APPLIED PHYSICS LETTERS 99, 141913 (2011)
Pyramidal inversion domain boundaries revisited T. Remmele,1,a) M. Albrecht,1 K. Irmscher,1 R. Fornari,1 and M. Straßburg2 1
Leibniz-Institut fu¨r Kristallzu¨chtung, Max-Born-Str. 2, 12489 Berlin, Germany OSRAM Optical Semiconductors GmbH, Leibniz Straße 4, 93055 Regensburg, Germany
2
(Received 5 May 2011; accepted 7 September 2011; published online 6 October 2011) The structure of pyramidal inversion domain boundaries in GaN:Mg was investigated by aberration corrected transmission electron microscopy. The analysis shows the upper (0001) boundary to consist of a single Mg layer inserted between polarity inverted GaN layers in an abcab stacking. The Mg bound in these defects is at least one order of magnitude lower than the chemical Mg concentration. Temperature dependent Hall effect measurements show that up to 27% of the Mg acceptors is C 2011 American Institute of Physics. [doi:10.1063/1.3644132] electrically compensated. V Pyramidal inversion domain (PID) boundaries are defects that form in Mg-doped GaN at Mg-concentrations exceeding 2 1019 cm3.1–4 These defects are GaN pyramids with inverted polarity inside the GaN matrix, confined by six f11 2lg side facets, typically l is found to be 3, 4, or 2 and a hexagonal shaped (0001) top facet. They have typical sizes in the range of 2-6 nm in metal organic chemical vapor deposition (MOCVD) grown material.1,3 According to energy dispersive x-ray spectroscopy and electron energy loss spectroscopy, Mg is incorporated into the top and side facets of these defects.1,5 The experimental observation that the Mg concentration of 2 1019 cm3, at which pyramidal inversion domains start to form, coincides with the concentration beyond which the free carrier concentration drops led several authors1,2,6 to conclude that incorporation of Mg in form of Mg3N2 into these defects could explain this drop. As an alternative explanation for the reduced free carrier concentration, compensation of the Mg acceptor by, e.g., nitrogen vacancies (VN) has been put forward.7,8 A prerequisite for a quantitative evaluation of the Mg incorporated into PIDs is the precise knowledge of the structure of the defects down to an atomic level. Various models have been proposed. They essentially differ in the number of Mg layers that are incorporated into the boundaries of the polarity inverted GaN, in the coordination of the Mg with N and in the alignment of the Ga- and N-layers between the PID and surrounding matrix. Liliental-Weber et al.9 proposed this interface to consist of a single monolayer of Mg in a stacking sequence abcac, corresponding to GaNMgNGa with a stacking fault at the interface. In contrast, Venne´gue`s et al.10 considered a bilayer of Mg where Mg atoms are coordinated with N like in an antibixbyite structure. From careful density functional theory calculations, Northrup11 concluded that the (0001) boundary of the PID exhibits a sequence of GaNMgNGa layers in registry abcab. He showed that for reasons of charge neutrality, 0.25 monolayers of MgGa below and above the Mg layer are required. The two N layers are separated from each other by an average distance of 0.30 nm in the [0001] direction. Up to now, the determination of the atomic structure of this interface has been hampered due to the limited resolution of the electron microscopes and the small size of the defects, a)
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which in most cases are completely covered inside the thin electron-transparent foil. Therefore, the comparison of image simulations with experimental high resolution transmission electron microscopy (HRTEM) images has been used which, however, led to contradicting results.2,9,10 In this letter, we report a study on structure and density of pyramidal inversion domain boundaries with an aberration corrected microscope in a series of samples with doping levels ranging from 4 1019 cm3 up to 1.5 1020 cm3. We study defects in areas with a thickness below 5 nm, with focus settings that enable an amplitude contrast. Under these imaging conditions, the obtained image represents to a certain degree the projected potential and allows for a more intuitive analysis of the structure. Our HRTEM images clearly reveal a single layer of Mg atoms in the top (0001) facet of the PID and support the model proposed by Northrup.11 Temperature dependent Hall-effect (TDH) measurements show compensation of 0.15-0.27 by intrinsic donors, i.e., nitrogen vacancies, hydrogen-nitrogen vacancy complexes, or complexes of Mg with these defects. A series of three 700 nm thick GaN:Mg layers with three different Mg concentrations were grown on a 3 lm thick nominally undoped GaN layer deposited on a sapphire substrate by MOCVD. Mg concentrations of 4.2 1019 cm3, 6.5 1019 cm3, and 1.5 1020 cm3 were measured with an accuracy of 610% by secondary ion mass spectroscopy (SIMS) in the respective layers. TEM cross sectional samples, in [1100] and [1120] orientation, were prepared by grinding with diamond films and final argon ion milling with low voltage ion sources using acceleration voltages from 4 kV down to 100 V. The TEM investigations were performed with an FEI Titan 80-300 microscope equipped with an image Cs-corrector and operated at 300 kV. The corrector was tuned to a Cs value magnitude less than 2 lm and minimized residual aberrations to allow a resolution close to the limit of the instrument of 0.07 nm. TDH measurements were performed in the temperature range between 100 and 600 K on the activated sample with the lowest Mg concentration (4 1019 cm3) to determine the degree of compensation by donor impurities. Fitting of the measured hole concentration, p, was based on the charge neutrality equation in the simple form valid for a partly compensated non-degenerate p-type semiconductor, assuming a negligible electron concentration and complete donor ionization. NV ¼ 2ð2pmh kT=h2 Þ3=2 represents the effective density of states (DOS) in the valence
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FIG. 1. HRTEM images of the PIDs (a) in ½11 20 projection and (b) in ½1100 projection. Image simulations for a PID according to Northrup (c) in ½1120 projection with a foil thickness of 5.4 nm and a defocus of 4.5 nm (d) in ½1100 projection with a foil thickness of 5 nm and a defocus of 5 nm.
band, NA ¼ NA/{1 þ gA exp[(EA EF)/kT]} is the concentration of ionized acceptors, NA and ND are the total acceptor and donor concentrations, EA and EF are the acceptor energy level and the Fermi level, respectively. We assumed an effective DOS hole mass of 1.5 m0 (Refs. 12 and 13) and a degeneracy factor gA ¼ 2.14,15 Fig. 1 shows a HRTEM image of a pyramidal inversion domain boundary for the ½1120 and ½1100 projection next to corresponding image simulations showing amplitude contrast is achieved, i.e., atomic columns appear dark. Since the thickness of the layer corresponds roughly to the lateral extension of the PID, we can assume that the central part of the upper boundary proceeds through the whole film thickness, which allows a rough intuitive analysis of the structure of that boundary directly from the experimental image. In both projections, the images show the presence of an additional layer at the top (0001) inversion domain boundary between the PID and the GaN matrix. In the ½1120 projection, the layer consists of a row of atoms, that appear grayish, i.e., they have a lower Z, and are shifted by 1=3½1100 with respect to the lower polarity inverted GaN layer inside the PID. The GaN layer on top of this inserted plane is shifted again by 1=3½1 100. The spacing between the two GaN layers that are separated by the inserted layer is 0.3 nm. These results already indicate a possible agreement with the model proposed by Northrup,11 i.e., an abcab stacking corresponding to GaNMgNGa at the upper (0001) facet of the defect. In the Venne´gue`s model,10 we would indeed expect two rows of Mg atoms, with the Mg in register with Ga atoms in the upper and lower interface of the (0001) facet of
Appl. Phys. Lett. 99, 141913 (2011)
the PID in the ½1120 projection. For a more detailed analysis of the structure, image simulation is needed. Fig. 2(b) shows the atomic model of the PID with the Mg layer in the c-stacking sequence as suggested by Northrup.11 The PID structure is embedded in the GaN matrix and the PID itself has a height of 9 monolayers (0002) and a lateral extension at the upper facet of about 5 nm. The six side facets are of f1123g-type and for simplicity, no Mg atoms are included in the side facets as they are not recognizable in the experimental images and no relaxation has been taking into account. In the model by Northrup, the (0002) monolayers of the polarity inverted GaN inside the PID are shifted along the [0001] direction so that the N atoms in the PID are nearly at the same height as the N atoms of the GaN matrix (Fig. 2(b)). Since the volume of the PID is identical for both structures, we restrict ourselves for the Venne´gue`s model to the (0001) boundary (Figs. 2(c) and 2(d)). In the models, no relaxation has been taken into account for the atomic positions. The structural models were divided in slices suitable for multislice calculations in ½1120 and in ½1100 projection. The simulations were computed with the ems software package16 and the modulation transfer function of the recording charge coupled device was taken into account.17 The results of the simulations are displayed in Figs. 1(c) and 1(d) and in Figs. 2(c) and 2(d). For the Northrup model in ½1120 projection, the Mg layer is seen in the simulation as inserted lattice plane appearing as grey dots between the dark dots that correspond to Ga atom columns. N atoms appear as faint grey dots close to the Ga atoms. For the Venne´gue`s model, we find N and Mg at almost identical contrast forming a sort of dumb bell structure close to the Ga atoms, while at the center of the (0001) boundary, no atomic contrast is present. This does not match our experimental observation of atomic contrast (gray dots) at the c-stacking position. Thus comparing our simulations with the experimental image, we find the best agreement for the model by Northrup.11 Even the spacing of the Ga columns on the top facet inversion domain boundary fits well with his calculations. Turning to the volume of the PID, we clearly see the contrast pattern that is generated by the shift along the c-axis between Ga atoms inside and outside the PID. Residual contrast differences can be mainly attributed to strain in the sample and the, therefore, unavoidable bending of atomic columns on a local scale and an overall bending of the sample which makes it nearly impossible to orient the sample in the exact zone axes as in the simulations. Next, we compare the simulations in the ½1100 projection. Again, we find the best agreement for the Northrup model. While the inserted Mg plane is clearly visible in the Northrup model, a grayish double line is expected in the Venne´gue`s model. In the TABLE I. Measurements of Mg concentration by SIMS, free hole concentration (FHC) by Hall effect at 300K, density and mean size w of the PIDs by TEM, and the estimated amount of Mg bound in the PIDs. [Mg] (cm3)
FIG. 2. (Color) PID (a) geometrical model, (b) atomic model according to Northrup in ½1120 projection. The left part shows the PID embedded in the GaN matrix, the right part only the central slice of the PID, (c) model of the (0001) inversion domain boundary of Venne´gue`s and corresponding simulation in ½1120 projection, and (d) in ½1 100 projection.
4.2 1019 6.5 1019 1.5 1020
FHC (cm3)
PID (cm3)
w (nm)
[MgPIDs] (cm3)
3.3 1017 3.0 1017 2.8 1017
1.5 1014 1.2 1016 3.0 1016
3.5 4.5 5
3.0 1016 4.3 1018 1.3 1019
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FIG. 3. (Color online) Temperature dependence of the hole concentration measured by temperature dependent Hall-effect (circles) and calculated by the neutrality equation using the parameters EA EV ¼ 160 meV, NA ¼ 4.2 1019 cm3, ND ¼ 7 1018 cm3, mh ¼ 1:5m0 , and gA ¼ 2 (line).
contrast simulation and in the experimental image the cplanes inside the PID seem to be bent, which is caused by the superposition of the matrix GaN and the polarity-inverted PID GaN and is a result of the PID geometry. Based on the structural model proposed by Northrup,11 we estimate the amount of Mg incorporated into the PIDs. We evaluated the size and density of PIDs from TEM brightfield images for three samples with a measured Mg content of 4.2 1019 cm3, 6.5 1019 cm3, and 1.5 1020 cm3, respectively. The amount ofP Mg incorporated into the PIDs is calculated by ½MgPIDs ¼ q B AB ðwÞ rB , where AB(w) is the area of a specific boundary facet B of a PID with a base width w, rB is the density of Mg atoms for the corresponding boundary, and q denotes the volume density of the PIDs in the sample.18 We assume the (0001) boundary to consist of a full Mg monolayer, with two neighboring (0002) planes exhibiting a Mg occupation of 0.25 for reasons of charge neutrality, i.e., the basal plane of one unit cell is occupied by 1.5 Mg atoms. For the f11 23g facets, we used 3 Mg atoms per unit area for rB (according to Romano et al.19). The results of our estimation are shown in Table I. The amount of Mg bound in the PIDs is about one order of magnitude lower than the total Mg concentration. Hence, the incorporation of Mg as electrically inert Mg3N2 into the boundaries of the PIDs cannot explain the observed drop in free hole concentration found in GaN:Mg when Mg concentrations exceed 2 1019 cm3. To measure the amount of active Mg and the degree of electrical compensation by donors and its effect on the reduction of the free carrier concentration temperature dependent Hall effect measurements were performed. Fig. 3 shows an example of such a measurement of an activated sample with the lowest Mg concentration (4.2 1019 cm3) and the fitting based on the neutrality equation.7,8 We obtain an ionization energy of EA EV ¼ 160 meV in good agreement with values reported by others for the mid 1019 cm3 Mg doping level.20 Taking this activation energy and the effective hole mass of mh ¼ 1:5m0 , a compensation ratio of ND/NA between 0.15 (for gA ¼ 2) and 0.27 (for gA ¼ 1) is found.21 The fact that our SIMS measurements show oxygen, silicon, and carbon concentrations to be around the detection limit (
