Martienssen W., Warlimont H. (Eds.). Handbook of Condensed Matter and Materials Data

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1002 Part 5 Special Structures

E (eV)

–2

–4

–6

–8

–10

–

––

–

––

Au(110)

E (eV)

–1

–

––

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

⎮⎮

(Å

–1

)

Au(110)

Fig. 5.2-27 Comparison of experimental results [obtained by

KRIPES for the empty states (dots) and by ARUPS for the initial

states (triangles)] with the theoretical calculations of Fig. 5.2-26.

Notice the splitting of the state near

Y(X



) probably due to the 2× 1

reconstruction [2.40,41]

Fig. 5.2-26 Theoretical projected band structure for the

unreconstructed Au(110) surface. Note that in the notation

of this ﬁgure,



and M correspond to YandS, respectively,

in the SBZ of Fig. 5.2-18 [2.39]

E (eV)

–2

–4

–6

–

––

Pd (111)

Fig. 5.2-28 Theoretical projected band structure (shaded

area) for Pd(111), showing an empty surface state

(near

Γ) and various occupied surface states and reso-

nances [2.42]

E (eV)

–

––

Pd (111)

Fig. 5.2-29 Comparison of the dispersion of the empty sur-

face state of Fig. 5.2-28 with experimental results obtained

by KRIPES [2.43]

Part 5 2.3

The Physics of Solid Surfaces 2.3 Electronic Structure of Surfaces 1003

E (eV)

2.0

–

––

– 5.0

– 0.5

– 1.0

– 1.5

– 2.0

– 2.5

– 3.0

– 3.5

– 4.0

– 4.5

– 5.0

0.4 0.8 1.21.2 1.6

⎮⎮

(Å

–1

)

SHSH DD

W(100)

ω/ω

0.92

0.88

0.84

0.80

0.76

0.72

0.68

0.1 0.2 0.3 0.4 0.5 0.6 0.7

⎮⎮

(Å

–1

)

Al(111)

RPA

RDA

Fig. 5.2-31 Experimental dispersion of the surface plas-

mon in Al(111) as a function of q



(squares)and

comparison with theoretical results obtained with two dif-

ferent approximations [2.46]

Fig. 5.2-30 Dispersion of surface states for W(100) along

the

ΓM line obtained by ARUPS and comparison with

theory [2.44,45]

5.2.3.2 Semiconductors

The data on elemental semiconductors (including dia-

mond) are ordered according to the atomic number.

They are followed by data on some of the compound

semiconductors. For a more detailed discussion of the

various subjects, the reader may consult [2.8, 10,11] or

the books [2.47,48].

Surface Ionization Energies

The ionization energy is deﬁned as the distance of the top

of the valence band at the surface from the vacuum level.

At low impurity concentrations, the ionization energy is

independent of doping and should, preferably, be meas-

ured in place of the work function. Table 5.2-14 reports

the ionization energies for a number of semiconductors.

Surface Core Level Shifts

In semiconductors, core levels are shifted because of

charge transfer between surface atoms. Table 5.2-15

Table 5.2-14 Ionization energies at semiconductor sur-

faces

Crystal Face Reconstruction Ionization

energy (eV)

Diamond (111) 2×1 6.25 (25)

(100) 2×1 5.33

(111) 2×1 5.24 (9)

7×7 5.30

(111) 2×1 4.77 (2)

c(2 × 8) 4.70

GaP (110) 1×1 5.98 (3)

GaAs

(100) c(2 × 8) 5.40 (7)

c(4 × 4) 5.34 (5)

4×6 5.05

(110) 1×1 5.48 (6)

GaSb (110) 1×1 4.79 (9)

InP (110) 1×1 5.77 (8)

InAs (110) 1×1 5.37 (6)

InSb (110) 1×1 4.84 (6)

CdS (110) 1×1 6.7 (6)

CdSe (110) 1×1 6.62

CdTe (110) 1×1 5.79 (1)

Data are average values from various authors. Errors are

standard deviations. References to the original papers and

individual errors are given in [2.47]

Part 5 2.3

1004 Part 5 Special Structures

Table 5.2-15 Surface core level shifts for elemental semiconductors

Crystal Face Reconstruction Core level

Surface shifts (eV )

Diamond (111) 2×1 1s −0.8

(100) 2×1

−0.49 (3) −0.230 0.062 0.29 (5)

c(2 × 4) −0.485 −0.205 0.062 0.22

(111) 2×1 −0.46 (9) −0.14 0.23 (6) 0.64

7×7 −0.74 (5) −0.07 (5) 0.30 (6) 0.52 (3)

(100) 2×1

−0.49 (7) −0.21 (3)

c(4 × 2) −0.60 −0.24

(111) 2×1 −0.49 (8) 0.44

c(2 × 8) −0.73 (3) −0.24 (3)

Data are average values from various authors. Errors are standard deviations. References to original papers and individual errors

are given in [2.47]

Table 5.2-16 Surface core level shifts at Ga and As sites in

GaAs

Face Reconstruction

Surface shift (eV )

Ga(3d) As(3d)

(100) c(4 × 4) +0.49 −0.285 (5)

+0.55

c(2 × 8) +0.3 −0.26 (1)

+0.55 (0)

4×6 +0.4 −0.45 (16)

−0.21

(110) 1×1 +0.28 (0) −0.373 (5)

Data are average values from various authors. Errors are

standard deviations. References to the original papers and

individual errors are given in [2.47]

gives the shifts for the C(1s), Si(2p), and Ge(3d) lev-

els for various faces and reconstructions. The surface

shifts of the 3d levels at the Ga and As sites of GaAs

(110) and (100) faces are given in Table 5.2-16.

The p and d levels are spin–orbit split and give rise

to doublets. Nonequivalent atoms increase further the

number of surface shifts. Up to four components are

observed in Si and Ge and up to two in GaAs.

Unresolved surface shifts for various III–V com-

pounds are given in Table 5.2-17.

Surface State Bands

The origin and nature of surface states have been dis-

cussed in the introduction to Sect. 5.2.3. Here the energy

versus k



along signiﬁcant directions of the SBZ and/or

the density of states are reported for various recon-

structed/relaxed surfaces. The experimental data were

Table 5.2-17 Surface core level shifts at (110) surfaces of

III–V compounds

Crystal Surface shifts (eV )

Cation Anion

AlSb +0.38 −0.38

GaP +0.31 (2) −0.41 (0)

GaAs +0.28 (0) −0.370 (5)

GaSb +0.30 −0.36

InP +0.30 (2) −0.30 (1)

InAs +0.27 (1) −0.30 (0)

InSb +0.23 (1) −0.29(1)

Data are average values from various authors. Errors are

standard deviations. References to the original papers and

individual errors are given in [2.47]

obtained mainly with ARUPS and KRIPES or by optical,

energy loss, and STM techniques.

Because of the large amount of available data, only

a selection of dispersion curves and surfaces has been

given. For more detailed information, the reader is re-

ferred to [2.10,11].

The rearrangement of unsaturated dangling bonds at

the surface is considered to be the driving force for re-

construction of semiconductors. An example of DBs is

shown in Fig. 5.2-32a,b that give contours of the charge

density for the ﬁlled (P) and empty (Ga) surface states

on the (110) surface of GaP. In Fig. 5.2-32c, a com-

parison is made with an STM image taken with a bias

voltage that allows the observation of ﬁlled and empty

states.

Figures 5.2-33 – 5.2-36 and 5.2-38 – 5.2-40 give the

E(k



) curves for selected surfaces of diamond, Si, Ge,

Part 5 2.3

The Physics of Solid Surfaces 2.3 Electronic Structure of Surfaces 1005

4Å

[001]

[11

–

Fig. 5.2-32 (a) Theoretical charge density contours for the ﬁlled DB states at P sites on the relaxed GaP(110) surface,

(b) the same for the Ga site empty states, (c) comparison with constant current STM images for GaAs(110). The two STM

images refer to ﬁlled (As) states (left) and empty (Ga) states (right). The two images are obtained with positive (left)and

negative (right) bias. The rectangular unit cell is in the same (absolute) position.

(d) Schematic representation of the unit

cell. As atoms are shown as empty circles; Ga atoms as black circles [2.49,50]

E (eV)

–2

–4

C(111) 2 × 1

–

––

–

GaAs, and CdSe. The local density of states for Si(111)

7× 7 as obtained from ARUPS and STM spectroscopy

is shown in Fig. 5.2-37.

Transitions Between Surface States

Transitions between surface state levels give rise to

optical absorption and electron energy loss. Such tran-

sitions have been observed by SDR, RAS, ellipsometry,

and EELS. As an example, the arrows in Figs. 5.2-36

and 5.2-38 show the transitions observed in Si and

Ge(111)2 ×1. Notice the high joint density of states

caused by the quasi-parallelism of the bands along

JK.

Fig. 5.2-33 Theoretical surface state bands (full lines)and

resonances (dashed lines) for a relaxed π-bonded chain

model of diamond(111)2× 1. Comparison with experimen-

tal results (open circles) obtained by ARUPS along the

ΓJ

line [2.51,52]

Part 5 2.3

1006 Part 5 Special Structures

Fig. 5.2-35 Dispersion curves of Si(100)2× 1 observed by ARUPS

at 21.2 eV. Prominent peaks are indicated by open circles, while

weak peaks and shoulders by dots. S and B peaks have surface and

bulk characters. The experimental bands should be compared with

the surface structures of Fig. 5.2-34. No optical transition clearly

associated to S

(or D

down

, D

in Fig. 5.2-34) has been observed

in spite of the essential parallelism of the two bands (meaning a high

JDOS) [2.54,55]

E (eV)

–2

–4

–6

–8

–10

–12

–14

–

––

–

Si(001) 2 × 1

down

Fig. 5.2-36 Surface band structure of Si(111)2 × 1. Comparison be-

tween theoretical structure based on pseudopotential calculations

for the π-bonded chain model (see Sect. 5.2.2.3, Fig. 5.2-11) and

experimental results from ARUPS. Photoemission from the excited

surface states (around the B point in the ﬁgure) is obtained by using

highly doped samples. Arrows indicate optical transitions observed

in SDR and EELS (see Figs. 5.2-41 and 5.2-43) [2.56, 57]

–

E (eV)

⎮⎮

–

= 0

–1

–2

–3

–4

–5

–6

–7

–8

KKW.X

Si(001) 2 ×1

Fig. 5.2-34 Theoretical surface band structure of Si

(100)2× 1, obtained with the asymmetric dimer model (see

Sect. 5.2.2.3, Fig. 5.2-7). D

down

and D

refer to the DB

bands at the down and up atoms. The bands labeled S

–S

and B

–B

are back-bond states (modiﬁed by the surface)

[2.53]

E (eV)

––

2.0

1.5

1.0

0.5

– 0.5

–1.0

–1.5

–

––

Si(111) 2 ×1

Part 5 2.3

The Physics of Solid Surfaces 2.3 Electronic Structure of Surfaces 1007

E(eV)

–5

IPE

STS IPE

–4 –3 –2 –1 0 1 2

Si(111) 7 × 7

Adatoms

Rest atoms

Si(111) 7 × 7

Fig. 5.2-37a–c Density of states associated with the dan-

gling bonds(on the adatoms and “restatoms”) of theSi(111)

7×7 surface (see Fig. 5.2-13), obtained

(a) by ARUPS (inte-

grated over all atoms), and

(b) and (c) by STM spectroscopy.

Notice that the gap (if present) occurs at the Fermi energy

[2.57–59]

E (eV)

––

–

2.5

2.0

1.5

1.0

0.5

– 0.5

– 1.0

– 1.5

–

––

Ge(111) 2 × 1

Fig. 5.2-38 Surface band structure of Ge(111)2 ×1. Com-

parison between theoretical structure (in the frame of

the chain model) and experimental results obtained with

KRIPES (open dots and triangles) and ARUPS (black

dots). Photoemission from excited states has been reached

by using highly doped Ge. Arrows indicate optical tran-

sitions observed in SDR and EELS (see Figs. 5.2-42

and 5.2-44) [2.60–62]

In the dielectric theory of the surface re-

sponse, the transition probability is proportional

to –Im

ε = ε



in the optical absorption and to

Im[1/1+

ε]=ε



/[(1+ε



)

+ε



]inEELS,

ε = ε



−iε



being the dielectric function of the surface layer. The two

techniques give essentially the same results, as shown in

Fig. 5.2-45.

The great anisotropy of some reconstructed sur-

faces, as shown in Figs. 5.2-41 and 5.2-42, is reﬂected

in second-harmonic generation, which is specially

sensitive to the symmetry of the surface, being for-

bidden for centrosymmetric media (see Fig. 5.2-46 for

Si(111)2 × 1).

Surface anisotropy has given rise to the technique

of reﬂectance anisotropy spectroscopy (RAS), in which

linearly polarized light is modulated between two prin-

cipal directions (of the surface tensor) and the difference

Part 5 2.3

1008 Part 5 Special Structures

E (eV)

–3.2

–2.4

–1.6

– 0.8

0.8

1.6

–

––

' Γ

–

⎮⎮

GaAs (110)

Fig. 5.2-39 Surface band structure of GaAs(110). Comparison be-

tween theoretical structure (continous brown line) and experimental

determinations: KRIPES ( ﬁlled and open circles), ARUPS (dashed

line), and two-step photoemission (triangles). It can be noticed that

the surfacestates nearlycoincide with the band edgesof the projected

bulk band structure [2.63–67]

E (eV)

–2

–4

–6

–

––

' Γ

–

(ideal)

CdTe (110)

(relaxed)

Fig. 5.2-40 Electronic band structure of the CdTe(110) surface.

The open circles show experimental points obtained by ARUPS.

Theoretical surface states and resonances are shown by solid and

dashed lines, respectively [2.68,69]

∆R/R

×10

–2

123

hν (eV)

Si(111) 2 ×1

[01

1] [2

11]

Fig. 5.2-41 Surface differential reﬂectivity (SDR) spectra

for Si(111)2× 1, obtained with two polarizations: with the

electric vector parallel ([0

11], ﬁlled circles) and perpendic-

ular ([

211], open circles) to the chains of the π-bonded

chain model. For the transitions shown by arrows in

Fig. 5.2-36 (hν<1 eV) the change in reﬂectivity can be

observed only with the electric vector parallel to the

chains. The spectrum for hν>1 eV is associated to tran-

sitions along

ΓJ in the SBZ. The change of anisotropy

at approximately 1.2 eV is conform to the “sum rule”:



ωdω =



ωdω [2.70]

in the reﬂected light is recorded. Figure 5.2-47 gives an

example of RAS spectra for GaAs(100).

5.2.3.3 Magnetic Surfaces

The magnetic moments of atoms near the surface

plane, p

(n = 1 for the surface), differ from those for

the bulk, p

. The total incremental moment at the surface

is deﬁned as

∆ p

∞



n=1

( p

− p

Table 5.2-18 gives the values of p

, p

,and∆ p

for

various ferromagnetic surfaces.

Temperature is more effective in destroying the

magnetic order at the surface than in the bulk. This

Part 5 2.3

The Physics of Solid Surfaces 2.3 Electronic Structure of Surfaces 1009

(meV)

0.2 0.4 0.4 0.8 1.0

loss

(arb. units)

Si(111)2 ×1

×100

× 333

20K300K

300K

Fig. 5.2-43 EELS spectra at T = 20 K and 300 K for

Si(111)2× 1 ( full and dashed lines) compared with the re-

sults of SDR of Fig. 5.2-41 (brown dashed line). The peak

of EELS is slightly displaced towards higher energies be-

cause of the energy dependence of the factor in front of the

loss function Im



ε +1



[2.70,71]

I (arb. units)

×100

×1000

580 meV

415 meV

Ge(111)2 ×1

T = 295 K

20 meV

Fig. 5.2-44 EELS spectrum of Ge(111)2 ×1 at room tem-

perature. The same considerations done in the caption of

Fig. 5.2-43 hold also here [2.73]

effect is shown in Fig. 5.2-48, where the ratio of

the polarization P at a given temperature to that

at absolute zero is plotted versus temperature. The

Curie temperature at the surface T

is approxi-

mately equal to that of the bulk (T

) in most cases.

Table 5.2-19 reports the ratio T

for a number of

materials.

A more detailed discussion of the magnetic proper-

ties of surfaces is given in [2.13].

∆R/R (%)

Energy (eV)

3.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

along [011]

along [2

11]

Fig. 5.2-42 Surface differential reﬂectivity versus energy for

Ge(111)2 × 1 with polarization parallel and perpendicular to the

chains of the π-bonded model. The anisotropy for hν<1eV is

smaller than for Si(111)2 ×1. The same considerations done in the

caption of Fig. 5.2-41 hold also here [2.72]

''d (Å)

Energy (eV)

3.5

150

Si(111) 2 ×1

100

0.5

1 1.5 2 2.5 3

Fig. 5.2-45 Comparison of SDR (dotted line) [2.70,

74], EELS (solid line) [2.75] and ellipsometry (dashed

line) [2.76] spectra for Si(111)2 ×1. The qualitative agree-

ment is remarkable [2.70,74–76]

Part 5 2.3

1010 Part 5 Special Structures

∆r/r

E (eV)

1.5

5.5

0.004

0.002

GaAs(001)

2.5 3.5 4.5

– 0.002

0.002

– 0.002

0.002

– 0.002

– 0.004

0.002

– 0.002

0.002

– 0.002

∆r/r

(2 × 4)

T = 585 °C

c(4 × 4)

189 °C

(4 × 2)

609 °C

(1 × 6)

488 °C

(4 × 6)

220 °C

Fig. 5.2-47 Reﬂectance anisotropy spectra for GaAs(100) grown

by MBE at different substrate temperatures in an As

ﬂux of

2.8×10

−6

torr. The corresponding reconstructions (as determined

by RHEED) are also reported [2.78]

Si(111) 2 × 1

[21

]

[011

]

[21

]

[011

]

[21

]

[011

]

Fig. 5.2-46a–c Intensity of the secondharmonic (SH) gen-

eration signal as a function of polarization of the incidence

pump beam (1.17 eV), for Si(111)2× 1.

(a) total SH signal;

(b) SH component polarized along [2

1]; (c) SH component

polarized along [01

1] [2.77]

Part 5 2.3

The Physics of Solid Surfaces 2.3 Electronic Structure of Surfaces 1011

Table 5.2-18 Surface magnetizations at given temperatures. The theoretical values are averages from various authors

(obtained with linearized-augmented-plane-wave or tight-binding methods). References to original papers are given

in [2.13]

Crystal Face T (K) Magnetic moment (Bohr magnetons) Technique

p

(100) 0 2.25 2.96 2.34 2.45 1.0 Theory

(110) 0 2.22 2.60 2.37 2.28 0.66 Theory

300 2.2 2.9 (3) 0.7 (3) SPLEED

(100) 0 0.57 0.67 0.59 0.60 0.13 Theory

300 0.03 (3) SPLEED

(110) 0 0.62 0.63 0.64 0.58 0.11 Theory

(111) 0 0.58 0.63 0.64 0.58 0.11 Theory

300 0.06 (12) SPLEED

P/P

T/T

1.0

0.8

0.6

0.4

0.2

0.2 0.4 0.6 0.8

Fe(110)

SPLEED

Kerr

Table 5.2-19 Surface Curie temperatures (T

). References to original papers are given in [2.13]

Crystal Face T

(K) T

Technique

(100) 630 1 SPLEED

(110) 630 1 SPLEED

(111) 630 1 ECS

(100) 1040 1 SPARPES

(110) 1040 1 Spin-polarized secondary electrons

EuS (111) 16.71 (5) 1.000 (4) SPLEED

Gd (0001) 293 1.05–1.07 SPLEED

Tb (0001) 220 1.14 ECS

Fig. 5.2-48 Temperature dependence of magnetic order-

ing. Kerr ellipticity (representing bulk magnetization) and

normalized polarization P/P

of scattered electrons in

SPLEED (representing surface magnetization) as a func-

tion of T/T

.Thesolid curves are ﬁts to a Bloch law:

(0) −m

(T ) = bT

3/2

, m

being the magnetization of

the ﬁrst layer [2.79]

Part 5 2.3