6.8 Diamond Structured Si and Pb
127
0
10
20
10
20
-14.0
-13.5
-13.0
-12.5
0
10
0
10
20
(b)
GGA Rb 44
E-E f (eV)
Local Density of States
atom 1
atom 2
atom 3
atom 4
(c)
GGA Rb 46
atom 1
atom 2
atom 3
(d)
GGA Rb 55
atom 1
atom 2
atom 3
atom 4
atom 5
atom 6
(a)
atom 3
GGA Rb 28
atom 1
atom 2
5
10
5
-11.0
-10.5
-10.0
5
5
10
(f)
E-E f (eV)
Local Density of States
GGA Cs 44
atom1
atom2
atom3
atom4
(g)
GGA Cs 46
atom1
atom2
atom3
(h)
GGA Cs 55
atom1
atom2
atom3
(e)
GGA Cs 28
atom4
atom5
atom6
atom1
atom2
atom3
0
0
10
0
10
-11.5
0
0
20
Fig. 6.21 DFT derived atomic site-resolved energy shift of the local DOS for a, e C I28 , b, f O h44 , c,
g C 3v46 , and d, h O h55 clusters of Rb and Cs [85]. Atoms counts from the outermost inward with an
increase of the effective atomic CN. Table 6.9 list the detailed information on the undercoordination
effect on the properties of the Cs and Rb clusters [85]
surface charging during experiment. The missing of one electron in the Si
+
N cluster
weakens the screening on the crystal potential, which enhances the shift accordingly.
BOLS theory reproduction of the measurements turns out the E 2p (0) of 96.74 eV for
an isolated Si atom and its bulk shift 2p (12) of 2.46 eV.
A fitting to the size trends for porous Si [99] and Si
+
N clusters [96] results in the
K dependent Si 2p energy shift of both atomic clusters and nanostructured Si:
⎧
⎨
⎩
E 2 p (K ) = E 2 p (∞) + b/K = 99.06 + 9.68/K [ p − Si]
E 2 p (K ) = 102.60 + 13.8/N
1/3
= 102.60 + 10.69/K [Si
+
N ]
E vb (K ) = 4.20 + 10.89/K [Si
+
N ]
Figure 6.22d compares the DFT optimized valence DOS for the (100) and the
stepped (210) skins. Bond contraction of the undercoordinated (210) edge bond
entraps the valence DOS by about 1.0 eV without polarization. Results show consistently that Si atoms undercoordination in the skin of clusters and the terrace-edge
entrapped electrons and deepen both the 2p and the valence bands of Si simultaneously. These observations are in consistency with that derived from skin XPS
analysis, as shown in Sect. 4.5.
127
0
10
20
10
20
-14.0
-13.5
-13.0
-12.5
0
10
0
10
20
(b)
GGA Rb 44
E-E f (eV)
Local Density of States
atom 1
atom 2
atom 3
atom 4
(c)
GGA Rb 46
atom 1
atom 2
atom 3
(d)
GGA Rb 55
atom 1
atom 2
atom 3
atom 4
atom 5
atom 6
(a)
atom 3
GGA Rb 28
atom 1
atom 2
5
10
5
-11.0
-10.5
-10.0
5
5
10
(f)
E-E f (eV)
Local Density of States
GGA Cs 44
atom1
atom2
atom3
atom4
(g)
GGA Cs 46
atom1
atom2
atom3
(h)
GGA Cs 55
atom1
atom2
atom3
(e)
GGA Cs 28
atom4
atom5
atom6
atom1
atom2
atom3
0
0
10
0
10
-11.5
0
0
20
Fig. 6.21 DFT derived atomic site-resolved energy shift of the local DOS for a, e C I28 , b, f O h44 , c,
g C 3v46 , and d, h O h55 clusters of Rb and Cs [85]. Atoms counts from the outermost inward with an
increase of the effective atomic CN. Table 6.9 list the detailed information on the undercoordination
effect on the properties of the Cs and Rb clusters [85]
surface charging during experiment. The missing of one electron in the Si
+
N cluster
weakens the screening on the crystal potential, which enhances the shift accordingly.
BOLS theory reproduction of the measurements turns out the E 2p (0) of 96.74 eV for
an isolated Si atom and its bulk shift 2p (12) of 2.46 eV.
A fitting to the size trends for porous Si [99] and Si
+
N clusters [96] results in the
K dependent Si 2p energy shift of both atomic clusters and nanostructured Si:
⎧
⎨
⎩
E 2 p (K ) = E 2 p (∞) + b/K = 99.06 + 9.68/K [ p − Si]
E 2 p (K ) = 102.60 + 13.8/N
1/3
= 102.60 + 10.69/K [Si
+
N ]
E vb (K ) = 4.20 + 10.89/K [Si
+
N ]
Figure 6.22d compares the DFT optimized valence DOS for the (100) and the
stepped (210) skins. Bond contraction of the undercoordinated (210) edge bond
entraps the valence DOS by about 1.0 eV without polarization. Results show consistently that Si atoms undercoordination in the skin of clusters and the terrace-edge
entrapped electrons and deepen both the 2p and the valence bands of Si simultaneously. These observations are in consistency with that derived from skin XPS
analysis, as shown in Sect. 4.5.