as given by [11, 73–75]. In comparison with the curves obtained for Cij of Wright [11], the maximum relative error of x is obtained for the elastic constants given by Azuhata et al. [73] and amounts to 8% in case of r = 0 and 25% in case of r = 1. Typically, the relative errors of the In concentration are less than 5%. The systematic error due to the not well known Cij is not further considered for the evaluated samples in this work.
0.53 0.55 0.57 0.59 0.61
c lattice spacing [nm]
0 0.2 0.4 0.6 0.8 1.0
x
cGaN c
InN
unstrained InxGa1-xN Kim et al., r = 1 Kim et al., r = 0 Chisholm et al., r = 1 Chisholm et al., r = 0 Azuhata et al., r = 1 Azuhata et al., r = 0 Wright, r = 1 Wright, r = 0
Figure 3.17: In concentration x in dependence of the c lattice spacing for thick TEM specimens (r = 1), thin TEM specimens (r = 0) and totally relaxed InxGa1−xN. The results for different elastic constants as given by Kim et al. [74], Chisholm et al. [75], Azuhata et al. [73], and Wright [11] are displayed.
beam is used. For practical reasons this should be done at the beginning of the microscope session. Mader and Reˇcnik [77] determined the polarity of different polar materials using CBED patterns from ZA orientations. For small sample thicknesses, the CBED discs of the reflections show an approximately homogeneous intensity. The intensity of the reflections under consideration can then be compared directly. For example, the intensity of the 0002 beam is stronger than the intensity of the 0002 beam for sample thicknesses of more than 40 nm for the h1100i ZA orientation (figure 3.4 b). The effect of small mistilt from the exact ZA orientation is visualised in figure 3.18. In the following , the intensities are again normalised to the intensity of the incident electron beam. The difference of the normalised intensities ∆I = I(0002)−I(0002) of the 0002 beam and the 0002 beam is shown for mistilts around the h1100i(left column in figure 3.18) andh1120i (right column in figure 3.18) ZA orientations for different specimen thicknesses t. The tilt is given in parts s of the COLC, i. e. s(0001) =−2 denotes a COLC of 0002, which means a strong excitation of the 0004 beam. The COLC range given corresponds to a mistilt of±0.55◦ for s(0001),±0.45◦ fors(1100) and±0.90◦ fors(1120). For theh1120iZA orientation I(0002) is more intense than I(0002) for the whole analysed tilt region up to a specimen thickness of 10 nm. For theh1100iZA orientation this is valid for a thickness up to 7 nm. At 15 nm thickness the mistilt corresponding to s(0001) has to be smaller than 0.14◦, and at 20 nm smaller than 0.07◦ for both ZA orientations. Considering that a TEM sample can be bent at thin regions, it is obvious that an unambiguous determination of the polarity and/or the 0002 beam is possible at very thin sample regions only. Simulations of CBED patterns using Bloch wave calculations for h1120i andh1100iZA orientations show the appearance of HOLZ lines in the CBED discs for thicknesses & 10 nm. If the CBED discs in the experiment are of homogeneous intensity without HOLZ lines, this is taken as indicator that the observed intensity difference is reliable for the polarity measurement.
t = h1100i ZA h1120iZA 5 nm
a)
I(0002)-I(0002)_ 0.06 0.048 0.036 0.024 0.012 0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(11-20) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
f)
I(0002)-I(0002)_ 0.077 0.061 0.046 0.031 0.015 0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(1-100) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
10 nm
b)
I(0002)-I(0002)_ 0.331 0.265 0.199 0.132 0.066 0.0 -0.0 -0.011 -0.022 -0.033 -0.044 -0.055
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(11-20) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
g)
I(0002)-I(0002)_ 0.064 0.051 0.039 0.026 0.013 0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(1-100) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
10 nm
c)
I(0002)-I(0002)_ 0.52 0.416 0.312 0.208 0.104 0.0 -0.0 -0.041 -0.081 -0.122 -0.163 -0.204
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(11-20) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
h)
I(0002)-I(0002)_ 0.142 0.114 0.085 0.057 0.028 0.0 -0.0 -0.01 -0.02 -0.029 -0.039 -0.049
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(1-100) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
Figure 3.18: To be continued.
20 nm
d)
I(0002)-I(0002) _ 0.414 0.331 0.248 0.166 0.083 0.0 -0.0 -0.054 -0.109 -0.163 -0.217 -0.271
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(11-20) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
i)
I(0002)-I(0002) _ 0.265 0.212 0.159 0.106 0.053 0.0 -0.0 -0.015 -0.029 -0.044 -0.058 -0.073
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(1-100) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
25 nm
e)
I(0002)-I(0002)_ 0.401 0.321 0.241 0.161 0.08 0.0 -0.0 -0.071 -0.143 -0.214 -0.286 -0.357
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(11-20) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
j)
I(0002)-I(0002)_ 0.206 0.165 0.124 0.082 0.041 0.0 -0.0 -0.024 -0.047 -0.071 -0.094 -0.118
-1.0 -0.5 0.0 0.5 1.0
-1.0
s(1-100) -2.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
s(0001)
Figure 3.18: Intensity difference ∆I =I(0002)−I(0002) between the normalised intensities of the 0002 beam and the 0002 beam for wurtzite GaN in dependence of mistilt around the h1100i (left column,a toe) and h1120i ZA orientation (right column, ftoj) for different specimen thicknesses t. The tilt is given in parts sof the COLC. The scalebar ranges from the maximum value of ∆I to the minimum value if negative or zero for each individual image. Reddish colour levels denote positive ∆I, i. e. I(0002) is stronger than I(0002), and grey levels denote negative ∆I.
Pyramidal defects in Mg doped GaN
While n-type doping of GaN using Si is possible up to high doping levels, p-type doping of GaN caused problems for a long time. Different acceptors were analysed, among which Mg is most suitable and now commonly used. For growth of GaN:Mg with MOVPE, the material is of high resistivity. For a long time, it was not clear why this is the case or how to reach p-conductivity using this growth technique. It was not until 1989, when Amano et al. [78, 79] accidentally discovered thatp-type conductivity can be obtained in GaN:Mg if a low energy electron beam irradiation (LEEBI) treatment is performed after MOVPE growth. Nevertheless, this is a quite elaborate method, and only the irradiated material near the surface exhibits p-type conductivity. The exchange of the LEEBI treatment with an easier post growth thermal heating process carried out in a N2 atmosphere by Nakamura et al. [80, 81] represents a breakthrough for the commercial manufacturing of GaN based optoelectronic devices.
It was proposed that GaN:Mg is passivated by H [81], which is inevitably present during MOVPE growth of GaN, and Mg−H complexes are formed. These Mg−H complexes compensate the holes, and the resistivity of the GaN:Mg film is increased [81]. The post growth heat treatment is thus used to dissociate the Mg−H complexes and to remove H from the crystal [81]. Despite the passivation of GaN:Mg, H should also exhibit beneficial effects on GaN:Mg growth. Based on DFT calculations, Neugebauer et al. [82] and van de Walle et al. [19, 20, 83] concluded that the concentration of N vacancies VN is reduced and that the achievable Mg concentration in GaN is increased if H is present. The latter result of increased Mg concentration was experimentally demonstrated by comparison of MBE grown GaN:Mg samples with GaN:Mg codoped with H [84, 85]. Nevertheless, codoping with H also changes the microstructure and extended defects like inversion domains (IDs) can be created [85], which is detrimental for device application.
Despite the fact that Mg was found to be the most suitable acceptor for p-type doping of GaN, there are some drawbacks. For example, the ionisation energy of Mg in the range of approximately 200 meV is very high. Therefore, only a small amount of the MgGa is
59
ionised [86]. Thus, to reach a certain hole concentration in GaN films, a much higher Mg concentration is necessary. Nevertheless, the hole concentration starts to decrease for Mg concentrations exceeding approximately 1019 cm−3 [87]. This is usually attributed to extended defects forming at these high Mg concentration. These extended defects are of pyramidal shape. Therefore, they are called pyramidal defects (PDs). The PDs were found to be Mg rich, thus reducing the amount of active Mg in GaN and affecting the free hole concentration.
McCluskey et al. [88] first observed PDs in GaN:Mg. They analysed as-grown and annealed MOVPE samples. While no PDs were observed in the as-grown sample, PDs were formed in samples annealed at 1400◦C for 15 minutes. Comparing the structure of the PDs with defects formed in GaN due to implantation of H [89, 90], these authors conjectured that H may play a role in pyramidal defect (PD) formation. In the following time, further analyses of the PDs were conducted. The base of the PDs lies in the{0001} plane [88, 91], with six side facets composed of a combination of second order pyramidal planes (see appendix A.4 for nomenclature of special planes in hexagonal crystals). These are {1213}, {1212}, and {1216} [92]. The tips of the pyramids always point in the [0001]
direction of the surrounding GaN matrix material [91, 93]. A schematic of a PD viewed in different directions is shown in figure 4.1.
The nature of the PDs has been studied in the literature and different models were suggested. All models comprise an enrichment of Mg at the boundaries or inside the PDs. Hansen et al. [94, 95] stated that the PDs are Mg3N2 precipitates. Mg3N2 is the only compound of Mg and N which is reported [5]. The crystal structure of Mg3N2 was analysed by David et al. [96] and Partin et al. [97]. They report that Mg3N2 crystallises in the antibixbyite structure, which simplified can be described by a face centred cubic (fcc) N lattice with three quarters of the tetrahedral lattice sites occupied by Mg. Due to the unoccupied tetrahedral lattice sites, the lattice is distorted. The structure can be seen in
a) b) c)
Figure 4.1: Schematic structure of a PD viewed alongathe [0001] direction of the surround-ing GaN matrix material,b [1120], and c[1100]. The side facets of PDs are combinations of {1213}, {1212}, and {1216} planes [92].
[010] and [110] projection in figure 4.2 a and b, respectively.
The a lattice constant is 0.9953 nm [97]. The space group of antibixbyite is Ia3 (no. 206, Pearson symbol cI80) [5]. The band structure of Mg3N2 was calculated with DFT by Fang et al. [98] and Orhan et al. [99]. They report that Mg3N2 has a direct energy gap. The experimentally obtained band gap energy at the Γ point is 2.8 eV [98].
In contrast to the interpretation of the PDs as Mg3N2 precipitates, Liliental-Weber et al. report the observation of hollow cavities inside PDs [28, 91, 100, 101] and suggest that the boundaries of the PDs are decorated with Mg and covered by GaN of reversed polarity [6, 102–104]. Venn´egu`es et al. [92] studied Mg doped bulk GaN grown by a high-pressure, high-temperature method exhibiting rather large PDs with basal plane diameters of approximately 100 nm. They showed that these defects are IDs using CBED in cross section TEM. Convincing evidence was presented that the Mg enrichment at the inversion domain boundary (IDB) can be explained in terms of the presence of a thin layer of the antibixbyite structure Mg3N2. It has still to be shown that this model is also valid for PDs in highly Mg doped GaN grown by MOVPE.
MOVPE grown GaN:Mg contains much smaller PDs with basal plane diameters of
a) b)
Figure 4.2: Antibixbyite structure of Mg3N2. The small spheres represent N and the large spheres represent Mg atoms. In athe unit cell is shown in [010] projection. b displays the unit cell in [110] projection.
(5. . .20) nm. Therefore, an analysis of the PDs using CBED is not practical. HRTEM analysis turned out to be challenging because the PDs have to be positioned in an extremely thin sample area to minimise an overlap of the PD boundary, which is to be analysed, with the surrounding GaN matrix material.
In the following, the nature of the basal plane IDB of PDs in MOVPE grown GaN:Mg will be illucidated. For this, first results obtained from energy dispersive x-ray spectroscopy (EDS) and scanning transmission electron microscopy (STEM) measurements will be pre-sented, which qualitatively agree with a Mg enrichment at the boundaries. This is followed by a description of the experimental HRTEM results and HRTEM image simulations. With the microscope CM20 UT, which was used for recording the HRTEM images,{1120}planes cannot be resolved. Therefore, HRTEM was restricted to the h1120i ZA. The experimen-tally obtained HRTEM image of a basal plane boundary of a PD will be compared with simulated HRTEM images. For the simulations, a variety of boundary models were set up.
All models assume that the boundary is an IDB, and that antibixbyite is present.
4.1 Experimental
The growth of the samples was done by MOVPE using ammonia (NH3) with TMG and Cp2Mg as precursors1. The substrates consisted of 2 µm thick undoped MOVPE GaN on (0001) sapphire. On top of this 4 µm GaN:Mg was grown at Tg = 1050◦C with a Cp2Mg flow of 350 sccm, TMG flow of 20 sccm, and NH3 flow of 5000 sccm. This corresponds to a doping level of approximately 2·1019 cm−3.
TEM samples were prepared by a tripod method. Ion milling was performed in a PIPS (Gatan) equipped with two ion guns. For the milling Ar+ ions were used. The angles between the sample surface and the two incident Ar+ ion beams was ±5◦. The acceleration voltage of the ions was 5.4 eV. With these settings, the duration of the ion milling was usually about 20 minutes to reach electron transparency. EDS and STEM analysis, employing also a high angle annular dark field (HAADF) detector, were performed on a JEM 2010F equipped with a field emission gun (FEG) at 200 kV2, while HRTEM was done with a CM20 UT equipped with a LaB6 filament at 200 kV. The polarity of the GaN matrix material was measured using the method described in section 3.4. HRTEM image simulations employing the multislice approach (see section 3.1.2) were performed using the electron microscopy image simulation (EMS) software package of Stadelmann [57].
1The samples were grown by Dr. Stephan Figge, semiconductor epitaxy group (Prof. Dr. D. Hommel).
2The EDS and HAADF STEM measurements were done at the Joˇzef Stefan Institute, Ljubljana (Slove-nia) in cooperation with Dr. Aleksander Reˇcnik and Dr. Nina Daneu from the Joˇzef Stefan Institute and Dr. Roland Kr¨oger from the University of Bremen, electron microscopy group (Prof. Dr. A. Rosenauer).