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SPM Probe tips
CNT attached to a Si
probe tip
Slide # 1
Microcantilevers: Mechanical properties
Rectangular Cantilever:
Spring constant:
Resonant frequency:
f res
E: Young’s Modulus
I: Moment of inertia
L: length, W: width, h: height
3EI
k 3
L
0.162 E 0.5 h3W
k

 0.323
0.5 2
 L
m
Wh 3
I 3
L
m  hLW
Triangular Cantilever:
 4W 3

Eh W
k
cos  1  3 3 cos   2
2 L3
b


3
 i2
k
k
fi 
 0.323
m
2 3 M
1
 i  1.875
Slide # 2
Microcantilevers II
Cantilever quality factor Q: Quality factor depends on loss mechanisms.
Usually the quality factor is ~50 in air. In vacuum, it can go up to several
thousand or more.
Detection Of Cantilever Deflection:
There are 3 common techniques for cantilever detection:
(i) Optical detection: commonly used for scanning robe microscopy.
This is well suited for a single cantilever, but not suitable for an array
of cantilevers
(ii) Piezoresistive detection: used for sensing purposes and in
integrated circuit applications. Not as sensitive as the
(iii) Capacitive detection: used in some transducers. Highly sensitive for
short distances, but not for long distances.
Ultimately, the resolution of the cantilever
deflection is limited by its thermomechanical
noise given as
2
x tm
12
 4Qk BTB k0 
12
Slide # 3
Midterm Review: Important topics
• Mobility and Hall effect
• Excitonic effects
• Photoluminescence for impurity and composition
determination
• Atomic force microscopy modes
– Contact
– Tapping
– Non-contact modes
Slide #
Problems 1
• Calculate the maximum excitonic
binding energy for excitons in GaN.
Effective masses: 0.2m0 and 0.75m0
for electrons and holes. k = 9.5.
• Calculate the bandgaps of AlN and
GaN from 2 PL peak positions given
for two compositions: x = 0.11, peak at
340 nm; x = 0.45, peak at 290 nm.
• What are the two major factors that
affect mobility? Choose one of these
factors and design a device to reduce
the scattering factor drastically
• Why is small magnetic field used
during Hall mobility measurement?
bind
Eex
*
13.6 mred
1
 2
n m0  2
1  x EGaN  xEAlN  Eg , AlGaN
1  y EGaN  yE AlN  Eg , AlGaN
Slide #
Problems 2
• In the force vs. distance curve point out the regions where contact mode
and non-contact modes are operated. Sketch the AFM topography
image of a perfectly square ridge with vertical edges, with a tip that has
a conical shape with half angle of 20 degrees. How does the shape
looks like if the tip has a parabolic edge?
• Mention three major information that you can get from PL. Do you
expect PL peak intensity for GaAs and GaN, similar order as for Si and
SiC? Explain in detail.
• For a very pure material, without defects and doping, the lowest energy
and most prominent PL peak is observed at 1.40 eV at 4 K. The
bandgap of the material is 1.42 eV, and the dielectric constant is 13. The
typical donor and acceptor activation energies are 7 meV and 130 meV.
Assuming that the momentum relaxation time is 1 ns for both type of
carriers, calculate
(i) Electron and hole effective masses
(ii) Electron and hole mobility values
(iii) How would the peak position change with increase in temperature?
Slide #
Short questions and problems
• Explain briefly:
– Why is scanning capacitance performed in contact mode but
potential measurement in non-contact mode
– Why is optical phonon scattering only at higher temperature but
acoustic scattering at lower temperature
– Calculate the low field mobility for GaN if the saturation velocity is
2x107 cm/s and the critical electric field is 4x105 V/cm. Why does
velocity saturate at higher field?
– Draw the band diagram for a metal tip and an n-type semiconductor
sample, with a surface barrier. Show the change in surface barrier
as super bandgap illumination is incident on it.
– How does the intensity and peak position of PL peak vary for a
quantum well with (a) AlGaAs/GaAs, (b) with AlGaN/GaN
Slide #