Zengqi Zhang, Zongwei Xu,,a) Ying Song, Tao Liu, Bing Dong, Jiayu Liu, and Hong Wang

AFFILIATIONS 1 State Key Laboratory of Precision Measuring Technology and Instruments,Centre of MicroNano Manufacturing Technology,Tianjin University,Tianjin 300072,China

2State Key Laboratory of Separation Membranes and Membrane Processes,School of Materials Science and Engineering,Tianjin Polytechnic University,Tianjin 300387,China

ABSTRACT As an important wide-bandgap semiconductor,gallium nitride(GaN)has attracted considerable attention.This paper describes the use of confocal Raman spectroscopy to characterize undoped GaN,n-type GaN,and p-type GaN through depth profilin using 405-,532-,and 638-nm wavelength lasers.The Raman signal intensity of the sapphire substrate at different focal depths is studied to analyze the depth resolution.Based on the shift of the E2H mode of the GaN epitaxial layer,the interfacial stress for different types of GaN is characterized and calculated.The results show that the maximum interfacial stress appears approximately at the junction of the GaN and the sapphire substrate.Local interfacial stress analysis between the GaN epitaxial layer and the substrate will be very helpful in furthering the applications of GaN devices.

KEYWORDS Confocal Raman spectroscopy,Gallium nitride,Heteroepitaxial growth,Interfacial stress

I.INTRODUCTION

Gallium nitride (GaN) is a third-generation semiconductor material that has a high breakdown electric field large forbidden bandgap,high thermal conductivity,high electron saturation velocity,and strong radiation resistance.Its high electron mobility makes GaN highly suitable in the fabrication of high-frequency microwave devices.The suitability of high-frequency device materials is often evaluated using Johnson’s figur of merit.The Johnson’s figur of merit is 1 for Si,2.96 for GaAs,and 22 for SiC—for GaN,it can be up to 37.1Both SiC and GaN can output high power.Moreover,GaN can output high power at high frequencies.1Therefore,GaN has obvious advantages in the fiel of 5G radio frequency,power amplifie materials,power devices,and fast charging.

The GaN epilayer(EPI)exhibits two types of epitaxial growth:homoepitaxial and heteroepitaxial.To date,heteroepitaxial growth has been widely used for producing GaN epitaxial layers using metal organic chemical vapor deposition(MOCVD)or halide vapor phase epitaxy.The selection of heterogeneous substrates generally follows the principles of structure matching,lattice constant matching,and thermal expansion coefficien matching.The substrate material has a significan influenc on the crystal quality of heteroepitaxial GaN.The main substrate materials used for GaN heteroepitaxial growth are sapphire,SiC,Si,diamond,and LiAlO2,among which sapphire,SiC,and Si are the most commonly used.2–4

The main problems with GaN heteroepitaxial growth stem from lattice mismatch and thermal stress mismatch of heterogeneous substrates.The epitaxial growth of GaN on a substrate with a large lattice mismatch will cause a high density of dislocations(108–1010cm-2)in the GaN epitaxial layer.High-density dislocations reduce the carrier mobility,lifetime,and material thermal conductivity,while forming nonradiative recombination centers and lightscattering centers,thus reducing the luminous efficienc of optoelectronic devices.In addition,electrode metal and impurity metal elements will diffuse into the dislocations to form a leakage current path,thus reducing the output power of the device and seriously affecting its stability.5Growing GaN on a substrate with an excessively different coefficien of thermal expansion will produce a large biaxial stress during the cooling process and may cause microcracks,which will degrade the optoelectronic properties of the epitaxial layer.4In addition,the existence of residual stress can lead to the separation of the GaN from the substrate,whereby thermal mismatch stress and shear stress become the driving force for interface separation.5,6Adding a buffer layer or an insertion layer is a good way of controlling the interfacial stress.Common buffer layers for GaN include AlN and AlGaN graded buffer layers.Therefore,interfacial studies on defect characterization,stress analysis,and new buffer layer settings are the key to preparing high-quality GaN epilayers.

Confocal microscopes use a pinhole or slit placed on the backimage plane of the microscope objective to block light outside the confocal plane.Confocal Raman spectrometry offers greatly improved depth resolution and achieves rapid,nondestructive,and noncontact detection.7Songet al.used confocal Raman spectrometry to distinguish the longitudinal optical phonon (LO) mode of the epitaxial layer and the longitudinal optical phonon–plasmon coupled (LOPC) mode of a 4H-SiC substrate layer,8while Yamaguchiet al.applied this technique to characterize the mechanical stress of Si.9Through confocal micro-Raman spectroscopy,Kladkoet al.revealed the epitaxial structure of the nitride layer and the micrometer-scale depth distribution of the deformation gradient in a sapphire substrate interface region.10Tadaet al.studied the stress distribution in the shallow trench isolation structure of Si,11Kudrinet al.identifie the cleavage edge section of the heterostructure of a GaMnAs layer,12and Holmiet al.characterized the volumetric stress distribution inα-GaN grown by the ammonothermal method,and further determined the types of linear dislocations.13However,for the stress analysis of GaN on a sapphire substrate,previous analyses have focused on the sample surface rather than depth profiling

In this paper,undoped,n-type,and p-type GaN materials on a sapphire substrate are characterized with depth profilin through confocal Raman spectroscopy.The interfacial stress distribution and resolution corresponding to different excitation light wavelengths and different depths are analyzed and discussed.

II.EXPERIMENTAL

A.Measurement procedure

The experiments described in this paper were carried out at room temperature using two confocal Raman spectrometers.The firs was a Horiba iHR550 spectrometer with a focal length of 550 mm.The spectral excitation light source was generated by a solidstate Nd:YAG SHG laser with wavelengths of 405 nm at 20 mW and 532 nm at 200 mW.The second was a Horiba XploRA PLUS spectrometer with a 250-mm focal length.The spectral excitation light source was generated by a solid-state Nd:YAG SHG laser with a wavelength of 638 nm at 9.53 mW.Different wavelength lasers have different excitation efficiencies and so choosing different powers ensures that the Raman scattering intensity of the different wavelength lasers can obtain a clear spectrum without damaging the sample.To avoid photocarbonization during Raman characterization,the laser power attenuation ratio was selected to be 25%,1%,and 100% for the 405-,532-,and 638-nm wavelengths,respectively.

All tests were carried out using a 100×objective lens(NA=0.9)and 1800 lines/mm grating.The Horiba iHR550 spectrometer uses the slit confocal method with a slit width of 100μm,blocking the light outside the confocal plane.According to the optical limit,the spatial resolution is better than 1μm in the horizontal direction and 2μm in the vertical direction(parallel to the optical axis).The integration time of spectrum acquisition was 10 s,and two accumulations were conducted.The LabSpec 6 software was used to fi the collected Raman spectrum according to the Gaussian–Lorentzian function to obtain the position,peak intensity,and half-width of the characteristic peak.The equipment was operated on a highprecisionXYZmechanical automatic platform,which could be adjusted through coarse and fin focusing,and a single-point depth test was performed in theZdirection with a minimum step size of 0.25μm.To ensure the accuracy of the experiment,the singlewindow mode was used in the single-point depth test to avoid any possible errors from the movement of the grating during a multiwindow scanning process.The center of the spectrum range was 568 cm−1.

During the experiment,the focus depth was changed by controlling the position of theXYZ-stage in theZ-axis direction.As shown in Fig.1,a focus depth of 0μm corresponds to the surface of the sample.Negative focus depths correspond to the inside of the sample,and positive focus depths correspond to the equipment being above the sample.In this way,the depth of the GaN layer was probed by changing the focus depth.

FIG.2.Illustrations and details of GaN samples.(a)GaN wafer samples:(from left to right)n-type,undoped,and p-type.(b)Illustration of the internal structures of the GaN samples.

B.Sample description

All samples of GaN epitaxial wafers used in this paper were purchased from Hengchuan Electrical Co.,Ltd.The samples were prepared using MOCVD.The GaN wafers were cut into pieces by laser for the Raman spectroscopy characterizations [see Fig.2(a)].

The test samples measured 5 mm × 5 mm,with a thickness of around 0.43 mm,roughness of approximately 0.5 nm,and dislocation density of 107cm−2.The carrier concentration of the ndoped and p-doped layers was between 1017and 1018cm−3.The resistance was 0.005 Ω⋅cm.The detailed structures of the samples are shown in Fig.2(b).There are AlN buffer layers of thickness 25 nm on the sapphire substrate to reduce the lattice mismatch,and 2000-nm-thick undoped GaN was grown on the buffer layer.The surface layer for the n-type GaN sample was a 2000-nm-thick n-type GaN thin layer,whereas the undoped sample had an additional 500-nm-thick undoped GaN thin layer and the p-type GaN sample had an additional 200-nm-thick p-type GaN layer.

III.RESULTS AND DISCUSSION

For wurtzite GaN,the phonon normal mode at theΓpoint,as predicted by group theory,has eight groups of the form 2A1+2B1+2E1+2E2.Among them,theA1andE1modes both have one set of acoustic modes,while the remaining six modes(A1+E1+2B1+2E2) are optical.The modes with Raman activity are 2A1+2E1+E2L+E2H,a total of six types.14As shown in Fig.3,the phonon dispersion of the hexagonal structure along[0001](Γ→Ain the Brillouin zone)is approximated by folding the phonon dispersion of the cubic structure along[111](Γ→L).This folding reduces the transverse optical(TO)phonon mode at theLpoint of the Brillouin zone in the cubic structure to theE2mode at theΓpoint of the Brillouin zone in the hexagonal structure.This mode is written asE2H,where H denotes the higher-frequency branch of theE2phonon.In the hexagonal structure,the polar phonons induce anisotropy in the macroscopic electric field The atomic displacements of theE1andE2modes are perpendicular to the c-axis,while the others run along the c-axis.The atomic shift of theE2Hmode is performed by the N atom,as shown in Fig.3.14

FIG.3.Optical phonon modes in the wurtzite structure.14

TABLE I.Typical phonon frequencies of wurtzite GaN(cm−1).

Table I lists the typical phonon frequencies of GaN observed by Raman scattering.15For the GaN single crystal with a wurtzite structure,there is anAl(TO) mode centered at 533 cm−1.TheAlg(S)mode centered at 418.1 cm−1is the characteristic peak of the sapphire substrate.10In addition,the 578 cm−1and 750 cm−1peaks of theEg(S)mode relate to the sapphire substrate.16

A.Analysis of the sapphire signal intensity

The 532 nm laser was used to perform Raman characterizations of the three samples by focusing the laser beam on the samples’surface.The Raman spectra are shown in Fig.4.The Raman spectra have been fitte to a Gaussian–Lorentzian function using Lab-Spec 6.The main peak of the GaN Raman spectra is theE2Hmode peak at about 568 cm−1.14The Raman characteristic peak intensity of the sapphire at 418.1 cm−1is 771,687,and 330 counts for the n-type GaN,undoped GaN,and p-type GaN,respectively.As shown in Fig.2,the n-type GaN has the largest GaN thickness,whereas the p-type GaN has the smallest thickness.The ntype GaN has the strongest sapphire substrate signal,while the p-type GaN has the weakest sapphire substrate signal,as shown in Fig.4.The absorption coefficient of the samples for the 532-nm laser are in the order p-type GaN >undoped GaN >n-type GaN.

FIG.4. Raman spectra with 532-nm-wavelength laser using Horiba iHR550 spectrometer.

From Fig.4,it is clear that the p-type GaN has an extra peak on the left side of theE2Hmode.The p-type GaN is doped with Mg ions.This peak may be due to the Mg ion doping in the p-type GaN,which increases the number of defects in the sample and enhances the dislocation.23

B.Depth profiling of GaN and sapphire signals

Depth profilin of the GaN and sapphire signals was performed on the three samples using the 532 nm laser.Each sample was tested at three different points,as shown in Fig.5.The depth analysis from 15μm to −15μm was achieved by moving the stage along theZaxis,where negative depths correspond to focusing the laser beneath the surface and positive depths correspond to focusing the laser above the sample.Figure 5(a) shows the variation of the phonon line intensity ofA1g(S)in the three samples with respect to the focus depth.The sapphire phonon line intensity gradually decreases as the focus depth moves from the inner part to the sample surface.Figure 5(b)shows the Raman spectra results for the surface and at a depth of −15μm in the n-type GaN.When focusing at −15μm,the Raman intensity of the sapphire phonon modeA1g(S) significantl exceeds theE2Hmode of GaN.When focusing on the sample surface,theE2Hmode is the main Raman signal,and the sapphire signal is weak.

FIG.5.Depth profilin of three samples by the excitation of 532-nm laser from the Horiba iHR550 spectrometer.(a)Curve of sapphire A1g(S)mode Raman peak intensity and focal depth for three samples with 100×objective lens with step size of 1 μm.(b)Raman spectra results when focusing on the surface and at −15 μm with n-type GaN.(c)Depth profilin of n-type GaN with a fine step size of 0.5 μm.

The depth test was repeated with the n-type GaN and a 532-nm laser with a fine step size of 0.5μm.As shown in Fig.5(c),theA1g(S)andEg(S)signals gradually decrease as the focus depth moves from the inside of the sample to the surface,whereas theE2Hmode signal for GaN gradually increases.The effective depth profilin of different layers indicates that the Horiba iHR550 spectrometer has a good resolution in the depth(Z)direction.

C.Confocal Raman depth analysis and calculation of interfacial stress

Different wavelength lasers have different penetration depths.The penetration depth can be calculated from the absorption coeffi cient as24

wheredpis the penetration depth andαis the absorption coefficient The absorption coefficien can be determined using the relation25

wherekis an extinction coefficien andλis the wavelength of the laser.Therefore,the relationship between penetration depth and extinction coefficien can be obtained as

The extinction coefficien of bulk GaN has been investigated in previous studies.The curve of extinction coefficien with respect to wavelength is shown in Fig.6.26The extinction coefficien of bulk GaN at 405,532,and 638 nm can be obtained from the curve.The absorption coefficien and penetration depth can then be calculated using Eqs.(1)–(3)(see Table II).

FIG.6.Extinction coefficien of bulk GaN.26

The generation of the Raman scattering spectrum is related to the lattice vibration of the sample.Raman spectroscopy can accurately measure the lattice vibration energy of the material.When there is no stress in the crystal,the crystal lattice vibrates at an intrinsic frequency corresponding to the elastic constant.When the sample is subjected to tensile or compressive residual stress,its atomic bond lengths will extend or shorten accordingly,and the lattice vibration energy will change.Given the relationship between the force constant and the bond length,the force constant of the sample will increase or decrease,so the vibration frequency of the atom will change and the peak of the Raman spectrum will shift to a lower or higher frequency.27–29

The frequency shift of the Raman spectrum is sensitive to the stress of the sample.Generally,when there is compressive stress inside the sample,the bond length of the molecule will decrease and the force constant will increase.This increases the vibration frequency and shifts the Raman spectrum to the right,with the wave number increasing (more inelastic energy lost during scattering).Conversely,when there is a tensile stress inside the sample,the Raman spectrum shifts to the left and the wave number decreases.Therefore,a frequency shift in the characteristic peak of the Raman spectrum can effectively characterize the local stress of the sample.

The frequency shift has a linear relationship with the stress in the material.The stress at different depths can be calculated according to the frequency shift as

where Δωis the frequency shift,σis the stress,andKis the stress coefficient30

According to previous studies,the position of theE2Hmode of a standard GaN single crystal is 568 cm−1,and the stress coefficien of GaN grown on c-direction sapphire is 2.56.30In previous research on different types of GaN substrates,Jiang31found the compressive stress to be 1.277 GPa when the position of theE2Hmode of GaN on sapphire substrate was 571.27 cm−1.

Raman spectrometry has a certain spectral resolution,but data fittin can effectively increase the sensitivity and elucidate the Raman spectrum shift.For a grating of 1800 lines/mm,the spectral resolution is 1.17 cm−1,and a nominal sub-pixel resolutionof 0.02 cm−1can be obtained after fittin the Raman peak with a Gaussian–Lorentz function,greatly improving the measurement accuracy.32

TABLE II.Extinction coefficient absorption coefficient and penetration depth of bulk GaN by different lasers.

TABLE III.Depth profilin of GaN E2H mode Raman spectra with 532 nm laser(frequency shift and stress of n-type GaN,undoped GaN,and p-type GaN,100×objective lens,1800 lines/mm grating,Horiba iHR550 spectrometer).

The three kinds of GaN samples were characterized by Raman spectroscopy depth profilin from −15μm to 15μm with 405 and 532 nm lasers.The Raman spectra of theE2Hmode under different focal depths were fitte and further analyzed according to the above calculation method.The frequency shift over all depths was found to be greater than 0.02 cm−1,indicating that the measurement accuracy was sufficient The interface stress value was then calculated according to the frequency shift.The peak fittin results,frequency shifts,and corresponding stress values of theE2Hmodes are presented in Tables III and IV.All samples exhibit a frequency shift toward the red end of the spectrum.Therefore,the interfacial state iscompressive stress,which is consistent with the compressive stress of the sapphire substrate sample.15,31

TABLE IV.Depth profilin of GaN E2H mode Raman spectra with 405 nm laser(frequency shift and stress of n-type GaN,undoped GaN,and p-type GaN,100×objective lens,1800 lines/mm grating,Horiba iHR550 spectrometer).

FIG.7.(a)Stress depth profilin of GaN samples with step length of 1 μm under the parameters in Table III.(b)Stress depth profilin of GaN samples with step length of 1 μm under the parameters in Table IV.Red triangles represent the depth at which the E2H mode peak intensity of the GaN is the strongest.

According to the Raman spectrum characterization results,the depth profilin of the calculated interfacial stress values is shown in Fig.7.The intensity of the main characteristic peak of the epitaxial layer should be the strongest when the laser focuses on the sample’s surface.7,33In this paper,the red triangles mark the depth at which the peak intensity of theE2Hmode is the strongest.TheE2Hmode shift and the calculated local stress display variations around the interfacial layers,where the maximum interfacial stress value appears a few micrometers below the sample surface for both the 405 and 532 nm lasers.The thermal conductivity coefficien of GaN is four times greater than that of sapphire below 100° C.There is a large lattice mismatch and thermal mismatch between the sapphire and GaN layers,although the 25-nm AlN thin layer should lessen the mismatch to some extent.Interfacial residual stress will be generated during the growth process of the GaN epitaxial layer.Large residual stress appears at the interface between the sapphire and GaN andextends to the surface of the sample,as shown in Fig.7.The residual stress gradually drops as the focus point moves towards the sample surface.This is mainly because of the high lattice quality of the EPI layer of the GaN samples.

TABLE V.Depth profilin of GaN E2H mode Raman spectra with 638 nm laser(frequency shift and stress of n-type GaN,undoped GaN,and p-type GaN,100×objective lens,1800 lines/mm grating,Horiba XploRA PLUS spectrometer).

Compared with the results from using the 532-nm wavelength laser,characterization by the 405 nm laser produces a larger difference between the maximum and minimum values of the interfacial stress.The stress results characterized by the 532 nm laser exhibit smoother transitions during the depth profiling The difference between the two results is mainly due to the different penetration depths of the lasers.

The residual stress characterized by 532 nm laser Raman spectroscopy shows that the stress can be ordered as undoped GaN>ntype GaN>p-type GaN.Among the three samples,the p-type GaN has the thinnest GaN layer.However,the n-type GaN was found to have a smaller stress value when characterized by the 405 nm laser.Because the laser wavelength influence the attenuation(absorption)coefficien and Raman scattering efficiency34there may be a significant difference between the n-type GaN and the other two samples when using the 405 nm laser.Moreover,the penetration depth of GaN with the 405-nm wavelength laser is 2.86μm(Table II),which is less than the thickness of the n-type GaN.This may affect the accuracy of the characterization,although the actual penetration depth can be more than 2.86μm due to the influenc of the refractive index.8

To determine the cause of the difference in the residual stress of n-type GaN,confocal Raman depth characterization was performed using the 638-nm wavelength laser of the Horiba XploRA PLUS spectrometer.The peak fittin results,frequency shift,and corresponding stress values of theE2Hmodes are presented in Table V,and the depth profilin of the calculated interfacial stress values is shown in Fig.8.The residual stress characterized by 638 nm laser Raman spectroscopy also runs in the order undoped GaN>n-type GaN>p-type GaN.Although the characterization with the 638-nm wavelength laser was not performed using the same spectrometer as for the 532-and 405-nm wavelength lasers,the magnitude relationship and trends for the three samples are the same.This proves that penetration depths of less than the sample thickness may degrade the accuracy of interfacial stress measurements for n-type GaN when using a 405 nm laser.

FIG.8.Stress depth profilin of GaN samples with step length of 1 μm under the parameters in Table V.

IV.CONCLUSIONS

Confocal Raman spectroscopy has been used to nondestructively characterize and analyze the interfacial stress of GaN on a sapphire substrate by depth profiling The distribution of interfacial stress for n-type,undoped,and p-type GaN was characterized and calculated using 405-,532-,and 638-nm wavelength lasers.By calculating theE2Hmode Raman shift,the interfacial compressive stress between the GaN and sapphire substrate was found to run in the order undoped-GaN>n-type GaN>p-type GaN.The stress results characterized by the 532 nm laser showed smoother transitions during the depth profiling The depth profilin of interfacial stress is useful for solving key problems in the preparation of new semiconductor materials with high-quality GaN substrates and functional devices.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China(Grant Nos.51575389 and 51761135106),the National Key Research and Development Program of China(Grant No.2016YFB1102203),the State Key Laboratory of Precision Measuring Technology and Instruments(Pilt1705),and the‘111’Project of the State Administration of Foreign Experts Affairs and the Ministry of Education of China(Grant No.B07014).