Determining the Thickness of Pb Film Similar to Bulk with Energy Dispersion Derived from Quantum Well States

It is known that the energy spacing between adjacent empty quantum well (QW) states in Pb islands on Cu(111) would reveal the shrinking characteristic originating from the effect of the image potential. Using the phase accumulation model, including a phase factor contributed from the image potential, the shrinking energy spacing can be quantitatively explained with the assumption of the parabolic energy versus wave vector (E–k) dispersion. However, an experimental dispersion acquired from analyzing the energies of the QW state reveals a linear E–k relationship corresponding to the Pb bulk band structure, implying the assumed parabolic dispersion is not appropriate. By combining the linear dispersion with the image potential effect in the calculation, it is found that the calculated values of energy spacing of island thickness below eight atomic layers are not in agreement with the experimental measurements. This implies that the electronic structure of Pb islands would be similar to that of the bulk when their thicknesses reach eight-atomic layers.

[1]  H. Jeng,et al.  Field-induced expansion deformation in Pb islands on Cu(111): evidence from energy shift of empty quantum-well states. , 2012, Physical review letters.

[2]  T. Tsong,et al.  Suet al.Reply , 2011 .

[3]  A. Borisov,et al.  Comment on "Phase contribution of image potential on empty quantum well states in Pb islands on the Cu(111) surface". , 2011, Physical review letters.

[4]  T. Tsong,et al.  Electron relaxation in empty quantum-well states of a Pb island on Cu(111) studied by Z-V (distance-voltage) spectroscopy in scanning tunneling microscopy , 2010 .

[5]  Wang Yao,et al.  Quantum size effects on the work function of metallic thin film nanostructures , 2010, Proceedings of the National Academy of Sciences.

[6]  R. Berndt,et al.  Scattering and lifetime broadening of quantum well states in Pb films on Ag(111) , 2010 .

[7]  T. Tsong,et al.  Quantum size effect on ultra-thin metallic films , 2010 .

[8]  T. Tsong,et al.  Effects of electronic confinement and substrate on the low-temperature growth of Pb islands on Si(1 0 0)-2 × 1 surfaces , 2010 .

[9]  K. Bohnen,et al.  Decay mechanisms of excited electrons in quantum-well states of ultrathin Pb islands grown on Si(111): Scanning tunneling spectroscopy and theory , 2009 .

[10]  T. Tsong,et al.  Phase contribution of image potential on empty quantum well States in pb islands on the cu(111) surface. , 2009, Physical review letters.

[11]  U. Bovensiepen,et al.  Ultrafast electron dynamics in Pb/Si(111) investigated by two-photon photoemission , 2008 .

[12]  R. Berndt,et al.  Quantum modulation of the Kondo resonance of Co adatoms on Cu/Co/Cu(100) , 2008, 0804.2967.

[13]  Xi Chen,et al.  Manipulating the Kondo resonance through quantum size effects. , 2007, Physical review letters.

[14]  S. Heike,et al.  Tip-induced energy shift in Au/Fe(100) quantum wells , 2007 .

[15]  T. Tsong,et al.  Strength modulation of quantum-well states in Pb islands with periodic distortions , 2007 .

[16]  M. Chou,et al.  Persistent superconductivity in ultrathin Pb films: a scanning tunneling spectroscopy study. , 2006, Physical review letters.

[17]  Q. Xue,et al.  Band structure and oscillatory electron-phonon coupling of Pb thin films determined by atomic-layer-resolved quantum-well states. , 2005, Physical review letters.

[18]  A. Bauer,et al.  Electronic structure and dynamics of quantum-well states in thin Yb metal films. , 2004, Physical review letters.

[19]  Yang Guo,et al.  Superconductivity Modulated by Quantum Size Effects , 2004, Science.

[20]  A. Mans,et al.  Quantum electronic stability and spectroscopy of ultrathin Pb films on Si(111)7×7 , 2002 .

[21]  R. Miranda,et al.  Observation of preferred heights in Pb nanoislands: A quantum size effect , 2002 .

[22]  V. Narayanamurti,et al.  Imaging subsurface reflection phase with quantized electrons. , 2002, Physical review letters.

[23]  H. Petek,et al.  Optical intersubband transitions and femtosecond dynamics in Ag/Fe(100) quantum wells. , 2002, Physical review letters.

[24]  R. Berndt,et al.  Luminescence from metallic quantum wells in a scanning tunneling microscope. , 2001, Physical review letters.

[25]  L. J. Chen,et al.  Correlation between quantized electronic states and oscillatory thickness relaxations of 2D Pb islands on Si(111)-(7 x 7) surfaces. , 2001, Physical review letters.

[26]  M. Chou,et al.  Quantum electronic stability of atomically uniform films. , 2001, Science.

[27]  M. Tringides,et al.  Uniform, self-organized, seven-step height P b / S i ( 111 ) − ( 7 × 7 ) islands at low temperatures , 2000 .

[28]  R. Miranda,et al.  Can electron confinement barriers be determined by STM , 2000 .

[29]  Miller,et al.  Quantum-well states as fabry-Perot modes in a thin-film electron interferometer , 1999, Science.

[30]  E. Rotenberg,et al.  Quantum-well states in copper thin films , 1999, Nature.

[31]  Dean Cvetko,et al.  Step height oscillations during layer-by-layer growth of Pb on Ge(001) , 1997 .

[32]  Dongmin Chen,et al.  Electron Fringes on a Quantum Wedge , 1997 .

[33]  Kuo-Jen Chao,et al.  Formation of Atomically Flat Silver Films on GaAs with a "Silver Mean" Quasi Periodicity , 1996, Science.

[34]  Evans,et al.  Observation of quantum size effects in photoemission from Ag islands on GaAs(110). , 1993, Physical review letters.

[35]  Fischer,et al.  Lifetime of image-potential states on metal surfaces. , 1992, Physical review. B, Condensed matter.

[36]  Bauer,et al.  Quantum size and surface effects in the electrical resistivity and high-energy electron reflectivity of ultrathin lead films. , 1988, Physical review. B, Condensed matter.

[37]  Smith,et al.  Phase analysis of image states and surface states associated with nearly-free-electron band gaps. , 1985, Physical review. B, Condensed matter.

[38]  J. Pendry,et al.  The existence and detection of Rydberg states at surfaces , 1978 .