Surface roughness estimation of MBE grown CdTe / GaAs ( 211 ) B by ex-situ spectroscopic ellipsometry

Spectroscopic ellipsometry (SE) ranging from 1.24 eV to 5.05 eV is used to obtain the film thickness and optical properties of high index (211) CdTe films. A threelayer optical model (oxide/CdTe/GaAs) was chosen for the ex-situ ellipsometric data analysis. Surface roughness cannot be determined by the optical model if oxide is included. We show that roughness can be accurately estimated, without any optical model, by utilizing the correlation between SE data (namely the imaginary part of the dielectric function,  or phase angle, ψ) and atomic force microscopy (AFM) roughness.  and ψ values at 3.31 eV, which corresponds to E1 critical transition energy of CdTe band structure, are chosen for the correlation since E1 gives higher resolution than the other critical transition energies. On the other hand, due to the anisotropic characteristic of (211) oriented CdTe surfaces, SE data ( and ψ) shows varieties for different azimuthal angle measurements. For this reason, in order to estimate the surface roughness by considering these correlations, it is shown that SE measurements need to be taken at the same surface azimuthal angle. Estimating surface roughness in this manner is an accurate way to eliminate cumbersome surface roughness measurement by AFM. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4959223]


INTRODUCTION
Spectroscopic ellipsometry provides experimental data that can be modeled to obtain optical properties of the material.Ellipsometry allows one to obtain important aspects of the material such as alloy composition, surface temperature during growth, surface roughness etc. 1 In in-situ SE analysis, the surface roughness layer is in general modeled using effective medium approximation (EMA). 2,3his model yields results that are in significant positive correlation with those obtained by AFM measurements. 4,5However, in ex-situ SE data analysis, due to the formation of the oxide layer once the sample is exposed to air, EMA cannot give the correct surface roughness value if both EMA and oxide layer are used in the model.Therefore, only oxide layer can be used on the top layer of the optical model. 6dTe is most widely used as a buffer layer between alternative substrates (such as GaAs, Si or Ge) [7][8][9][10] and HgCdTe, as an alternative to the standard substrate CdZnTe.11,12 HgCdTe is the leading material for use in infrared detectors, especially for strategical applications.13 The crystal quality and the surface roughness of the CdTe buffer layer are extremely important for the successful growth of HgCdTe by molecular beam epitaxy (MBE).Because of the large lattice mismatch between CdTe and the alternative substrates, some difficulties have been encountered in optimization of the growth process.Non-optimal growth conditions will negatively affect CdTe growth and, hence, HgCdTe epi-layer growth.Some undesired obstacles of the CdTe buffer layer, such as a large number of dislocations and other defects, and surface roughness, will deteriorate the crystal quality of HgCdTe; they hence need to be minimized by optimizing the growth conditions.
The (211) oriented surface is preferred for the MBE growth of HgCdTe focal plane array technology since this surface is free of common growth defects such as hillocks, oval defects, twinning, and antiphase domains that are present on other orientations such as (110), (100) and (111)B. 14e-terminated (211)B surface of CdTe is also required because this surface provides larger absorption of the Hg atoms to the surface.15 HgCdTe IR detectors grown by MBE on CdTe/GaAs (211)B have being fabricated with good crystal quality and high operability.8,16 An atomically smooth surface of CdTe is required for the consecutive growth of HgCdTe.For this reason, characterization of surface properties is important.The most reliable surface roughness measurement method is AFM. Hoever, this measurement may take a long time, and is also only carried out after growth on what is usually a limited sample size and limited local area.The measurement must be repeated at different positions to get an accurate measurement of overall surface roughness.
In this study, we show that surface roughness of CdTe/GaAs (211)B buffer layers can be determined by ex-situ SE data without constructing an optical model.Furthermore, the optical properties and thickness of the CdTe layers were determined exclusively by constructing an oxide/CdTe/GaAs optical model.

EXPERIMENTAL
The CdTe films were grown on epi-ready GaAs(211)B substrate by a Veeco Gen-20MZ MBE system.(211)B represents a B-phase (Te-terminated) CdTe (211) oriented surface.The samples mentioned in this paper were grown under various growth conditions and thicknesses between 0.3 and 6 µm.8][19] These de-oxidation processes were controlled by in-situ Reflection High Energy Electron Diffraction (RHEED), which yielded data related to surface crystal quality.Substrate temperature was controlled by pyrometer.After oxide removal, a CdTe nucleation layer was grown at a colder temperature (∼210 • C) than that for CdTe film (∼330 • C). 19 Before CdTe growth, the nucleation layer was annealed under Te 2 flux in order to stabilize the surface.The growth parameters are summarized in Table I.Surface oxides of the substrates were thermally removed under As 4 flux for samples 1-11 and the de-oxidation temperatures were between 580 and 650 • C. The de-oxidation processes were carried out under In overpressure for samples 12-16, and oxide removal temperatures were between 488 and 532 • C according to pyrometer measurements.After oxide desorption of the substrate, a CdTe nucleation layer (∼150 nm) was grown in order to achieve improved B-face nucleation and better crystallinity for the growth of the epitaxial CdTe layer.The nucleation processes were carried out at about 210 • C.After the growth of CdTe nucleation layer, an annealing was performed for samples at about 380 • C to improve the crystal quality and to prevent the formation of the treading dislocations for samples 8-16.Then, the CdTe layers were grown at about 300 • C.However, some samples (1-3) were grown at higher temperatures (330-370 • C).
A Woollam M-2000X ellipsometer was used to determine optical constant, thickness and surface roughness of the CdTe epilayers.Ellipsometric measurements were performed in ambient conditions.A Xenon arc lamp was used as a light source in measurements.The photon energy range was 1.24 eV to 5.05 eV.This range was divided into 479 numbers of wavelengths.The angle of incidence was constant at 65.82 • for all measurements.Surface morphologies of epilayers were examined by AFM operated at semicontact mode.

DATA ANALYSIS
Ellipsometric data were fitted by constructing a three-layer optical model (oxide/CdTe/GaAs) to obtain the thicknesses and optical properties of CdTe films.The Woollam library of optical constants was used for GaAs substrate.For the top oxide layer the Couchy model, which is often used to obtain the dielectric function for transparent material, was used. 20Nine general oscillators were used  to construct the dielectric function of CdTe epilayer, including Gaussian, Harmonic, Lorentzian and Pseni-Tri oscillators. 21,22Here, thickness of oxide, thickness of CdTe and CdTe oscillator parameters (such as the amplitude at oscillator center energy, center energy, broadening etc.) were left free in the fit.Oxide thicknesses, CdTe film thicknesses and some critical transition energies of CdTe were obtained using this optical model for each sample.Sample 8 was chosen as a representative example and the measured pseudo dielectric function data and fitting results are given in Figure 1(a).As can be seen from the figure, the experimental data and the model were in close agreement for all samples, including this sample.The dielectric function of CdTe obtained from these fittings can be also seen in Figure 1(b) for sample 8.The peak of ε 1 at ∼1.5 eV is related to photon absorption and band gap energy (E g ). 23he SE characterization results are summarized in Table II.The critical transition energies E 1 , E 1 + ∆ 1 , and E 2 were measured by using peaks of ε 2 .E 1 energies were obtained as ∼3.326 eV for samples 7, 8, 10, 11, 12 and 15; and E 1 ∼3.312 eV for other samples.On the other hand, the samples that have E 1 ∼3.326 eV also have E g between 1.503 and 1.506 and E 1 + ∆ 1 between 3.871 and 3.890 eV.Other samples that have E 1 ∼3.311 eV also have E g between 1.508 and 1.514 eV and E 1 + ∆ 1 between 3.833 and 3.852 eV.These two groups are clearly distinguishable also in terms of ε 2 (Figure 2) and absorption coefficient (α) behavior (Figure 3).The samples were ranged according to their absorption coefficients at E 1 , and absorption coefficients and E 1 critical energies for all samples were plotted in Figure 4 to show two distinct groups.These differences might be related to stress in the material due to thermal mismatch or incomplete relaxation of the CdTe epilayer. 24Nevertheless, at room temperature, this effect is expected to be insignificant.The variation in ε 2 and α can be attributed to the relative density of imperfections in the crystallinity, 25 and the low absorption coefficient values can be associated with the void formation in the material. 26n our data analysis, oxide layer was used as the top layer due to best SE fit result.When we used EMA for the top layer, roughness values were neither physically meaningful nor consistent with AFM measurements.EMA layers with three components (CdTe, oxide and void) were also examined but unphysical surface roughness values were obtained.Therefore, the oxide/CdTe/GaAs model was chosen to analyze SE data for all samples.A new ex-situ data analysis was carried out to determine the surface roughness due to the insufficiency of this model in determining the surface roughness.In this new data analysis, peak intensities of the imaginary parts of the pseudo dielectric functions and psi functions at 3.31 eV were examined.A decrease of the ellipsometric data (<ε 2 > and ψ) intensity is consistently observed with increased surface roughness.The decrease was further analyzed by probing its correlation with AFM measurements.

RESULTS AND DISCUSSIONS
In SE data analysis, we used the pseudo dielectric function 27 as experimental data.The pseudo dielectric function is a function of energy dependent polarization angle (ψ and ∆) and angle of incidence (θ i ), function is a complex quantity and it has real <ε1> and imaginary <ε 2 > parts, 28 <ε> = <ε 1 > + i <ε 2 > FIG. 4. Absorption coefficients at E 1 and E 1 critical energies for all samples.The samples were ranged according to their absorption coefficients, showing two distinct groups.
The surface morphology of a sample interferes with the correct determination of surface roughness because the ellipsometric measurements can display differences for the different azimuthal angles on the same point of the surface.These differences of the measured data vary according to the degree of surface anisotropy. 29Anisotropy was found to be largest for the roughest surfaces.However, for the smoothest samples, slight anisotropy occurred.For this reason it is necessary to take ellipsometric data at the same azimuthal angle according to surface normal in order to determine the surface roughness from ellipsometric data analysis.
As the surface orientation of our samples was (211), therefore, other orientations (0-11) and (-111), which are perpendicular to the surface normal or parallel to the surface, were chosen as reference directions (Figure 6).The samples were mounted to the ellipsometer stage such that the (0-11) orientation of the sample was perpendicular to the incident light.The azimuthal angle was chosen as reference angle (0 • ) for this position.The ellipsometric measurements were taken at 65.82 • incident angle at room temperature.Imaginary parts of the pseudo dielectric functions of these samples, which were mounted on a sample stage such that incident light was perpendicular to the (0-11) orientation,  (Figure 7) was obtained between these two intensities and surface roughness: The adjustment R-square values were 0.973 and 0.965 for these two fittings <ε 2 > and ψ respectively.This relation was valid only for the 65.8 • incident angle, room temperature and (211) oriented CdTe with zero degree azimuthal angle.The RMS roughness values were obtained from 10x10 µm 2 AFM scans.On the other hand, the spot size of the ellipsometer on the sample was about 2x7 mm 2 in size.Even though there is a large difference between the sizes of two measurement areas, correlation obtained was sufficiently acceptable.If it were possible to take the measurement on the same point of the sample from both AFM and SE, the correlation may be obtained with less error.
Fang et al. reported two different linear correlations between ψ and AFM roughness for two different chemically etched Si(100) samples, 30 examining ψ intensity at 1.96 eV (632.8 nm).This energy corresponds to HeNe laser operation energy used in their experiments, which is in the red part of the visible spectrum.On the other hand, E 1 critical transition energy of silicon is at 3.42 eV.We also examined ψ intensity at 1.96 eV for our samples and similarly obtained a linearly dependent correlation.However, some samples could not be fitted to this correlation.Therefore the E 1 transition energy point 3.31 eV was considered appropriate for the determination of the CdTe surface roughness.It should be examined whether E 1 transition energy points of other semiconductor materials are appropriate for the determination of the surface roughness or not.
AFM surface images of samples 7, 8, 9 and 13 are given in Figure 8. RMS values were 22.08 nm, 14.36 nm, 6.15 nm, and 4.10 nm respectively.As it is known that there are three types of surfaces, mirror-like, hazy, and milky, 29 it can be said that sample 13 has a mirror-like surface and sample 7 has a hazy or milky surface.These hazy and milky surfaces have high anisotropy and we assume that these types of surfaces are more likely to occur on high indices orientations such as (211) due to non-optimal growth conditions.
Variation of intensity of <ε 2 > with azimuthal angle indicates an anisotropic surface. 31Then, the anisotropy was checked by varying the azimuthal angle of the samples.Using sample 12 as an example, the pseudo dielectric function data measured from this sample at different azimuthal angles are given in Figure 9.When the incident light was perpendicular to the (0-11) or (2-13) or (-111) orientations, azimuthal angles were 0 • , 45 • and 90 • respectively.A variation of the intensity of the <ε 2 > values was observed with angle.As seen in Figure 9, the difference at E 1 transition point 3.31 eV is more pronounced compared to other transition points.In Figure 10, for three different azimuthal angles, the peak values of <ε 2 > at 3.31 eV of samples 1, 16, 14, 4, 15 and 12 versus the AFM roughness is also presented.A sort of proportionality between roughness and anisotropy can be observed, with higher roughness inducing larger anisotropy.We can infer from this that if we want to estimate the surface roughness using this method, it is necessary to always use the same azimuthal angle for measurement consistency.From data presented in this work, an incidence of 65.8 • seems a sensible angle for the surface roughness estimation.

CONCLUSIONS
We used a three-layer optical model (oxide/CdTe/GaAs) to obtain the thickness and optical properties of CdTe films that were grown on GaAs(211) from ex-situ ellipsometric data analysis.However, surface roughness could not be obtained from the model with good agreement with AFM measurements obtained from other possible models, such as (roughness/oxide/CdTe/GaAs) or (roughness/CdTe/GaAs).In this study, we have shown that without constructing any optical model, roughness can be determined by using the exponentially dependent relations between SE data (<ε 2 > or ψ) and AFM roughness.It is also supposed that these relations will make determination of surface roughness easier during growth by in-situ ellipsometry.In the correlations, E 1 critical transition energy of CdTe band structure, which occurs around 3.31 eV, was chosen because it yielded better correlation between SE data and AFM roughness than the other critical transition energies.Due to the anisotropic surface characteristic of (211)B orientation, a certain azimuthal angle has to be chosen in consistent determination of surface roughness from SE data.This fast and reliable method would yield rapid feedback for the optimization of the growth process by minimizing surface roughness.

FIG. 1 .
FIG. 1.(a) Experimental and model data of pseudo dielectric function and (b) CdTe dielectric function obtained by this fitting procedure for sample 8.

FIG. 5 .
FIG. 5. Imaginary parts of pseudo dielectric functions of the samples.These functions were measured from the same directions, i.e. the incident light was perpendicular to the (0-11) orientation of the sample surface.
FIG. 9. Pseudo dielectric function data of sample 12 measured from three different orientations; Incident light was perpendicular to the (-111) orientation (black curve) and (0-11) orientation (blue curve) and (2-13) orientation (red curve).Due to the anisotropy, the intensity of the <ε 2 > values shows differences for this sample, having a surface roughness of 19 nm.The most explicit difference was shown at E1 transition point, 3.31 eV.

TABLE I .
Growth parameters of the samples.

TABLE II .
Thickness values and critical energies of CdTe obtained from ellipsometric data characterization and surface roughness values obtained from AFM.