Structural properties and analysis of defect structures

Hall measurements was performed using the Van der Pauw configuration (Bio-Rad Microscience HL5500 Hall System) at 23 °C and yielded a background electron concentration 2.87×10¹⁶ − 7.06×10¹⁸ cm^-3 with mobility 28.2 - 40.9 cm²⋅V^-1⋅s^-1 and resistivity 0.771-0.0216 Ω⋅cm. The strong PL peak of free exciton at 3.28 eV with FWHM of 105 meV is inspected at room temperature, as shown in Fig.

4-1. No defect emission is also observed at the visible region, ensuring a good optical quality of the ZnO films.

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

PL intensity (a.u)

Photon energy (eV) PL @ RT

Fig. 4-1 PL spectrum measured at room temperature

X-ray diffraction (XRD) is well established for quantitative exploration of the defect structure over a macroscopic length scale in accordance with crystal imperfection [7]. Radial (2θ−ω ) scans along surface normal were conducted and only the (000l) reflections of both sapphire and ZnO were observed, elucidating the c-plane orientation of the grown ZnO layers. Azimuthal cone scans (φ scans) across the off-normal ZnO {2022} and sapphire {2022} peaks, as illustrated in Fig.

4-2(a), were measured to examine the in-plane epitaxial relation. Six ZnO diffracted peaks (FWHM ~ 0.57°) that are evenly spaced 60^o apart confirm that the ZnO film has 6-fold rotational symmetry against surface normal and is grown epitaxially on the c-plane sapphire. The 30° offset between the {2022} reflections of ZnO and

sapphire verifies the in-plane epitaxial relationship of [1010] sapphire || [1120] ZnO and [1120] sapphire || [0110] ZnO.

To characterize the structural quality of the grown films, the ω−rocking curve of

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the ZnO (0002) reflection, as shown in Fig. 4-2(b), was measured. The rocking curve of the nearly resolution-limited sapphire (0006) reflection was also shown as a reference. The narrow width, 0.0072°, of sapphire (0006) reflection reveals that the contribution of instrumental broadening to the ZnO width is negligible. The obtained mosaic spread of the ZnO film, 0.0482°, is much smaller than other reported values, typical of ~0.2°, of ZnO films prepared with PLD [8, 9]. It is also noticed that the line widths of ZnO specular (0002) and off-normal {2022}reflections are different by more than an order of magnitude. Such a prominent difference of diffraction features in these two groups reveals the structural characteristics of the films.

TDs in a film produce crystalline plane distortions and the associated lattice deformation depends on the geometry of the TDs [10]. For a c-plane ZnO layer, TDs with their dislocation lines lying along the [0001] direction, i.e. normal to the ZnO/sapphire interface are most often observed [2, 11]. In our case, the majority of TDs have their lines along the [0001] direction, which will be discussed in more details in TEM results. For a (0001) oriented thin film with wurtzite structure, the TDs are classified to three different types according to the direction of the corresponding Burgers vector (b) relative to the [0001] line direction. They are edge dislocation with bE = 1/3⋅<11 2 0>, screw dislocation with bC = <0001>, and mixed

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dislocation with bM = 1/3⋅<11 2 3>, which is a combination of bE and bC. Pure edge TDs twist surrounding ZnO lattice about [0001], leading to the formation of vertical grain boundaries [2, 12]. Under this circumstance, the (hkil) crystalline planes with nonzero in-plane component, i.e. either h or k is not zero, are distorted. On the other hand, the pure screw TDs result in the tilting of the ZnO lattice, generating a pure shear strain field [13], and the crystalline planes with nonzero l are deformed.

Therefore, to investigate the influence of edge TDs, we measured the profiles of ( 0 0)h h surface reflections, which are not sensitive to lattice distortion caused by pure screw TDs. Such scans were performed in the grazing incidence diffraction geometry by keeping the surface normal almost perpendicular to the vertical scattering plane. The FWHMs of ω-rocking curves reflect the lattice twist and the widths of radial scan yield the lateral strain field and domain size. As a complement, we also recordemeasured the line widths of the (000l) normal reflections, which are not affected by the pure edge TDs. The ω-rocking curves and radial scans provide the lattice tilt angle and coherence size as well as strain profile along surface normal, respectively.

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-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Fig. 4-2 (a) Azimuthal scans of ZnO {2022} and sapphire {2022} peaks. (b) Comparison of ω scans of ZnO (0002) and substrate sapphire (0006) peaks.

(All marked values denote FWHM.)

-1.0 -0.5 0.0 0.5 1.0

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.0

Fig. 4-3 Superimposed radial (a) and symmetric ω scans (b) of ZnO (0002) and (1010)reflections. The abscissa of Fig. (a), Δqr, is the deviation of the scattering vector, q = 2πsin(θ )/λ, away from the corresponding reflection in the radial direction. (All values denote FWHM.)

Figure 4-3 (a) displays the intensity distribution of scattered X-rays along the radial scans across ZnO (0002) and (1010) reflections, of which the former is along the growth direction and the latter lies on the sample surface. The FWHM of the former, 0.00816 nm^-1, is significantly smaller than that of the latter, 0.01565 nm^-1,

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indicating the strain along surface normal caused by screw TDs is much smaller than that along lateral direction caused by edge TDs. The profiles of ω-rocking scans

across ZnO (0002) and (1010) reflections are illustrated in Fig. 4-2(b). Similarly, the FWHM of the (0002) reflection, 0.048°, is much smaller than that of the (1010) reflection, 0.578°, revealing the tilt angle to be smaller than the twist angle. This pronounced difference of widths between (0002) and (1010) reflections strongly indicates that the density of pure edge TDs is greater than that of pure screw TDs.

These observations are qualitatively similar to what observed for GaN grown on c-sapphire [10, 14]. Analogous phenomena are attributed to the same crystal

structure of ZnO and GaN, both belonging to space group P63mc, and the similar lateral lattice parameter, with a difference ~1.8 %.

0 2 4 6 8 10 12 Fig. 4-4 Williamson-Hall plots for a ZnO layer of radial scans (a) and ω-rocking

curves (b). The symmetric radial scans and ω-rocking curves were measured for (000l) and ( 0 0)h h reflections as indicated in the figures.

Dashed lines are linear fits of the data.

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To obtain meaningful quantitative results, we employed a Williamson-Hall plot, Δqr vs. q plot with q = 2sinθ/λ denoting the scattering vector and Δqr standing for the line width in q along the radial direction, to separate the broadening due to finite structural coherence length from strain induced broadening. The inverse of ordinate intercept yields the coherence length, i.e., the effective domain size, and the slope yields the root-mean-square (RMS) inhomogeneous strain averaged over the effective domains [15]. Figure 4-4(a) illustrates the Williamson-Hall plot of radial scans

along ZnO (000l) and (h0h0) reflections. The correlation lengths obtained are 159.8 nm along the surface normal, which is only a fraction of the film thickness, and 86.1 nm along the lateral direction. The average lateral strain is 1.49×10^-3, about three times that along the surface normal, 0.51×10^-3, manifestingedge dislocations to be the dominant cause of distortion of the ZnO lattice. Analogous to the Williamson-Hall plot for radial scans, Fig. 4-4 (b) shows a Δqt vs. q plot, where Δqt = Δω × q denoting the line width in q along the transverse direction, for ω-scans across

the (000l) and in-plane (h0h0) reflections, of which the slopes yield the spreads of tilt and twist angle, respectively. The obtained tilt angle (αΩ) is 0.089^o, which is only one sixth of the twist angle (αΦ), 0.542^o. The density of TDs can be evaluated from the corresponding Burgers vector and the tilt/twist angular. For screw TDs, the

density NS is calculated according to

2

and bC denotes the length of corresponding Burgers vector bC, which is [0001] with bC

= 0.5225 nm in this case. Applying the values determined from XRD, we obtained NS = 2.03×10⁸ cm^-2. For edge TDs, the formula employed to calculate the density, NE, depends on the spatial arrangement of the TDs [17]. Assuming a random

distribution, we apply

case of TDs accumulating at a small-angle boundary, we adopt the formula

2.1 α_Φ

E =

E

N b L, where L denotes the correlation length along the in-plane direction.

In both formulae of NE, bE is the length of associated Burgers vector bE =

1/3< 1120 >, 0.3238 nm. The edge TDs densities for a random distribution and for accumulating at small-grain boundaries so obtained are 2.00×10¹⁰ cm^-2 and 1.62×10¹⁰ cm^-2, respectively. Even though the authentic distribution of edge TDs is uncertain, we expect it to be between a random distribution and an accumulation at a small-angle grain boundary, and the density NE to be of order 10¹⁰ cm^-2. The results indicate that NE is about 100 times higher than NS, hence edge TDs are indeed the dominant type of dislocations in ZnO films grown on c-plane sapphire, in agreement with a conclusion drawn from a qualitative comparison of the FWHMs of (0002) and (1010) reflections.

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Fig. 4-5 The profile of a radial scan across ZnO (1014) reflection measured in an asymmetric geometry.

In a further examination of those results, we measured the radial scan profile of an off-normal (1014) reflection, of which both edge and screw TDs contribute to the line width broadening. The radial scan measured in an asymmetrical geometry is displayed in Fig. 4-5. The obtained width was compared with the calculated value by using the characteristic parameters of the edge and screw TDs respectively determined from ( 0 0)h h and (000l) reflections. The mean square strain of (1014)

planes induced by three edge dislocation systems with bE = 1/3 < 1120 > and slip planes {1100} and the screw dislocation with bC = <0001> can thus be calculated using the TDs density obtained above (NE =1.62×10¹⁰ cm^-2, NS =2.03×10⁸ cm^-2) [14].

The strain broadening of the (1014) Bragg reflection in the radial direction is subsequently calculated based on such strain fields to yield an average 0.078^o. This

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value is in good agreement with the measured one, 0.074^o.

TEM contrast analysis was also performed to characterize the nature of the TDs.

On the basis of the invisibility criterion, g · b = 0, where g denotes the diffraction vector, the dislocations with Burgers vector b perpendicular to the diffraction vector g are invisible in the images. We thus took bright-field cross-sectional TEM images under a two-beam contrast condition with the zone axis near [10 1 0] and diffraction vectors g equal to (0002), (11 2 0) and (11 2 2), as shown in Fig. 4-6(a), (b) and (c), respectively. Pure edge TDs with bE = 1/3⋅<11 2 0> are invisible in images recorded with g = (0002) but are in contrast in images with g = (11 2 0) and (11 2 2). On the contrary, pure screw TDs with bC = <0001> are out of contrast in the g = (11 2 0) case and are visible as g = (0002) and (11 2 2). As to the TDs of mixed type with bM = 1/3⋅<11 2 3>, they are visible in all three images. In all three micrographs, TDs seen as dark lines stem from the ZnO/sapphire interface with their dislocation lines primarily along the [0001] direction. The number of TDs is significantly less in Fig.

4-6(a) as compared with those in 6(b) and 6(c), manifesting that only a small fraction of TDs belongs to pure screw type. Taking the specimen thickness 90±10 nm into account, we calculated the densities of edge, screw and mixed TDs to be approximately 1.5±0.2×10¹⁰ cm^-2 (~ 77%), 4.3±0.3×10⁸ cm^-2 (~ 2%), and 4.1±0.5×10⁹ cm^-2 (~ 21%), respectively. Amounting to 98% of the total TDs contains the edge

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component as determined from the TEM measurements.

In some regions, as shown in Fig. 4-6(d), the mergence of dislocation lines to form half loops was observed, especially in the bottom half of the film close to the interface, revealing the strong interaction between the TDs. It appears that the annihilation of two nearby dislocations of opposite Burgers vectors leads to the formation of these loops. The presence of many half loops and the difference of TDs density in depth may explain the smaller vertical structural coherence length found in XRD measurements as compared with the film thickness.