doi:10.1016/j.physrep.2003.09.001 
Copyright © 2003 Elsevier B.V. All rights reserved.
Harold J. W. Zandvliet
, 
Solid State Physics group & MESA+ Research Institute, University of Twente, P.O. 217, 7500 AE, Enschede, The Netherlands
Accepted 1 September 2003;
editor: G. Comsa
Available online 29 October 2003.
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Abstract
Although germanium (Ge) (0 0 1) has a relatively small surface unit cell, this surface displays a wealth of fascinating phenomena. The Ge(0 0 1) surface is a prototypical example of a system possessing both a strong short-range interaction due to dimerization of the surface atoms, as well as an energetically weaker, long-range interaction related to the ordering of the dimers. In this review, I show how the key energetic parameters that govern the thermodynamic behavior of Ge(0 0 1) are extracted from scanning tunneling microscopy measurements. These energetic parameters are used to interpret several surface phase transitions: the 2D equilibrium shape evolution of islands and vacancy islands; the order-disorder c(4×2)→(2×1) phase transition; the orientational phase diagram; and, the faceting of [0 1 0] oriented steps. Particular attention is paid to the differences between Ge (0 0 1) and the closely related and technologically important silicon (Si) (0 0 1) surface.
Author Keywords: Germanium (0 0 1) surface; Surface thermodynamics; Scanning tunneling microscopy
PACS classification codes: 68.35.Bs; 68.35.Md; 68.35.Rh
Fig. 1. Ball and stick model of the Ge(0 0 1) surface: (a) (1×1) (unreconstructed) surface; (b) p(2×1) dimer reconstruction; (c) p(2×2) dimer reconstruction; (d) c(4×2) dimer reconstruction.
Fig. 2. Side-view schematic drawing of a buckled dimer (asymmetric dimer). There is an effective charge transfer of about 0.1e from the down atom of the dimer to the up atom of the dimer. The dimer bond tilts slightly out of the surface plane.
Fig. 3. Scanning tunneling microscopy empty-state image of Ge(0 0 1). The sample bias is +1.6 V, and the tunneling current is 1 nA. The image size is 53 nm×55 nm.
Fig. 4. Filled-state scanning tunneling microscopy images of various types of defects on Ge(0 0 1): (a) single dimer vacancy (A-DV); (b) double dimer vacancy (B-DV); (c) (2+1) dimer vacancy (2+1 DV).
Fig. 5. Scanning tunneling microscopy image of very clean Ge(0 0 1) showing local c(4×2), p(2×2), and (2×1) reconstructions. Sample bias is −1.6 V, tunneling current is 1 nA, and image size is 45 nm×45 nm.
Fig. 6. Scanning tunneling microscopy image of a well-ordered striped (2×1)−c(4×2) domain pattern on Ge(0 0 1). Sample bias is −1.6 V, tunneling current is 1 nA, and image size is 40 nm×40 nm. Inset: buckling registry near a single-layer A-type step edge (
SA). The widths of the (2×1) and c(4×2) domains are denoted by
l and
L, respectively.
Fig. 7. Schematic diagram of a single-layer stepped Ge(0 0 1) surface. The dumbbells represent surface dimers. The two different types of single-layer steps are labeled
SA and
SB (
a0=5.66 Å and
a=4.0 Å).
Fig. 8. Schematic diagram of rebonded and a non-bonded
SB-step edges.
Fig. 9. Schematic drawing of a meandering
SB-step trapped between two neighboring straight
SA-step edges.
Fig. 10. Schematic diagram of a [1 1 0] oriented step edge containing a thermally excited kink pair. The nearest-neighbor and next-nearest-neighbor interaction energies are shown.
Fig. 11. Plot of the free energy of
SA and
SB step edges versus temperature.
Fig. 12. Schematic diagram of a 100% kinked [0 1 0] step edge. The nearest-neighbor and next-nearest-neighbor interaction energies are shown.
Fig. 13. Free energy of a [0 1 0] oriented step on Ge(0 0 1) versus temperature.
Fig. 14. Schematic diagram of a vacancy island on Ge(0 0 1), with rectangular shape of length
l and width
w.
f=σ
||−σ
represents the elastic force monopole along the vacancy island periphery arising from the surface stress anisotropy.
Fig. 15. Aspect ratio (
l/
w) of a vacancy island on Ge(0 0 1) versus temperature in the absence of surface stress anisotropy. The experimentally measured aspect ratio with error bar (1.4±0.1) is also shown.
Fig. 16. Filled-state STM image of a Ge(0 0 1) surface after low-dose Ar-ion bombardment and annealing at 500 K. Image size 20 nm×15 nm, sample bias −1.6V, and tunneling current 0.5 nA.
Fig. 17. Anisotropy of the surface stress,
f, versus the aspect ratio of a vacancy island. Lower curve, vacancy island size of 24
D/
a; middle curve, vacancy island size of 48
D/
a; upper curve, vacancy island size of 96
D/
a. The inset shows the distribution of aspect ratios of the vacancy islands.
Fig. 18. Excess surface-free energy per atom versus the aspect ratio of a vacancy island for
f=0.08 eV/ Å
2.
Fig. 19. Schematic diagram of the effective couplings between adjacent dimers.
Fig. 20. Schematic diagram of a [0 1 0] oriented step and a pair of [1 1 0] oriented steps running from point A to point B.
Fig. 21. Plot of the step free energies of a [0 1 0] oriented step and a pair of [1 1 0] oriented steps versus temperature. For temperatures smaller then 630 K, it is energetically favorable for the [0 1 0] step to meander around its mean direction rather than to facet into local [1 1 0] segments.
Fig. 22. Scanning tunneling microscopy image of [0 1 0] oriented steps on Ge(0 0 1). Faceting into [1 1 0] segments (as occurs on Si(0 0 1)) doesn't occur. Image size 55 nm×55 nm. The sample bias is −1.6 V and the tunneling current is 1 nA.
Table 1. Energy differences for the (2×1) family of reconstructions of Ge(0 0 1) with respect to the (2×1) reconstruction
χ (
0.1–0.15) refers to the charge transfer from the lower to upper atom of the dimer.
Table 2. Total energies for the (2×1) family of the Ge(0 0 1) surface (per spin in the Ising model and per dimer in the dipole model)
The disordered non-buckled (2×1) reconstruction is taken as zero energy. C is a constant.
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