parameters with the error bars are given in Table 1. E (LO) phonon mode. The increase in carrier concentra- 17 18 −3 It should be noted that obtainedinthe fittingprocess layer tion in the range of 2 × 10 –3×10 cm (Fig. 5) leads to thicknesses are in good agreement with the SEM data. significant high-frequency shift and broadening of the LPP −1 Referring to Fig. 6a, the reflectance peak at ~450 cm branch, which indicates the increase in interaction between can be attributed to the sapphire substrate. The features LO phonon and plasmon and the decrease in mobility of −1 + observed in the range of 500–740 cm are due to a charge carriers. This behavior of LPP branch agrees well combination of overlapping features from GaN layers with the experimental data on IR reflectance of Si-doped and sapphire reststrahlen bands. For the deeper analysis, GaN films grown on sapphire by Z.F. Li et al. [30], and Table 1 Best fit oscillator parameters for GaN layers of the investigated structure (layers are numbered from top to bottom) -1 −1 −1 −1 −1 −1 Layer no. ω (cm ) γ (cm ) ω (cm ) γ (cm ) ω (cm ) γ (cm )d (μm) d (μm) ε LO LO TO TO p p IR Nominal ∞ 1 740.2 (±0.5) 10.7 (±1.1) 561.1 (±0.8) 15.7 (±0.9) 507.8 (±1.2) 350.5 (±1.0) 0.47 (±0.02) 0.401 5.25 (±0.07) 2 740.7 (±0.8) 12.8 (±0.9) 560.8 (±0.2) 14.4 (±0.5) 55.7 (±0.5) 155.7 (±0.5) 1.73 (±0.06) 1.752 5.01 (±0.03) 3 740.4 (±0.3) 11.4 (±1.0) 562.3 (±0.4) 6.83 (±0.5) 537.1 (±0.9) 390 (±0.7) 0.8 (±0.02) 0.82 5.35 (±0.08) 4 740.1 (±0.7) 6.22 (±0.7) 560.7 (±0.1) 17.8 (±0.5) 132.3 (±0.5) 249.1 (±0.5) 0.27 (±0.03) 0.31 5.35 (±0.1) 5 742.1 (±0.2) 8.68 (±0.8) 560.4 (±0.7) 18.4 (±0.5) 436.1 (±0.7) 383.3 (±0.5) 0.01 (±0.001) - 5.3 (±0.09) Template 741.5 (±1.0) 13.14 (±1.3) 560.2 (±0.3) 7.16 (±0.1) 51.39 (±0.8) 180 (±0.9) 3.48 (±0.05) 3.51 4.99 (±0.07) Thickness of interface layer was not determined from SEM data Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 7 of 9 Table 2 Optically determined values of carrier concentration and mobility for each analyzed GaN layer of the investigated + + n /n /n -GaN structure 17 −1 2 −1 −1 Layer no. N ×10 (cm ) μ (cm V s ) 1 28.8 (±0.13) 133.3 (±1.20) 2 0.37 (±0.01) 300.0 (±0.90) 3 34.4 (±0.12) 119.7 (±0.75) 4 2.04 (±0.03) 187.4 (±0.67) 5 22.20 (±0.07) 121.9 (±0.52) Template 0.31 (±0.01) 259.4 (±1.27) lowers with increasing n-type doping [34]. It should be mentioned, that carrier concentration for the n layers in 18 −3 the order of ~10 cm is in good agreement with the re- sults of our Raman studies of similar GaN structures based Fig. 7 Experimental (solid line) IR reflectance spectra of the + + on analysis of LOPC modes [6]. Obtained decrease of investigated n /n /n -GaN structure and calculated reflectance spectra of 6.78-μm-thick GaN layer on sapphire (dash-dot line) and carrier mobility μ with carrier concentration is also in good bulk GaN (dash line) agreement with Hall experiments in GaN [35] and theoret- ical modeling [36]. Raman measurement in bulk GaN [10] and epitaxial layers The values of high-frequency dielectric permittivity ε [31]. It should be noted that the low-frequency LPP were found to be in the range of 4.99–5.35 (Table 1). branch of the LOPC cannot be reliably defined in our case, The increase in ε for the doped n layers as compared as s-polarized IR reflectance spectra were not measured in to n layers can be related to the red shift of the α-GaN −1 low-frequency range below 300 cm . band gap [37]. It should be noted that values of ε can Values of carrier concentration and mobility listed in be determined with relatively small error only for low- Table 2 were calculated using Eqs. (8) and (9) with electron conductive films. Accuracy in the determination of ε effective mass m* of 0.2 m [32]. It can be seen, that calcu- decrease with carrier concentration, which is related to lated carrier concentration profile is similar to the Si impur- the fact that the ε parameter accounts for “the high- ity concentration profile obtained by SIMS measurements frequency” limit when the dielectric model function is (Fig. 3), but with the order of magnitude lower carrier con- extrapolated to shorter wavenumbers than those studied −1 centrations as compared to concentration Si impurity. Such here [11]. The wide spectral range of 300–4000 cm discrepancy in concentrations of carriers and doping im- was analyzed in order to decrease the error in the deter- purities was observed earlier by M. Bockowski et al. [33], mination of ε and other parameters involved in model- and was related to compensation effects by acceptor states ing the IR reflectance spectra of n layers. (likely by gallium vacancies), formation energy of which Conclusions IR reflectance spectra of the multilayer structure consist- ing of GaN layers grown on a sapphire substrate and doped with different concentrations of Si impurity were measured and analyzed in details. Analysis of the investi- gated structure by SEM of photo-etched cross-section showed good correlation with the technological parame- ters of the GaN layers. SIMS analysis also revealed the presence of thin delta layer near the GaN buffer/GaN- template interface with higher content of Si and O impur- ities, which is related to homoepitaxial regrowth interface. Modeling of IR reflectance spectrum of the studied multi- layer structure by including into analysis the additional layer made it possible to obtain the best fitting of the experimental spectrum. Obtained thicknesses of GaN layers are in good agreement with the SEM and SIMS Fig. 8 Calculated imaginary part of dielectric function obtained for data. Calculated from the spectral dependence of dielectric each analyzed GaN layer from the best-fit data analysis permittivity LOPC modes for each GaN layer showed Tsykaniuk et al. Nanoscale Research Letters (2017) 12:397 Page 8 of 9 high-frequency shift and broadening of LPP branch with 3. Nakamura S, Mukai T, Senoh M (1991) High-power GaN p-n junction blue- light-emitting diodes. Jpn J Appl Phys 30:L1998–L2001 the increase in carrier concentration. Concentration and 4. Nakamura S, Senoh M, Nagahama S, Iwasa N, Yamada T, Matsushita T, mobility of charge carrier for each GaN layer were calcu- Kiyoku H, Sugimoto Y (1996) InGaN-based multi-quantum-well-structure lated from the plasmon frequency and damping param- laser diodes. Jpn J Appl Phys 35:L74–L76 5. Koschnick F, Michael K, Spaeth J, Beaumont B, Gibart P (1996) Optical eter. Obtained carrier concentration profile is similar to detection of electron nuclear double resonance on a residual donor in those obtained by SIMS, but with values of carrier concen- wurtzite GaN. Phys Rev B 54:R11042–R11045 tration one order of magnitude less than the concentra- 6. Belyaev AE, Strelchuk VV, Nikolenko AS, Romanyuk AS, Mazur YI, Ware ME, DeCuir EA, Salamo GJ (2013) Depth profiling of strain and carrier tion of Si doping impurity, which can be attributed to concentration by cleaved surface scanning of GaN Gunn-diode: confocal compensation effects by the defect acceptor states. Thus, Raman microscopy. Semicond Sci Technol 28:105–111 it is demonstrated that IR reflectance spectroscopy and 7. Sobotta H, Neumann H, Franzheld R, Seifert W (1992) Infrared lattice vibrations of GaN. Phys Status Solidi 174:K57–K60 2 × 2 transfer matrix method can be successfully used for 8. Everall NJ (2009) Confocal Raman microscopy: performance, pitfalls, and analysis of epitaxial multilayer GaN structures with non- best practice. Appl Spectrosc. doi:10.1366/000370209789379196 uniform doping profiles, and allow for the determination 9. Barker AS, Ilegems M (1973) Infrared lattice vibrations and free-electron dispersion in GaN. Phys Rev B 7:743–750 of the fundamental electron and phonon parameters of 10. Perlin P, Camassel J, Knap W, Taliercio T, Chervin JC, Suski T, Grzegory I, each GaN layer. Porowski S (1995) Investigation of longitudinal-optical phonon-plasmon coupled modes in highly conducting bulk GaN. Appl Phys Lett 67:2524–2526 Abbreviations 11. Kasic A, Schubert M, Einfeldt S, Hommel D, Tiwald TE (2000) Free-carrier and IR: Infrared; FTIR: Fourier transform infrared spectroscopy; SEM: Scanning electron phonon properties of n- and p-type hexagonal GaN films measured by microscopy; SIMS: Secondary ion mass spectrometry; LOPC: Longitudinal optical infrared ellipsometry. Phys Rev B 62:7365–7377 phonon–plasmon coupled 12. Mirjalili G, Parker TJ, Shayesteh SF, Bulbul MM, Smith SRP, Cheng TS, Foxon CT (1998) Far-infrared and Raman analysis of phonons and phonon interface Acknowledgements modes in GaN epilayers on GaAs and GaP substrates. Phys Rev B 57:4656–4663 This work was supported by NATO SfP Grant 984735 and by the US National 13. Dumelow T, Parker TJ, Smith SRP, Tilley DR (1993) Far-infrared spectroscopy Science Foundation Engineering Research Center for Power Optimization of of phonons semiconductor superlattices and plasrnons in semiconductor Electro Thermal Systems (POETS) with cooperative agreement EEC-1449548. The superlattices. Surf Sci Rep 17:153–212 authors are thankful to Ivan Karbovnyk for critical reading of the manuscript. 14. Lee SC, Ng SS, Abu Hassan H, Hassan Z, Dumelow T (2014) Crystal orientation dependence of polarized infrared reflectance response of Authors’ Contributions hexagonal sapphire crystal. Opt Mater (Amst) 37:773–779 BTs was responsible for IR reflectance measurements, analysis of obtained 15. Kroon RE (2007) The classical oscillator model and dielectric constants extracted results, modeling of spectra, participated in discussion of results, and was from infrared reflectivity measurements. Infrared Phys Technol 51:31–43 involved in the drafting of the manuscript. AN performed formulation of the 16. Mitsas CL, Siapkas DI (1995) Generalized matrix method for analysis of research problem, participated in discussion of results, was involved in the coherent and incoherent reflectance and transmittance of multilayer structures drafting of the manuscript. VS was involved in the discussion of the manuscript with rough surfaces, interfaces, and finite substrates. Appl Opt 34:1678–1683 and gave final approval of the version to be published. VN assisted in IR 17. Katsidis CC, Siapkas DI (2002) General transfer-matrix method for optical reflectance measurements. YM, MW, and EADC were responsible for the growth multilayer systems with coherent, partially coherent, and incoherent of the studied structures. BS and JLW performed photo-etching and SEM analysis. interference. Appl Opt 41:3978–3987 RJ performed SIMS analysis. GS and AB were involved in the discussion of the 18. Weyher JL, Tichelaar FD, Van Dorp DH, Kelly JJ, Khachapuridze A (2010) The manuscript and gave final approval of the version to be published. All authors K2S2O8KOH photoetching system for GaN. J Cryst Growth 312:2607–2610 read and approved the final manuscript. 19. Lewandowska R, Weyher JL, Kelly JJ, Konczewicz L, Lucznik B (2007) The influence of free-carrier concentration on the PEC etching of GaN: a calibration with Raman spectroscopy. J Cryst Growth 307:298–301 Competing Interests 20. Weyher JL, Van Dorp DH, Kelly JJ (2015) Principles of electroless The authors declare that they have no competing interests. photoetching of non-uniformly doped GaN: kinetics and defect revealing. J Cryst Growth 430:21–27 Publisher’sNote 21. Katsidis CC, Ajagunna AO, Georgakilas A (2013) Optical characterization of Springer Nature remains neutral with regard to jurisdictional claims in free electron concentration in heteroepitaxial InN layers using Fourier published maps and institutional affiliations. transform infrared spectroscopy and a 2 × 2 transfer-matrix algebra. J Appl Phys 113:1–12 Author details 22. Gervais F, Piriou B (1974) Anharmonicity in several-polar-mode crystals: V. Lashkaryov Institute of Semiconductor Physics, National Academy of adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit Sciences of Ukraine, Pr. Nauky 41, Kiev 03680, Ukraine. Institute for infrared reflectivity. J Phys C Solid State Phys 7:2374 Nanoscience and Engineering, University of Arkansas, West Dickson 731, 23. Harima H (2002) Properties of GaN and related compounds studied by Fayetteville, AR 72701, USA. Institute of High Pressure Physics, Polish means of Raman scattering. J Phys: Condens Matter 14:R967–R993 Academy of Sciences, Sokolowska str. 29/37, 01-142 Warsaw, Poland. 24. Yu P, Cardona M (2010) Fundamentals of semiconductors. Physics and Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, materials properties, 4th edn. Springer-Verlag, Berlin PL-02-668 Warsaw, Poland. 25. 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Nanoscale Research LettersSpringer Journals

Published: Jun 8, 2017

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