Chapter 4 Ag Films on Ge(111)
4.4 Discussion
(4.1) where a Pade function (radio of polynomials) is employed to account for the band distortion; a, b, c, d, and the zone-center effective mass m∗ are treated as fitting parameters.
4.4 Discussion
The dispersion relations are governed by Bohr-Sommerfeld quantization rule:
2k⊥N t + φ = 2nπ (4.2)
where k⊥ is the wave vector component perpendicular to the film surface, N is the film thickness in monolayers, t is the monolayer thickness, φ ≡ φ(k⊥, kk) is the total phase shift at the boundary, and n = N − ν is a quantum number.
The allowed k⊥ determines the binding energy of a quantum well peak through the bulk band dispersion relation. Analyzing the EDC curve at normal emission,
Figure 4.5: The total phase shift as a function of k⊥ at kk= 0.
the peak positions were fit to a set of Lorenzian functions on a smooth background and the corresponding values of k⊥ were obtained by the Ag bulk band calculation from Γ to L. Apply the quantization rule, the total phase shift at normal emission are calculated, shown in Fig. 4.5.
For increasing in-plane momentum, each quantum well state exhibits a dispersion relation Eν(kk). The k⊥ is dependent on kk due to the quantization rule. This yields the subband dispersion through the bulk band dispersion E(k⊥, kk) :
Eν(kk) = E(kν⊥(kk), kk) (4.3) The zone-center effective mass of each subband is given by :
1
mν∗ = 1
~2
d2Eν(kk)
dk2k (4.4)
When the phase shift derived from both k⊥ and kk dependence is taken into consideration in the quantization rule, a straightforward calculation of the zone-center effective mass are obtained
where the first term on the right hand side of (4.5) is the inverse of the effective
mass in the bulk limit of N → ∞; that is
To simplify the problem, we assume the phase shift as
φ(k⊥, kk) = φ0(1 + Ak⊥)(1 + Bkk2) (4.7) where the only squared term of kk is used for symmetry. At normal emission, where kk is zero, the phase shift reduces to a linear function.
Using this model and our assumption, the effective mass can be fit by the fitting function :
⊥ and mbulk can be obtained from the calculated bulk band dispersion from Γ to L point taken from an empirical analysis of Smith et al [30].
We performed simultaneous fitting of the phase shift with k-dependence, the thickness, and energy dependence of effective mass at kk = 0. The numerical values of the fitting parameters are φ0 = 7.42, A = −0.56 and B = 3.92. The solid curve in Fig. 4.5 is the result from a simultaneous fitting. Combining the Bohr-Sommerfeld quantization rule and the fitting of phase shift, we obtained the theoretically ex-pected energies of each quantum well state for all thickness at normal emission, as shown in Fig. 4.6. The fitting results are accordant to the experiment data. The outcome for effective mass are also fit well, as shown in Fig. 4.7. The small discrep-ancies can be attributed to inaccuracies in the band structure and the assumption of phase shift in the model. The effective mass is expected to diminish as 1/N for in-creasing film thickness. This phenomena can be explained by the Bohr-Sommerfeld quantization rule with a simple assumption that the phase shift is a function of k⊥
and kk.
Figure 4.6: Energies of quantum well resonance as a function of thickness at normal emission.
Figure 4.7: Thickness and energy dependence of the zone center subband effective mass.
Chapter 5
Submonolayer Pb on Ge(111)
Lead deposits on Ge surfaces have received a large amount attention. Pb on Ge is considered ”prototypical” system for study metal/semiconductor interface.
(√ 3 ×√
3)R30◦ is a common reconstruction in metal/semiconductor interface. It is stabilized by the minimization of the Ge dangling bonds. The study of the sub-monolayer Pb on Ge(111) was reported by many groups. When the highly-doped n-type Ge(111) are used, the electronic structures are different from those previously reported.
When Pb atoms are absorbed on highly-doped (dopant concentration of 1 × 1017 ∼ 1 × 1018 cm−3) n-type Ge(111), the valence band of Ge including the heavy-hole, light-heavy-hole, and split-off hole bands are reflected and probed by angle-resolved photoemission spectroscopy. The effective masses of carriers in the conduction band and valence bands near the band edges have been measured by cyclotron resonance in many semiconductors.
5.1 Experiment
The Ge(111)-c(2 × 8) was prepared by cycles of sputtering at 500◦C with Ne gas, followed by annealing at 600◦C. The cleanness of sample was checked by LEED pattern and photoemission spectrum.
2 ML of Pb (in substrate unit) was deposited by EFM3 with a rate of 0.2 ML/min
(a) (b)
Figure 5.1: The LEED pattern of (√ 3 ×√
3)R30◦ reconstruction with electron energy 40eV.
onto the substrate at room temperature . The sample was then annealed to 200◦C and a (√
3 ×√
3)R30◦ reconstruction was formed. The LEED pattern of the (√ 3 ×
√3)R30◦ reconstruction was shown in Fig. 5.1. This reconstruction can be also obtained by deposing several monolayer Pb film at 120 K followed by annealing to 300◦C. A sharp (√
3×√
3)R30◦LEED pattern can be obtained by different condition and we can conclude that the reconstruction is stable.
The dispersion relation along two symmetry directions, ¯Γ ¯M ¯Γ and ¯Γ ¯K ¯M , are recorded at 120 K. The measured direction can be calibrated by LEED pattern, which reflects corresponding surface Brillouin zone (SBZ) as shown in Fig. 5.2. The dashed line represents the SBZ of Ge(111) and the solid line represents the SBZ of the (√
3 ×√
3)R30◦ reconstruction. A photon energy of 21.2 eV (He I α) is used.
The electronic structures are measured both at room temperature and low temper-ature ( 120 K ).
To distinguish between bulk or surface emission bands, different photon energies are applied. In contrast to bulk state, the peak position of a surface state in photoe-mission spectra is independent of the photon energies used. Synchrotron radiation source provides tunable photon energies. The experiments using synchrotron radi-ation light source were performed on the BL21B1 beamline at NSRRC in Taiwan.
This is an ultra-high resolution and high flux beamline, covering the photon energies from 5 to 100 eV. The reconstruction was obtained by the same procedure. The band dispersion were also measured along two symmetry directions with different
Γ
Figure 5.2: The corresponding SBZ of the (√ 3 ×√
3)R30◦ reconstruction.
photon energies.
5.2 Result
Figure 5.3 (a) and (b) show the series of energy distribution curves with increas-ing emission angles. Normal emission corresponds to θ = 0 and the surface electronic structure can be probed from ¯Γ toward to the surface zone boundary by varying kk.
Figure 5.3 (a) shows three electronic state features along ¯Γ ¯M ¯Γ direction. These states are clearly observed and labeled as A, B, I, H1, H2 and H4. State A is ob-servable for emission angles 19◦ - 26◦ at binding energy at 0 to 0.6 eV; state B2 is observable for emission angles 16◦-30◦ at binding energy at ∼ 0.8 eV. A and B are combine to state I , observed at large emission angles ≥ 30◦.
Figure 5.3 (b) shows the electronic state features along ¯Γ ¯K ¯M direction. These states are clearly observed and labeled as C-G and h1-h2. State C is observable for emission angles 15◦ - 22◦ at binding energy ∼ 0.35 eV; state D is observable for emission angles 17◦-22◦ at binding energy at ∼ 0.8 eV. Both E and G are symmetry to ¯M , observed at large emission angles 22◦-33◦ and 18◦-33◦. State F is observable for emission angles 17◦ - 22◦ at binding energy ∼ 0.7 eV.
Dispersion relations were mapped along the ¯Γ ¯M ¯Γ and ¯Γ ¯K ¯M directions , as shown
Figure 5.3: The EDCs along (a) ¯Γ ¯M ¯Γ and (b) ¯Γ ¯K ¯M directions.
in Fig. 5.4 and 5.5. The vertical axis is the energy, and the horizontal axis is the in-plane momentum of the photoelectron, kk, calculated from the polar emission angle. The 2D dispersion of the electron band along two symmetry directions, are measured both at room temperature and low temperature. The red vertical lines denote high symmetry points of the (√
3 ×√
3)R30◦ unit cell. The high symme-try points in the fcc(111) surface are ¯M and ¯K, where ΓM = √
The electronic states labeled in energy distribution curve (EDC) are also labeled in 2D images. Near the zone center ¯Γ, some electronic states with weak intensity are not noticeable in EDC’s, but they are easier to see in the 2D image. The states are labeled H1-H4 and h1-h4 for the two measured directions, respectively.
The electron structure of the Pb/Ge(111)-(√ 3 ×√
3)R30◦ were reported in previ-ous research. With angle-resolved photoemission spectroscopy (ARPES), Carlisle at al. observed that the α and γ reconstructions of Pb/Ge(111) system have the same electronic structure in the two symmetry directions although their atomic structures are different. Their spectrum show that surface states cross the Fermi level and both two phase are metallic, as shown in Fig. 5.6.
The bands dispersions are very different from the previous reports. This may be caused by the substrate doping concentration (dopant concentration of 1 × 1017 -1×1018cm−3). The band dispersions observed from our experiment have the feature of the (√
3 ×√
3)R30◦ reconstruction. Along the ¯Γ ¯M ¯Γ direction, state I is centered at the second ¯Γ point around 0.9 eV. The band folding effected are observed. State B centered at the second ¯Γ point and a weak feature, label as B’, centered at the zone center are observed. Along the ¯Γ ¯K ¯M direction, state C and D are centered at K; state E and G are centered at ¯¯ M point. The faint feature C’ observed at low temperature are centered at ¯K.
Figure 5.4: The 2D image along ¯Γ ¯M ¯Γ direction.
Figure 5.5: The 2D image along ¯Γ ¯K ¯M direction.
Figure 5.6: The energy dispersion of surface states detected along two symmetry directions with photon energy 20 eV at room temperature. [17]
5.2.1 Difference at RT and LT
Usually, measurements of photoemission spectra are done at low temperature to reduce the background and thermal broadening. The electronic states detected at room temperature and low temperature are essentially equivalent. Spectra show rather broad peaks at room temperature. As shown in Fig. 5.7 (c), the peaks of EDC at kk = 0.65 ˚A−1 are sharper and the peaks can be resolved at low temperature.
The main difference is the presence of the C’ state along the ΓKM direction.
Along the ¯Γ ¯K ¯M , a faint feature at ∼ 0.6 eV close to ¯K is observed at low temper-ature. This state is not easy to observe in the EDC or 2D image. Figure 5.7 shows the gradient of the 2D image from the Fig. 5.5. The EDC at kk = 0.78˚A, shown in Fig. 5.7 (c), shows clearly that a new peak emerges at binding energy 0.6 eV.
5.2.2 2D Dispersion
To know that the electronic states are 2D or 3D states, different photon energies were applied. The band dispersion along ¯Γ ¯M ¯Γ and ¯Γ ¯K ¯M directions are measured with photon energies 17, 21, and 25 eV, as shown in Fig. 5.8 and 5.9. The features look the same as different photon energies are used.
Figure 5.7: A new band emerges at low temperature.
Figure 5.8: The 2D image along ¯Γ ¯M ¯Γ direction with different photon energies.
Figure 5.9: The 2D image along ¯Γ ¯K ¯M direction with different photon energies.
Figure 5.10: The EDCs along ¯Γ ¯M ¯Γ and ¯Γ ¯M ¯Γ direction with different photon energies.
Analyzing the photoemission spectra amply, the EDC curves of various photon energies are shown at varying kk. Along the ¯Γ ¯M ¯Γ and ¯Γ ¯K ¯M directions, most peak positions do not move as changing photon energies, shown as Fig. 5.10 (a) and (b).
The electronic states H1-H4, h1-h4, A-I and C’ are all surface states.
5.2.3 Observation of Substrate Band Edges
The interesting feature are the states near the zone center, H1-H4 and h1-h4.
Their peak position did not vary with photon energies, as shown as Fig. 5.11. The central portion of the 2D image shows four concave bands, three of them correspond-ing well to the bulk Ge valence band edges ( heavy hole, light hole, and split-off hole
Figure 5.11: The 2D image with different photon energies.
bands). As shown in Fig. 5.12 (a), those bands detected along the ¯Γ ¯M ¯Γ correspond well to the Ge bands along the [110] direction [31]. They match well with the bands H1, H2, and H4.
5.3 Discussion
In our experiment, a remarkable change of the electronic structure between RT and LT is that a new surface state band emerges when the temperature is cooled down. Pb/Ge(111) have been well studied. A phase transition of 1/3 monolayer Pb on Ge(111) from a room temperature (√
3 ×√
3)R30◦ phase to a 3 × 3 phase below 200 K. This have been observed from LEED pattern or a STM image [32]. The angle-resolved photoemission study of the electronic structure on Pb/Ge(111) has been probed and the remarkable change is that the upper surface state is much more clearly split into two bands at LT [33]. Many explanations were proposed to explain
Figure 5.12: Comparison the experimental data to the calculated Ge bulk band with the (a) spin-orbit coupling and (b) non-spin-orbit coupling.
Figure 5.13: The band splitting around the ¯K points at LT.[33] Solid lines denote high symmetry points of the (√
3 ×√
3)R30◦ unit cell (upper panel) and 3 × 3 unit cell (lower panel) [33].
the phase transition, such as nesting instability, defect-mediated density waves, and dynamical fluctuations.
Mascaraque at al. reported the appearance of a different surface band with a 3 × 3 periodicity at low temperature using photons with 32 eV [33], as shown in Fig.
5.13. The band found in the vicinity of the Fermi level was detected as shoulder in the low temperature peak. The phase transition was considered to be induced by the thermal disorder and should be an order-disorder type. Maybe the structure has two kinds of Pb atoms, whose vibrational movement is stabilized at low tem-perature. The driving force of the phase transition in our system is not clear. The possible explanation can not be proved only on the basis of the electronic structure and the detailed information on the atomic structures of the (√
3 × √
3)R30◦ and 3 × 3 are required.
However, the LEED pattern was not observed to change in our experiment when the temperature is cooled down to 50 K, while the new surface bands centered at K¯√3 become resolved at low temperature. It is possible that the atomical change of
the Pb-√
3 surface was not sensitive to LEED pattern.
The more interesting bands are those faint bands centered at zone center. They match well with the Ge bulk band edges ( heavy hole, light hole, and split-off hole bands) from calculation.
Depending on the species and the structure of the adsorbed atoms, the surface states act as donor-type or acceptor-type states. Depending on the position of the Fermi level, donor-type surface state can carry a positive charge and acceptor-type surface state a negative charge. The charge of surface states is compensated by an opposite charge inside the semiconductor. The charge screens the surface charge is called the space charge QSC and the spatial regions of redistributed screening charges are called space charge layers. The occupied surface states induce strong band bending. Fig. 5.14 shows the band scheme for a n-type semiconductor space charge layer. Partially occupied acceptor type surface state carrying negative charge is compensated by the space charge. Bulk donor states are lifted above the Fermi level and are empty of electrons. The exact position of Fermi energy at the surface is determined by charge neutrality. The distribution of space charge is related to the curvature of the electronic bands. Due to the band bending, free electrons are pushed away from the surface and their density is lowered. This space charge layer is called a depletion layer. Higher density of acceptor surface states at lower energies in the band gap can induce stronger upward band bending. The space charge layer extends deeper into the semiconductor and the band bending is stronger that the intrinsic energy crosses the Fermi energy. This space layer is called a inversion layer.
Pb atoms adsorbed on Ge surface form an ordered structures and create surface states in the band gap. The surface states of the (√
3 ×√
3)R30◦ reconstruction on normal doped Ge(111) consists of upward parabolic bands. If the surface states are acceptor-type and carry negative charge, which is screened by an opposite charge inside the semiconductor. Electron occupation in the surface states induce strong upward band bending. The surface states can penetrate into the bulk and the interaction of the surface states and the Ge bulk band in the inversion layer are
Figure 5.14: Bans scheme of a (a) depletion and (b) inversion space charge layer on a n-type semiconductor [2].
considered. Near the zone center, the surface states occupation in (E, k) diagram is coincident with the Ge bulk band, leading to the strong interaction between the surface state and Ge bulk bands. Due to the fact that Ge bulk continuum dominates the density state, the surface state band reflects the Ge bulk band edge as a result of strong interaction.
The surface bands H1, H2, and H4 can be well explained by the surface bands inducing space charge layer. We compare the non-spin-orbit coupling Ge bands with it. They match well. The result suggests that Ge bands form spin-orbit and non-spin-orbit coupling coexists.
The band gap of Ge is an inverted gap, where the gap is p-like at the bottom and s- like at the top. Surface state derived from the conduction band are more s-like. The valence band edge of Ge is derived from p3
2 and p1
2 states of free atoms.
There are no bands splitting off from the s-type band by the spin-orbit interaction.
A strong interaction between p-type Ge band edges and the s-like surface band may broke the symmetry of p-type Ge band. Therefore, the spin-orbit splitting and non-spin-orbit splitting bands coexist.
Chapter 6
Conclusion
The electronic structures of the ultrathin metal films on the semiconductor have been investigated by high resolution angle-resolved photoemission. The electronic structures of Ag/Ge(111) and Pb/Ge(111) are studied.
Atomically uniform Ag film on Ge(111) were prepared at the thickness ranging 5-18 monolayers. A detailed investigation of the subband dispersion relations in Ag films of various thickness deposited on Ge(111) is probed by angle-resolved pho-toemission. The effective mass at the zone center were extracted through a fitting model of a Pade function.
That effective masses at the zone center of subbands for the Ag/Ge(111) were found to increase with decreasing thickness. The effective mass at the zone center of each subband is coupled to the kk dependence of k⊥ for the quantum well state band structures due to the Bohr-Sommerfeld quantization rule. This behavior is simply caused by a boundary effect through both k⊥ and kk momentum dependent phase shift.
Submonolayer Pb film deposited on Ge(111) results in (√ 3 ×√
3)R30◦ recon-struction. The electronic structures are probed both at room temperature and low temperature. A new surface state band centered at ¯K√3 emerges at T = 120 K while no phase transition is observed by LEED pattern.
The electronic structures are different from the previous report. The surface state band dispersion reflects the Ge bulk band edges, including the heavy-hole, light-hole, and split-off hole bands. We propose that a space charge layer is induced on the highly-doped n-type Ge(111) surface by a Pb-induced acceptor type surface state, resulting large band bending and strong hybridization interaction between the surface state and the Ge substrate bands. It is the first time observation that spin-orbital splitting and non-spin-orbital splitting bands coexist at the interface of metal/semiconductor.
Bibliography
[1] Stefan H¨ufner, Photoelectron Spectroscopy, Springer
[2] Hans L¨uth, Surfaces and Interfaces of Solid Materials , Springer [3] G Sch¨onhense, and U Heinzmann, J. Phys. E: Sci. Inst. 16, 74 (1983)
[4] P. S. kirchmann, M. Wolf, J. H. Dil, K. Horn, and U. Bovensiepen, Phys. Rev.
B. 76, 075406 (2007)
[5] K. Horn, B. Reihl, A. Zartner, D. E. Eastman, K. Hermann, and J. Noffke, Phys.
Rev. B. 57, 14758 (1998)
[6] http://www.nsrrc.org.tw/english/lightsource.aspx , NSRRC [7] User Manual SCIENTA R3000 , VG SCIENTA
[8] Peter Y. Yu and Manuel Cardona, Fundamentals of Semiconductors, Springer [9] http://cst-www.nrl.navy.mil/bind/static/index.html
[10] J. J. M´etois and G. Le Lay, Surf. Sci. 133, 422 (1983) [11] G. Le Lay and J. J. M´etois, Appl. Surf. Sci. 17, 131 (1983) [12] T. Ichikawa, Solid State Commun 46, 827 (1983)
[13] T. Ichikawa, Solid State Commun 49, 59 (1983)
[14] R. Fiedenhans’l, J. S. Pedersen, M. Nielsen, F. Grey, and R. L. Johnson, Appl.
Surf. Sci. 178, 927 (1986)
[15] H. Huang, C. M. Wei, H. Li, B. P. Tonner and S. Y. Tong, Phys. Rev. Lett. 62, 559 (1989)
[16] J. A. Carlisle, T. Miller, and T. C. Chiang, Phys. Rev. B. 47, 3790 (1993) [17] J. A. Carlisle, T. Miller, and T. C. Chang, Phys. Rev. B. 47, 10342 (1993) [18] S. A. de Vries, P. Goedtkindt, P. Steadman, and E. Vlieg, Phys. Rev. B. 59,
13301 (1999)
[19] E. Ganz, F. Xiong, Ing-Shouh Hwang, and J. Golovchenko, Phys. Rev. B. 43, 7316 (1991)
[20] R. D. Bringans, and H. H¨ochst, Phys. Rev. B. 25, 1081 (1982)
[21] J. Aarts, A. J. Hoeven, and P. K. Larsen, Phys. Rev. B. 37, 8190 (1988) [22] A. R. Smith, K. J. Niu, C. K. Shih, Science 273, 226 (1996)
[23] M. H. Upton, T. Miller, and T. C. Chiang, Appl. Phys. Lett. 85, 1235 (2004) [24] T. Valla, P. Pervan, A. B. Hayden, and D. P. Woddruff, Phys. Rev. B. 54,
11786 (1996)
[25] Y. Z. Wu, C. Y. Won, E. Rotenberg, H. W. Zhao, F. Toyoma, N. V. smith, and Z. Q. Qiu, Phys. Rev. B. 66, 245418 (2002)
[26] P. D. Johnson, K. Garrison, Q. Dong, N. V. Smith, Dongqi Li, J. Mattson, and S. D. Bader, Phys. Rev. B. 50, 8954 (1994)
[31] U. Schmid, N. E. Christensen, and M. Cardona, Phys. Rev. B. 41, 5919 (1990) [32] Joseph M. Carplinelli, Hammo H. Weitering, E. Ward Plummer, and Roland
[31] U. Schmid, N. E. Christensen, and M. Cardona, Phys. Rev. B. 41, 5919 (1990) [32] Joseph M. Carplinelli, Hammo H. Weitering, E. Ward Plummer, and Roland