Physics 243A - Surface Physics of Materials
Midterm Examination
November 13, 2008
(100 points total, open books, notes, and class handouts)
Name:______________________________
[1] (15 points) Suppose that the sticking probability for oxygen molecules (O2) incident on a W(110)
surface at 298 K and an ambient pressure of 1 x 10(-8) torr is constant at 1.0 until a coverage of atomic
oxygen of 0.5 monolayers (as measured relative to the W atom surface density of 1.41 x 1015 atoms/cm2) is
reached. Above this coverage, assume that the sticking probability drops to 0.1. Calculate the time
variation of the coverage of atomic oxygen on the surface, make a qualitative plot of coverage versus time,
and determine how long it will take to reach a full coverage of 1.0 monolayer.
[2] (25 points) A Hartree-Fock calculation for the CO molecule yields a total energy for the system of -
112.75 atomic units (1 a.u. = 27.211 eV) and one-electron eigenvalues εC1s = -20.65 a.u. and εO1s = -11.30 a.u.
The distance between C and O in the calculation was set to be the equilibrium distance of 1.18 A.
(a) Estimate the O 1s and C 1s binding energies in eV from this data.
(b) What additional theoretical total energies would you need to be able to calculate the relaxation
energies involved with the O1s and C 1s binding energies? Specify these as precisely as you can.
(c) After photoelectron ejection from the C 1s orbital, what other molecule's outer electron orbitals
would best represent the final outer electron orbitals of the resulting ion?
(d) Write down the equations for the coulomb and exchange integrals between the C 1s and O 1 s
orbitals. Then provide numerical estimates for both of these integrals, using a simple classical
model if appropriate. Note that these two core orbitals are on two different centers and so overlap
negligibly. Also, it may be convenient to note that two classical electron point charges separated
by a distance of 1 Ă have a repulsive potential of 14.4 eV.
[3] (20 points) Consider KLL Auger emission from Cu metal, with some relevant binding energies being:
Cu: Z = 29 Zn: Z = 30
M4,5 ?.? 10.2
M3 75.1 88.6
M2 77.3 91.4
M1 122.5 139.8
L3 932.5 1021.8
L2 952.3 1044.9
L1 1096.7 1193.6
K1 8980.5 9660.8
(a) What will be the most energetic Auger electron in this series? Make the most accurate estimate
you can of its energy, indicating the type of formula you have used.
(b) After the Auger transition in (a), what type of hole state will be left behind? If we now want to
estimate the effect of this hole state on the surrounding valence electrons, we might treat the final
state as an "impurity atom" in the Cu lattice. What would be the atomic number of the atom we
would choose for the impurity in this case?
