Abstract— Design, simulation, fabrication and testing of p-type polycrystalline diamond (poly-C) piezoresistive RFMEMS is reported for the first time. The use piezoresistive detection in RFMEMS can lead to an output impedance in the ranges of 20 - 500 Ω and several MΩ for intra- and inter-grain piezoresistors, respectively. The inter-grain gauge factor of the poly-C film with a resistivity of 22 ⋅Ω cm was estimated to be over 20. An Ohmic contact with a contact resistance of 5.21 MΩ was achieved by using a highly-doped poly-C interlayer between metal and lightly-doped piezoresistor.

I. INTRODUCTION

ADIO frequency micro electro mechanical systems (RFMEMS) can yield on-chip micromechanical resonators with ultra high quality factors over 10,000 at

GHz frequencies in both vacuum and air making them excellent candidates for broadband wireless communications [1]. However, various types of single micromechanical resonator structures usually have a large motional resistance of over 100 KΩ [2-4] at GHz frequencies, which are preventing them from directly coupling to an antenna or low noise amplifier in wireless communications applications, where matching impedances in the range of 50 - 377 Ω are often required. The large output impedance results from the use of capacitive detection in capacitive RFMEMS. The most direct methods for lowering the motional resistance are to 1) raise the dc-bias voltage; 2) increase the overlap areas between electrodes; 3) decrease the electrode-to-resonator gap; 4) increase the quality factor and 5) sum together the outputs of an array of identical resonators. However, this leads to (a) challenges in microfabrication, (b) increase in the size of devices, and (c) expensive signal processing electronics. Since the first report of piezoresistivity in single crystal and polycrystalline (poly-C) diamond by researchers at Michigan State in 1992 [5], there has been enormous interest in the utilization of p-type poly-C prepared by chemical vapour deposition (CVD) as a material for sensor applications owing to its unique physical and chemical properties and potential application at high temperatures. For the first time, this paper reports the piezoresistive detection in RFMEMS using poly-C piezoresistive sensors. The piezoresistive detection, which is receptive to device scaling without decreasing the detection sensitivity, can help adjust

Manuscript received April 29, 2001. (Write the date on which you submitted your paper for review.) This work was supported by the Engineering Research Centers Program (ERC) of the National Science Foundation under Award Number EEC-9986866

Zongliang Cao and Dean Aslam are with Electrical and Computer Engineering Department of Michigan State University, Lansing, MI 48910 USA, phone: 517-282-6531; e-mail: caozongl@ msu.edu.

the output impedance by (a) adjusting the piezoresistor dimensions and (b) increasing the mobility of holes by using intra-grain piezoresistor (which also leads to a piezoresistive gauge factor of over 4000 [6]). While the intra-grain detection will be the subject of subsequent publications, the inter-grain piezoresistors, with a gauge factor in the range of 20, are discussed in the current paper. Another unique feature of the current work is the use of single-material MEMS (SMM) [7]. An overview of poly-C piezoresistive MEMS is shown in Fig. 1. The actuation of poly-C piezoresistive MEMS can be capacitive or piezoelectric.

Fig. 1 Conceptual 3D-graph and SEM images of piezoresistive sensor made

of polycrystalline diamond.

II. FUNDAMENTALS OF POLY-C PIEZORESISTOR For p-type semiconducting material, the piezoresistive

effect is attributed to the band structure of valence band. As stress is applied, two degenerate bands, the so-called heavy and light hole bands, at the upper P3/2 state of the valence band at k = 0 shift with respect to each other along the energy of the E - k band diagram. A redistribution of holes between the shifting bands leads to a resistivity change, sign of which depends on whether the piezoresistor is in compression or tension. Gauge factor (GF), an index of the sensitivity of a

Piezoresistive Sensor Technology for RFMEMS using p-type Polycrystalline Diamond

Zongliang Cao, Dean Aslam Member, IEEE

R

2009 IEEE Nanotechnology Materials and Devices ConferenceJune 2-5, 2009, Traverse City, Michigan, USA.

978-1-4244-4696-4/09/$25.00 ©2009 IEEE 190

piezoresistive sensor device, is defined as the ratio of relative change in resistance to the relative applied strain ε :

R R R RGFL L ε

Δ Δ= =

Δ (1)

where, R and L are the original resistance and length of the piezoresistor, respectively. A more general expression for GF is:

1 2GF υ ρ ρε= + + Δ (2) where υ is the Poisson’s ratio and ρ is the resistivity. The term 1 2υ+ , mainly depending upon the geometry, is normally less than 5.

In general, the polycrystalline materials consist of crystalline grains interconnected by grain boundaries. Grains are considered as single crystals with a diamond lattice. The grain boundaries (GBs) are composed of disordered atoms and contain a large number of defects and dangling bonds which act as trapping states and/or segregation sites [8]. Trapping of holes creates a potential barrier at the boundary and a depletion region into the grains. The film can be modeled as grains of length gL with boundary thickness δ and depletion width dw [9].The fractional change in resistivity per unit strain of the polycrystalline materials can be represented as [10]:

(2 ) (2 )1 1 1g d g d b

g g g b

L w wL L

δ ρ δ ρρρ ε ρ ε ρ ε

− + Δ + ΔΔ= + (3)

where gρ and bρ are the resistivity of grain and grain boundary. Normally, it is believed that the piezoresistive effect of the GBs is much lower than the grain crystal. The random orientations of the GBs also lower the overall piezoresistive effect of grain. This is consistent with the reported low GF of polycrystalline materials than that of their single crystal counterparts. The effect of GBs on the gauge factor was studied in [11] and presented as below assuming there is no gauge factor for GBs:

11 gGF GF

α⎛ ⎞≈ ⎜ ⎟+⎝ ⎠

(4)

where α is the ratio of GBs resistance to grains resistance along the conduction path when film has no strain and gGF is the gauge factor of single-crystalline material. This explains why polycrystalline film with high resistivity results in larger GF.

III. EXPERIMENTAL The piezoresistive property of poly-C was studied for

different structures, doping levels and temperatures using cantilever beams, three point bending fixture and differential pressure setup before. Piezoresistive micro-sensors, such as pressure sensor, accelerometer and the strain sensor in cochlear probe, were also reported in [11-16]. Generally, GF of poly-C increases with the increase of resistivity, grain size and operation temperature. Since the GF of poly-C inter-grain piezoresistor is only 1%-10% of that of poly-C intra-grain piezoresistor, it is essential to improve the sensitivity of the piezoresistive sensor for its application.

By using the new diamond patterning technique, a new piezoresistive micro-sensor consisting of three poly-C layers with different doping level, as shown in Fig. 1, was fabricated to improve sensitivity from three aspects. Firstly, the resistivity of undoped poly-C layer is increased from 103 cmΩ ⋅ to 108-109 cmΩ ⋅ with addition of O2 during poly-C growth, making undoped poly-C a good insulation layer. This is because O2 i) can reduce the doping efficiency of boron in diamond; ii) can suppress the sp2 bonded carbon species and increase the concentration of atomic carbon; iii) selectively etches non-diamond carbon residing on diamond surfaces. All these effects improve the overall quality of diamond (e.g., higher sp3/sp2 ratios and resistivity). Secondly, the doping level of the piezoresistive sensor which is made of lightly-doped poly-C is selected carefully to improve the signal-to-noise ratio (SNR). Lastly, highly-doped poly-C with resistivity of 10-3 cmΩ⋅ is added between the lightly-doped poly-C and metal layer to reduce the contact resistance. The structure in Fig.1 includes three poly-C layers with various doping levels serving as insulation layer, semiconducting layer (piezoresistor) and conducting layer, respectively. This all-diamond structure was demonstrated in more detail in [7], which can help (a) alleviate problems related to multi-material layers (thermal mismatch, adhesion, inter-layer diffusion, contact resistance), (b) utilize unique properties of the material and (c) lower the overall fabrication cost.

A. Poly-C Film Technology Poly-C film is grown by Microwave Plasma Chemical Vapor Deposition (MPCVD) at 800oC after being seeded by spinning diamond-powder-loaded-water (DPLW) over Si, SiO2 or Si3N4 layer. In situ boron doping is achieved by introducing Trimethylboron (B(OCH3)3, TMB) diluted in hydrogen (TMB/H2=0.098%) during the poly-C growth environment. The doping level is controlled by adjusting the ratio of TMB/CH4 in order to make the poly-C semiconducting or metallic (highly-doped with boron). The measurement of doped poly-C resistivity as a function of TMB/CH4 ratio was performed by first fabricating doped poly-C resistors of various dimensions on thermal SiO2, and then patterning Cr/Au (50 nm/400 nm) interconnects in a four-point probe measurement setup as shown in Fig. 2a. The doped poly-C resistivity as a function of TMB/CH4 ratio is plotted in Fig. 2b.

For different doping levels in the piezoresistor, the Cr/Au-piezoresistor contact resistivity, with and without a highly-doped poly-C interlayer, was measured using a Kelvin Bridge structure (Fig. 2a). The contact resistivity, Cρ , was then calculated by:

( )C CR A V I Aρ = ∗ = ∗ (5) where CR is the contact resistance, A is the contact area and V and I are measured as shown in Fig. 2a. Fig. 2c shows a plot of Cρ as a function of resistivity. The result, as measured by a Kelvin bridge structure, shows that the highly-doped poly-C

191

interlayer can reduce the contact resistances to 30%-45% of the original values.

(a)

(b)

(c)

Fig. 2 Measurement on resistivity and contact resistivity of doped poly-C Dry etching of poly-C is performed by Reactive Ion Etching (RIE) technique using the new two-step etching recipe [17]. Al is used as masking layer due to high selectivity of Al to poly-C in RIE. Smooth underlying layer (Si, SiO2 or Si3N4) is achieved as shown in Fig. 3a. If one poly-C layer needs to be patterned on another poly-C layer (for example, piezoresistive sensor needs to be patterned on top of cantilever made of undoped poly-C), CF4/Ar plasma is used to eliminate the micro-columns on the etched surface in O2 plasma (Fig. 3c) and smoothen the etched poly-C surface as shown if Fig. 3b. AFM is used to check the directionality of etching at 50 mTorr. More anisotropic etching is achieved under 15 mTorr with almost 90 degrees but at the expense of higher density of micro-masks in O2 plasma and higher etch rate of Al masking layer in CF4 plasma.

Fig. 3 a) poly-C patterning on Si with two-step etching b) poly-C patterning

on poly-C in CF4 plasma c) in O2 plasma d) profile of sidewall by AFM

B. Chip Design and Resonator Technology Different types of RFMEMS resonators made of only

poly-C were fabricated for potential piezoresistive applications, as shown in Fig. 4. However, only the cantilever beams with various length (250-800 µm) and width (60-100 µm) were used to characterize piezoresistive detection due to its simplicity.

Fig. 4 SEM of RFMEMS made of polycrystalline diamond

Fig. 5 presents the fabrication process of cantilever beams. At step#1, undoped poly-C with resistivity of 108-109 cmΩ ⋅ was grown on n-type Si substrate as insulation layer which was followed by the growth of lightly-doped poly-C layer with resistivity of 22 cmΩ ⋅ . The lightly-doped poly-C layer was patterned using RIE in CF4/Ar plasma to form the piezoresistor. A 3 um-thick-PECVD SiO2 was deposited and patterned using dry etching to form the mould for the selective growth of highly-doped poly-C as interconnects. This SiO2 layer was annealed in N2 at 750 oC to improve the quality because low quality SiO2 is etched at faster rate in MPCVD till continuous poly-C film forms. After the selective growth of highly-doped poly-C, shown at step #2, the undoped poly-C was patterned using two-step RIE technique to create the shape of cantilever beams with smooth Si surface, as shown at step #3. At step #4, PECVD SiO2 was deposited at the back side of the sample to protect the back side of Si in KOH etching at step #6. Cr/Au was deposited at step #5 for two reasons: i) it decreases the length

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of poly-C interconnect so that the total resistance of interconnects are reduced which results in the improvement of sensitivity; ii) the gold bonding is more stable on Cr/Au pad rather than on poly-C with high roughness. Finally, the cantilever beams were released by KOH wet etching, as shown in step #6. The growth condition for three poly-C layers is given in Table I.

Fig. 5 Cross-sections of the fabrication sequence

TABLE I GROWTH CONDITIONS FOR BOTTOM AND TOP POLY-C LAYERS

Microwave Power: 2.3 kW, Pressure: 40 Torr Growth Temperature: 800 oC

Time (Hour) Thickness

H2:CH4 (sccm) 100:1.5 0.5 Undoped poly-C

H2:CH4:O2 (sccm) 100:1.5:0.4 14.5 ~2.5 um

Lightly-doped poly-C H2:CH4:TMB(sccm) 100:1.5:0.5 4.0 ~0.6 um

Highly-doped poly-C H2:CH4:TMB(sccm) 100:1.5:10 0.5 ~0.08 um

Fig. 6 Tip displacement versus average strain of the piezoresistive sensor

The average strain of the U-shape piezoresistor at the tail end of the cantilever is simulated using Coventorware (Fig. 6). Theoretical calculation is also plotted by using the given equation in Fig. 6. Theoretical calculation is only 85% of the simulation because it assumes the piezoresistor has no effect on the stain of the cantilever and it also neglects the piezoresistor thickness. Simulation results provide the average strain value to calculate the GF. Theoretical results tell us how to decide the value of each parameter in order to improve the sensitivity.

C. Piezoresistor Design and Piezoresistive Detection The design of piezoresistor is very important for

obtaining output impedance values that make piezoresistive

detection superior to capacitive detection. Table II shows the design parameters for the piezoresistor:

TABLE II Design Parameters for the Piezoresistor

Average GF

ρ Ω.cm

ρC

Ω.cm2 RC L/w Rpzr

GF·S

0.2 20 Ω 7.35 1 100 Ω 7.47 7.5 0.01 ~2.0x10-5 0.4 Ω 5 500 Ω 7.49

0.2 14 KΩ 17.8 1 70 KΩ 19.5 20 7 8.8x10-2 1.76 KΩ 5 350 KΩ 19.9

0.2 44 KΩ 18.3 1 220 KΩ 21.1 40 22 4.5x10-1 9 KΩ 5 1.1 MΩ 21.8

0.2 86 KΩ 56.1 1 430 KΩ 41.7 65 43 6.8x10-1 13.6 KΩ 5 2.15 MΩ 42.7

where GF is extracted from the graph in [10] . L and w denote the length and the width of the piezoresistor, respectively. Resistivity and corresponding contact resistivity comes from Fig. 2. The definition of S is given by equation 6. The sensitivity of the piezoresistive detection is proportional to GF·S. In addition, it is also assumed the thickness of piezoresistor is 1 um and the contact areas between piezoresistor and metal are 5x10-5 cm2 by considering both contacts at the two ends of piezoresistor. From Table II, the sensitivity of piezoresistive detection increases with the increase of the resistivity and the decrease of length/width aspect ratio. The lowest output impedance is achieved at very high doping level in the ranges of 20 - 500 Ω but with very low sensitivity due to the low gauge factor. Considering the above two effects, the trade-off value of the resistivity is selected to be 22 cmΩ ⋅

Fig. 7 measurement setup for piezoresistor

The measurement setup is shown in Fig. 7. The tip of the cantilever beam was pressed down using micromanipulator with 0.1 um resolution of vertical movement. The change of the resistance was read out by multi-meter by every 5 um change of the displacement

The measurement result is given in Fig. 8a. The relative change of the resistance as a function of the micro-strain is plotted in Fig. 8b by using the points in the middle. The last several points are abandoned because the cantilever’s tip may already touch the bottom of the cavity. The slope of 8.0 indicates the minimum estimation of GF. The contribution of contact resistance to the total resistance is calculated by equation 6.

( )( )2

2

241.5%

2 2c c

c PZR c l l t t

R aS

R R a t l w l wρ

ρ ρ= = =

+ + + (6)

193

Here, cR =3.7 MΩ is the contact resistance,

PZRR =5.21 MΩ is the resistance of piezoresistor.

cρ =0.45 2cmΩ ⋅ is the contact resistivity when resistivity ( ρ ) of poly-C is 22 cmΩ⋅ .

(a)

(b)

Fig. 8 piezoresistive detection by bending the cantilever GF is 14 by considering the contribution of contact

resistance. Actually, the contact area is usually 50%-70% of 2a due to the misalignment on the small dimensions. As a result, the actually GF is 20~28. Larger contact area will be used for the next generation of design to reduce the influence of contact resistance on the purpose of achieving higher sensitivity.

D. Noise Analysis For future RFMEMS application, noise analysis of

piezoresistive sensor is necessary. The noise power spectral density of the piezoresistor, 2 2 -1

noise (V Hz )V , is mainly composed of thermal noise power spectral density 2 2 -1

T (V Hz )V and flicker noise power spectral density 2 2 -1

f (V Hz )V , which can be expressed as the addition of two noise components.

2 2 -1 2 2 -1 2 2 -1noise T f(V Hz )= (V Hz )+ (V Hz )V V V (7)

The thermal noise arises from the random motion of mobile carriers in resistive electrical material, such that

( ) ( )2T 4 4 2B B l l t tV k TR k T t l w l wρ= = + (8)

The direct way to reduce thermal noise is to reduce the length/width ratio of the piezoresistor. If using the parameters given in Fig. 7, 2

TV equals to 290 nV Hz and the total rms thermal noise voltage within 1 MHz bandwidth is 1 mV. The magnitude of flicker noise is inversely proportional to the frequency f , often called1 f noise. The flicker noise is caused by fluctuation in the electrical conductivity, which can be presented as

2 2f in

1( )l l l t t

V Vqt l w l w f

α=

+ (9)

where, inV is the input voltage of Wheatstone bridge measurement setup. α is a device dimensional independent parameter. q is carrier’s concentration. The direct way to reduce flicker noise is to increase the surface area of piezoresistor. According to equation (8) and (9), high resistivity gives rise to high thermal noise and flicker noise spectral density, whereas high resistivity also results in high GF. This is the reason why the resistivity of piezoresistor is selected to be 22 cmΩ ⋅ in terms of SNR.

IV. CONCLUSION Design, simulation, fabrication and testing of p-type

polycrystalline diamond (poly-C) piezoresistive RFMEMS is reported for the first time. The major factor that worsens the sensitivity of the piezoresistor is the large contact resistance. The contact area will be increased by 100 to reduce the contact resistance significantly. The total resistance of the piezoresistor in our current design is on the order of MΩ leading to large thermal noise. The width of the piezoresistor will be increased by 6 to improve the thermal noise. Piezoelectric actuation will be applied on the cantilevers. Frequency response will be obtained through piezoresistive detection. Intra-grain piezoresistor will also be studied for high-sensitive piezoresistive detection.

ACKNOWLEDGMENT This work is supported by the Engineering Research

Centers Program (ERC) of the National Science Foundation under Award Number EEC-9986866.

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