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Atomic resolution with an atomic force microscope usingpiezoresistive detection

M. Tortonese, R. C. Barrett,a) and C. F. QuateEdward L. Ginzton Laboratory, Stanford University, Stan&-d, Calr~ornia 94305

(Received 1 October 1992; accepted for publication 30 November 1992)

A new detection scheme for atomic force microscopy (AFM) is shown to yield atomic

resolution images of conducting and nonconducting layered materials. This detection scheme

uses a piezoresistive strain sensor embedded in the AFM cantilever. The cantilever is batchfabricated using standard silicon micromachining techniques. The deflection of the cantilever is

measured directly from the resistance of the piezoresistive strain sensor without the need for

external deflection sensing elements. Using this cantilever we achieved 0.1 A,,, verticalresolution in a 10 Hz-l kHz bandwidth.

The atomic force microscope ( AFM) ’ is able to image

the surfaces of conducting and nonconducting materials

with very high vertical and lateral resolution. It is cur-

rently being used in a variety of scientific and technological

applications.2 The AFM works by bringing a cantilever in

contact with a sample. The sample is then scanned and the

cantilever is deflected according to the topography of thesample. By measuring the deflection of the cantilever a

three-dimensional image of the surface of the sample can

be recorded. The detector used to measure the deflection ofthe cantilever is crucial in determining the performance of

the microscope and its range of applicability. Conventional

detectors are based on vacuum tunneling,lT3 optical inter-ferometry,&’ optical lever,8 and capacitance.’ All of these

methods require a sensing element external to the cantile-

ver. Piezoelectric’oV” and piezoresistive” cantilevers pro-

vide alternative detection schemes in which the deflection

detector is integrated in the cantilever. An integrated sen-

sor provides several advantages over conventional AFM.

Currently, external deflection sensors make up a large frac-

tion of the size and complexity of an AFM. They also

require alignment to the cantilever, which must be main-

tained during scanning. This normally requires that the

sample be moved while the cantilever and detector are held

fixed. This requirement makes imaging of large samples

difficult. In this letter we present the first atomic scale

images taken with a piezoresistive cantilever. First, we will

review the principle of the piezoresistive detection scheme,

then we will characterize the devices that we fabricated,

and finally we will show atomic scale images.

The variation of bulk resistivity with applied stress is

known as the piezoresistive effect. Silicon exhibits a strongpiezoresistive effect.13 At the same time it is a suitable

material for fabricating cantilever beams. 4 The resistance

of a resistor built into one of these beams will change whenthe cantilever is stressed with deflection. Figure 1 shows a

diagram of an AFM with a piezoresistive element. In our

implementation two wires connect the piezoresistive canti-lever to an external dc-biased Wheatstone bridge which

directly measures the deflection by measuring the cantile-

ver’s resistance. Figure 2 is a schematic drawing of our

“Present address: IBM Almaden Research Center, San Jose, CA 95120.

piezoresistive cantilever. The shape of the cantilever per-mits the current to flow in one leg and out the other. Al-

though the resistor could be lithographically defined to

occupy the most highly stressed region toward the base of

the cantilever; our choice of a uniformly doped cantileversimplifies the fabrication process. Metal lines connect the

piezoresistor to bonding pads on the silicon chip and therethe cantilever is connected to the external Wheatstonebridge. The cantilever is electrically isolated from the sub-

strate by a thin layer of silicon dioxide. It is important that

the resistor be made shallow, so that the current flows as

close as possible to the surface of the cantilever, where thestress is maximum. As an extreme case, a cantilever with a

uniform doping profile would have zero net piezoresistive

response because opposite sign stresses on the top and bot-tom of the cantilever would give an equal but oppositecontribution to the change in resistance. The cantilevers

presented here have a thickness of 4.5 ,um and the averagedepth of the resistor is 0.5 pm. The resistor is p type with

a sheet resistance of 220 a. The cantilever is oriented alongthe ( 110) crystallographic axis of the silicon, where the

piezoresistive coefficient is maximum. The fabrication has

been described elsewhere.”

Two parameters are of fundamental importance in

AFM: the spring constant of the cantilever and the mini-

mum detectable deflection of the sensor used to measure

the deflection of the cantilever. The minimum detectable

deflection of the deflection sensor defines the vertical reso-

lution of the microscope. Small spring constant and highvertical resolution are usually desirable. Unfortunately,soft cantilevers are less sensitive than stiff cantilevers for

the’same cantilever thickness or length. This can be seen nthe following two equations.

vz

VI-v,=-v-g

FIG. 1. Schematic diagram of the piezoresistive detection scheme forAFM.

a34 Appl. Phys. Lett. 62 (a), 22 February 1993 0003-6951/93/080834-03$06.00 @I 1993 American institute of Physics a34

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CD”bXtmcla,ine

I Iondingpad

b

f

/ ‘”,

piezorcsistor

A (110) Silicon orientation

axrde metal

dopehsilicoo

FIG. 2. Schematic drawing of a piezoresistive cantilever. Plane view (a)and cross section (b) .

The spring constant of an undeflected cantilever with

the structure shown in Fig. 2 is given by

Et3wbkc- -

2b(L:-L;)+6wL;(1)

where E is the Young’s modulus of silicon along the ( 110)

direction, t is the thickness of the cantilever, and w, b, L,,

and L2 are defined in Fig. 2.

The sensitivity of the cantilever can be expressed as the

resistance change per unit deflection. When the cantileveris deflected the only stress that will affect the resistance of

the piezoresistor is the stress along the longitudinal direc-

tion of the cantilever, which is the direction of the current

flow. From the analysis of the stress in the cantilever, as-

suming that the top triangular region of the cantilever does

not contribute to the resistance, we find

AR--R -‘4 [ ;;;:?$$&h’ (2)

I I I I I

1 10 100 1000 10000

Frequency (Hz)

(a)

where R is the resistance of the cantilever and AR is the

resistance change due to a deflection AZ at the free end of

the cantilever. rrL is the longitudinal piezoresisti ve coefli-

cient for silicon along the ( 110) direction at the operating

temperature and with a given doping concentration in the

piezoresistor and /3 is a correction factor to account for the

fact that the resistor is not at the surface of the cantilever.

P depends on the thickness of the cantilever and on the

depth profile of the silicon doping, which is determined by

the implantation parameters and the subsequent thermal

processes. using SUPREM3l’ to simulate our fabricationprocess we found /!?=0.79.

The minimum detectable deflection of the cantilever

depends not only on its sensitivity, but also on the noise in

the measurement system. The fundamental noise limit in

the measurement of resistance is given by the Johnson

noise in the piezoresistor, which is

vn= (4k,TRhf, (3)

where V, is the thermal electrical noise, k, the Boltzmann

constant, T the temperature, and Af the bandwidth. Inaddition, there are other sources of noise. One is the noise

in the electronics used to measure the resistance. With

careful selection of the electronic components this noise

can be made negligible at room temperature. Another is

l/f noise which becomes dominant in our piezoresistive

cantilevers as we increase the voltage applied to the bridge.

This noise can arise from many sources, such as carrier

trapping at surface defects, or from the contacts. As can be

seen in Fig. 1 the output signal increases with the voltage

applied to the bridge, so that it may seem advantageous to

operate with a voltage as high as possible. However, given

the l/f noise, the signal to noise ratio flattens out after a

certain voltage. We found it convenient to use a bridge

supply voltage near 8 V. This tends to maximize the signal

to noise ratio and keeps the power dissipated in the canti-

lever within a few mW. Figure 3 shows the noise spectral

density for one of our cantilevers for a bridge supply volt-

age of 4 V, with little l/f noise (a) and for a bridge supply

voltage of 12 V, where the l/f noise is dominant (b).

ridge Supply Bias: 12 V

orner frequency = 750 Hz

1 10 100 1000 10000

Frequency (Hz)

(b)FIG. 3. Noise spectral density for one of the fabricated cantilevers. The voltage applied to the bridge is 4 V in (a) and 12 V in (b). Even though thel/j- noise is dominant in (b), the minimum detectable deflection in a bandwidth from 10 Hz to 1 kHz is lower because the output of the detectorincreases linearly with the bridge supply voltage.

a35 Appl. Phys. Lett., Vol. 62, No. 8, 22 February 1993 Tortonese, Barrett, and Quate a35

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FIG. 4. Scanning electron micrograph of a piezoresisti ve cantilever.

Figure 4 is a scanning electron micrograph of a pi-

ezoresistive cantilever. The metal contacts are visible on

the left side of the micrograph. We have fabricated piezore-

sistive cantilevers with lengths Li and widths w varying

from 400 to 75 pm and from 50 to 10 pm, respectively.

Correspondingly, the spring constants vary from 5 to 100N/m, the minimum detectable deflections in the band-

width from 10 Hz to 1 kHz vary from 0.7 to 0.1 A,,, themeasured resonant frequencies vary from 40 to 800 kHz

with a resonance sharpness in air varying from 200 to 800.

(Cl Cd)

FIG. 5. Unfiltered atomic resolution images of graphite (a), boron nitride(b), molybdenum disul fide (c), and tantalum di selenide (d).

The resistance of the different cantilevers ranges between2.5 and 7 kfI. For operation in our AFM the cantilevers

are wire bonded to standard 8 pin DIP packages which are

directly housed in our microscope.We used our cantilevers in repulsive mode AFM to

image atomic corrugations on a number of layered mate-

rials. Figure 5 shows unfiltered images of graphite, boron

nitride (an insulator), MoS, and TaSe,

We find that the piezoresistive detection scheme is at-

tractive because of its simplicity and reliability. It has dc

response, requires only low voltage and uses simple cir-cuitry. The cantilever a long with its integrated deflection

sensor can be conveniently batch fabricated. The absenceof external deflection sensing elements simplifies the design

of an AFM for imaging large samples and for operation in

controlled or adverse environments such as ultrahigh vac-uum. The operation of the microscope is simplified as well,

since the precise alignment of complex components is un-

necessary. A further improvement will be to include an

integral tip on the cantilever to improve the imaging o f tall

structures.

The authors wish to acknowledge Tom Albrecht for

helping to generate the original idea for this detection

scheme and Hirofumi Yamada for contributing to the early

stages of this work. One of the authors (R.C.B.) acknowl-edges the support of the Hertz Foundation. This research

was supported by the National Science Foundation and by

the Office of Naval Research.

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