Bifunctional effects of the ordered Si atoms intercalated between quasi-free-standing epitaxial graphene and SiC(0001): graphene doping and substrate band bending

As shown in figures 1(a) and (b), both STM and LEED images obtained from the surface prepared by postannealing the oxide-removed 6H–SiC(0001) sample at 1150 °C for 5 min displays a well-known image and pattern of the $(6\sqrt{3}\times 6\sqrt{3})R30^\circ$ ZL [39–41]. In this STM image, the solid (dotted) rhombus represents a unit cell of $(6\sqrt{3}\times 6\sqrt{3})R30^\circ$ (6×6). The LEED pattern contains brightest spots of the SiC substrate (S) and bright spots of the graphene-like ZL (G) together with dim superstructure spots surrounding the S and G spots [42]. The ARPES spectrum obtained from this surface does not show any graphene-like π bands, as seen in figure 1(c). Instead, only two localized states, g1 and g2, appear at binding energies near 0.5 and 1.5 eV, respectively [43]. These results say that the surface is covered with the ZL without any ML graphene.

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After 3.3 ML Si deposition on this ZL at RT and subsequent annealing at 650 °C for 5 min, the obtained STM image shows large and round clusters covering most of the surface, as shown in figure 1(d). The corresponding LEED pattern shows weak 3 × 3 spots whose unit cell is outlined by a solid rhombus and dim $(6\sqrt{3}\times 6\sqrt{3})R30^\circ$ spots inside the white circle, as shown in figure 1(e). As shown in figure 1(f), in the vicinity of the $\bar{K}$ point, a pair of π bands appear; one having a charge neutrality point (E_D) at 0.42 eV below the Fermi level (E_F) and the other with a weaker E_D difficult to appoint its position exactly. This is supported by a momentum distribution curve at a binding energy of 0.16 eV on the lower part of figure 1(f) [44]. From the LEED pattern and the π bands, it can be concluded that the deposited Si atoms are partially intercalated and part of the ZL is decoupled from the substrate. Due to electron transfer from the intercalated Si layer, the decoupled graphene with a structure of 3 × 3 exhibits an electron doping of $n=1.1\times {10}^{13}$ cm⁻², since $n={({E}_{D}-{E}_{F})}^{2}/(\pi {{\hslash }}^{2}{v}_{F}^{2}$), where ${E}_{D}-{E}_{F}$ is 0.42 eV, ℏ is the Planck constant divided by 2π and the Fermi velocity v_F is $1.1\times {10}^{6}$ m s⁻¹ [45].

After an extended postannealing at 750 °C for 5 min, as shown in figure 1(g), the STM image shows only a one-dimensional (1D) structure with three directions equivalent to the $[10\bar{1}0]$ direction together with scattered 0.5 nm high craters. In the corresponding LEED pattern, figure 1(h), the ZL-related spots disappeared totally and there appear dim rows of spots along the three equivalent directions (i.e., having an angle of ${120}^{\circ }$ between any two) as well as bright S and G spots. Such a LEED pattern except G spots was already depicted by Naitoh et al for a new kind of Si-rich structure on the SiC(0001) surface having neither graphene nor ZL [46]. In here, a unit cell is marked by a long rhombus. In the vicinity of the $\bar{K}$ point, as shown in figure 1(i), only a single sharp π band appears as expected for pristine graphene. This means that through full intercalation of Si between the SiC(0001) substrate and the ZL, the ZL becomes QFMLG. Therefore, it can be deduced that the 1D structure shown in figure 1(g) is reconstructed on the SiC(0001) substrate and imaged through this decoupled graphene. Since Si atoms cannot be intercalated through defect-free graphene, it can be concluded that they penetrate through the ZL by way of the observed craters, which appear as dark spots in the LEEM images reported by Xia et al [33]. When the amount of Si deposition at RT was less than 2 MLs, even after 750 °C annealing, Si atoms remaining on the ZL and do not intercalate, since the craters were not formed. It was also reported that Li atoms create defects/cracks on the graphene layer and penetrate through those defects to the ZL [18]. This decoupled graphene shows a E_D at 0.21 eV below the E_F in figure 1(i), which appeared already as the faint π band in figure 1(f). This decoupled graphene exhibits a much-reduced electron doping of $n=2.7\times {10}^{12}$ cm⁻², which implies that the 1D structure shown in figure 1(g) is well ordered and passivates the substrate more effectively than the ZL or the Si-intercalated 3 × 3 structure shown at 650 °C annealing. This decoupled graphene having E_D = 0.21 eV survives even at 800 °C annealing.

However, after postannealing at 850 °C, as shown in figures 1(j) and (k), the surface is covered with the well-known three-layer 3 × 3 structure (as designated by solid rhombuses) which appears on the Si-rich SiC(0001) surface [47]. Its accepted model composed of a Si adlayer (bound to the top Si atoms of the substrate), Si trimers and Si adatoms was proposed by Starke et al through density functional theory analysis on STM and LEED results [48]. The band structure around the $\bar{K}$ point shows neither decoupled graphene-related π band nor ZL-related localized states, g1 and g2. This implies that the decoupled graphene is destroyed as a result of formation of SiC layers through reaction between C atoms of the decoupled graphene and Si atoms provided from either the intercalated Si layer or the craters, while extra Si atoms form the three-layer 3 × 3 structure at this temperature.

Additional annealing at 1000 °C induced the well-known $(\sqrt{3}\times \sqrt{3})R30^\circ$ structure composed of Si adatoms on the clean bulk-terminated SiC(0001) surface. Finally postannealing at 1150 °C for 5 min gave rise to the recovery of the ZL (not shown here) [36, 49].

In figure 2, the STM images of the intercalated Si atoms between the decoupled graphene and the SiC(0001) substrate are shown. Magnified images, figures 2(a) and (b), obtained from the same area in a terrace of the 650 °C annealed surfaces shown in figure 1(d) are characterized by a 3 × 3 structure whose unit cell is marked by solid rhombuses. As expected from the faint LEED pattern in figure 1(e) and the strong doping estimated from figure 1(f), the surface is not so well-ordered and there exist a lot of defects such as dark dips; especially, the filled-state STM image of figure 2(b) shows a lot of disorder. Even though this 3 × 3 structure is thought to be composed of a Si adlayer and Si adatoms, it is different from the one in figure 1(j), which emerges in the Si-rich SiC(0001) surface (without any graphene layer) composed of an adlayer, three trimers and an adatom having a dangling bond per 3 × 3 unit cell [47, 48]. In figure 2(c) shown is the image of the decoupled 1 × 1 graphene layer on the 3 × 3 Si interfacial layer, which was obtained by a tip different from that used in obtaining figures 2(a) and (b), probably a C-end tip. A graphene 1 × 1 unit cell marked by a small rhombus (lattice constant: 0.246 nm) is rotated by ${30}^{\circ }$ relative to the 3 × 3 structure designated by a large rhombus.

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In figures 2(d) and (e) shown are an empty- and a filled-state STM images obtained from the same area of the 750 °C annealed surface. They correspond to magnified images of the 1D structure already shown in the terrace of figure 1(g). Such a 1D structure, composed of narrow two-protrusion rows and broad four-protrusion rows along the [$10\bar{1}0$] direction, was also reported from on Si-rich SiC(0001) having neither graphene nor ZL [37, 46, 50]. Considering the symmetry of this structure, a conventional (primitive) unit cell is drawn by a solid rectangle (dotted rhombus) on the upper part in figure 2(e). In here, a thick solid (dashed) line represents an axis of reflection (glide reflection). So this 1D symmetry belongs to plane group cm [51]. For simplicity, from now on, this structure will be named as $c(14\times 2\sqrt{3})$ (lattice constants: 4.31 nm × 1.07 nm) referring from the conventional unit cell's length and width relative to the lattice constant of SiC(0001)-1 × 1, 0.308 nm. Naitoh et al, who also observed the identical structure from Si-rich SiC(0001), proposed a two-layer model composed of an adlayer with two holes (twenty-six atoms) and eight adatoms per primitive unit cell for this 1D structure by removing the third layer of the 3 × 3 structure and rearranging the first and the second layers [46]. This model is depicted on the STM images of figures 2(d) and (e). The side-view model is also drawn at the bottom of figure 2(d). The brightness asymmetry to the [$10\bar{1}0$] direction in the filled-state STM image in figure 2(e) can be explained by two types of Si adatom sites depending on existence of underlying C atoms [46]. The Si coverage of the corresponding model, 34/28(=1.214) ML, is less than that of the three-layer 3 × 3 structure, 13/9(=1.444) ML [48]. The annealing period was increased long enough at 750 °C, but the intercalated Si structure remained as $c(14\times 2\sqrt{3})$. Even though the dangling bond density is increased from 1/9(=0.111) ML of the three-layer 3 × 3 structure to 10/28(=0.357) ML of the $c(14\times 2\sqrt{3})$ structure, the interaction with the decoupled graphene prevents the SiC(0001) surface from forming the three-layer 3 × 3 structure under the graphene, since the $c(14\times 2\sqrt{3})$ structure is the most stable under the present condition. In figure 2(f) shown is the image of the decoupled graphene on the $c(14\times 2\sqrt{3})$ structure at a low bias voltage of $-0.1$ eV. At the same time, the $c(14\times 2\sqrt{3})$ structure appears vaguely, whose primitive unit cell is marked by a long dotted rhombus. The graphene superstructure appears to be $\sqrt{3}\times \sqrt{3}$, instead of 1 × 1, as marked by a small rhombus (0.427 nm × 0.427 nm) in figure 2(f). Such a reconstruction of the decoupled graphene is known to be due to quantum interferences generated by static impurities at low bias voltages [52, 53].

With postannealing the sample at 800 °C, as shown in figure 2(g), broad four-protrusion rows almost disappear and narrow two-protrusion rows become dominant. In figure 2(h) and (i) shown are the detailed images of the area having only two-protrusion rows. The corresponding atomic structural model, constructed through removing the four-adatom rows and rearranging two-adatom rows of Naitoh et al's $c(14\times 2\sqrt{3})$ model, is overlapped with the image. The corresponding side-view model is also shown above the top-view model in figure 2(i). As marked by the dotted rectangle in figures 2(h) and (i) (corresponding to a unit cell), such a structure belongs to plane group pg having only axes of glide reflection marked by dashed lines [51]. For simplicity, from now on, this structure will be named as $4\times 2\sqrt{3}$ (1.23 nm × 1.07 nm) referring from the unit cell's length and width relative to the lattice constant of SiC(0001)-1 × 1. The Si coverage of this model is 18/16(=1.125) ML, 7% less than that of the $c(14\times 2\sqrt{3})$ structure, 1.214 ML, meaning that a small amount of Si atoms has been deintercalated. The dangling bond density is also increased by 5% from 10/28(=0.357) ML of $c(14\times 2\sqrt{3})$ to 6/16(=0.375) ML.

In figure 3, high-resolution synchrotron photoemission spectra of the C 1s core levels obtained in the steps of Si intercalation are shown. These spectra were obtained by bulk-sensitive 520 eV photons (left panel) and surface-sensitive 326 eV photons (right panel). The corresponding fitting parameters including binding energies (E_Bs), relative intensities (RIs) referred to that of component B of the ZL and Gaussian widths (GWs) are listed in table 1.

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Table 1.  Fitting results for binding energies (E_Bs) and Gaussian widths (GWs) of the C 1s spectra shown in figure 3 obtained by photon energies (E_Phs) of 520 and 326 eV. Relative intensities (RIs) are referred to the photoemission intensity of component B of the ZL. Lorentzian width: 0.20 eV and asymmetry parameter of component G: 0.08.

Spectrum		(a) ZL			(b) RT			(c) 650 °C			(d) 750 °C			(e) 850 °C			(f) 1150 °C
component	EPh	EB	RI	GW	EB	RI	GW	EB	RI	GW	EB	RI	GW	EB	RI	GW	EB	RI	GW
	(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)
B	520	283.73	1.00	0.63	283.60	0.38	0.63	283.85	0.28	0.56	283.89	0.07	0.52	283.80	0.08	0.62	283.70	1.00	0.66
	326	283.73	1.00	0.63	283.64	0.15	0.63	283.83	0.29	0.56	283.92	0.11	0.52	283.80	0.06	0.62	283.70	0.83	0.66
B${}^{\prime }$	520							282.88	0.31	0.56	282.83	0.56	0.52	282.98	1.05	0.62
	326							282.79	0.21	0.56	282.76	0.36	0.52	282.81	0.85	0.62
T	520	284.15	0.20	0.63	284.02	0.08	0.63	284.27	0.06	0.56	284.31	0.01	0.52	284.22	0.02	0.62	284.20	0.33	0.66
	326	284.15	0.48	0.63	284.08	0.04	0.63	284.36	0.03	0.56	284.34	0.01	0.52	284.22	0.02	0.62	284.16	0.77	0.66
T${}^{\prime }$	520							283.46	0.17	0.56	283.23	0.14	0.52	283.37	0.24	0.62
	326							283.37	0.11	0.56	283.16	0.10	0.52	283.20	0.35	0.62
S1	520	284.89	0.94	0.80	284.79	0.55	0.62	284.98	0.61	0.69	284.87	0.35	0.44	284.85	0.24	0.76	285.06	0.78	0.82
	326	284.82	3.17	0.71	284.75	0.97	0.60	284.97	2.10	0.69	284.96	0.42	0.61	284.88	0.73	0.76	285.00	2.77	0.74
S2	520	285.67	1.56	0.83	285.51	0.41	0.87	285.72	0.48	0.69	285.63	0.11	0.69	285.72	0.09	0.72	285.73	1.53	0.82
	326	285.59	5.30	0.93	285.56	0.81	0.86	285.72	1.21	0.69	285.70	0.26	0.69	285.69	0.24	0.76	285.70	5.26	0.88
G	520							284.72	0.97	0.34	284.67	1.81	0.31	284.74	0.30	0.35
	326							284.70	3.81	0.32	284.67	8.36	0.30	284.74	1.13	0.34

In figure 3(a), the spectra of the ZL before Si deposition are decomposed to four components. One bulk-related component B at E_B = 283.73 eV and two ZL-related components, S1 at E_B = 284.89 eV and S2 at E_B = 285.67 eV, are identified. Component S1 originates from the ZL C atoms bonding to the underlying top Si atoms of the SiC substrate, while component S2 originates from the remaining ZL C atoms [43]. From the ratio, RI(S1)/[RI(S1) + RI(S2)] = 0.38, it can be deduced that 38% of the C atoms of the ZL belong to component S1. The fourth component T at E_B = 284.15 eV was introduced for consistent E_B(s) of the other components at E_Phs of both 510 and 326 eV. This is assigned to the top C atoms of the SiC bulk, since it [RI(326 eV)/RI(520 eV) = 2.4] is more surface-sensitive than component B [RI(326 eV)/RI(520 eV) = 1] and less surface-sensitive than components S1 and S2 [RI(326 eV)/RI(520 eV) = 3.4].

After 3.3 ML Si deposition at RT, the C 1s spectra have the same B, S1, S2 and T components, as shown in the twice-expanded spectra of figure 3(b). Their RIs are quite reduced owing to the thick Si overlayer on the ZL. One distinct difference between before and after Si deposition is in the ratio of the RIs, RI(S1)/[RI(S1)+RI(S2)], which changes from 0.38 to 0.55. In other words, 17% of the C atoms in the ZL are additionally bonded with deposited Si atoms, since some of the C atoms of the ZL are chemically active differently from pristine graphene. These Si atoms bonding with the C atoms of the ZL make craters for Si atoms to penetrate. It has been reported that the existence of an sp²-to-sp³ rehybridization originating from the up- and down-relaxation in the ZL is associated with enhancement of the chemical reactivity of the ZL C atoms [54–57]. The buckled-up sp³-like C atoms with upward dangling bonds, estimated at least to be 17% of the ZL's C atoms, can be the origin of strong bonding to deposited Si atoms. So, Si atoms in the intercalated area move to the non-intercalated area, when postannealing the sample at 650 °C, since the decoupled graphene is inert.

After 650 °C postannealing, as shown in figure 3(c), three additional components ${{\rm{B}}}^{\prime }$, ${{\rm{T}}}^{\prime }$ and G appear along with the original components B, T, S1 and S2 as a result of partial intercalation. Surface-sensitive component G [RI(326 eV)/RI(520 eV) = 4.0] at E_B = 284.72 eV with asymmetry can be assigned to the conductive graphene decoupled by Si intercalation and bulk-sensitive components ${{\rm{B}}}^{\prime }$ [RI(326 eV)/RI(520 eV) = 0.68] at E_B = 282.88 eV and ${{\rm{T}}}^{\prime }$ [RI(326 eV)/RI(520 eV) = 0.65] at E_B = 283.46 eV are assigned, respectively, to the bulk C atoms of the SiC substrate and to the top C atoms of the SiC substrate under the intercalated Si 3 × 3 layer shown in figures 1(d)–(f) and figures 2(a)–(c). Component ${{\rm{B}}}^{\prime }$ (E_B = 282.88 eV) has a lower binding energy by 0.85 eV than component B (E_B = 283.73 eV) of figure 3(a), which implies that the intercalated Si 3 × 3 layer induces 0.85 eV more band bending than that of the ZL.

After 750 °C postannealing, as shown in figure 3(d), the RIs of components B, T, S1 and S2 originating from non-intercalated ZL area decreased, while the RIs of components ${{\rm{B}}}^{\prime }$, ${{\rm{T}}}^{\prime }$ and G increased. Since the corresponding STM images shown in figure 1(g) and figures 2(d)–(f) indicate the Si intercalation on the terrace, such components related to the remaining ZL area shown in figure 3(d) must be due to some of defective areas like craters and steps, where Si intercalation is blocked. The RI of component G at 750 °C annealing (1.81 at E_Ph = 520 eV and 8.36 at E_Ph = 326 eV) becomes about twice that at 650 °C annealing (0.97 at E_Ph = 520 eV and 3.81 at E_Ph = 326 eV). The RI of component ${{\rm{B}}}^{\prime }$ also increases by 81% (i.e., from 0.31 to 0.56 at E_Ph = 520 eV). These mean that, at 650 °C annealing, the intercalated area is about half the total surface. The binding energy difference between component ${{\rm{B}}}^{\prime }$ (E_B = 282.83 eV) and component B (E_B = 283.73 eV) of figure 3(a) indicates that the intercalated Si $c(14\times 2\sqrt{3})$ layer induces 0.90 eV more band bending than that of the clean ZL. When increasing the postannealing temperature from 650 °C to 750 °C, even though the E_D moves by 0.21 eV as shown in figures 1(f) and (i), the E_B of component G shows almost no change. This fact indicates that the doping level movement of the decoupled graphene is not directly related to the Fermi level movement of the substrate.

After 850 °C annealing, as shown in figure 3(e), the RI of component G decreases to 15%, while the RI of component ${{\rm{B}}}^{\prime }$ becomes twice, since most of the decoupled graphene was destroyed by the reaction with Si, forming the three-layer 3 × 3 structure on SiC layers, as shown in figure 1(j). The remaining graphene exists as small flakes, which can be rotationally disordered on the three-layer 3 × 3 structure, as on the SiC($000\bar{1}$) surface [43, 58]. As a result, π band crossing around the $\bar{K}$ point does not appear in figure 1(l). The E_B of component ${{\rm{B}}}^{\prime }$, 282.98 eV, is similar to that a previously reported result, 283.05 eV for the three-layer 3 × 3 structure [49]. This structure shows 0.75 eV more band bending (i.e., 283.73–282.98 eV) than that of the clean ZL in figure 3(a).

After 1150 °C annealing for 5 min, as shown in figure 3(f), the ZL has been recovered. The ratio of component S2's RI to component S1's RI approaches to 2 [43]. Since the SiC(0001)-1 × 1 unit vectors are 0.308 nm long and the graphene 1 × 1 unit vectors are 0.246 nm long, a $(6\sqrt{3}\times 6\sqrt{3})R30^\circ$ cell contains 108 Si atoms on the top layer and a commensurate 13 × 13 graphene cells have 338 C atoms (two C atoms per unit cell) [41]. So, 108 C atoms can be bonded to the Si atoms on the top layer and the other 230 C atoms remain unbound; thus their ratio is close to 1:2. Both processes, Si intercalation and graphene destruction, induce larger ZL terraces with less contamination or defects, since the ZL or graphene acts as a barrier to the release of impurities from the surface and to the removal of the defect-related Si and C atoms.

In figure 4 shown are high-resolution synchrotron photoemission spectra of Si 2p obtained in parallel with C 1s shown in figure 3. The spectra were obtained using both bulk-sensitive 326 eV photons (left panel) and surface-sensitive 132 eV photons (right panel). Their fitting results are listed in table 2.

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Table 2.  Fitting results for binding energies (E_Bs) and Gaussian widths (GWs) of the Si 2p spectra shown in figure 4 obtained by photon energies (E_Phs) of 326 and 132 eV. Relative intensities (RIs) are referred to the photoemission intensity of component B of the ZL. Lorentzian width: 0.10 eV, spin–orbit splitting energy: 0.60 eV and branching ratio: 0.5.

Spectrum		(a) ZL			(b) RT			(c) 650 °C			(d) 750 °C			(e) 850 °C			(f) 1150 °C
component	EPh	EB	RI	GW	EB	RI	GW	EB	RI	GW	EB	RI	GW	EB	RI	GW	EB	RI	GW
	(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)	(eV)		(eV)
B	326	101.44	1.00	0.60	101.33	0.29	0.60	101.46	0.34	0.60	101.54	0.05	0.60	101.49	0.06	0.60	101.44	0.91	0.60
	132	101.43	1.00	0.60	101.30	0.11	0.60	101.45	0.18	0.60	101.50	0.03	0.60	101.48	0.03	0.60	101.44	0.93	0.60
B${}^{\prime }$	326							100.56	0.26	0.60	100.58	0.42	0.60	100.72	0.68	0.60
	132							100.54	0.12	0.60	100.58	0.16	0.60	100.84	0.39	0.60
D	326	100.74	0.07	0.60	100.80	0.07	0.60	101.02	0.19	0.60	100.97	0.06	0.60	101.09	0.21	0.60	100.83	0.09	0.60
	132	100.79	0.14	0.60	100.75	0.04	0.60	101.00	0.03	0.60	101.17	0.01	0.60	101.18	0.04	0.60	100.82	0.20	0.60
Z	326	101.80	0.13	0.60	101.69	0.06	0.60	101.81	0.04	0.60							101.83	0.22	0.60
	132	101.81	0.12	0.60	101.67	0.04	0.60	101.78	0.03	0.60							101.86	0.16	0.60
T	326							100.03	0.20	0.60	100.13	0.32	0.60	100.25	0.65	0.60
	132							100.04	0.22	0.60	100.13	0.31	0.60	100.28	1.08	0.60
S${}^{*}$	326				99.43	0.96	0.68
	132				99.42	2.04	0.73
S	326							99.46	0.29	0.49	99.44	0.32	0.60	99.61	0.37	0.60
	132							99.48	0.55	0.59	99.47	0.55	0.60	99.63	1.08	0.60
C	326				98.67	0.01	0.24	98.86	0.02	0.60	98.72	0.02	0.60	99.02	0.04	0.60
	132				98.78	0.07	0.45	98.79	0.06	0.54	98.81	0.08	0.60	99.00	0.12	0.60

In figure 4(a), the spectra of the ZL before Si deposition are decomposed to a SiC bulk-related component, B, at E_B = 101.44 eV (similar to a previously reported result, 101.45 eV [49]), and two additional components, Z at E_B = 101.80 eV and D at E_B = 100.74 eV at a E_Ph of 326 eV. Component Z arises from the substrate Si atoms bonded to the C atoms of the ZL and component D is attributed to Si-terminated defect areas, which is not transformed to ZL [10]. After 3.3 ML Si deposition at RT, component S^* originating from deposited Si atoms is detected and the RIs of components B and Z are attenuated by deposited Si atoms, as shown in figure 4(b). A weak surface-sensitive component C probably due to Si atoms adsorbed to defects/steps is detected additionally at the lowest E_B.

In the Si 2p spectra of figure 4(c) obtained after 650 °C annealing, components ${{\rm{B}}}^{\prime }$, T and S have been added to components B, Z, D and C. Component ${{\rm{B}}}^{\prime }$, originating from the SiC bulk under the decoupled graphene, is bulk-sensitive [RI(132 eV)/RI(326 eV) = 0.46]. Less bulk-sensitive component T [RI(132 eV)/RI(326 eV) = 1.1] is assigned to both the Si adlayer and the substrate Si atoms bonded to the Si adlayer. Surface-sensitive component S [RI(132 eV)/RI(326 eV) = 1.9], which has almost the same E_B as component S^*, is assigned to both the adatoms with dangling bonds in the intercalated Si atoms and still-not-intercalated Si atoms on the ZL. The band bending, estimated from the binding energy difference between component B of the ZL in figure 4(a) and component ${{\rm{B}}}^{\prime }$ of the 650 °C annealed surface in figure 4(c), is 0.88 eV, which turns out to match well with that (0.85 eV) estimated in figures 3(a) and (c).

From the 750 °C annealed surface, as shown in figure 4(d), the same components as those in figure 4(c) except component Z are detected. The depletion of component Z implies that the whole ZL is decoupled from the SiC substrate by the intercalated Si $c(14\times 2\sqrt{3})$ layer. The survival of components B and D is due to the remaining ZL area such as the craters and steps shown in figure 1(g), where Si intercalation is blocked. The band bending estimated from the binding energy difference between component B in figure 4(a) and component ${{\rm{B}}}^{\prime }$ of the 750 °C annealed surface in figure 4(d) is 0.86 eV, which is similar to that (0.90 eV) estimated in figures 3(a) and (d). This band bending related to the appearance of components T and S of the intercalated Si $c(14\times 2\sqrt{3})$ layer is not so much different from that of the intercalated Si 3 × 3 layer.

After 850 °C annealing, as shown in figure 4(e), the RIs of components ${{\rm{B}}}^{\prime }$, T and S have become much stronger than those of figure 4(d). Their enhancements originate from the destruction of the decoupled graphene. The E_B of component ${{\rm{B}}}^{\prime }$, 100.72 eV, is the same as the previously reported result, 100.72 eV for the three-layer 3 × 3 structure [49]. This shows a band bending of 0.72 eV (i.e., 101.44–100.72 eV) compared to the clean ZL in figure 4(a), which is close to that (0.75 eV) estimated in figures 3(a) and (e). After 1150 °C annealing for 5 min, as shown in figure 4(f), the ZL has been recovered.

The valence band spectra obtained at normal emission during Si-intercalation process are shown in figure 5. Each valence band maximum at the surface (E_VBM) marked by a vertical line is estimated by the difference [$(\alpha )-(\beta )$] between $(\alpha )$ (the E_B of C 1s component B in the cases of (a) ZL, (b) RT, (c) 650 °C and (f) 1150 °C or C 1s component ${{\rm{B}}}^{\prime }$ in the cases of (c) 650 °C, (d) 750 °C and (e) 850 °C, listed in table 1 at E_Ph = 520 eV) and $(\beta )\;([$ 281.0 eV, which is the energy difference between the C 1s core level and the valence band maximum of bulk SiC, reported earlier) [49]. For example, the E_VBM of spectrum 'd' is estimated by $(\alpha )282.83$ eV $-\;(\beta )281.0$ $\mathrm{eV}=1.8$ eV below E_F. Spectrum 'a' of the ZL before 3.3 ML Si deposition is in good agreement with the previous reports on the $(6\sqrt{3}\times 6\sqrt{3})R30^\circ$ ZL [59]. Two ZL-related localized states existing close to E_F are marked by g1 and g2 [43]. Features between 2 and 12 eV originate from hybridization of C 2p and Si 3s + 3p states [33]. The 3.3 ML Si deposition at RT reduces the overall ZL-related states but the Si-cluster-related states around 2 eV increases, as shown in spectrum 'b'. Spectrum 'c' obtained after 650 °C annealing has features of both spectrum 'b' and spectrum 'd' due to partial intercalation. So it has two E_VBMs. Postannealing the sample at 750 °C gives spectrum 'd' with features around E_B = 0.7, 2–12 and 21 eV. The peak around 0.7 eV marked by L1 is related to the surface states caused by residual dangling bonds of the Si $c(14\times 2\sqrt{3})$ structure. A relatively strong feature around 3 eV is related to the Si 3s + 3p states of the Si $c(14\times 2\sqrt{3})$ interfacial layer, which is also seen in spectrum 'e'. A swollen area around 8 eV and a broad peak around 21 eV originate from a π band and a σ band of the decoupled graphene, respectively [5, 43]. Postannealing at 850 °C gives spectrum 'e' in good agreement with that of the three-layer Si 3 × 3 structure [49]. Spectra 'c', 'd' and 'e' say that all of the Si-rich structures on the SiC(0001) are semiconducting from nonexistence of surface states at E_F² . The semiconducting nature of the three-layer 3 × 3 structure arise from a Mott–Hubbard metal–insulator transition due to strong electron correlation effects of states localized at the Si adatom sites, leading to a filled lower Hubbard band and an unfilled upper Hubbard band inside the band gap [49, 60–62]. Since the $c(14\times 2\sqrt{3})$ structure also has adatoms as the three-layer 3 × 3 structure, the same kinds of Hubbard bands will be induced. In reality, spectra 'd' and 'e' are similar except graphene-related areas around E_B = 8 and 21 eV. As a result, the $c(14\times 2\sqrt{3})$ layer is semiconducting and the lower Hubbard band L1 is formed inside the band gap as the three-layer 3 × 3, which can be seen in spectra 'd' and 'e' of figure 5. Postannealing this sample at 1150 °C for 5 min recovers the clean ZL having a broad density of states which extend up to E_F, as shown in spectrum 'f '.

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The above-mentioned experimental results can be depicted by the band diagrams of the n-type 6H–SiC(0001) with the ZL and the $c(14\times 2\sqrt{3})$ layer, as shown in figures 6(a) and (b), respectively. Figure 6(a) [6(b)] has been drawn using the 520 eV spectra of figure 3(f), figure 4(f) [figure 3(d), figure 4(d)], figure 5 and tables 1 and 2. In addition to these experimental results, referred are its band gap (E_g = 3.0 eV), its energy difference (281.0 eV) between the bulk C 1s core level and the valence band maximum (E_VBM) and its theoretical bulk E_F position, 2.9 eV above E_VBM (i.e., 0.1 eV below the conduction band minimum (E_CBM)), which were previously reported [49, 63].

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In the diagram of the ZL in figure 6(a), since the E_B of C 1s bulk component B is 283.70 eV, the surface E_F is located at 2.7 eV above E_VBM and the surface band bending (Schottky barrier) for the ZL turns out to be only 0.2 eV (0.3 eV). This surface E_F is positioned near the upper limit of the g1 state located in the band gap, as shown in figure 1(c) and in spectra 'a' and 'f ' of figure 5. The filled (g1) and empty (g1${}^{*}$) surface states are superimposed with band D associated with carbon (as well as silicon) dangling bonds and some defects extending up to the E_F [36, 57, 59, 64]. If there existed ML graphene on this ZL, as the Dirac cone represented by dotted lines in figure 6(a), the graphene would show a very high electron doping level (E_D = 0.42 eV below E_F and $n=1.1\times {10}^{13}$ cm⁻²) due to charge transfer from the ZL having high-density surface states [7, 10]. When the dangling bonds of the 6H–SiC(0001) surface is perfectly passivated by hydrogen intercalation and there is no surface state, the ML graphene exhibits a p-type conductivity with E_D = 0.30 eV above E_F and a hole density of $5.5\times {10}^{12}$ cm⁻² [11]. According to Ristein et al, this is due to the spontaneous polarization, P, of the substrate creating an acceptor layer, which is marked by minus signs in circles (⊖s), negative effective polarization charge, in figure 6 and the n-type doping of the ML graphene on the ZL was explained by donor-like states associated with the ZL which overcompensate this polarization doping [64]. If this is the case, the electron charge density provided by the ZL is estimated to be $n=1.7\times {10}^{13}$ cm⁻², which results in an electron doping of $1.1\times {10}^{13}$ cm⁻² to the decoupled graphene by compensating a hole density of $5.5\times {10}^{12}$ cm⁻²due to spontaneous polarization.

In the diagram of the $c(14\times 2\sqrt{3})$ layer in figure 6(b), since the E_B of C 1s bulk component ${{\rm{B}}}^{\prime }$ is 282.83 eV, the surface E_F is located at 1.8 eV above E_VBM and the surface band bending (Schottky barrier) for the ZL turns out to be only 1.1 eV (1.2 eV). Inside the band gap, the lower Hubbard band marked by L1 is filled with electrons and the normally empty upper Hubbard band marked by U1 is partially filled with electrons originating from the conduction band [49]. The surface E_F is therefore fixed at a position close to the lowest states of band U1, inducing a band bending [36, 60, 61]. The electrons in band U1 in turn are transferred to the decoupled graphene and give n-type graphene doping of $2.7\times {10}^{12}$ cm⁻² corresponding to E_D = 0.21 eV below E_F. The electron charge density provided by the $c(14\times 2\sqrt{3})$ layer is estimated to be $n=8.2\times {10}^{12}$ cm⁻². When the intercalated Si layer structure is transformed into $4\times 2\sqrt{3}$ through postannealing at 800 °C as shown in figure 2(g), the E_F and the E_D show almost no difference from those of $c(14\times 2\sqrt{3})$, since their basic structures are commonly composed of an adlayer and adatoms and even after full transformation the dangling bond density increases by only 5% from 10/28(=0.36) ML of $c(14\times 2\sqrt{3})$ to 6/16(=0.38) ML of $4\times 2\sqrt{3}$ in the models of figure 2. Since the dangling bond density of the $c(14\times 2\sqrt{3})$ layer is 0.36 ML per SiC(0001)-1 × 1 unit cell, under the assumptions that there exist essentially no unsaturated Si dangling bonds at the interface [43, 56] and that the electron charge density given to the ML graphene is proportional to the dangling bond density, the ZL has by itself about 0.75 dangling bond per SiC(0001)-1 × 1 unit cell [i.e., dangling bond density of $c(14\times 2\sqrt{3})\cdot$ {electron charge density provided by ZL}/{electron charge density provided by $c(14\times 2\sqrt{3})$} = 0.36 ML$\cdot 1.7\times {10}^{13}$ cm⁻²/$8.2\times {10}^{12}$ cm⁻²]. Since the number of the ZL's C atoms per SiC(0001) unit cell is 338/108 (= 3.1), 0.75 ML is only 24% of the ZL's total C atoms. Even though, in section 3.3, it was mentioned that at least 17% C atoms of the ZL has dangling bonds, in reality more C atoms must have dangling bonds, since all of the C atoms with dangling bonds cannot bond to the deposited Si atoms due to dense C atoms in the ZL with a C–C bond-length of 0.142 nm. The intercalated 3 × 3 layer of the 650 °C annealed surface has almost the same E_F position as the $c(14\times 2\sqrt{3})$ layer as shown figures 3(c) and 4(c), but its density of surface states is as high as that of the ZL, as shown in figure 1(f). This is due to the defect-related surface states, as shown figures 2(a) and (b).