Van Der Waals Epitaxial Growth of Bismuth Thin- lm on Silicon (111) Substrate by MBE

Crystallinity of an 80-nm-thick bismuth thin film grown on Si(111) substrate by MBE was investigated. The highly (0003) textured Bi film contains two twinning domains with different bilayer stacking sequences. The basic lattice parameters c and a as well as b, the bilayer thickness, of the two domains were determined from a series of X-ray diffraction (XRD) measurements, and found that the differences are within 0.1% as compared with those of bulk Bi reported in literature, suggesting that the Bi film has been nearly fully relaxed. From the XRD φ-scans of asymmetric Bi (01-14), (10-15), (11-26) planes and Si (220) plane as well as selected area electron diffraction patterns and electron back scatter diffraction pole figures, we confirmed the well registration between the lattices of Si and Bi lattice, i.e. the ω angle difference between Bi[0003] and Si[111] and the φ angle different between Bi[01-14] and Si[220] are 0.056° and 0.25°, respectively, and thus concluded that the growth is a quasi-van der Waals epitaxy. Introduction Bismuth is an unusual semi-metal with a highly anisotropic Fermi surface and a very narrow inter-band overlap. Its intrinsic carrier concentration at room temperature is ~1018/cm3, just slightly higher than that of the narrow gap semiconductor InSb. Because of the small effective mass in certain orientations and the low intrinsic carrier density, using quantum-size effect to realize the semi-metal/semiconductor transition in Bi thin-film have drawn attentions for decades [1-2]. In addition, recent researches on the surface of (0003) Bi observed metallic surface states formed by spin-orbital interaction [3-4], revealing that the potential applications of Bi and Bi-based materials to the magnetic devices. However, both the researches and applications of the versatile Bi properties depend mainly on the well-ordered structures, and the growth of nanoscale Bi thin films with high quality is of great importance. Bi lattice is a layered structure. Each Bi atom covalently bonds three others to form a hexagonal bilayer network and the bilayers stack in ABC closed pack sequence along its trigonal direction (c-axis) (Fig. 1). Atoms in the adjacent bilayers still have covalent charges form a much weaker “semi-covalent” bonding [5] or van der Waals bonding [5]. The coexistence of different bonding in the lattice may result in difficulties in the epitaxial growth. However, the weaker bonding also allows the growth through the van der Waals bonding interfaces to mitigate the effect of biaxial strain resulting from the huge lattice mismatch, on the crystallinity. Various substrates including Si, BaF2 and glass have been used for the growth of Bi thin film [2, 7-10]. Among them, Si substrate is of great importance because it is the platform of integrated circuits. The feasibility of applications on semiconductor devices [11] as well as on interconnection [12] have been reported very recently for Bi thin films. For the growth of Bi thin film on Si (111) substrate, a previous work utilized in-situ low energy electron diffraction technique to


Introduction
Bismuth is an unusual semi-metal with a highly anisotropic Fermi surface and a very narrow inter-band overlap. Its intrinsic carrier concentration at room temperature is ~10 18 /cm 3 , just slightly higher than that of the narrow gap semiconductor InSb.
Because of the small effective mass in certain orientations and the low intrinsic carrier density, using quantum-size effect to realize the semi-metal/semiconductor transition in Bi thin-film have drawn attentions for decades [1][2]. In addition, recent researches on the surface of (0003) Bi observed metallic surface states formed by spin-orbital interaction [3][4], revealing that the potential applications of Bi and Bi-based materials to the magnetic devices. However, both the researches and applications of the versatile Bi properties depend mainly on the well-ordered structures, and the growth of nanoscale Bi thin films with high quality is of great importance.
Bi lattice is a layered structure. Each Bi atom covalently bonds three others to form a hexagonal bilayer network and the bilayers stack in ABC closed pack sequence along its trigonal direction (c-axis) (Fig. 1). Atoms in the adjacent bilayers still have covalent charges form a much weaker "semi-covalent" bonding [5] or van der Waals bonding [5]. The coexistence of different bonding in the lattice may result in difficulties in the epitaxial growth. However, the weaker bonding also allows the growth through the van der Waals bonding interfaces to mitigate the effect of biaxial strain resulting from the huge lattice mismatch, on the crystallinity.
Various substrates including Si, BaF2 and glass have been used for the growth of Bi thin film [2,[7][8][9][10]. Among them, Si substrate is of great importance because it is the platform of integrated circuits. The feasibility of applications on semiconductor devices [11] as well as on interconnection [12] have been reported very recently for Bi thin films. For the growth of Bi thin film on Si (111) substrate, a previous work utilized in-situ low energy electron diffraction technique to observe a structure transition from disordered pseudo-cubic Bi (110) grains into twinned hexagonal Bi (111) grains [8] when the coverage of Bi is 7 monolayers, revealing the van der Waals epitaxial growth of Bi on Si (111) substrate. However, very few reports on the in-plane structure or the granular properties of Bi thin films [10]. In this work, we present a detailed study on the structural properties of a Bi thin film grown on Si (111) substrates by molecular beam epitaxy (MBE). Bi lattice parameters including a, c, and b, the bilayer thickness, were determined by high-resolution X-ray diffraction (HRXRD) on different planes. The registry between Bi and Si lattice was checked by HRXRD φ-scan and selected area electron diffraction (SAED) and electron back scatter diffraction (EBSD). Twinning and granular properties in Bi thin film was also investigated using HRXRD φ-scan, SAED and EBSD.    Fig. 2 shows the setup of HRXRD with the angles which will be referred hereafter. Fig. 3 shows the result of ω-2θ HRXRD scan of a Bi thin film with a thickness of ~80 nm, deposited on Si (111) substrate by molecular beam epitaxy (MBE). In the figure, the strong peak at 22.45° is from the diffraction of Bi (0003) planes. The FWHM Δ(2θ) of the peak is 0.11°, close to the value calculated from Scherrer equation for 80 nm thickness. Besides, the clear thickness fringes around the peak indicates the film has a rather smooth surface. These findings reveal that the growth is mainly along the c-axis with a well-ordered sequence, despite the ~18% lattice mismatch between Bi and Si. The peak at 27.16° is the diffraction of Bi (10)(11)(12) planes. The existence of this peak reveals the granular in-plane structure of the Bi film. To understand the in-plane structure, we performed electron backscatter diffraction (EBSD) measurement and the inverse pole figure (IPF) Z mapping and IPFX mapping are shown in Fig. 4(a) and (b), respectively. The orientation can be identified by the colored circular sector with the coordinate system for hexagonal lattice. As shown in Fig. 4(a), the whole region is almost red except some black spots, indicating that the Bi film is [0003] textured. The black spots are located at the grain boundary where the defects make the orientation unresolvable.

Results and Discussion
The (10)(11)(12) phase (purple or yellow color), however, is not visible in Fig. 4(a). In Fig. 3, the intensity ratio of (10-12) to (0003) is 1/60. Considering that the structure factor of (10-12) is about 10 times larger than that of (0003), the probability ratio of appearing (10)(11)(12) grain to (0003) grain is ~1/1600. Since the IPF mappings covers only several hundred grains as  shown in Fig. 4(b), the grain of (10-12) could omit this measurement area due to its low probability. The IPFX mapping, shown in Fig. 4(b), clearly depicts grains with sizes in several microns. Almost all the grains are either in grass green or in deep blue except several scattered grains in light blue. The number of grass green is much more than that of deep blue, indicating that [01-10] represented by grass green is the preferential direction. The second largest color is along  which is 60º with respect to [01 -10]. To further elucidate the relation between the lattices of Bi twinning phases and the Si substrate, the TED images took from two different twinning phases are shown in Fig are much brighter than other Bi spots, which is due to their strong structure factor.
To further understand the relationship between the Si substrate and the preferential growth of the Bi film, we performed XRD measurements for the tilting planes (01-14), (10)(11)(12)(13)(14)(15), and (11-26) of the Bi twinning phases as well as the (220) planes of the Si substrate. Note that a trigonal lattice becomes an FCC lattice when its lattice constants have the relation: c = √6 a. In this situation, {0-1-14} of the hexagonal trigonal system is equivalent to the {220} of the cubic FCC system, and the c/a of Bi is larger than √6 by only ~6.5%. In here, we compare the φ scans of Bi (01-14) and Si (220) to understand which twinning phase follows the stacking sequence of Si. The φ-scan of the four tilting planes are shown in Fig. 6(a), 6(b), 6(c), and 6(d), respectively. In the measurement, the  of the Si substrate parallel to the diffraction plane when φ = 0°. For the measurement of (01-14), (10)(11)(12)(13)(14)(15), and (220) planes, the sample was rotated to φ = 90° to let the projection of the plane normal on the sample surface perpendicular to the diffraction plane. Then, the plane for measurement was tilted with a χ angle to let its normal on the diffraction plane to perform ω-2θ scan. The schematic diagram for aforementioned procedures can be find as Supplementary Fig. S1 online. After a fine-tuning procedure, we obtained a best Bragg's angle, at which φ scan was performed. The same procedures were used for (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26) plane except that the initial φ angle was set at 60°. As  on Si (111) [13]. Although the Si substrate is slightly mis-orientated, the tilting direction of the Bi film suggests that it is still affected by the steps on the Si substrate.
The ω-2θ scans of Bi (01-14), Bi (10-15) and Bi (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26) are shown in Fig. 7(c)-(e). The scans were performed at six different φ angles, indicated in the figures. In contrast to Bi (0003), the Bragg's angles of the three planes are in much larger variation for different φ angles and the FWHM's are also much broader. For some cases, the Bragg's reflection clearly can be decomposed into two peaks resulting from two groups of grains, which is consistent with the low intensity skirt observed from the φ-scan of plane (01-14) shown in Fig. 6(d). Therefore, we conclude that the vertical structure of Bi film is in much better order than its in-plane structure. The latter clearly contains different grains and could suffers from defects and strains resulting from huge lattice mismatch between Bi and Si substrate as well as the defects at grain boundaries.
The determination of the lattice parameter a and c allows us to understand more detailed structural properties. Since the vertical structure of the Bi film is in much better order, we performed XRD measurement on (0003) The lattice parameter c was set as the average value listed in Table 1 and the parameter a can thus be uniquely determined for each d(pqrs). In total, we have 18 measurements for 3 different titling planes at 6 different φ angles. The average and standard deviation for a are 4.545 Å and 0.0096Å, respectively. The values are also listed in Table 1. For comparison, the lattice parameters determined from Barret [14] are also listed in Table 1. Barret's results were determined from zonerefining Bi single crystal and are considered free from defects and strains. Our parameter a is very close to Barret's value.
However, the difference is much smaller than our standard deviation and further discussion in a becomes inappropriate. But the difference between two c parameters is small than our standard deviation. Therefore, we believe that the epitaxial Bi thin film is nearly fully relaxed but might with a very small in-plane compressive stain in the range of 10 -4 . Kammler and Horn-von Howgen estimated 2% compressive strain in the 7 ML bismuth film deposited on Si (111) from their LEED observation [8]. In contrast, our 80-nm-thick film is about 200 ML and has been nearly fully relaxed. Both results indicate the effect of van der Waals gap on the heterepitaxy.
In addition to lattice parameters c and a, the bilayer thickness, b, is also an important parameter which cannot be directly determined from XRD measurements. Notice that the top atoms and bottoms atoms in a bilayer belong to different basis atoms as shown in Fig. 1. Therefore, the bilayer thickness affects the structure factor of the lattice and thus the integrated XRD intensity. In this work, we derive the thickness by comparing the integrated XRD intensities of different planes.
However, the integrated intensity is also a function of Bragg's angle, θ, and Debye-Waller factor which contains average mean square of atomic displacement. In here, we list a simplified formula (2) [15], considering only the terms relevant to bilayer thickness, b, Bragg's angle, θ, Debye-Waller factor, e -2M , and the Miller indices of the (p q r s) plane, for the integrated XRD intensity, I, as follows, where d is the distance between two adjacent bilayers which is c/3, A is a constant independent of Bragg's angle and orientation, fj is the atomic scattering factor, L is the Lorentz factor, and Ac is the absorption correction factor. The details of the parameters are described as follows. For the Debye-Waller factor, e -2M , the factor M is proportional to the average mean square displacement of the atoms to their lattice points along the normal of plane (p q r s). The atomic displacement is due to thermal vibration and lattice imperfections. In here, because of the aforementioned severe disorder in tilting planes, which could hinder the obtaining of accurate intensity, we consider only (0 0 0 s) planes. We thus used the following equation to express the M factor [16], where 〈r  2 ̅ 〉 is the vertical average mean square atomic displacement and B = 8π 2 〈r  2 ̅ 〉. Atomic scattering factor of Bi atom, fj, is a function of Bragg's angle and wavelength. The value used in this work was calculated using the polynomial formula from Ref. [16]. The Lorentz factor, L, includes the polarization factor and the angular velocity. Our XRD has a Ge (220) first crystal and L is given by, where θM is the Bragg's angle for Ge (220) and cos 2θM = 0.7033. The Cu-Kα absorption coefficient of Bi, μ, is 2391 /cm and the film thickness is only 80 nm, the effect of absorption much be considered, the correction factor Ac is given by Finally, we may obtain a function F(b/d) by divided Eq. (2) by the measured X-ray intensity, Iexp. The function is expressed as, Intuitively, the F value of different planes should be the same if we select correct b/d value and Debye-Waller factor. In addition to b/d and Debye-Waller factor, the final F value is also unknown, we thus need at least three planes to find the three unknown variables. We selected the integrated XRD intensities of (0006), (0009) and (00012) Table 1. In the solving, (0003) plane was not chosen because of the extinction effect resulting from its small Bragg's angle, suggested in Ref. 14. However, as shown in Fig. 9, the curve of (0003) is also very close to the point of intersection. Its F(b/d) value is slightly lower than that of the point of intersection by 0.9%. Table 1 also lists the b/d and B values reported by Barret. Our b/d is very close to Barret's value. For the B values, ours is larger than Barret's value by 63% [17]. Barret's results were obtained from a Bi single crystal produced by zone-refining method and the B value is believed mainly from thermal vibration. In contrast, our B value is from an epitaxial Bi thin-film, must suffer from defects and strains resulting from the huge lattice mismatch as well as the granular in-plane structure. However, the b/d value is close to the value of single crystal and the B value is low despite the aforementioned in-plane disorder. We believed that the van der Waals gap must play an important role.

Conclusion
In conclusion, the lattice structure of an 80-nm-thick Bi thin film grown on (111) Si substrate by MBE has been investigated.
Most of the grains in the film were grown along [0003] direction but with two different stacking sequences, i. e., in two twining phases. From EBSD, XRD φ-scan, and SAED measurements, we found that the preferential twining phase well register the lattice of the bottom Si substrate. The lattice parameters, c, a, and b as well as the Debye-Waller factor of the (0003) grains have been determined. The parameters are close to those of bulk Bi single crystal, implying that the grains are nearly fully relaxed despite the huge ~18% lattice mismatch. From these findings, we believe that the growth is a van der Waals epitaxy.

MBE of nanoscale Bi
Bi thin film was deposited on Si(111) substrate by MBE. Before the growth, Si wafers were degreased in acetone, methanol and isopropyl alcohol each for 2 minutes and then soaked into 2% HF solution for 1 min to remove the native oxide. The wafers were then loaded into SVTA MBE system and were baked at 300°C under UHV environment for 1 hour in the buffer chamber and desorbed at 850°C for 5 minutes in the growth chamber. The temperature of substrate was a critical parameter during the growth, which was fixed at 130°C and the growth time was 30 minutes.

HRXRD spectra
HRXRD spectra of Bi film were carried out on Bruker New D8 Discover with an X-ray wavelength of 1.5406 Å (Cu K-α) and an integration time ranging from 0.1 s to 1 s.

SAED pattern
SAED pattern of Bi grains were carried out on JEOL JEM-2010F TEM with an accelerating voltage of 200 kV.

EBSD maps
EBSD maps of Bi film were performed on JEOL JSM-7800F PRIME with EBSD NordlysMax3 detector. The accelerating voltage is 20 kV.
between two adjacent bilayers, respectively.