Influence of incoherent twin boundaries on the electrical properties of β−Ga2O3 layers homoepitaxially grown by metal-organic vapor phase epitaxy A. Fiedler, R. Schewski, M. Baldini, Z. Galazka, G. Wagner, M. Albrecht, and K. Irmscher Citation: Journal of Applied Physics 122, 165701 (2017); View online: https://doi.org/10.1063/1.4993748 View Table of Contents: http://aip.scitation.org/toc/jap/122/16 Published by the American Institute of Physics Articles you may be interested in Growth and characterization of β-Ga2O3 thin films by molecular beam epitaxy for deep-UV photodetectors Journal of Applied Physics 122, 095302 (2017); 10.1063/1.4985855 Epitaxial structure and electronic property of β-Ga2O3 films grown on MgO (100) substrates by pulsed-laser deposition Applied Physics Letters 111, 162101 (2017); 10.1063/1.4990779 Phase formation and strain relaxation of Ga2O3 on c-plane and a-plane sapphire substrates as studied by synchrotron-based x-ray diffraction Applied Physics Letters 111, 162104 (2017); 10.1063/1.4998804 Valence and conduction band offsets of β-Ga2O3/AlN heterojunction Applied Physics Letters 111, 162105 (2017); 10.1063/1.5003930 Interface characterization of atomic layer deposited high-k on non-polar GaN Journal of Applied Physics 122, 154104 (2017); 10.1063/1.4986215 Ab initio velocity-field curves in monoclinic β-Ga2O3 Journal of Applied Physics 122, 035702 (2017); 10.1063/1.4986174 JOURNAL OF APPLIED PHYSICS 122, 165701 (2017) Influence of incoherent twin boundaries on the electrical properties of b-Ga2O3 layers homoepitaxially grown by metal-organic vapor phase epitaxy A. Fiedler,a) R. Schewski, M. Baldini, Z. Galazka, G. Wagner, M. Albrecht, and K. Irmscherb) Leibniz-Institut f€ ur Kristallz€ uchtung, Max-Born-Str. 2, 12489 Berlin, Germany (Received 30 June 2017; accepted 9 October 2017; published online 23 October 2017) We present a quantitative model that addresses the influence of incoherent twin boundaries on the electrical properties in b-Ga2O3. This model can explain the mobility collapse below a threshold electron concentration of 1 1018 cm3 as well as partly the low doping efficiency in b-Ga2O3 layers grown homoepitaxially by metal-organic vapor phase epitaxy on (100) substrates of only slight off-orientation. A structural analysis by transmission electron microscopy (TEM) reveals a high density of twin lamellae in these layers. In contrast to the coherent twin boundaries parallel to the (100) plane, the lateral incoherent twin boundaries exhibit one dangling bond per unit cell that acts as an acceptor-like electron trap. Since the twin lamellae are thin, we consider the incoherent twin boundaries to be line defects with a density of 1011–1012 cm2 as determined by TEM. We estimate the influence of the incoherent twin boundaries on the electrical transport properties by adapting Read’s model of charged dislocations. Our calculations quantitatively confirm that the mobility reduction and collapse as well as partly the compensation are due to the presence of twin lamellae. Published by AIP Publishing. https://doi.org/10.1063/1.4993748 I. INTRODUCTION Monoclinic gallium sesquioxide (b-Ga2O3) belongs to the transparent semiconducting oxides. It is distinguished by its large band gap of about 4.7 eV,1 which is the reason for a transparency range extending deep into the ultraviolet and for a high electrical break down field estimated at 8 MV/cm. Combined with the feasibility of n-type doping by Sn or Si,2,3 b-Ga2O3 has great potential as a material for solar-blind photodetection4–6 and for power electronics where it might outperform GaN and SiC.7–11 To fully exploit the favorable properties of b-Ga2O3, single-crystalline material of high structural perfection and controlled electrical characteristics is a prerequisite. Usually, this can be accomplished by epitaxial growth of deliberately doped, crystalline films. An advantage of b-Ga2O3 over conventional wide band gap semiconductors is the availability of native substrates obtained from crystals grown from the melt by edge-defined film-fed growth,12 floating zone technique,13–15 and Czochralski growth.16–19 Homoepitaxial growth of b-Ga2O3 layers on such substrates is therefore the method of choice and has been performed by molecular beam epitaxy (MBE),20,21 halide vapor phase epitaxy (HVPE),22 or metal-organic vapor phase epitaxy (MOVPE).23–25 Using MOVPE, we observed low doping efficiencies and low electron mobilities (10–30 cm2/Vs) for Sn doped layers grown on (100) oriented substrates.24 Below an electron concentration n of about 5 1017 cm3, a Hall effect could not be measured at all, equivalent to a mobility collapse. Recently, similar electrical behavior was reported for b-Ga2O3 layers heteroepitaxially grown on c-plane sapphire substrates by low pressure chemical vapor deposition.26 On the other hand, doped b-Ga2O3 bulk crystals grown from the melt a) Electronic mail: email@example.com Electronic mail: firstname.lastname@example.org b) 0021-8979/2017/122(16)/165701/7/$30.00 exhibit much higher electron mobilities at room temperature: ln 130 cm2/Vs at n 1018 cm3.27 Such mobility values are in agreement with theoretical predictions that take account of the most important mechanisms of phonon and impurity scattering.28–31 Hence, other mechanisms must be responsible for the observed reduction of the mobility and its collapse below a certain electron concentration. Since we showed in previous studies that layers grown homoepitaxially on (100) oriented substrates by MOVPE may suffer from a high density of twin lamellae,24,32 it seems likely that these extended defects have detrimental effects on the electrical properties. This assumption is corroborated by our study of Sn and Si doped layers homoepitaxially grown by MOVPE on (010) substrates.25 These layers are free of twin lamellae and exhibit high, bulk-like mobilities and no compensation. In Ref. 32, we analyzed in detail the formation of twin lamellae and showed that their formation can be suppressed by defined offorientation from (100), but we did not examine the impact of the twin lamellae on electrical transport. In the present paper, we report on the electrical transport properties of Si doped b-Ga2O3 layers homoepitaxially grown on (100) substrates of no or only slight offorientation. These layers behave electrically very similar to the Sn doped layers of Ref. 24 with respect to low mobility values and mobility collapse below a threshold electron concentration (here, n ¼ 1 1018 cm3) as well as low doping efficiency. By using transmission electron microscopy (TEM), we show that the layers contain a high density of twin lamellae. High resolution scanning transmission electron microscopy (STEM) allows us to analyze the atomic structure of the twin boundaries, which can be classified into coherent boundaries parallel to (100) and incoherent ones parallel to (001). While the former ones preserve the atomic coordination, this is not the case at the incoherent twin boundaries (ITBs). Our atomic model of an ITB suggests 122, 165701-1 Published by AIP Publishing. 165701-2 Fiedler et al. that one dangling bond per unit cell is present. The dangling bonds are arranged along the ITBs of thin twin lamellae and may act as acceptor states. This is in analogy to the model of electrically active dislocations originally suggested by Read33 and further developed to explain unusual carrier mobility behavior in highly dislocated GaN.34–36 Here, we adapt this model to ITBs in b-Ga2O3. Based on the density and geometry of the ITBs, estimated by TEM measurements, corresponding calculations quantitatively confirm that mobility reduction and collapse as well as partly the compensation are due to the presence of twin lamellae. II. EXPERIMENTAL b-Ga2O3 layers of about 250 nm thickness were grown by MOVPE on (100) oriented substrates. The respective MOVPE growth process is explained in detail in Ref. 24. Tetraethylorthosilicate (TEOS) was used as the metalorganic precursor for the n-type doping by Si. The substrates were wafers of dimensions 5 5 0.5 mm3 prepared from bGa2O3 bulk crystals grown by the Czochralski method.18,19 The surface orientation of the square-shaped substrates was (100) with unintentional miscut deviations below 0.4 as determined by atomic force microscopy measurements of the step heights and widths on epitaxy-ready substrate surfaces. The edges were parallel to  (b-direction) and  (c-direction), respectively. Most of the used substrates were electrically insulating due to Mg doping of the bulk crystals. In addition, some conductive substrates were used, which were sliced from unintentionally n-type doped crystals. Electrical characterization of the layers on insulating substrates was performed by resistivity and Hall effect measurements at room temperature using a commercial setup (Lake Shore HMS 7504) and contacting the samples in van der Pauw configuration. Point-like contacts were prepared by applying InGa eutectic in the four corners of the samples. Current-voltage measurements of these contacts showed ohmic behavior for all samples under investigation. In order to detect deep electron traps, we applied deep level transient spectroscopy (DLTS) to the layers on conductive substrates. Circular Schottky contacts (diameter 0.4 mm and 0.8 mm) prepared by using a shadow mask and depositing 30 nm Ni by electron beam evaporation served as test structures. The DLTS measurements were performed in the temperature range from 100 K to 540 K using a BioRad DL8000 system with Fourier transform correlation of the capacitance transients. In this way, electron traps with energy levels of up to 1.3 eV below the conduction band edge (i.e., within the upper quarter of the band gap) are recorded. The structural properties of the layers were investigated by transmission electron microscopy (TEM) and high resolution scanning transmission electron microscopy (STEM) using an aberration corrected FEI Titan 80–300 microscope operated at 300 kV. The microscope is equipped with a Fischione high angle annular dark-field detector (HAADF) and a highly brilliant field emission gun (X-FEG). Details on the chosen TEM operating parameters and on the preparation J. Appl. Phys. 122, 165701 (2017) of cross-sectional TEM samples along the (010) orientation can be found in Ref. 32. The Si dopant concentration was determined by secondary ion mass spectrometry (SIMS) performed by RTG Mikroanalyse GmbH. Calculations of the influence of ITBs on the electrical transport properties were implemented in MATLAB.37 III. RESULTS AND DISCUSSION A. Electrical properties Conductivity and Hall effect, as well as DLTS measurements, reveal the following electrical properties of the Si doped b-Ga2O3 (100) layers: (i) (ii) In Fig. 1, the electron Hall mobility l is plotted versus the electron concentration n. An unambiguous Hall effect is measurable only in layers with n > 1 1018 cm3. Above this threshold, the mobility decreases from 30 cm2/Vs to 10 cm2/Vs for an increase in electron concentration by an order of magnitude, a dependence qualitatively consistent with dominant scattering at ionized impurities. For n < 1 1018 cm3 the layers are still conductive, but a measurement of the Hall effect is impossible which is ascribed to a sudden drop in electron mobility with decreasing electron concentration (mobility collapse). A similar mobility collapse below a critical carrier concentration is observed in GaN and is explained by the presence of a high density of dislocations forming walls of potential barriers for electron transport.34–36 The four-terminal resistances of the van der Pauw measurement in the (100) plane of our layers are strongly anisotropic: the four-terminal resistance R with current flow along the  direction is about ten times higher than the resistance R with current flow along . This large difference cannot be explained by the monoclinic crystal structure of b-Ga2O3, since its electron transport properties have turned out to be almost isotropic.14,27,30,31,38 Rather it suggests that anisotropically arranged, electrically FIG. 1. Electron Hall mobility as a function of the electron Hall concentration at 300 K for b-Ga2O3 homoepitaxially grown by MOVPE on (100) oriented substrates (black squares). The blue dashed line represents the calculated bulk mobility. The green dashed-dotted lines represent the calculated mobility due to incoherent twin boundaries of the lowest (1 1011 cm2) and highest (1.5 1012 cm2) density determined by TEM. The redshaded area illustrates the total calculated mobility within these bounds. 165701-3 (iii) (iv) Fiedler et al. active inhomogeneities, such as extended defects, are present in the layers. The electron concentration, measurable by the Hall effect above 1 1018 cm3, is lower by a factor of 3 to 30 than the Si dopant concentration measured by SIMS in the respective range from 3 1018 cm3 to 2 1020 cm3 as represented in Fig. 2. This indicates high compensation of the Si donors by acceptors and possibly, electrically inactive Si incorporation. Compensating acceptors could be point defects (e.g., Ga vacancies) and extended defects rather than impurities in our layers. In Fig. 3, a typical DLTS spectrum of a layer is compared with that of a conductive substrate. The spectrum of the substrate is dominated by the DLTS peak of an electron trap at 0.7–0.8 eV below the conduction band edge that is omnipresent in melt-grown b-Ga2O3 bulk crystals in the mid 1016 cm3 concentration range.27,39 This peak shows no broadening due to non- or multiexponential thermal emission. Therefore, the peak should be due to a point defect. In contrast, the DLTS spectrum of the layer consists of broadened, overlapping peaks, while the “bulk” peak is strongly suppressed. This suggests that the underlying defects possess closely spaced or continuously distributed energy levels as it is usually assumed for extended defects. For the approximate center of gravity of the broad DLTS peak distribution, we determine a thermal activation energy of 0.34 eV. Since we assume that these defects significantly contribute to the electrical compensation, the DLTS evaluation of their concentration, maximum of the peak distribution is at about 1 1016 cm3, reflects only a small part of their real concentration. This is because the electron concentration available for recharging during a DLTS filling pulse, which is given by the difference between the concentration of shallow donors and the concentration of compensating deep level defects, is much smaller in the present case than the concentration of the deep level defects, leading to incomplete filling. FIG. 2. Electron Hall concentration n at 300 K as a function of the silicon atomic concentration measured by SIMS for b-Ga2O3 layers homoepitaxially grown by MOVPE on (100) oriented substrates (black squares). The black line marks the upper electron concentration limit in the ideal case of completely ionized, uncompensated Si donors. The red-shaded area predicts the electron concentrations in the presence of incoherent twin boundaries with densities between 1 1011 cm2 and 1.5 1012 cm2. J. Appl. Phys. 122, 165701 (2017) FIG. 3. DLTS spectrum of an (100) oriented, conductive b-Ga2O3 substrate (red dots) and of a layer (black squares) grown by MOVPE on such a substrate. The time window setting of 20 ms used here corresponds to the emission rate in the peak maximum of en,max ¼ 114 s1. In conclusion, our observations suggest that electrical transport in the layers is ruled by anisotropically arranged, extended defects. A structural analysis by TEM, presented in the subsequent paragraph, will provide direct evidence of extended defects and their type. B. Structural analysis The TEM analysis of the layers reveals the presence of a high density of planar defects. A typical example is shown in Fig. 4(a) by a cross sectional dark field image of a 150 nm thick layer grown on a substrate with a nominal miscut of 0.1 . While the substrate is free of planar defects and shows only speckled contrast due to unavoidable surface damage caused by ion milling, the layer contains a high density of planar defects. These defects turn out to be twin lamellae. Structural details on the atomic scale of the boundaries of the twin lamellae are uncovered by Z-contrast STEMHAADF images. Figure 4(b) shows a region of coalescence of the two possible twin orientations projected along the  zone axis. Since the atomic number of oxygen (Z ¼ 8) is much smaller than the atomic number of gallium (Z ¼ 31), the contrast in these images arises from the gallium columns only. The image has been overlaid with a stick and ball model of b-Ga2O3. The stacking can be analyzed from the lozenge-shaped arrangement of the Ga atoms in the b-Ga2O3 along this projection. The boundary in the (100) plane is marked by the red dashed line. The lattice in this region can be continued by mirroring at the (100) plane combined with a translation by a half c lattice parameter along . This produces a twinned crystal orientation, described by a c/2 glide reflection. Let us focus on the (100) twin boundary first. The structural model shown in Fig. 4(c), derived from the Ga positions in Fig. 4(b), shows that all atoms in the boundary are fully coordinated, i.e., the twin boundary at the (100) plane is coherent. We consider now the twin boundary formed by coalescence along  of two twinned nuclei marked by I and II in Fig. 4(b). The boundary (highlighted by a yellow, dotted line) can be recognized by the different orientation of the lozenge-shaped arrangement of the Ga atoms. In the stick 165701-4 Fiedler et al. J. Appl. Phys. 122, 165701 (2017) FIG. 5. Scheme of the distribution of incoherent twin boundaries (ITBs) as seen in a cross sectional TEM image. The yellow stripes represent the ITBs at the (001)-plane. B is the thickness of the layer, A is the width of the image, L is the thickness of the TEM sample, D is the mean distance between each two neighboring ITBs, t is the distance between two adjacent dangling bonds within an ITB, and hi are the heights of the ITBs. FIG. 4. (a) Cross sectional TEM dark field image of a typical MOVPE layer. For imaging, we used a g vector parallel to . (b) High resolution STEM-HAADF image showing a region where two twin orientations coalesce. The red dashed line indicates the (100) twin boundary, while the yellow dotted line represents the (001) twin boundary. (c) Structural model of the boundaries developed from the STEM image. Bright green and grey indicating octahedrally bound Ga atoms, and dark green and black correspond to tetrahedrally bound Ga atoms, respectively. Red balls correspond to oxygen atoms. (d) and (e) represent enlarged models of atomic bonding at the (001) boundary corresponding to the, respectively, highlighted structural units in (c). and ball model of Fig. 4(c), the oxygen atoms, invisible in STEM and TEM images, have been placed based on the principle of plausibility, i.e., considering their coordination and the distortion of the bonds. According to this model, the boundary is formed of two structural units that are highlighted by violet, dashed and blue, solid rectangles. In the first structural unit [enlarged in Fig. 4(d)], an oxygen column is coordinated by two octahedral gallium columns and arranged in a planar geometry. This is very likely an energetically unfavorable configuration and may lead to local lattice relaxation. The second structural unit [enlarged in Fig. 4(e)] is formed of two columns of tetrahedrally bound gallium atoms bound to an oxygen column. The oxygen atoms in this column are only coordinated by two gallium atoms, i.e., a single nearest Ga neighbor is missing compared to the corresponding undisturbed lattice site. The (001) twin boundary thus is an incoherent boundary that exhibits dangling bonds and local lattice relaxations. It is natural to assume that these (001) twin boundaries introduce deep states in the energy gap of b-Ga2O3 which influence the electrical properties of the layers in a negative way. A corresponding quantitative model will be developed in Sec. III C. A prerequisite for any quantitative model is the knowledge of the density of active defects introduced by these boundaries. Therefore, we measure the dimensions and density of the incoherent twin boundaries (ITBs), i.e., their average height, lateral extension, and mean distance as sketched in Fig. 5, from TEM micrographs. From the analysis of 3566 twins in b-Ga2O3, we find that their heights hi range from half a unit cell up to several 10 nm with 96% below 10 nm and an average value of 3.2 nm. Additionally, we extract the mean distance D ¼ (40 6 20) nm between each two neighboring ITBs by measuring each distance of related neighboring (001) boundaries. The thickness of the TEM sample is L 50 nm, which is a lower bound for the length of the ITBs, because we see no distortion of the atom columns in the high-resolution STEM-HAADF images [see Fig. 4(b)]. Since hi D and hi L and the average vertical separation (along a*) is about 10 nm, it is possible to treat the ITBs as separate line defects. According to our model of atomic bonding, one dangling bond per unit cell is present in the ITB. Hence, we can quantify the density of columnar arranged dangling bonds by P i hi Nitb ¼ ; (1) A B a sinðbÞ where i is the index of the ITBs, a ¼ 1.223 nm is the lattice parameter,40 b ¼ 103.7 is the monoclinic angle,40 A is the width of the image, and B is the thickness of the layer. The hereby determined density of ITBs ranges from Nitb ¼ 1 1011 cm2 to Nitb ¼ 1.5 1012 cm2 with the mean value hNitbi ¼ 6 1011 cm2. The distance t between two dangling bonds within an ITB is equal to the lattice parameter b ¼ 0.304 nm,40 since there is one dangling bond per unit cell. C. Transport model in the presence of incoherent twin boundaries From the structural analysis, we know that the incoherent twin boundaries (ITBs) at the (001) plane contain dangling bonds. These normally form acceptor-like deep states 165701-5 Fiedler et al. J. Appl. Phys. 122, 165701 (2017) 1 e2 Nd3 Ec Ed ¼ 36:3 meV 1:46 : 4pe0 e FIG. 6. Scheme of the band bending due to dangling bonds introducing acceptor states (negative sign in a rectangle) in an n-type semiconductor. The axis system illustrates the potential energy in the b-c plane in the case of incoherent twin boundaries (ITBs). Cylindrical space charge regions of radius R and axis along  form around the ITBs. D represents the mean distance between each two neighboring ITBs. in an n-type semiconductor.41 Since we investigate moderately to highly n-type doped material, the Fermi level is located above or pinned by the deep dangling bond state. Hence, the dangling bond acceptor catches a free electron and forms a negatively charged region. The valence and conduction band edges are bent and a spherical space charge region forms around the dangling bond. Since the dangling bonds are columnar arranged, like line defects, the resulting space charge region around an ITB has a cylindrical shape with the radius R and the cylinder axis along  as shown in Fig. 6. Due to charge neutrality, we can define R in such a way that the cylinder contains an amount of fixed positive charge equal to the negative charge at the ITB42 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ f f ; (2) pR2 Ndþ Na ¼ ) R ¼ b pb Ndþ Na where Ndþ is the density of ionized donors, þ Na is the density of ionized acceptors, the difference Nd Na is the electron concentration of an n-type semiconductor without extended defects, b is the distance between two dangling bonds within an ITB, and f is the filling factor of the dangling bonds. Due to Coulomb repulsion, the occupation of the closely spaced dangling bonds by electrons is limited. Hence, the filling factor is somewhere between 0 and 1. The filling of dangling bonds is determined using Read’s minimum energy approximation for line defects given in Ref. 42, f 0:232 ; (3) E ¼ E0 f 3ln fc 2 e 1 being the energy of the interaction of two with E0 ¼ 4pe 0e b electrons in adjacent sites, where e0 e ¼ 10:2e0 is the product of the absolute dielectric constant and the relative static one,43 1 fc ¼ b p Ndþ Na 3 , and E ¼ ðEc Eitb Þ ðEc Ed Þ is the thermal activation energy of dangling bonds. Formula (3) is exact for T ¼ 0 K and gets more inaccurate with increasing temperature by underestimating the filling of dangling bonds. Nevertheless, it is an appropriate approximation at 300 K and gives a lower bound for f. For the ionization energy of the ITBs, we take Ec Eitb 0:34 eV, the center of gravity of the broad DLTS peak distribution (Fig. 3), as a reasonable assumption. The shallow donor ionization energy is calculated after Ref. 27, (4) Assuming a homogeneous distribution of the ITBs, a periodical electrostatic potential / occurs. For the in-plane electrical transport through the layer, the electrostatic potential along  is crucial (see Fig. 6), since the ITBs form at the (001)-plane. The potential barrier that an electron has to overcome when flowing in  is the difference between the potential maximum at the ITB and the potential minimum at half way D/2 between adjacent ITBs. The analytical calculation of / was done by Krasavin for dislocations in GaN, which are also columnar arranged,35 and is adopted by us for the case of ITBs in b-Ga2O3, 4e2 Ndþ Na R3 e2 f lnð2Þ: (5) e/ðR; D; bÞ ¼ 3 e0 eD 2bpe0 e For the current flow between twinned regions, this barrier has to be overcome by thermionic emission, like in polycrystalline or powdered semiconductors.44 Therefore, a twin boundary can be assumed as a back-to-back Schottky barrier and it is possible to define an effective resistance for such a barrier. Using the effective resistance, it is possible to define a quantity litb, which has the dimensions of a carrier mobility44 eL e/ðR; D; bÞ ; (6) litb ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ exp kB T 8kB Tpm where m* ¼ 0.28m0 is the effective electron mass.38 litb can be interpreted either in terms of a constant carrier density associated with a thermally activated mobility or conversely in terms of a constant mobility and thermally activated carrier density.44 Following Matthiessen’s rule, the total mobility results from 1 1 1 ¼ þ ; ltot lbulk litb (7) where lbulk is the bulk mobility of b-Ga2O3 due to normal scattering processes. The bulk mobility is calculated using an empirical expression given in Eq. (7) of Ref. 28. To obtain the dependence of the mobility l on the electron concentration n like in Fig. 1, it is necessary to calculate n by solving (iteratively) the charge neutrality equation. Since the dangling bonds within an ITB show acceptor-like behavior, the charge neutrality equation as well has to be adjusted35 Nitb : n ¼ Ndþ Na f b (8) Using the well-known expressions for the density of ionized donors (Ndþ ) and ionized acceptors (Na ) as a function of the Fermi energy (EF), the temperature and the respective ionization energies, and assuming Boltzmann statistics, one can calculate the electron concentration n for a certain density of donors Nd, point defect related acceptors Na, and acceptors related to ITBs Nitb. For Na, we take 5 1015 cm3, a value measured by DLTS for layers on (100) substrates off-oriented 165701-6 Fiedler et al. by about 6 towards  which do not contain extended defects, and hence, we assume that this value accounts for point defect related acceptors. Furthermore, we assume for the calculation that all Si atoms are incorporated as electrically active shallow donors, i.e., Nd is taken equal to the Si atomic concentration. The resulting mobility due to the presence of ITBs versus the electron concentration n is plotted together with the experimental results in Fig. 1. Nearly all experimental values are in the calculated range given by the bounds for the density of ITBs using the model of homogeneously distributed, charged barriers. The mobility collapse at a critical electron concentration of about 1 1018 cm3 is also reproduced by our model. The electron concentration n in the presence of ITBs versus the Si atomic concentration is plotted together with the experimental results in Fig. 2. The calculation shows that the given density of ITBs in the layers account for the strong compensation, in particular, in the low Si doping range up to 3 1019 cm3. For higher Si atomic concentrations, however, the model fails. Two reasons may be responsible for this failure: (i) the underestimation of the filling factor f by Eq. (3) and (ii) our assumption that all Si atoms are incorporated as electrically active shallow donors. In particular, the latter assumption is probably inapplicable for high Si doping concentrations since incorporation on electrically inactive sites, including the formation of defect complexes and gettering of Si at ITBs, may take place. Finally, we point out that a strong conductivity anisotropy is inherent to our simple model. Since we have regarded only space charge cylinders expanded in the  direction, the barrier for current flow along  has a maximum and reduces for current flow away from this direction. This assumption is in accordance with the principal arrangement of the twin lamellae and explains qualitatively the anisotropy in the four-terminal resistances measured by the van der Pauw method (see above). The measured ratio R/R of about 10 overestimates the actual conductivity anisotropy which should correspond to a ratio of only 2 according to Ref. 45. The reason for this unexpectedly low conductivity ratio may be due to the incoherent twin boundaries, which form on the (010)-plane when two twinned islands coalesce and which are not taken into account in the present model. From atomic force microscopy images of the layers an aspect ratio of the length of an island in  direction to the length in  direction of about 2 is obtained for every island forming during MOVPE growth.32 This is an indication for the density of ITBs in  direction and might explain a two-to-one anisotropy in conductivity. IV. CONCLUSIONS b-Ga2O3 layers grown homoepitaxially by MOVPE on (100) substrates of slight off-orientation below 0.4 showed a low mobility of at most 30 cm2/Vs, a mobility collapse below a threshold electron concentration of 1 1018 cm3, as well as low doping efficiency with electron concentrations being a factor of up to 30 lower than the silicon donor doping concentration. Combining the structural investigations of twin lamellae in these layers, in particular, the geometry and J. Appl. Phys. 122, 165701 (2017) density of ITBs, with a transport model for charged dislocations in GaN,35 the low mobility and the mobility collapse at low n-type doping can be well explained. The low doping efficiency is at least partly described by the model. Thus, we conclude that point defects like Ga vacancies, which are considered to be important compensating acceptors in n-type b-Ga2O3,46 play only a minor role for compensation in our samples. Our model may also explain the electrical behavior of n-type b-Ga2O3 layers grown on sapphire (0001) substrates by low pressure chemical vapor deposition, where a similar trend in mobility over electron concentration was reported.26 Such heteroepitaxial growth results in 60 rotational domains of b-Ga2O3 as we observe by MOVPE growth on (0001) sapphire and already reported by Lv et al.47 We expect that the grain boundaries between these domains behave electrically in a similar way as the ITBs. As it has been shown in previous work, twinning occurs due to possible double positioning of the Ga adatoms on the (100) plane. 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