Integrated piezoresistive sensors for atomic force-guided scanning Hall probe microscopy

Abstract

We report the development of an advanced sensor for atomic force-guided scanning Hall probe microscopy whereby both a high mobility heterostructure Hall effect magnetic sensor and an n- Al _0.4 Ga _0.6 As piezoresistive displacement sensor have been integrated in a single III–V semiconductor cantilever. This allows simple operation in high-vacuum/variable-temperature environments and enables very high magnetic and topographic resolution to be achieved simultaneously. Scans of magnetic induction and topography of a number of samples are presented to illustrate the sensor performance at 300 and 77 K. © 2003 American Institute of Physics.

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Integrated piezoresistive sensors for atomic force-guided scanning Hall
probe microscopy
A. J. Brook, S. J. Bending,a)and J. Pinto
Department of Physics, University of Bath, Bath, BA2 7AY United Kingdom
A. Oral
Department of Physics, Bilkent University, 06533 Ankara, Turkey
D. Ritchie and H. Beere
Cavendish Laboratory, Cambridge University, Cambridge, CB3 OHE United Kingdom
M. Henini
Department of Physics, University of Nottingham, Nottingham, NG7 2RD United Kingdom
A. Springthorpe
Nortel Networks Optical Components Inc., 3500 Carling Avenue, Ottawa, Ontario K2H 8E9, Canada
?Received 21 October 2002; accepted 31 March 2003?
We report the development of an advanced sensor for atomic force-guided scanning Hall probe
microscopy whereby both a high mobility heterostructure Hall effect magnetic sensor and an
n-Al0.4Ga0.6As piezoresistive displacement sensor have been integrated in a single III–V
semiconductor cantilever. This allows simple operation in high-vacuum/variable-temperature
environments and enables very high magnetic and topographic resolution to be achieved
simultaneously. Scans of magnetic induction and topography of a number of samples are presented
to illustrate the sensor performance at 300 and 77 K. © 2003 American Institute of Physics.
?DOI: 10.1063/1.1576914?
The demonstration of p-Si atomic force microscopy
?AFM? cantilevers with piezoresistive detection1represented
a major milestone in the field of scanning probe microscopy
as it allowed variable temperature atomic-resolution topo-
graphic imaging without the need for optical sensing ele-
ments with precise alignment criteria. There is much to be
gained by the extension of piezoresistive detection to III–V
semiconductor cantilevers since it would allow one to exploit
the direct band gaps and high carrier mobilities in these ma-
terials. In particular scanning tunneling microscope ?STM?-
guided scanning Hall probe microscopy ?SHPM?,2,3which is
noninvasive and yields quantitative low-noise magnetic im-
ages, could be extended to nonconducting or electrically un-
connected samples. While the use of GaAs as a piezoresis-
tive material has been limited by its low piezoresistive
coefficient,4the Al content of n-AlxGa1?xAs alloys can be
tailored to give large piezoresistive coefficients.5We have
recently shown that high sensitivity piezoresistive detection
can be achieved using a cantilever with an n-Al0.4Ga0.6As
layer as the piezoresistive sensing element.6Since our sensor
is composed exclusively of AlxGa1?xAs alloy layers, which
can be grown with almost perfect epitaxy, it allows us to
realize an integrated low-noise Hall probe in a high-mobility
Al0.3Ga0.7As/GaAs two-dimensional electron gas ?2DEG?
grown at the surface of the cantilever.
Figure 1?a? shows a scanning electron micrograph of a
completed cantilever revealing the two primary sensors re-
quired for dual magnetic and topographic imaging. The first
sensor, a Hall cross ?inset Fig. 1?a?? situated near the very
end of the cantilever, is electrically contacted via the four
gold leads at either side of the cantilever. The piezoresistor is
placed at the base of the cantilever where bending stresses
are at a maximum. In addition a sharp (?100 nm diameter?
AFM tip has been micromachined at the very end of the
a?Electronic mail: pyssb@bath.ac.uk
FIG. 1. ?a? SEM of a fabricated piezoresistive cantilever. Inset shows a blow
up of the Hall probe and pyramidal AFM tip. ?b? Epilayer structure for our
integrated cantilever.
APPLIED PHYSICS LETTERSVOLUME 82, NUMBER 2019 MAY 2003
35380003-6951/2003/82(20)/3538/3/$20.00
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© 2003 American Institute of Physics

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sensor, close to the Hall probe. The entire cantilever has been
fabricated from a single GaAs/AlGaAs epilayer structure
?sketched in Fig. 1?b??, grown by molecular beam epitaxy at
590°C. From top to bottom the stack comprises a modula-
tion doped n-Al0.3Ga0.7As/GaAs structure forming a 2DEG
?100 nm from the surface which is separated from the
n-Al0.4Ga0.6As piezoresistive layer by an electrical isolation
region composed of two undoped GaAs layers and an
Al0.3Ga0.7As/GaAs superlattice. The micromachining steps
developed to realize the cantilever are reported elsewhere.6
The performance of the cantilever as an AFM sensor can
be estimated from its geometry and material properties. For
the rectangular cantilever shown in Fig. 1?a? the spring con-
stant is well described by
k?Ewt3
4L3,
?1?
where t is the thickness, w is the width, L is the length of the
cantilever, and E is the Young’s modulus in the ?011? direc-
tion (E?12.2?1010Pa).7The fractional resistance change
is given by
?R
R?3?LEt?1?l/?2L???1?tr/t?
2L2
?z,
?2?
where ?z is the deflection of the cantilever tip, tris the
thickness of the piezoresistor, and ?Lis the longitudinal pi-
ezoresistive coefficient. Using our known cantilever dimen-
sions (L?400 ?m, w?150 ?m, t?6 ?m, l?60 ?m, and
tr?0.5 ?m) andpiezoresistive
?10?9Pa?1in n-Al0.4Ga0.6As at 300 K?6,8we calculate that
k?15 N/m and ?R/(R?z)?8.0?10?7Å?1. The figure-of-
merit of AFM sensor performance is the minimum detectable
deflection ?MDD? whose fundamental limit is set by the
Johnson noise (Vn??4kBTR?f ) from the piezoresistor and
the three identical resistors in the Wheatstone bridge into
which it is incorporated. We estimate a MDD of 0.02 Å/?Hz
at 300 K for a typical piezoresistor with resistance 25 k?.
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coefficient(?L?1.35
The performance of the Hall probe is also determined by
its dimensions and the Johnson noise limit. The x–y resolu-
tion of the sensor shown in Fig. 1?a? is limited to ?1 ?m by
the optical lithographic processing, although submicron
probes could easily be realized by electron-beam lithography.
The Johnson noise-limited minimum detectable field is given
by Bmin??4kBTR?f/IHRHwhere R is the series resistance
of the voltage leads, IHis the Hall current and the RHHall
coefficient. For a 1 ?m Hall cross, with typical values of R
?80 k?, RH?3000 ?/T, and IH?4 ?A at 300 K, a MDF
of 3?10?6T/?Hz is estimated.
Plots of measured noise spectra for the piezoresistor and
Hall probe at 300 and 77 K are given in Figs. 2?a? and 2?b?.
At low frequencies 1/f noise dominates the response of both
piezoresistor and the Hall probe, while above a corner fre-
quency the indicated Johnson noise limit is rapidly ap-
proached. The noise figures fall abruptly when the sensor is
cooled to 77 K due to the explicit temperature dependence of
the Johnson noise as well as that of the piezoresistive coef-
ficient and the resistance of the Hall probe leads.
Measurements were performed with the cantilever
mounted in a low temperature STM which had been modi-
fied for AFM use. The deflection of the cantilever was mea-
sured in a Wheatstone bridge driven at 5 V dc, composed of
the piezoresistor and three almost identical resistors. The
output was passed through a low noise high gain amplifier
and detected with a phase sensitive detector. The resonant
frequency of our cantilevers ranged from 18 to 21 kHz and
quality factors of 300–500 could be achieved in air (Q
?10000 under vacuum?.
The cantilever was tested in AFM mode by scanning a
patterned 100-nm-thick gold film comprising of triangles
?side length 5 ?m? in a hexagonal array with 10 ?m period
FIG. 2. Measured noise spectra of ?a? the piezoresistor and ?b? the Hall
sensor at 300 K and 77 K. Dotted horizontal lines indicate the Johnson noise
limits.
FIG. 3. ?a? AFM image of an hexagonal array of Au triangles ?image size
?IS? ?20 ?m?20 ?m, grayscale spans ?GS? ?100 nm]. ?b? Linescan in
the direction indicated in ?a?. ?c? Magnetic image of a magnetic imaging
reference sample ?MIRS? (IS?20 ?m?18 ?m,GS?18 mT). ?d? Linescan
of ?c? in direction indicated. ?e? Topographic image of MIRS (IS?20 ?m
?12 ?m,GS?100 nm). ?f? Linescan in direction indicated in ?e?.
3539Appl. Phys. Lett., Vol. 82, No. 20, 19 May 2003Brook et al.

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along a given lattice vector ?Fig. 3?a? and linescan in Fig.
3?b??. The image was scanned in noncontact mode with the
cantilever slightly inclined (1°–2°) with respect to the
sample. The cantilever was oscillated close to its resonance
frequency and approached towards the sample until the os-
cillation amplitude dropped to a predetermined value. The z
motion of the scanner tube was then used to keep this am-
plitude constant while scanning the sample surface.
Figure 3?c? shows a scan of the local induction at the
surface of a magnetic imaging reference sample9at 300 K.
The sample is a high density data storage disk with a com-
plex bit track written on it with a repeat distance of
?10.5 ?m. Two bit tracks are clearly resolved with the ex-
pected repeat distance as illustrated in the linescan shown in
Fig. 3?e?. Figure 3?d? is a topographic image of a small re-
gion of the same sample showing striping due to laser tex-
turing performed prior to writing the bit track in order to
smooth the film ?see also linescan in Fig. 3?e??.
Figure 4?a? shows a 77 K magnetic image of part of a 10
periodsquarearrayof
YBa2Cu3O7???YBCO? squares. The 0.35-?m-thick ?001?
YBCO film was grown on a MgO substrate at 690°C by
electron beam coevaporation of the metals. It was patterned
using optical lithography and Ar ion milling, and subse-
quently annealed in atomic oxygen to optimize the stoichi-
ometry. The sample was zero field cooled to 77 K when a 2.5
mT field was applied perpendicular to the film. The sensor
was then scanned across the sample at a constant height of
?1 ?m. Dark areas where the YBCO squares have screened
the penetration of flux are clearly resolved, and are seen
more clearly in the adjacent linescan ?Fig. 4?b??.
In conclusion we have demonstrated an advanced inte-
grated sensor based around a III–V cantilever with piezore-
sistive detection, which allows one to perform AFM-guided
scanning Hall Probe microscopy. In this way the unique ad-
vantages of SHPM can be extended to the imaging of non-
conducting or unconnected magnetic samples. The sensor’s
ability to produce simultaneous topographic and magnetic
images has been demonstrated. Finally, we note that our pi-
ezoresistive cantilever also allows the direct integration of
other secondary III–V sensors during epitaxial growth which
can further exploit the properties of direct gap semiconduc-
tors, e.g., a vertical cavity surface emitting laser or a single
electron transistor.
?m5
?m superconducting
The authors acknowledge the financial support of
EPSRC in the UK ?Grant No. GR/M76119? and TU¨BY´TAK
in Turkey ?Grant No. TBAG-1878?.
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8Measured value from 2.5-?m-thick n-Al0.4Ga0.6As (1?1019cm?3Si
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FIG. 4. ?a? Magnetic image of a square array of YBCO squares (IS
?16 ?m?16 ?m,GS?2.5 mT), T?77 K, ?0Hz?2.5 mT. ?b? Linescan in
the direction indicated in ?a?.
3540 Appl. Phys. Lett., Vol. 82, No. 20, 19 May 2003Brook et al.
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