Transcript Chapter 18: Surface Effects

From Solid to Surface
A image of surface for
fcc(111)
Problem 12.2 due Thursday
Talks next week
In this course, most of the problems we deal with are
bulk properties.
In nature, crystals are not infinite but finite 3D objects
terminated by surfaces.
Many phenomena and processes occur at the interface
between a condensed phase and the environment.
Ch. 18: Surface Effects & Measurement
The (100) surface of group IV semiconductors contain atoms
that are paired together in dimers that lead to a (2x1)
reconstruction.
Even if the surface atoms don’t
move, there is a surface effect
Just like there were effects from having periodicity,
there are also effects from it suddenly stopping
If we assume the surface is just like the bulk
Negative value of Ef reflects the attractive force of the
positive ions
surface
The charge density if
there were no effect
from the surface
Does it make sense
that the electrons
abruptly stop at the
surface?
electrons
No electrons
What is the work function?
Two definitions:
Any difference?
MINIMUM ENERGY needed to remove an electron
from a solid to a point immediately outside the solid
surface (≈ 100 Å)
Energy needed to move an electron from the FERMI
LEVEL to VACUUM
<< 100 Å
Work function with dipoles
Corrections to before:
• For finite lattices in 3D,
there is a difference
compared to infinite lattices
   F  W S
• Also, non-equivalent crystal
faces will have different dipole
moments  work function
depends on the orientation
• Another possibility is that the
atoms near surface move
WS = dipole density arising from the
finiteness of the lattice, “double layer”
Measuring the Work Function
(1. Photoelectric Effect)
If the incident light does
not have an energy equal
or greater than W, then
electrons will not escape
due to the light.
What is another way to get electrons to leave?
2. Work function from thermionic emission
Richardson-Dushman
equation derived from
adding Fermi-Dirac
distribution to current
density

 

j  AT exp  

k
T
B


2
Richardson constant: A = 120 A/(cm2 K2)
Metals have different work functions
These answers vary ~5% based on how they are measured.
What happens when you touch to
metals together?
• each material’s energy state distribution is unique; different EF.
• focus on the electrons near the filled/empty boundary.
Minimum
energy to
remove
electron
from
sample
E=0 (vacuum level)
EF (Fermi level)
EF (Fermi level)
Metal 1
Metal 2
• the closer an electron is to the vacuum level, the weaker it is bound to the solid
• or, the more energetic is the electron
Opposite charges attracted to each other, so stay at interface
Two Conductors in Contact
–+
–+
This is an example of band bending and – +
its due to redistribution of charge.
–+
New vacuum level – +
electron flow
leads to charge separation (dipole)
Contact potential difference
Fermi level the same throughout sample
Example:
Conducting Tip
Microscopy
Thickness of Band Bending Region
for metals and semiconductors
Poisson’s Equation:
area A
E(x)
s : permittivity (F/cm)
 : charge density (C/cm3)
E(x+Dx)
Dx
for semiconductors
s =o for metals
Something similar occurs when bringing a metal and a
semiconductor or two semiconductors together. However,
there are several concepts needed that we will discuss in
Chapter 28 and 29.
All solid-state electronic and opto-electronic devices are
based on doped semiconductors.
Bringing Semiconductors Together
A Few Methods to Study Surfaces
The book is a little out of date on the methods to
analyze surfaces. There are many more now.
• Common: atomic force
microscopy and (scanning)
transmission electron
microscopy
• Others include: (angle resolved)
photoemission electron
spectroscopy and low energy
electron diffraction
Atomic Force Microscope
deflection sensor
force sensor
tip
tip
feedback
sample
scanner
The force between tip and sample
is measured. The interatomic force
between tip and sample deflect a
cantilever which carries the tip. In
this case the morphology of
surfaces can be measured.
vibration
damping
Data acquisition
Measure roughness to look at quality of film growth.
Oriented growth is referred to as epitaxy. Thin film growth is
controlled by the interplay of thermodynamics and kinetics.
Three growth modes:
• Layer-by-layer, or Franck van der Merve growth (typically ideal)
• Island, or Vollmer-Weber growth (very rough)
• Layer plus island, or Stranski-Krastanov growth (in between)
The occurrence of the individual growth modes is governed by the bond
strength between the atoms in the layer and the atom-substrate bonds.
Atomic Force Microscopy (AFM)
Deflections of 10-2 Å can be measured.
There are several methods to measure
the deflection of the cantilever:
Deflection of a laser beam
Measurement of capacitance between
cantilever and a second electrode.
Use of optical interferometry
Use of an STM to measure the cantilever
deflection
Scanning Tunneling Microscope (STM)
Based on quantum
mechanical
tunneling current
D. Eigler, IBM
Works for electrically
conductive samples
Imaging, spectroscopy and
manipulation possible
The AFM can be used in three different contact modes.
Contact mode:
The tip-sample distance is only few Å (light
contact). The spring constant of the cantilever is
small so that can bend and follow surface contours.
A constant-height mode or a constant-force mode
can be applied.
Non-contact mode:
The sample-tip distance is several 10 Å. The tip is
affected by the weak attractive forces. In this
case the cantilever vibrates and the resonance
frequency changes due to the interaction with the
sample.
Tapping mode:
In this mode the tip also vibrates and is closer to
the sample so that it touches the surface.
This mode is advantageous for surface with high
surface roughness.
Non-contact Si(100)(2x1)
Vicinal surfaces are created by cutting a crystal
a small angle away from a typical surface
orientation (e.g. close to 001 or 110)
Vicinal surfaces comprise a lot of steps.
In case of vicinal Si(100) monoatomic
steps appear, with alternating dimer
orientation. The step energies are
different for both cases (SA, SB).
In case of SB much more kinks appear.
For higher vicinal angle also double
steps show up.
Facetting:
Depending on the step and terrace energies,
stepped surfaces may change to faceted
surfaces. This can also be induced by
adsorption. It also depends on temperature.
Example: Faceting of a Si(111) surface misoriented
by 10°.
Example: Gold induced faceting of a vicinal
Si(100) surface
Warning about image processing
Beware of introducing image processing artifacts !
Understand and know what you are doing
Raw data shows ‘jumps’ in
slow scan direction. (Due to
pointing instabilities of laser).
Processing (here ‘flatten’) can
remove them, but can create
new artifacts.