Delayed crystallization of ultrathin Gd2O3 layers on Si(111) observed by in situ X-ray diffraction

We studied the early stages of Gd2O3 epitaxy on Si(111) in real time by synchrotron-based, high-resolution X-ray diffraction and by reflection high-energy electron diffraction. A comparison between model calculations and the measured X-ray scattering, and the change of reflection high-energy electron diffraction patterns both indicate that the growth begins without forming a three-dimensional crystalline film. The cubic bixbyite structure of Gd2O3 appears only after a few monolayers of deposition.


Background
Binary rare-earth metal oxides became increasingly important as gate dielectrics in metal oxide semiconductor field-effect transistor technology [1,2] and as catalysts. The application of these oxides as gate dielectrics is based on their high dielectric constants [3], large bandgaps [4], high thermal stability of their interfaces to silicon [5], and large band offsets with silicon. Gd 2 O 3 is a promising candidate among the lanthanide oxides due to its close lattice match to silicon ( a Gd 2 O 3 = 10.812Å; 2a si = 10.862 Å). Epitaxial growth of Gd 2 O 3 has been demonstrated for a variety of substrates, including GaN [1], Si [6], and SiC [7] by atomic layer deposition [8] and molecular beam epitaxy (MBE) [9].
Here, we present an MBE growth study of Gd 2 O 3 on Si(111), applying synchrotron-based X-ray diffraction with particular focus on the formation of the very first crystalline layers. These measurements were done during sample growth in situ, in a continuous way without any growth interruption.

Molecular beam epitaxy
All samples were grown in a dedicated MBE chamber under ultrahigh vacuum (UHV) conditions. The 2 × 2cm 2 Si(111) substrates were prepared by a 10-min dilute (5%) HF treatment, to remove the thermal oxide, followed by a 10-min H 2 O rinse. Next, they were loaded into the MBE system, degased at 300°C in the load lock for 20 min, and annealed in the growth chamber under UHV at 720°C (measured using a thermocouple between heater and substrate) for 60 min to prepare a (7 × 7) reconstructed Si(111) surface. The sample temperature was subsequently ramped to the growth temperature of 700 C. During the growth, Gd 2 O 3 powder (99.999%) was evaporated from a special effusion cell (TUBO), which allows for cell temperatures in excess of 2,000°C [10]. Temperature and flux from this cell can be adjusted more accurately than with conventional e-beam evaporators. Throughout the experiment, the cell temperature was kept constant at 1,650°C (thermocouple temperature; the actual temperature of the source material is higher), resulting in a growth rate of 0.13 Å/min. Molecular oxygen at 10 -7 mbar was added 30 s prior to the growth sequence and throughout the entire layer deposition (OB, unpublished work).

X-ray diffraction
The X-ray scattering experiments were performed at the dedicated beamline U125/2-KMC at the synchrotron BESSY II (Helmholtz-Zentrum Berlin HZB, Berlin, Germany). This experimental setup [11] combines the MBE system described above with the ability to perform highresolution X-ray diffraction, which enables unique in situ growth studies. The primary X-ray beam with a size of 500 × 500 μm 2 enters and exits the growth chamber via X-ray transparent Be windows, whereas the scattered intensity can be probed in an angular range of 0°to 120°in-plane and 0°to 50°out-of-plane. Both the sample and the detector can be precisely moved during the growth to probe scattered intensity in a wide range of reciprocal space. An X-ray energy E of 12 keV, selected by a Si(111) double crystal monochromator (ΔE /E = 10 -4 ), is chosen as a compromise between the accessible area in reciprocal space and primary intensity. Throughout the experiment, the incidence angle was kept constant at a i = 0.2°.

Results and discussion
We index the reflections in surface (hexagonal) coordinates, marked with (HKL) hex , instead of using bulk indices, denoted by (HKL) cub [12]. Referring to the symmetry of the Si(111) cub substrates, we define the surface unit cell by vectors a, b, and c with lengths a = b = 3.84 Å, c = 9.405 Å and a = b = 90°, g = 120°. For example, the Si(022) cub bulk reflection refers to (104) hex in surface coordinates.
Post-growth X-ray diffraction Figure 1a shows a post-growth in-plane intensity distribution of a 13-monolayer (ML, 1 ML = 3.12 Å)-thick Gd 2 O 3 layer on Si(111) measured by in situ X-ray diffraction. All reflections are labeled in the sketch ( Figure  1b) which also addresses their different origin. There are basically three types of reflections: intense substrate peaks (red squares), layer reflections (blue circles), and intensity tails from crystal truncation rods (CTRs, green triangles), which are forbidden reflections for bulk Si. This diffraction pattern corresponds to the cubic bixbyite structure (space group 206) of Gd 2 O 3 with single orientation, in agreement with previous studies, which found an A-B twinning relation for Gd 2 O 3 /Si(111) heteroepitaxy [13]. Thus, the layer is 180°rotated with respect to the underlying substrate, referring to the Si-CaF 2 -type interface with the silicon atoms directly bonded to calcium [14].
In-situ X-ray studies during growth To study the epitaxial growth of Gd 2 O 3 on Si(111) in situ, we probed the evolution of the out-of-plane scattering by measuring three different CTRs, whose positions are indicated by green triangles in Figure 1b.   substrate contributions by L = ± 1 as shown in Figure 2. The onset of these layer reflections sensitively probes the appearance of a three-dimensional crystalline Gd 2 O 3 lattice.

Scattering calculations
For comparison, the CTR intensities were calculated using the structure model shown in Figure 3a. The semi-infinite silicon substrate and a finite number of the oxide layers, in a twinned orientation of the ABCABC packing with respect to the substrate, were included in the calculation. The intensity calculations were performed in the distorted wave Born approximation [15] since the incidence angle is close to the critical angle. A non-integer deposition was calculated as a sum of scattering amplitudes of two films, with the integer numbers of monolayers smaller and larger than the actual deposition, taken in the appropriate proportion. The time-dependent layer thickness was determined from the current growth time. The growth rate was obtained by dividing the total film thickness, determined from a post-growth CTR measurement, by the total growth time.

Layer formation at the interface
The measured (Figure 2a, b) and calculated (Figure 2c,  d)   . Layer peaks become stronger and are subsequently accompanied by thickness fringes whose separation in L shrinks with increasing thickness. However, in contrast to the calculations, which contain a fingerprint of a three-dimensional crystalline Gd 2 O 3 lattice already from the first monolayer on, there is no experimental evidence for a crystalline layer below the deposition of 2 to 3 ML. For a more detailed analysis, Figure 4 compares a selection of measured and calculated CTRs at different deposition thicknesses. The measured CTRs do not show an indication of the crystalline film for the deposition less than 2 ML, while the intensity changes due to the film are visible on the calculated CTRs from the very beginning of the growth. We cannot exclude an in-plane ordering in separate layers without any registry among one another.  Figure 4 Comparison between measured and simulated CTRs. One-dimensional intensity profiles along the CTR (10L) hex as measured (black curves) and calculated (red). The given values refer to nominally deposited layer thickness. In the beginning, the experimental profile does not change (gray), followed by a crystallization process (dark gray) which finally ends up with crystalline growth (yellow). about 4 ML, the measured curves become more and more close to the calculated ones, showing that the crystalline order develops in the film. For the film thickness larger than 4 ML, a crystalline film grows, and the thickness determined from the fringes on the CTRs agrees with the nominally deposited film thickness. This agreement proves that the sticking coefficient is constant for the entire growth starting from the layer-substrate interface -consistent with a constant deposition rate. Atomic force microscopy of the pure Si(111) substrate (not shown) yields a mean terrace size of 600 nm, which does not change after the deposition of 1 and 2 ML of Gd 2 O 3 . The roughness of 0.46 nm is preserved during growth. Post-growth X-ray reflectivity measurements prove the nominal layer thickness with an RMS roughness of less than 1 ML.
The evolution of the reflection high-energy electron diffraction (RHEED) pattern (not shown) during the first MLs is consistent with the 'delayed crystallization' scenario: During deposition of the first ML, the 2D streaky RHEED pattern from the Si(111) surface disappeared completely and transformed into a diffuse RHEED pattern with almost vanishing specular spot intensity -indicative of the lack of crystal order [13]. The specular spot intensity recovered after the deposition of (3 to 5 ML) together with the onset of pronounced RHEED oscillations.
For the final film, the fringes of CTRs (sensitive to crystalline film thickness only) and the X-ray reflectivity fringes (sensitive to total film thickness irrespective of crystalline order) correspond to the same thickness. Therefore, the crystalline order developed over the whole film thickness, without leaving a noncrystalline initial layer at the interface. This conclusion is in agreement with cross-sectional transmission electron micrographs in Figure 3b which demonstrates a pseudomorphic film and an atomically flat layer-substrate interface.

Conclusions
We have performed a synchrotron-based in situ X-ray diffraction study during the epitaxial growth of Gd 2 O 3 on Si(111). By comparing measured crystal truncation rods to X-ray scattering calculations, we found that the crystallization into three-dimensional cubic bixbyite structure was delayed: it started at a layer thickness of about 2 ML and proceeded up to 4 ML.