Transcript Slide 1

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
0.162E 0.5h3W
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
1  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 probe 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. Generally not as sensitive as the Optical detection technique
(iii) Capacitive detection: used in some transducers. Highly sensitive for short
distances, but not for long distances.
Ultimately, the resolution of the cantilever deflection in
resonance is mostly limited by its thermomechanical
noise given as
x tm2
12
 4QkBTB k0 
12
Slide # 3
Microcantilevers III
Cantilever based sensors:
The cantilever based sensors can be classified into three groups
(i) General detection of any short range forces: Scanning probe microscopy
(ii) Detection of mass attachment: based on changes in frequency response
(iii) Detection of molecular adsorption: based on changes in surface stress of a
functionalized cantilever. This can also be detected based on resonance
amplitude change.
(iv) Detection of radiation (IR or nuclear): based on deflection of a bimaterial
cantilever, or from deflection changes
(v) Detection of charges or electric or magnetic fields: Based on resonance
frequency or amplitude changes
Note that although cantilevers are highly sensitive to stress changes, but
resonance frequency based changes are the most sensitive due to quality factor
enhancement.
Slide # 4
Kelvin probe technique
Kelvin probe technique measures surface charge, surface potential, and surface work function. The
advantages are quantitative nature, and ease of operation.
Evac
qVcon = qVdc
semi
Si
Eg,Si
Ec
+
p Silicon
=  Si + Eg,Si - (semi + qs)
EC
qs
EF,semi
qVcon
Ev,EF,Si
Probe Tip
G. Koley and M. G. Spencer, J. Appl. Phys. 90, 337 (2001)
Semiconductor Sample
Slide #
Goutam Koley
Mathematical Model for SKPM
Qs Qtip
1 C
2
Vdc  Vac sin t  Vcon  
Ftotal 
2
2 d
40 d
 Ftotal  Fdc  F  F2
 C

F  
(Vdc  Vcon ) Vac sin  t
 d

G. Koley and M. G. Spencer, J. Appl. Phys. 90, 337 (2001)
Slide #
Goutam Koley
SKPM Measurement System
AMPLITUDE
DETECTOR
LASER
OSCILLATOR
POSITION
DETECTOR
LOCK-IN
CIRCUITRY
CONTROLLER
Z
CONTROLLER
Vdc
SCANNER
Vacsint
SAMPLE
Vdc
SURFACE POTENTIAL
IMAGE
G. Koley and M. G. Spencer J. Appl. Phys. 90, 337 (2001)
MORPHOLOGY
IMAGE
Slide #
Goutam Koley