Tutorial: Scanning Conductance Microscopy (SCM)
and Scanning Gate Microscopy (SGM).
By Douglas R. Strachan
SCM
conducting sample
V
insulator
ground plane
Fig. 1 SCM
This technique uses two passes of a conducting AFM tip over a sample which lies on top
of an insulating substrate with a ground plane below (Fig. 1). [See M. Bockrath, et al.,
Nano Lett. 2, 187 (2002) and C. Staii, et al., Nano Lett. 4, 859 (2004) as references.] In
the first pass the surface topography is measured with intermittent ("tapping") mode
AFM. In the second ("interleave") pass the tip is raised to a constant height (h) above the
surface of the sample and substrate. Typically, one uses an h of roughly 30 nm to 120
nm. The AFM tip can be modeled as a driven damped harmonic oscillator,
2
(1)
mx  F (t )  mx  m0 x  FP ( x) ,
where F (t ) is a driving force, m is the mass of the oscillator, x is the vertical position of
oscillator,  0 is the resonant frequency of oscillator, and FP (x) is the interacting force
between the AFM tip and the sample and substrate. Making the approximation

it
FP ( x)  FP ( x0 )  FP ( x0 )( x  x0 ) and trying a solution of x  x0  x0 e in Eq. 1
yields a relation with seven terms. Two of the terms are constants of time and determine
2
the equilibrium position of the oscillator x 0 , through FP ( x0 )  m0 x0 . The remaining
five terms all contain a factor of eit which can be cancelled out to yield



  2  FP ( x0 )    2  i
 0
m 
F0


x0 

(2)
.
2
m 



F (x )
  0 2  P 0    2    2  2


m 



The phase lag of the oscillating tip is given by
(3)
tan(  ) 




  2  FP ( x0 )    2
 0
m 


At resonance (with the tip driven at  0 ) the phase is  / 2 when the tip far away from the
sample, where the force gradient is zero. When the tip is close to the sample such that

FP ( x0 ) is significant, the phase will move a small amount (typically in the positive

sense since FP ( x0 ) is positive if we take the FP (x) directed downward in the negative
sense). (Note that phase shifts are opposite if one defines the oscillation to be ~ e it as
opposed to ~ eit .) We can take differences of  at different locations of the sample

where FP ( x0 ) varies. Using the small angle approximation of the numerator of Eq. 2
near  / 2 the phase difference is


F ( x )  FB ( x0 )
(4)
,
S  B  S 0
2
m0
where  S and  B are the respective phases over the conducting sample and just the

ground plane. FS ( x0 ) is the force gradient above the sample and ground plane, while

FB ( x0 ) is the background force gradient. Also note that the force gradients are assumed
to be measured at the same heights above the sample and background, which assumes
that the equilibrium position x 0 is approximately a constant distance h above the surface
during the interleave scan.
1


2
With the tip kept at a constant potential V the force gradient is FS ( x0 )  (V ) C S .
2
This gives a relation between the phase shifts and the changes in the capacitive coupling
between the background and the sample.
1 (V ) 2  

(5)  S   B 
 C S  C B .
2

2 m0 
This signal will be large for samples which have strong capacitive coupling to the
grounded back plane. The extent to which the entire sample capacitive couples to the
ground plane depends on the ability for the charge carriers in it to reorient themselves on
the time scales of the field variations. This time scale reflects the mobility of the carriers
through an RC time constant formed from the capacitance to ground in parallel to
redistribution resistance. For field variations slow enough the phase signal can be large
enough to measure. While for less conducting samples the phase signal will be smaller.
In this sense, this scanning probe technique can determine whether a sample is
conducting, thus the name SCM.
Fig. 2 SCM: Reproduced from C. Staii, A. T. Johnson, and N. J. Pinto Nano Lett. 4, 859 (2004).
An example of SCM is shown above in Fig. 2. The images are of a conducting nanotube
(b), an insulating nano-fiber (c), and a conducting nano-fiber (d). Line scans showing the
relative phase shifts are shown in the insets. Note that the phase shifts are opposite to
those in M. Bockrath et al. since they are calculated to be consistent with oscillations
going as ~ e it , as opposed to eit (which is simply a choice of notation).
SGM
V
insulator
ground plane
Vbias
Current Meter
Fig. 3 SGM
In SGM the sample has contact pads which connect it to a voltage source and a current
meter. As with SCM, SGM utilizes an interleave scan after determining the topography
of the sample surface. In this case, the tip is not driven during the interleave scan, but
instead kept at a fixed height above the sample with a fixed voltage. The tip acts as a
local gate, the same way a field effect transistor works, which can locally modify the
transport carrier density on a semi-conducting sample. As the tip is scanned across the
sample to gate different locations, the I-V characteristics can be mapped. This technique
can also be employed at higher frequencies (AC-SGM) as opposed to the DC case. An
example of this AC-SGM technique is shown in Fig. 4. The two color scale plots show
the impedance modulus (a) and the phase (b) of the nanotube measured at 300 KHz. The
two regions of higher impedance and lower phase are indicative of defects of the
nanotube where local gating of the tube is more effective.
Fig. 4 SGM: Reproduced from C. Staii, A. T. Johnson, R. Shao, and D. A. Bonnell Nano Lett. 5, 893
(2005).