Investigation on the Influence of Temperature Variation on the Response of Miniaturised Piezoresistive Sensors

Investigation on the Influence of TemperatureVariation on the Response of MiniaturisedPiezoresistive Sensors

G. Olmi

DIEM Department, Engineering Faculty, University of Bologna, Viale del Risorgimento, 2, 40136 Bologna, Italy

ABSTRACT: This paper deals with the analysis of temperature response of miniaturised piezore-

sistive strain sensors. Amorphous silicon sensors of different geometry were deposited on a glass

specimen: on the basis of previous studies, each sensor has a linear response and can be compared

with a full Wheatstone bridge, but dimensions and power consumption are much lower than those

of ordinary resistance strain gauges. A preliminary experiment was performed to prove the

robustness of sensor response, considering connections to the acquisition device having different

lengths. The main experimental campaign was aimed at investigating the influence on response

because of temperature variation during each test. Eight different sensor configurations were tested,

both under load and no-load conditions, with three replications. This paper describes test instal-

lation and measuring chain for simultaneous acquisition of both temperature and sensor voltage

output. Thermal response linearity and hysteresis effects were investigated. In addition, the results,

whose repeatability over the three replications was checked, made it possible to determine and

compare the sensitivities of each sensor configuration to temperature variations. Analysis of variance

(ANOVA) showed that, despite its different values for configurations with different geometry, sensi-

tivity remains the same under load or no-load conditions.

KEY WORDS: amorphous silicon, piezoresistive sensors, temperature variation, thermal sensitivity,

Wheatstone bridge

Introduction

Interest in measurements of strains, pressures and

forces in many fields of mechanical and electrical

engineering has recently increased. The increased

complexity and miniaturisation of modern mechan-

ical systems has also led to the development of micro-

electro-mechanical systems (MEMS), which required

exploration of the performance of strain sensors,

when their dimensions must shrink along with those

of the host structures. For example, in the biome-

chanics field, advanced diagnostic systems, such as

computed tomography and magnetic resonance

imaging, have enabled doctors to create 3D models of

human body vessels. Based on the analyses performed

by such tools, minimum invasive techniques were

studied and developed for neuro- and cardio-surgery.

An endovascular catheter is usually used for these

applications and micro-force sensors are required to

measure the contact force between the catheter and

vessel walls [1]. In addition, a demand on pressure

measurements is increasing in the automotive field

[2]. In robotics applications, more and more sophis-

ticated anthropomorphic hands are being developed

and miniaturised 6-degree of freedom force sensors

are usually required to improve possibilities of

autonomous grasping and fine manipulation [3, 4].

To fulfil these requirements, different types of

strain gauges were proposed: a first option could be to

use conventional resistance gauges (metal thin-film

strain gauges). They can be mass-produced at a low

cost, by using current thin-film technologies. In

addition, the large surface-to-volume ratio of the

sensing film increases the dissipation heat resulting

from self-induced heating. However, low electrical

resistivity (about 200 lW cm)1) prevents gauge and

device miniaturisation. In addition, such strain gau-

ges cannot be directly deposited on the device sur-

face, but require an additional adhesive substrate

with an obtrusive operation on the surface compo-

nent. The most used materials for pure metal thin

films are Mn, Au–Ni, Ni–Cr, Bi–Sb, Cu–Ni (the well-

known constantan).

An alternative could be to use ceramic thin-film

strain gauges. Chung [5] performed several investi-

gations on Ta-N (tantalum nitride) films, indicating

� 2008 The Author. Journal compilation � 2008 Blackwell Publishing Ltd j Strain (2009) 45, 63–76 63

them as a good choice, especially if they are to be

used in harsh environments, because of their high

corrosion resistance. A good linear response and a

high sensitivity were emphasised, results which sug-

gested the use of such gauges for micromachined

pressure sensors. However, a careful optimisation of

both deposition (by dc reactive magnetron sputtering

in an argon–nitrogen atmosphere on thermally oxi-

dised Si substrates) and post-deposition treatment

parameters was required, in order to improve the

piezoresistive properties.

Piezoresistive (based on the dependence of electri-

cal resistivity on stress/strain fields) strain gauges are

often used in MEMS, because of their high resistivity,

sensitivity and compatibility with miniaturisation

requirements. In a crystalline material, the electronic

states form quasi-continua in energy called ‘energy

bands’. This internal atomic arrangement and energy

bands can be altered by applying stress (or strain) on

the material, resulting in small changes in conduc-

tion in the presence of an applied electric field.

Semi-conductor materials are typically used as

piezoresistors: the best features are high hardness,

wear resistance, resistivity and the possibility of being

directly deposited on the component surface. Boron-

doped polycrystalline diamond (poly-C) exhibits a

considerable piezoresistive effect and a great sensi-

tivity. However, chemical vapour deposition (CVD)

which is conventionally used for the growth of poly-

C requires a substrate temperature of 500–900 �C, too

high a value for applications on many materials such

as plastics [6, 7]. Peiner et al. [8] suggested the

adoption of sputtered amorphous carbon (a-C) as a

material for use as piezoresistive strain gauges in

MEMS. Its main features are a low deposition tem-

perature (<150 �C) and good sensitivity and response

linearity. Wisitsoraat et al. [9] and Miller et al. [10]

deal with piezoresistive sensors made of indium–tin

oxide (ITO), whose best advantage is that the depo-

sition procedure can take place at near-room tem-

perature; however, such sensor types are rarely used

because of their high costs and limited supply of

indium.

An interesting alternative is to make use of amor-

phous (a-Si:H, the alternative proposed here) or

microcrystalline (lc-Si:H) silicon. Such materials can

be deposited by plasma-enhanced chemical vapour

deposition (PECVD) at the same low temperature

(<150 �C), with low costs and good linear perfor-

mance under static or impulsive loads [8, 11, 12].

Even porous silicon was applied with good results

[13]. Mechanical properties of PECVD-hydrogenated

amorphous silicon carbide were widely investigated

[14], also analysing composition and stoichiometry

of deposited films [15]. Moreover, with a suitable set

of process parameters, further desirable characteris-

tics can be achieved: resistance to wet etchants, high

resistivity and conformal coating capability [16].

The common feature of all the above mentioned

devices is that they are based on the use of piezore-

sistors connected as a Wheatstone bridge. For exam-

ple, in Ref. [17] an H-shaped piezoresistive strain

gauge is designed as a blood pressure measurement

device and is connected with three external resistors

in a full-bridge configuration (with one active gauge).

In the study [18], where a multifunctional surgical

tool was developed for epithelial tissue cutting and

characterisation, each strain component caused by

forces during cutting is measured by four piezoresis-

tors arranged in a full Wheatstone bridge configura-

tion (with four active gauges). Many other similar

devices have been developed in the fields of robotics

[3, 4, 19] and diaphragm pressure transducers [2, 13,

20]. This approach does, however, have some limi-

tations, such as large area, many connections to form

the bridge circuit, resistor value mismatches, or high

temperature drift.

Sensor Properties and Structure

In a previous stage of the current research [11], novel

hydrogenated amorphous silicon (a-Si:H) strain sen-

sors were developed and tested. They are deposited

by the PECVD [11, 21, 22] technique and differ from

the others because of the Wheatstone bridge struc-

ture, where a thin hydrogenated amorphous silicon

layer acts as sensitive area. As in a bridge, there are

four electrical terminals: two for voltage supply and

two for output voltage reading, where the resistance

among contacts is due to the distributed conductivity

of the sensitive area, subjected to variation as a strain

is applied.

The sensor described by Kuo et al. [23] consists of

four piezoresistors on a boron-doped silicon layer,

bonded by a commercial adhesive, and arranged in a

full bridge. The detected reading instabilities were

related to the poor stiffness of the adhesive substrate.

The proposed sensor [11] seems to overcome this

weak point and the sensor structure, for the direct

deposition and the integrated semi-conductor active

layer. Static and impulsive bending and torsion tests

showed good sensitivity and linearity, as well as

sensitivity to electro-magnetic fields, comparable

with conventional resistance strain gauges [11].

More detailed tests under four-point bending

moment were performed by Olmi et al. [22], involv-

ing several sensors with different geometries. The

64 � 2008 The Author. Journal compilation � 2008 Blackwell Publishing Ltd j Strain (2009) 45, 63–76

Experimentation and Discussion on Piezoresistive Strain Sensor Performance : G. Olmi

results confirmed the high response linearity

(linearity errors lower than 2%), acceptable hysteresis

and a good repeatability (standard errors between 2%

and 3%). A gain coefficient, formally equivalent to

the resistance strain gauge factor, was also

determined. A statistical approach [analysis of

variance (ANOVA)] was applied to show that the

defined gain factor is independent of the sensor

geometry or dimension and of load intensity, in

other words the sensor is linear. The gain factor is of

the same order of magnitude as the ordinary gauge

factor, implying a comparable sensitivity.

The aim of this paper was to determine the thermal

response of the above-described sensors. All the tests

reported in Refs [11, 22] were performed at room

temperature, so the subsequent step of the research

was oriented to investigation of temperature influence

on output voltage offset. A non-negligible offset had to

be expected, as suggested by temperature sensitivity of

silicon, confirmed by the results in Ref. [13], which

deals with the temperature characterisation procedure

of piezoresisitive porous silicon sensors.

Materials and Methods

Three sensors were deposited on a glass specimen

(Figure 1A,B; 101.5 mm long, 25.5 mm wide, 1.55

mm thick). The specimen material was borosilicate

barium, a type of glass manufactured by Corning

(Corning, NY, USA). The main mechanical charac-

teristics of the material are a Young’s modulus

comparable with that of aluminium alloy and

strength of about 40 MPa.

The sensor active area (Figure 1A) is composed of

a thin n-doped (500 nm thick) hydrogenated

amorphous silicon layer (a-Si:H). From the

mechanical point of view, the elastic modulus

(about 80 GPa, [24]) is of the same order as glass

and aluminium alloy moduli and is much lower

than steel modulus. This aspect, together with the

negligible layer thickness, makes it possible to

exclude any enforcement effect that may affect mea-

surements. The electrical contacts are manufactured

by using a chromium–aluminium–chromium three-

layered surface (layer thicknesses are 15/300/15 nm).

A chromium layer was chosen to reduce aluminium

penetration into the amorphous silicon layer. The

three-layered surface is patterned by photolitho-

graphic process and chemical etching, in order to

form the terminals.

Figure 1C shows all the configurations tested for

each sensor with indication of supply and output

directions and reciprocal orientation with respect to

the principal coordinate system (‘l’ and ‘t’ indicate

longitudinal and transverse directions in the

specimen layout, respectively). The three sensors

are octagonal, square and rhombic shaped. The first

(A)

(C)

(B)

Figure 1: Deposited sensors: structure (A), location on the glass specimen (B) and different electrical/dimensional configurations (C)


G. Olmi : Experimentation and Discussion on Piezoresistive Strain Sensor Performance

one has a sensitive area measuring 4.83 mm2, with

a side dimension of 1 mm. The octagonal sensor

can be fed along 45� directions (cases A and B) or

along vertical or horizontal directions (cases C and

D), while the output direction is always perpen-

dicular. The only difference between configurations

A and B or C and D is due to the inversion between

supply and output directions (the supply direction

for configuration A becomes the output direction

for configuration B and vice versa).

As a result of the statistical variation in the

deposition process (involving for example silicon

thickness, piezoresistive properties, terminals con-

ductivity), a physical dissymmetry may have

occurred in spite of the geometrical symmetry of the

sensors. Consequently, the a priori assumption of a

symmetrical robust (insensitive to symmetric layout

changes with respect to load direction) behaviour,

only on the basis of geometrical symmetry, did not

seem to be a rigorous approach. Symmetrical behav-

iour in static conditions at room temperature, as

shown by Olmi et al. [22], did not necessarily imply a

similar performance under temperature variation. By

considering symmetric configurations as different

ones, a sensitivity analysis could also be performed to

verify whether local physical variations (in symmet-

ric conditions) may have an influence on tempera-

ture response, or whether different responses were to

be expected only for different geometries.

The second sensor is square and its dimensions are

much shorter. In this case, the sensitive area mea-

sures only 0.09 mm2, while its side is 0.3 mm long.

Supply and output directions are ±45� inclined cor-

responding to configurations E and F. Finally, the

third rhomboid sensor has the same dimensional

characteristics as the square sensor, but in this case

voltage can be supplied only along horizontal

(configuration G) and vertical (configuration H)

directions (while the output signal is acquired along

vertical and horizontal directions). The octagonal

sensor has a significantly larger sensing area than the

other sensors, but is extremely flexible: four different

configurations are available with the possibility of

voltage supply along horizontal, vertical or ±45�inclined directions.

Previous studies and experimentations led to the

conclusion that output voltage depends on the

reciprocal orientation between the supply direction

and the maximum principal strain direction. Sensor

response is negligible (theoretically zero) when the

two directions are parallel or perpendicular

(configurations C, D, G, H), while it is maximum

(absolute value) when the reciprocal inclination is

±45� (configurations A, B, E, F) [11, 22].

As a result of the high value of the distributed

resistance of the sensitive area (7.5 kW), the power

required for sensor supply is very low (150 lV).

Feeding can be provided in current or voltage: in the

present case, a power supply of 2.5 V was applied.

Each sensor is formally equivalent to a Wheat-

stone bridge with equivalent strain gauges located

on each edge (or ideal line) connecting terminals

and with the same supply and output directions

(Figure 2). For configurations A, B, E, F, voltage

outputs were found to be proportional to a

combination of strains measured on the glass

specimen. As shown in Figure 2, this strain

combination corresponds to the measurements

recorded by the ideal strain gauges, combined in a

full bridge. The following equation, typically used

for Wheatstone bridges, can also be applied to

piezoresistive sensors, regarding the term k, as a

gain factor, replacing the strain gauge factor.

De and e0 indicate sensor output and supply voltage

(2.5 V), respectively. �l and �t are related to longitu-

dinal and transverse strains (Figures 1, 2), respec-

Figure 2: The analogy between piezoresistive sensors and strain gage full Wheatstone bridge



tively, and m to Poisson’s ratio of the glass specimen.

Olmi et al. [22] directly measured strain and Poisson’s

ratio values by using electrical strain gauges.

De

e0¼ 1

4k � 2el � 2etð Þ ¼ 1

2k � 1þ mð Þel , k ¼ De

e0� 2

1þ mð Þel

(1)

Experimental tests were performed in a controlled

temperature environment (Figure 3A). During each

test, temperature was varied according to a ramp law

both in the heating and in the cooling phases. Total

thermal gap between the initial minimum value and

maximum value was about 10–15 �C. Experimenta-

tions were performed on the eight sensor configura-

tions in no-load and in load conditions.

For the application of four-point bending load, the

same device described by Olmi et al. [22] was used. As

shown in Figure 3B, the specimen is clamped at its

borders (fixed by a couple of screws acting on a rubber

cover). A 2F force is centrally applied by a calibrated

mass and transmitted by a Kevlar wire, so that each

pinch is symmetrically loaded by a force F and is free to

rotate around its hinge. The bending moment acting

on the whole length of the specimen has a constant

distribution. The pinch [22] required a careful design.

In the present study, in order to evaluate the thermal

effect without loading, a few tests were performed

under the no-load condition, so it was essential that

the pinch’s own weight did not contribute to moment

distribution on the specimen. Each pinch was

designed so that the centre of gravity was vertically

aligned with the hinge hole, which implies that the

pinch’s own load is completely balanced by the hinge

reaction. The position of the centre of gravity can be

regulated in a small range by changing the position of

two nuts coupled to a threaded bar.

The load level was chosen so that a sufficiently

high strain was induced on the glass specimen and

transmitted to deposited sensors. A deposition on

glass was also performed in [10] and a similar testing

device for four-point bending moment was adopted:

the glass substrate was strained up to the value of

200 l�. This strain range is lower than that of some

commercial gauges, but encompasses the full range

which is usually important for MEMS applications,

mainly in biomechanics, that motivated the devel-

opment of the described sensors and of many other

piezoresistors.

For this reason, the value of 230 l� for maximum

principal strain (corresponding to 2F = 9.81 N, 1 kg

mass applied to Kevlar wire) was considered suitable

for tests in the loaded condition. In order to evaluate

measurement repeatability and to improve the sta-

tistical evidence, three replications were adopted.

Test Details

The measurement system (Figure 3A) required quite

long connections between the sensor under test and

the acquisition device. For simultaneous acquisi-

tions of temperature and sensor outputs, a T ther-

mocouple and the Scout55 (Hottinger Baldwin

Messtechnik, Darmstadt, Germany) were employed,

respectively. Analogic outputs from both devices

were interfaced to a SCB-68 platform, while the

DAQ card NI 6062E (National Instruments, Mopac

Expwy, Austin, TX, USA) was used for the laptop

connection. All the phases of data acquisition and

storing in memory were supervised by a LabView

(National Instruments) program personalised for

this application.

All the tests in static conditions were performed

with short connections and at constant room

temperature [11, 22]. After the repetition of some

of the previous tests, in order to check results

repeatability, additional tests were planned to

investigate the effects of cable length. A flat cable

(the same later used for tests under temperature

variation) of 3 m length and 0.5 W resistance was

used to connect the four terminals to the acquisi-

tion device. Tests were performed at constant room

temperature in static conditions at four different

load levels (more details below) both for increasing

and decreasing forces.

A force 2F was applied, by using the device in Fig-

ure 3B, so that the specimen was loaded in pure

bending condition (2F = 4.91 N, 9.81 N, 14.71 N,

19.61 N). The force was initially applied at its lowest

level and then statically increased up to the maxi-

mum. At each step the sensor output was measured

and an estimation of the gain factor was provided

according to Equation (1). The same procedure was

followed as the load was decreased to zero, and all

measurements were repeated three times. The

described tests involved all sensor configurations

with significant outputs (A, B, E, F). The results are

shown in the following diagrams (Figure 4),

comparing responses with short and long

connections. They show the ratio between output

and supply voltage versus the term 2(1 + m)�l.

Experimental results for all configurations in both

settings are very well interpolated by linear regres-

sion lines (R is the linear correlation coefficient,

varying in the range )1 to +1, where )1 and +1

values indicate perfect linearity, while the 0 value

refers to a completely scattered nonlinear distribu-

tion: consequently R2 varies from 0 to 1). Moreover,

linearity errors vary from 3% to 6% for all configu-

rations.



A constant gain factor is not a strict require-

ment (some semi-conductor gauges may be

nonlinear). However, a constant gain is surely a

preferable feature, as the nonlinearity needs a

calibration curve. In the present study the linear

trend of diagrams in Figure 4 (see also the static

(A)

(B)

Figure 3: Measuring chain for tests under temperature variation (A) and four-point bending loading configuration (B)



analysis in Ref. [22]) confirms a linear response of

sensors.

Olmi et al. [22] applied ANOVA to verify that sen-

sor static response was not influenced by geometric

or electrical configuration and by load intensity,

and in this study the same tool has shown the

same property as regards cable length. For each

configuration, ANOVA were applied (95% confidence

level), in order to compare the outputs at any load

level. Mean values of the outputs are summarised

in Figure 5, with the indication of the error bands.

The analysis confirmed that responses are quite

close (greatest differences for the highest load val-

ues in the cases of configurations A and F) and that

the cable length is generally not significant.

Temperature Effect

The procedure followed during each test can be so

summarised: first, the sensor selected for the test was

connected to the acquisition device and the related

circuit was balanced. Load was then applied, when

required. Finally, data acquisition on two channels

was started by the LabView command panel, as the

temperature was gradually increased according to a

ramp law. The cooling phase then took place in air,

and data acquisition was stopped only when initial

conditions were established again. Some of the

results (related to each configuration, with and

without load) are shown in Figures 6–8. Diagrams

show the thermal offset (expressed in mV and

Figure 4: The influence of connections length on the static responses of configurations A, B, E, F

Figure 5: Outputs for long and short connections at different load levels



Figure 6: Temperature response of configurations A, B C, D (octagonal shape)



normalised with respect to a supply voltage of 2.5 V)

versus the temperature variation from its initial

value. Each test took about 40 min.

The good linearity of sensor output versus tem-

perature variation is well confirmed by the high

value of R2, whose mean value is about 0.95, with

peaks up to 0.98. The linearity error was calculated

with respect to the maximum value of each trial.

These results are shown in Figure 9A, with reference

to mean values over the whole acquisition and to

maximum nonlinearity effects. This diagram shows

mean and maximum errors for each configuration

with and without load. It can be observed that

mean errors are always lower than 6%. Maximum

errors were observed at the highest values of tem-

perature, without any relationship with the appli-

cation of the load. The two highest values slightly

exceed 20% and were determined for configuration

G with load and configuration F without load. By

observing the diagrams in Figures 6–8, it can be

argued that such errors are strongly related to

hysteresis effects: for the same temperature varia-

tion the sensor response is different in the cases of

increasing and decreasing temperature. It was noted

that in the cooling phase the temperature offset is

higher than that in the heating phase. The only

exception was detected for the square-shaped sen-

sor in configuration E.

For this reason the hysteresis effect was also

investigated, emphasising the relationship with the

linearity properties. In order to determine a hysteresis

parameter for each of the 16 cases, the difference

between responses, in the heating and in the cooling

phases, was calculated for several values of tempera-

ture variation, with steps of 0.5 �C. All the difference

values were then normalised with respect to the

maximum output measured during each trial and a

mean value was calculated. On the basis of the his-

togram in Figure 9B it can be observed that this

parameter has a mean value of about 11%. The

maximum value corresponds to the maximum value

of the linearity error previously detected.

It can be observed that the modulus d

[mV (V �C))1] of the slope of the regression

lines (reported in dashed line in the diagrams of

Figures 6–8) has the physical meaning of thermal

offset per unit of temperature variation. This term

expresses the sensitivity of each configuration with

respect to temperature variations. The results are

shown in Table 1 and in Figure 10A.

Figure 7: Temperature response of configurations E and F (square shape)



The values of the parameter d are arranged in a

factorial plan (Table 1) with two factors: the config-

uration and the applied load. The first factor has

eight levels (eight different configurations), while the

second one has two levels (with or without load). The

three values for each case are the yields of the three

replications.

Result repeatability was checked by calculating the

standard error as a ratio between the standard devi-

ation and the mean value of d for each case. These

values, for any configuration and at any load level,

are shown in Figure 10B. It can be noted that the

values are all close to 4%. Only in one case (config-

uration E) was result repeatability worse than

expected: the gap between one of the values and the

other two led to a high value of the standard error, up

to 20%. In any case, the sensitivity of the square

sensor (configurations E and F) to temperature vari-

ations proved to be very low, so, despite a high rela-

tive error, the absolute differences between results

appeared to be acceptable.

The following question to be investigated con-

cerned the influence of sensor configuration and of

load level on temperature response, with reference to

the parameter d. It can be argued that the slope of

distributions and regression lines is the same with

and without external load, although it is different for

different configurations (Figures 6–8). This is con-

firmed by the histogram in Figure 10A, showing the

values of d for all configurations with and without

load.

A two-factor ANOVA [25] led to the conclusion (with

the 95% confidence level) that no significant differ-

ences are due to the load (conventionally, the ‘row

factor’) level. Nevertheless, differences because of the

configuration (the ‘column factor’) are significant.

The result is that each configuration has a different

thermal sensitivity, but the temperature response is

not influenced by the loading condition.

The last question to be addressed regarded the

comparison between responses of symmetric con-

figurations (configuration A versus conf. B; conf. C

versus conf. D; conf. E versus conf. F; conf. G versus

conf. H). In order to fulfil this requirement, the

ANOVA was completed by the decomposition of the

sum of squares between columns (SSBC), i.e. the sum

of squares representing the variance among different

configurations. The technique of the orthonormal

Figure 8: Temperature response of configurations G and H (rhombic shape)



decomposition [25] was applied and the final result

is shown in Figure 10C. The entire SSBC was split

into five components: four of them related to the

differences in responses between the symmetric

configurations, while the fifth one, named ‘residual’

accounted for all other differences among non-

symmetric (i.e. with a different geometry) configu-

rations. The pie chart clearly indicates that the

residual term is much higher than the others (about

95% versus 5%), meaning that the variance among

configurations is substantially due to macroscopic

differences in sensor geometry or supply direction

(horizontal/vertical or ±45� inclined). Symmetric

configurations (in particular A versus B, C versus D

and G versus H) do not have exactly the same

response, but the differences are of little signifi-

cance; non-significant differences are detected

between configurations E and F.

A similar experimental campaign was performed by

Pramanik et al. [13], with the aim of investigating the

thermal offset of a piezoresistive porous silicon pres-

sure sensor. Responses at different load (pressure)

levels proved to be slightly nonlinear, even if the

quadratic term appears to be almost negligible with

respect to the linear term. Assuming a linear

response, the mean value of voltage offset because of

temperature variation is about 0.15 mV �C)1. This

value can be compared with the results obtained in

Table 1: Parameter d [mV (V �C))1] for each of the tested configurations with and without load

Load

Configurations

Octagonal Square Rhombic

Cfg. A Cfg. B Cfg. C Cfg. D Cfg. E Cfg. F Cfg. F Cfg. H

Without load 0.0274 0.0358 0.0651 0.0804 0.0077 0.0052 0.0760 0.0960

0.0275 0.0359 0.0634 0.0754 0.0064 0.0054 0.0699 0.0930

0.0273 0.0366 0.0633 0.0793 0.0064 0.0060 0.0739 0.0899

With load 0.0272 0.0346 0.0631 0.0766 0.0078 0.0048 0.0675 0.0934

0.0272 0.0352 0.0609 0.0804 0.0088 0.0054 0.0682 0.0965

0.0260 0.0351 0.0639 0.0827 0.0059 0.0048 0.0683 0.0956

(A)

(B)

Figure 9: Linearity errors (A) and hysteresis effects (B) versus configurations



this study, considering the fixed value of supply

voltage, 2.5 V. Mean values of offsets are in the

range from 0.013 (configuration F) to 0.24 (configu-

ration H) mV �C)1, while the grand mean value, 0.12

mV �C)1, is of the same order and a little lower than

the result for porous silicon. Moreover, it is interest-

ing to observe that in Ref. [13] also offsets with close

values were observed even at very different load

(pressure) levels.

Conclusions

The main aim of this study was to investigate the

temperature response of novel piezoresistive sensors.

The performance of such miniaturised size devices had

been the subject of previous studies, regarding the

response under static bending and torsion loads [11,

22]. The main points can be summarised as follows.

• The sensors were deposited on a glass specimen, by

a chemical deposition procedure, which can also be

applied to metallic materials. The main features of

such sensors are their Wheatstone bridge structure,

small dimensions (about 0.1 mm), direct deposi-

tion on material surface (no adhesive substrates

required) and very low power consumption

(150 lW). On the basis of these characteristics,

interesting applications are possible, mainly in the

robotics and biomechanics fields.

• In a preliminary stage of tests, the possible influ-

ence of cable connections on sensor response at

(A)

(B)

(C)

Figure 10: Sensitivity to temperature variation (A), standard errors versus configurations (B) and orthonormal decomposition of

the SSBC (C)



constant room temperature was investigated. Sta-

tistical tests were applied to show that any influ-

ence can be excluded at the 95% confidence level

and that differences between sensor outputs un-

der different experimental settings, with short and

long connections, are negligible.

• The experimental campaign for temperature

response investigation was performed in a variable

(ramp law of about 10–15 �C) temperature

environment. Different sensor geometries

(octagonal, square and rhombic) with different

supply and output voltage directions were

investigated.

• The results emphasised a quite linear trend of the

thermal offset versus the temperature variation

during the test. The results were interpolated by

regression lines with high values of R2 (mean

value of about 0.95, with peaks of 0.98). The good

linearity is also confirmed by the low value of the

mean linearity error, close to 4%.

• The linearity error has its maximum values at the

highest temperature values. The tests emphasised

that such errors can be related to hysteresis effects,

more evident for some configurations. Hysteresis

(normalised to the maximum measurement of

each test) has a mean value of 11% and is

responsible for the observed nonlinearity effects.

• Results repeatability over the three replications is

very good. Low values of standard deviations and

errors were determined, and errors were generally

of few percentage points.

• ANOVA was performed on the sensitivity to

temperature variation d. At the 95% confidence

level it was shown that temperature response is

not influenced by the load level, but is different

for different configurations.

• A more detailed analysis was performed, by

splitting the SSBC into five components. It was

shown that symmetry between configurations

does not lead exactly to the same response, but

that differences are very small. Such a result

suggests that temperature behaviour is substan-

tially related to the geometry of the area crossed

by the current and is not sensitive to possible local

variations of physical properties.

• Numerical values of thermal offsets for all

configurations appear to be consistent with

previous research.

ACKNOWLEDGEMENTS

The author wishes to thank Prof. M. Lanzoni and

Prof. A. Freddi for their contributions in sensor manu-

facturing and in the discussion of experimental results.

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Documents

Investigation on the Influence of Temperature Variation on the Response of Miniaturised Piezoresistive Sensors