We discuss a low-cost atomic force microscope that we have designed and built for use in an undergraduate teaching laboratory. This microscope gives students hands-on access to nano-Newton force measurements and subangstrom position measurements. The apparatus relies mainly on off-the-shelf components and utilizes an interferometric position sensor known as the interdigitated (ID) cantilever to obtain high resolution. The mechanical properties of the ID readout enable a robust and open design that makes it possible for students to directly control it. Its pedagogical advantage is that students interact with a complete instrument system and learn measurement principles in context. One undergraduate experiment enabled by this apparatus is a measurement of Boltzmann’s constant, which is done by recording the thermal noise power spectrum of a microfabricated cantilever beam. In addition to gaining an appreciation of the lower limits of position and force measurements, students learn to apply numerous concepts such as digital sampling, Fourier-domain analysis, noise sources, and error propagation.

1.
R. S.
Newrock
, “
A new course: The physical principles of biological instrumentation
,”
Am. J. Phys.
46
(
1
),
32
34
(
1978
).
2.
G.
Binnig
,
C. F.
Quate
, and
Ch.
Gerber
, “
Atomic Force Microscope
,”
Phys. Rev. Lett.
56
(
9
),
930
933
(
1986
).
3.
S. R.
Manalis
,
S. C.
Minne
,
A.
Atalar
, and
C. F.
Quate
, “
Interdigital cantilevers for atomic force microscopy
,”
Appl. Phys. Lett.
69
(
25
),
3944
3946
(
1996
).
4.
S.
Alexander
,
L.
Hellemans
,
O.
Marti
,
J.
Schneir
,
V.
Elings
,
P. K.
Hansma
,
M.
Longmire
, and
J.
Gurley
, “
An atomic-resolution atomic-force microscope implemented using an optical lever
,”
J. Appl. Phys.
65
(
1
),
164
167
(
1989
).
5.
G. G.
Yaralioglu
,
A.
Atalar
,
S. R.
Manalis
, and
C. F.
Quate
, “
Analysis and design of an interdigital cantilever as a displacement sensor
,”
J. Appl. Phys.
83
(
12
),
7405
7415
(
1998
).
6.
Stephen C.
Minne
,
Scott R.
Manalis
, and
Calvin F.
Quate
,
Bringing Scanning Probe Microscopy Up to Speed
(
Kluwer
, Norwell, MA,
1999
), Chap. 4.
7.

Fcorr can be estimated by assuming a quadratic shape for the bent cantilever Fcorr=1mID2, where mID=LIDLT is the ratio of the distance of the ID fingers from the cantilever base to the total cantilever length. A more precise expression is Fcorr=2(3mID2mID3), which is derived from the equation for the shape of a simple rectangular beam, with an applied end-load P: z(x)=Px2(3LTx)(6EI), where x is the coordinate along the length of the cantilever, and E and I are the elastic modulus and moment of inertia of the beam, respectively. The tip deflection in this case is therefore z(LT)=PLT3(3EI).

9.
T. R.
Albrecht
,
S.
Akamine
,
T. E.
Carver
, and
C. F.
Quate
, “
Microfabrication of cantilever styli for the atomic force microscope
,”
J. Vac. Sci. Technol. A
8
(
4
),
3386
3396
(
1990
).
11.
For simplicity, we omit the intermediate parameter γ that is typically used. For an introductory treatment of harmonic oscillators, see
Atam P.
Arya
,
Introduction to Classical Mechanics
(
Prentice Hall
, Englewood Cliffs,
1998
), 2nd ed., Chap. 3
or
Richard P.
Feynman
,
Robert B.
Leighton
, and
Matthew L.
Sands
,
The Feynman Lectures on Physics
(
Addison-Wesley
, Reading, MA,
1989
), Vol.
1
, Chap. 23.
12.
J. P.
Cleveland
,
S.
Manne
,
D.
Bocek
, and
P. K.
Hansma
, “
A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy
,”
Rev. Sci. Instrum.
64
(
2
),
403
405
(
1993
).
13.
A.
Torii
,
M.
Sasaki
,
K.
Hane
, and
S.
Okuma
, “
A method for determining the spring constant of cantilevers for atomic force microscopy
,”
Meas. Sci. Technol.
7
(
2
),
179
184
(
1996
).
14.
J. E.
Sader
,
J. W. M.
Chon
, and
P.
Mulvaney
, “
Calibration of rectangular atomic force microscope cantilevers
,”
Rev. Sci. Instrum.
70
(
10
),
3967
3969
(
1999
).
15.
A. L.
Weisenhorn
,
M.
Khorsandi
,
S.
Kasas
,
V.
Gotzos
, and
H.-J.
Butt
, “
Deformation and height anomaly of soft surfaces studied with an AFM
,”
Nanotechnology
4
(
2
),
106
113
(
1993
).
16.
A.
Touhami
,
B.
Nysten
, and
Y. F.
Dufrêne
, “
Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy
,”
Langmuir
19
(
11
),
4539
4543
(
2003
).
17.
Veeco Contact Mode fluid cell, part # FC at http://www.veecoprobes.com
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