Influence of temperature and pressure on the static contact resistance of vacuum heat-treated...

In¯uence of temperature and pressure on the static contactresistance of vacuum heat-treated polyacrylonitrile ®lms

Sylvie Guessab*, Lionel Boyer, FreÂdeÂric HouzeÂ, Sophie NoeÈl, Olivier SchneegansLaboratoire de GeÂnie EÂ lectrique de Paris, UMR CNRS 8507, UniversiteÂs Paris VI et XI, SupeÂlec,

Plateau de Moulon, F91192 Gif-sur-Yvette Cedex, France

Received 23 February 2000; accepted 28 July 2000

Abstract

The protection against corrosion of low-level electrical contacts is usually insured by metallic terminal coatings. However, they can be

degraded by wear and corrosion, which ®nally causes the failure of the contacts. The ®eld we have been investigating, consists of replacing

the terminal metallic layer by an organic conducting ®lm, derived from polyacrylonitrile (PAN) by heat-treatment. In this paper, we present

results concerning the static contact resistance (Rc) measured in a ball/plane con®guration on metallic coupons over-layered with PAN ®lms

and heated under high vacuum at several temperatures: Rc at room temperature under a constant normal load; Rc at room temperature

varying the normal load; Rc at a constant normal load varying the temperature of the contact. These experiments reveal a transitional heat-

treating temperature. Above this temperature, the ®lm is very conducting and the behavior of the contact is ruled by the metallic electrodes.

Below this temperature, the ®lm is moderately conducting and then responsible for the contact resistance. In that case, pressure and

temperature dependencies of the contact show that variable-range hopping is the most probable transport mechanism. At the transitional

annealing temperature, the values of the contact resistance are scattered. Electrical investigations with a modi®ed atomic force microscope

(AFM) show that the ®lm is covered by a very thin layer, non-adherent and poorly conducting. # 2001 Elsevier Science B.V. All rights

reserved.

Keywords: Electrical contact resistance; Polyacrylonitrile; Heat-treatment; Piezoconductivity; Variable-range hopping; Atomic force microscopy

1. Introduction

We have been exploring for several years, an original way

for the improvement of the performances and the reliability

of low-level electrical contacts: the use of solid organic ®lms

as a substitute for terminal metallic coatings. Our researches

are focused on ®lms derived from polyacrylonitrile (PAN)

by annealing, that offer some decisive advantages:

� PAN can be grafted on metallic surfaces by electroche-

mical deposition, which allows to make very adherent and

covering films;

� though it is initially strongly insulating, it can be made

conducting by annealing.

Our process consists of depositing ®lms of PAN on

metallic substrates. After heat-treatment of the samples,

electrical properties are systematically evaluated, using a

speci®c device: the contact resistance Rc in a ball/plane

con®guration is measured, as a function of controlled para-

meters, such as the normal load (L) between the ball and the

plane, or the temperature of the contact (Tcont). Since the

beginning of our investigations on the potentialities of PAN-

derivative ®lms for a contact application, we have been

testing different con®gurations of samples, varying the

substrate, the thickness of the PAN layer, the modes of

deposition and heat-treatment. Our ®rst objective was to

elaborate samples in accordance with industrial require-

ments. Confronted with inexplicable results attributed to

the roughness of the substrate, we changed the orientation of

our study to make reproducible, perfectly de®ned and con-

trolled samples. Promising results extracted from previous

series of samples have already been presented [1±3].

This paper is concerning this last series of samples. We

®rst describe how they have been elaborated, then we

develop original electrical results, attesting for the transfor-

mation of the PAN ®lms induced by heat-treatment:

� Rc measured at room temperature under a constant normal

load;

Synthetic Metals 118 (2001) 121±132

* Corresponding author. Tel.: �33-1-69-85-14-09;

fax: �33-1-69-85-14-29.

E-mail address: [email protected] (S. Guessab).

0379-6779/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 9 - 6 7 7 9 ( 0 0 ) 0 0 4 0 0 - 8

� the evolution of Rc when the normal load L is varied from

4 to 100 gf (loading), then from 100 to 4 gf (unloading);

� the evolution of Rc when Tcont is varied from 100 to

ÿ1008C.

As an intermediate heat-treating temperature revealed

results dif®cult to analyze, we describe in the following

further investigations we achieved on the concerned sample,

using an original laboratory-made device, derived from an

AFM, which can achieve simultaneous cartographies of both

topography and local electrical contact resistance [4±5]. We

summarize our results, discuss them and conclude in the last

part of the paper.

2. Samples preparation

We have selected the substrate, considering it, ®rstly, to be

metallic to allow electrical measurements, secondly, to

present a very low roughness, and lastly, to form with

PAN ®lms an interface resisting to intense heat-treatments.

The chosen substrate consists of hard steel coupons

20 mm� 10 mm� 1 mm, carefully polished, with an

over-layer of 2 mm of nickel deposited by RF magnetron

sputtering. Some characteristics of the as received steel are

shown in Table 1. The conditions of deposition of nickel are

given in Table 2. The PAN ®lm is deposited by spin-coating.

Its thickness (1 mm) has been chosen to be more than 10

times greater than the maximum peak-valley height on the

substrate, and is systematically controlled by pro®lometry

measurements. The roughness and the morphology of the

surfaces are examined by atomic force microscopy (AFM) at

every stage of the elaboration.

The mode of heat-treatment was chosen intense enough to

perform signi®cant transformation of thick PAN ®lms. Thus,

the samples were pyrolyzed in a tubular furnace in high

vacuum (10ÿ6 Torr). The temperature was raised from the

ambient temperature up to a maximum (Tmax) at the rate of

28C minÿ1, and then quickly decreased to room temperature.

We have realized several heat-treatments, at Tmax � 550,

600, 650, 7008C. The electrical results we present in this

paper, revealed a crucial transition between 550 and 6008C.

Consequently, an intermediate annealing has been per-

formed at Tmax � 5758C.

Pro®lometry measurements show that our ®lms get nota-

bly thinner after the heat-treatment: the thickness, which

was initially 1 mm, falls down to 150 nm, whatever the value

of Tmax between 550 and 7008C. We propose three elements

of explanation:

� the loss of matter in the organic film caused by degassing,

already detected by other authors during PAN heat-treat-

ments [6];

� the reticulation of the film, that we have observed for

previous series of samples [7];

� inter-diffusion phenomena, that we have pointed out using

XPS surface analysis [8].

3. Experimental setup for contact resistancemeasurements

3.1. Principle

The dedicated device for the contact resistance measure-

ments has been described in detail in a previous paper [1]. It

is schematically represented in Fig. 1. The principle consists

of simulating the complex geometry of a contact of con-

nector by the idealized sphere/plane con®guration, which is

both representative of reality and is controllable. The plane

is one of the samples we describe above. The sphere is a

3.2 mm diameter copper±beryllium ball, over-layered with

2 mm of galvanic nickel and a 2 mm galvanic cobalt-doped

gold terminal coating. The dome is carefully polished in

order to minimize the effect of roughness. The sphere is

®xed in a `̀ ball holder'' preventing it from rolling. The

electrical study of these sphere/plane contacts is performed

in the static mode, allowing no lateral movement. For that,

the ball holder and the sample are clamped to elastic

diaphragms. We vary the normal load between the ball

and the plane using a stepping motor, and measure it with

a displacement capacitive sensor, via the spring constant of

the diaphragms (a preliminary calibration allows to convert

the measurement of the vertical displacement into the value

of the normal force).

Table 1

Some characteristics of the as received steel

Chemical composition (% in mass) C: 0.75; Si: 0.2; Mn: 0.5; Cr: �0.5; Fe: remainder

Tensile strength (MPa) 1420±1520

Heat-treatment Slow increase of the temperature up to 6508C, then heating at 8108C and quenching

Surface state Polished

Table 2

Conditions of deposition of nickel films, 2 mm thick on hard steel coupons

Deposition method RF magnetron sputtering

Substrate Polished hard steel coupons

Substrate temperature Cooled by a circulation of water

Substrate-to-target distance 8 cm

Target High-purity nickel (99.999%), diameter 6 in.

Residual pressure <3 � 10ÿ6 Torr

Sputtering gas Argon

RF power 300 W

Sputtering pressure 60 mTorr

Deposition time 25 min

122 S. Guessab et al. / Synthetic Metals 118 (2001) 121±132

The elements of the contact are connected to the electrical

setup following the four-wires method. The electrical circuit

mainly involves a Keithley 228A dc voltage/current source,

a Keithley 617 electrometer and a Keithley 182 digital

voltmeter, all controlled over the IEEE-488 bus. As very

low values of voltage or current are easier to measure than to

impose and control, current measurements are preferred

when Rc > 1 O (imposed voltage: 100 mV), whereas vol-

tage measurements are chosen in the opposite case (imposed

current: 10 mA).

3.2. Temperature control

A part of the control system which allows to regulate the

temperature from 100 to ÿ1008C is represented in Fig. 2.

The experimental setup is enclosed in a perspex box. The

sample support is encircled by a ¯ow of cooling gaseous

nitrogen terminally ejected towards the contact. Cool nitro-

gen production is achieved by an electrical resistance

plunged in a carboy of liquid nitrogen. The manual mod-

ulation of the dissipated power allows to vary the ¯ow of

cool evaporated gas. An electrical resistor supplies heat to

the sample support and is automatically commanded so that

the measurement provided by the temperature probe above

the sample support should equalize the demanded tempera-

ture. Beforehand, we gauged the system to make sure the

probe provided the real temperature of the contact (Tcont),

measured with a thermocouple inserted between the ball and

the sample. The software procedure for applying the normal

load was modi®ed in order to compensate the dilatation or

contraction of mechanical elements induced by the tem-

perature variations.

4. Results of the electrical measurements

4.1. Theoretical considerations

4.1.1. Contact between a sphere of material 1 and a plane

of material 2

In the general case, we consider a contact between a

sphere made of material 1 and a plane made of material 2, as

well as the following data:

r1,2 electrical resistivities (independent of pressure)

E1,2 Young's moduli

n1,2 Poisson's coefficients

R radius of the sphere

L normal load between the sphere and the plane

a radius of the contact area

The analytical expression for the contact resistance Rc can

be deduced from Hertz's and Holm's laws [9,10]. The

Holm's law [9] gives Rc (constriction resistance) as a func-

tion of a, r1 and r2.

Rc � Rconstriction � r1 � r2

4a(1)

The Hertz's law [10] provides a relation between a and L.

a�L� � 3RL

4E�

� �1=3

; with E� � 1ÿ n21

E1

� 1ÿ n22

E2

� �ÿ1

(2)

The expression for Rc then becomes

Rc�L� � r1 � r2

4

4E�

3RL

� �1=3

� K1Lÿ1=3 (3)

4.1.2. Presence of an interfacial layer between the sphere

and the plane

We now consider that there is an interfacial layer made of

material 3 (resistivity r3, thickness e) between the sphere

and the plane. In a ®rst approximation, we neglect the

interfacial effects (Schottky effect), which means that the

contact is ohmic (this is veri®ed experimentally by

plotting voltage versus current curves), and we consider

that the current lines are perpendicular to the plane. When

r3 and e are not pressure dependent, the expression for Rc

becomes

Rc � Rconstriction � Rfilm � r1 � r2

4a� r3e

pa2(4)

Fig. 1. Scheme of the setup for contact resistance measurement.

Fig. 2. Part of the temperature control system.

S. Guessab et al. / Synthetic Metals 118 (2001) 121±132 123

We have validated the formulation (4) for a normal load of

50 gf, using a finite elements modelization based on

MATLAB software [8]. We develop two extreme cases.

� If Rfilm ! Rconstriction, then we can refer to the Eqs. (1) and

(3) to express Rc.

� If Rfilm @ Rconstriction, then

Rc � r3e

pa2(5)

In this case, the next step consists of expressing Rc as a

function of L. Using Eq. (2) we obtain

Rc�L� � r3e

p4E�

3RL

� �2=3

� K2Lÿ2=3 (6)

When 1/r3 and e are linearly pressure dependent, it is shown

in the Appendix A that Rc may be expressed by

Rc � 1

AL� BL2=3(7)

where B � Kÿ12 and AL represents the effect of the pressure

on r3 and e.

4.1.3. Our case

In our case, we have several interfacial layers: three of

them are metallic, made out of nickel and gold, and one is

organic, derived from PAN. Calculations show that R®lm due

to the thin intermediate layers of nickel and gold is negli-

gible as compared to Rconstriction. Therefore, we just consider

a contact between a plane of steel and a sphere of copper±

beryllium, with an interfacial layer derived from PAN.

4.2. Contact resistance Rc measured at room temperature,

under a 50 gf normal load

The contact resistance has been measured at room tem-

perature (Tcont � 25�C), under a normal load of 50 gf

between the ball and the plane. For each sample, we have

performed 10 measurements, in 10 different points of con-

tact.

The results (minimal, maximal and average values) are

gathered in Table 3 and Fig. 3, as a function of the heat-

treating temperature. We note that the raw sample (Table 3)

presents very large resistance (>109 O), exceeding the lim-

itations of our experimental setup: the ®lm of PAN is

strongly insulating. Rc declines drastically when the inten-

sity of the heat-treatment increases, falling down to a few

mO for Tmax beyond 6008C. The samples heated at 600, 650

and 7008C show approximately the same minimal, maximal

and average values of Rc, which are of the order of magni-

tude of Rc measured on metallic coupons (constriction

resistance). We note that the sample heated at 5758C shows

values of Rc scattered on more than three decades (from 0.06

to 100 O).

4.3. Evolution of Rc as a function of the normal load (L)

A cycle of measurement of the contact resistance Rc as a

function of the normal load L consists of varying L from 4 to

100 gf (loading), then from 100 to 4 gf (unloading). Rc is

measured every 2 gf. For each sample, three points at least

have been tested. For each point, we have performed three

successive loading±unloading cycles.

Our main results are summarized hereafter.

1. The samples heated between 600 and 7008C, all present

a similar behavior, whatever the point and the rank of the

cycle. An example is shown in Fig. 4. The curves are

reversible, denoting that the contact is elastic. log Rc is a

linear function of log L. The slopes calculated by linear

®tting vary between ÿ0.29 and ÿ0.38, around the slope of

Table 3

Contact resistance (minimal, average and maximal values out of 10

measurements)a

Heat-treatment

Tmax (8C)

Rc min Rc ave Rc max

Raw >1GO >1GO >1GO550 1300O 2160O 3450O575 60mO 10O 100O600 3.3 mO 3.8 mO 4.2 mO650 3.1 mO 3.3 mO 3.9 mO700 3.1 mO 3.3 mO 4mO

a Measurements carried out at 258C under a normal load of 50 gf.

Fig. 3. Contact resistance (scattering and average values out of 10

measurements) measured at 258C under a normal load of 50 gf.

Fig. 4. Evolution of Rc as a function of L for a sample heated beyond

6008C.


ÿ1/3 predicted by the Eq. (3) supposed to be constant when

L varies. In that case, R®lm related to the ®lm derived from

PAN is negligible compared to Rconstriction so that Rc �Rconstricion.

2. For the sample heated at 5508C, the evolution of Rc as a

function of L is also rather reproducible, whatever the point

and the rank of the cycle. An example is shown in Fig. 5, on a

linear±linear graph. The dots representing the experimental

values for a loading±unloading cycle attest that the behavior

of the contact is reversible and then elastic. In this case,

Rconstriction (several mO) is negligible compared to Rc

(>1000 O) so that Rc � Rfilm. We have also represented

the ®ttings with two functions corresponding to the

Eqs. (6) and (7). For each function, the plotting software

we used (Microcal Origin 4.0) calculates the parameters (A,

B) to minimize w2 expressed underneath:

w2 � 1

N ÿ p

XN

i�1

oi� f �Li� ÿ y�Li��2 (8)

where N is the total number of experimental points used in

the fitting, p the total number of adjustable parameters

(p � 1 or 2 in our case), f(Li) the value of the fitting function

for the normal load Li, y(Li) the experimental value, oi

represents the weight of each experimental point. Four

different weighting methods are supported by Origin. The

values of Rc cover three decades. Therefore, we have chosen

the statistical method with oi � 1=y�Li�.We observe ®rst that the ®t obtained with the Eq. (6) is

bad. In contrast, a very good ®tting is obtained with the

Eq. (7) which takes into account the in¯uence of the pressure

on the conductivity and thickness of the ®lm.

As it is shown in the Appendix A, the parameter B

provided by the ®tting is linked to other data,

B � pk2

1002=3e0r0

(9)

with e0 � 150 nm, k � �3R=4E��1/3 and when L is in gf. We

then deduced that r0 � 70 O m. This value is intermediate

between the order of magnitude for the resistivity of raw

PAN (1016 O m) and the best performance mentioned in the

literature for heat-treated PAN (10ÿ5 O m).

In the same manner, the parameters a and b de®ned in the

Appendix A are linked to A and B by the relation

a� b � A

Bpk2 (10)

Replacing in Eq. (10), A and B by the values given by the

fitting gives a� b � 6:5� 109 Paÿ1. The maximum value

of the pressure for L � 1 N is Pmax � 0:75 GPa. Thus, we

have �a� b�Pmax� 4:9. Since physically aPmax

< 1, we

deduce that the relative increase of the conductivity due

to the pressure is very large (�5) when L � 1 N. Increases of

the conductivity of the same order of magnitude have

already been observed for poly(3-alkylthiophenes) films

subjected to an hydrostatic pressure of 0.5 GPa [11] and

for polypyrrole subjected to 1 GPa [12].

3. The intermediate sample heated at 5758C presents non-

reproducible and irregular curves that cannot be described

by any analytical model.

4.4. Evolution of Rc as a function of the temperature of the

contact (Tcont)

We have observed for three samples, the evolution of Rc

under a constant normal load (50 gf) when Tcont is varied

from 100 to ÿ1008C. The ®rst sample has been chosen

among those heated at Tmax � 6008C. The second sample is

the one heated at 5508C. The last sample corresponds to the

intermediate heat-treatment, Tmax � 5758C.

1. The experimental results obtained in the ®rst case are

represented by the dots and ®tted by the line in Fig. 6.

Despite ¯uctuations, Rc can be considered as a linear

increasing function of Tcont. This is coherent with the

Eq. (1): if we neglect the variation of a when Tcont varies,

Rc varies like r1 and r2, which are linear increasing func-

tions of the temperature, in the considered interval.

2. The results related to the 5508C sample are represented

by the dots in Fig. 7. Rc is a decreasing function of Tcont. This

could be predicted by the Eq. (7), which can be written as

Rc � e0r0

�a� b�L� pk2L2=3(70)

Here L is constant and if e0, a, b and k are not temperature

dependent and Rc varies like r0 (resistivity at atmospheric

pressure). Medium heat-treated PAN is a semiconductor

Fig. 5. Evolution of Rc as a function of L for a sample heated at 5508C.

Fig. 6. Evolution of Rc as a function of Tcont for a sample heated beyond

6008C.


[13], and thus, r0 is a decreasing function of the temperature.

We have tested three fitting equations that might describe the

evolution of Rc. Each of them is associated with a mode of

electrical conduction that has already been mentioned for

films derived from PAN [6,14±16]. The generic formula Ð

with T in Kelvin Ð is

Rc � R1 expT

T0

� �ÿn� �(11)

For n � 0:25, the Eq. (11) is the Mott's law describing the

variable-range hopping conduction in three-dimensions

[17]. For n � 0:5, it corresponds to a structure with con-

ducting clusters scattered in an insulating matrix [18]. For

n � 1, it is associated with thermally activated conduction in

ordered semiconductors.

The mode of ®tting is the same as previously described.

The values of w2 as a function of n are given in Table 4. It

appears that the thermally activated conduction in ordered

semiconductors has to be rejected. As a matter of fact, the

heat-treatment induces an inhomogeneous transformation in

the volume of the PAN ®lm, associated with inter-diffusion

phenomena. This probably leads to an amorphous structure.

The equations associated with n � 0:25 and n � 0:5 both

might be suitable, the Mott's law being the most adequate.

The corresponding ®tting curve is represented in Fig. 7. The

values we found for R1 and T0 (R1 � 1:7� 10ÿ6 O and

T0 � 4:8� 107 K) are coherent with those of the literature

[6,17].

3. The intermediate sample heated at 5758C presents non-

reproducible and irregular curves that cannot be described

by any analytical model.

5. Further investigations

The 5758C sample presenting results dif®cult to analyze,

we have studied its surface as well as that of the 6008Csample, with an original laboratory-made extension asso-

ciated with a commercial AFM. We have obtained simulta-

neously, topographical and local contact resistance surface

cartographies of a given area of each sample.

5.1. Experimental device

A schematic view of the laboratory-made system is

sketched in Fig. 8. The left half of the drawing corresponds

to the commercial AFM (Nanoscope1 III, Digital Instru-

ments); the right half sketches our speci®c home-built

extension for electrical measurements. The commercial

tip and cantilever were made of n-doped silicon coated

with p-doped diamond (Nanosensors DCT-FM). Sample

and cantilever holders were carefully insulated from the

Fig. 7. Evolution of Rc as a function of Tcont for a sample heated at 5508C.

Table 4

w2 as a function of n

n w2

0.25 3.2

0.5 5.9

1 19.8

Fig. 8. Schematic principle of the experimental device derived from classical AFM setup.


apparatus frame. When the tip is placed in contact with the

sample, a bias voltage (of typically 1 V) is applied. The x±y

displacement of the piezoelectric block then allows the

sample to be scanned line-by-line by the tip apex, whereas

the applied force is held constant by the z-displacement of

the sample. The resulting current at the input of the con-

version system then re¯ects the local tip/sample contact

resistance (in 102±1011 O range approximately) at each point

where the height datum is acquired. This leads to simulta-

neous cartographies of both the topographical and electrical

features of the studied surface in grey-scaled pictures. All

experiments have been performed at room temperature.

Topographical images are presented in the `̀ illuminate

mode''. For electrical images, the observed contact resis-

Fig. 9. Topographical and electrical images of the samples: (a) heated at 6008C; (b) heated at 5758C.


tance values are very high due to the small tip size and,

therefore, to the small tip/sample contact area.

5.2. Analysis of the 575 and 6008C samples

1. The 575 and 6008C samples were analyzed on an area

of 20 mm� 20 mm. The corresponding electrical and topo-

graphical images are shown in Fig. 9. The distributions of

the electrical resistance measured on each area are repre-

sented in Fig. 10 (the bars on the right are caused by the

saturation of the system of electronic conversion).

For the 6008C sample, the topographical image shows

small craters scattered on the `̀ moon-like'' surface. They

must be traces of the degassing induced by heat-treatment

[6]. As far as the electrical contact resistances are concerned,

the distribution is centered on 7� 107 O. Most of the contact

resistance values are counted between 3� 107 and

3� 108 O. This is associated with dark colors on the elec-

trical image. The surface looks uniformly conducting. We

note that the less conducting zones, generally ring-shaped,

correspond to the craters' ridges in the topographical image.

This correlation might reveal that the less conducting rings

have just a topographical cause: due to the high slope, the

side of the crater might not be scanned by the tip (Fig. 11).

However, we have measured this slope by pro®lometry and

it has proved to be gentle enough to be scanned by the

tip. Thus, the ring shapes in the electrical image do not have

Fig. 10. Distribution of the measured resistance: (a) sample heated at 6008C; (b) sample heated at 5758C.

Fig. 11. Effect of the topographical slope on the scanning of the tip.


a topographical cause. We believe, degassing traces could

present a higher electrical resistivity due to a special

chemical structure.

For the 5758C sample, less traces of degassing are

observed, which is logical since the heat-treatment is less

intense. The 5758C sample appears less conducting than the

6008C one; the values of contact resistance are 10 times

superior. This can be seen in the electrical image as well as in

the distribution of the contact resistance, which is centered

on 7� 108 O. It is dif®cult to ®nd correlation between the

topographical and the electrical images. We note that the less

conducting zones are uniformly distributed on the analyzed

surface. The observation of another 20 mm� 20 mm area on

the same sample has proved to be similar. The reproduci-

bility of electrical images on several areas of the 5758Csample, as well as the apparent homogeneity of each of

them, are not in accordance with the heterogeneous elec-

trical results in a ball/plane con®guration.

2. The 575 and 6008C samples were scanned on another

area of 50 mm� 50 mm, then on a larger area of

100 mm� 100 mm around this ®rst one. Fig. 12 shows the

last corresponding topographical and electrical cartogra-

phies for the 5758C sample. The area that had already been

scanned appears as more conducting, but no topographic

modi®cation is detected. This behavior has not been

observed for the 6008C sample. We then believe that there

is a very thin layer less conducting on the extreme surface of

the 5758C sample. It is poorly adherent and thus is elimi-

nated by the scanning of the probe. This behavior pointed

out at a nanocontact scale might also occur for microcon-

tacts in the ball/plane con®guration, due to the asperities at

the surface of the ball. It could explain the non-reproducible

results observed in the 5758C sample.

6. Discussion and conclusion

6.1. Summary of the results

Static contact resistance measurements in a ball/plane

con®guration point out the effect of vacuum heat-treatment

on PAN ®lms deposited on metallic coupons. They reveal a

transition around a critical heat-treating temperature

T trans � 5758C.

� Below Ttrans, Rc � Rfilm. The behavior of the contact

resistance when the normal load L varies can be described

by an original relation we derived from the Hertz's law,

taking into account the influence of the pressure on the

conductivity and thickness of the film. The evolution of

Rc, when the temperature of the contact Tcont varies, obeys

the Mott's law which denotes a variable-range hopping

conduction in the film.

� Above Ttrans, Rc � Rconstriction. The behavior of the contact

when L or Tcont varies is coherent and ruled by the metallic

electrodes.

� The intermediate sample shows non-reproducible results

and anomalous curves in a ball/plane configuration.

Coupled topographic and electrical AFM cartographies

suggest, this might be caused by a very thin poorly

adherent layer present at the extreme surface of the

sample.

Fig. 12. Degradation of the sample heated at 5758C by the scanning of the AFM probe.


6.2. Discussion

The improvement of the conductivity of PAN induced by

heat-treatment has already been mentioned in the literature

for various modes of annealing (atmospheric conditions,

duration, temperature, etc.), for ®lms [19±23] or ®bers

[14,24]. The conductivity of raw PAN is about

10ÿ14 Oÿ1 cmÿ1, whereas the best performance obtained

after heat-treatment listed in the literature is 103 Oÿ1 cmÿ1

[24]. It has also been largely proved that this increase of the

conductivity is caused by chemical modi®cations [22,25,26]

of PAN. The heat-treatment progressively transforms the

linear chains of PAN into a three-dimensional reticulated

lattice containing more and more cyclized groups. This is

accompanied by denitrogenation and dehydrogenation, so

that PAN evolves towards a graphite-like structure. Linear

chains of PAN present single bonds and localized electronic

states, whereas cyclized groups are associated with deloca-

lized electronic states, which enhances the electrical

conductivity.

Since the beginning of our investigations on heated PAN

®lms, we have been performing systematic surface analysis

by photoelectron spectroscopy, in some cases coupled with

infrared re¯exion/absorption spectroscopy. Our spectra for

every con®guration of samples we have considered are in

good correlation with the chemical transformation men-

tioned above. It has been developed in a previous paper

[1] for very thin PAN ®lms (50 nm) electropolymerized on

brass coupons coated by electroplated nickel and rapidly

heated in a lamp furnace.

Another phenomenon has to be taken into account. XPS

analysis performed on this series of samples not only reveals

the presence at the surface of carbon, oxygen and nitrogen,

but also the detection of nickel and iron for the samples

heated at and above 6008C, that are the ones presenting

satisfying electrical performances. The corresponding

approximate relative concentrations are shown in Table 5.

We underline the XPS analyses several nanometers in the

depth of each sample. We believe that the heat-treatment

causes the inter-diffusion of the metallic substrate with the

organic layer, as well as the chemical transformation of

PAN. For Tmax � 600�C, the whole terminal layer has a

mixed structure, presenting both metallic and organic com-

pounds. It is not possible at this point to tell how they are

arranged. For Tmax � 550�C, there is still a solid pure

organic layer at the surface, more than several nanometers

thick. Considering, on the one hand, the amount of nickel

detected by XPS on the 5758C sample and, on the other

hand, the AFM observations, we think there is a terminal

poorly conducting organic layer, less than several nan-

ometers thick, which is eliminated by the scanning of the

AFM probe.

Considering again the 5508C sample, we have found that

the Mott's law is the most suitable to describe the behavior

of the contact resistance when the temperature varies. When

the contact load varies, that is when the pressure applied to

the ®lm varies, we have found that the ®t by expression (7) is

good. From the values of A and B appearing in Eq. (7), the

ratio of the conductivities at 0.75 GPa and at 1 atm is

estimated close to 5. This value is in agreement with results

found in the literature for the poly(3-alkylthiophenes) [11]

and for the polypyrrole [12]. In these papers, the increase of

conductivity is attributed to a decrease of the Mott's para-

meter T0 due to the compression of the material. Hence we

have a con®rmation that the variable-range hopping is the

better candidate to describe the electrical transport mechan-

ism in the 5508C sample.

6.3. Conclusion

We have studied the electrical transport properties of ®lms

of PAN after transformation by heat-treatment in vacuum.

These ®lms are deposited on steel coupons with a terminal

coating of nickel. Since the industrial goal is to use these

®lms as terminal layers of electrical contacts, they are

studied in a `̀ contact situation'' that is pressed by a golden

ball. The annealing temperature has been the single para-

meter for the sample preparation, the maximum temperature

Tmax, during the process, varying between 550 and 7008C.

By means of a dedicated experimental device, we have

studied the variations of the contact resistance Rc versus

the temperature Tcont of the contact and versus the load L

applied to the contact. For the 5508C samples, the contact

resistance are large (�2000 O under 50 gf at 258C) and due

only to the ®lm. For the variations of Rc versus Tcont, three

®tting laws have been tested, the best being Mott's law. For

the variations of Rc versus L, a good ®t has been obtained

with an analytical law Ð taking into account the variation

of the conductivity with the pressure Ð we have derived

from the Hertz's law. From the parameters obtained with

the ®tting, we have deduced the value of the ®lm resistivity

and the ratio of the conductivities under 0.75 GPa and 1 atm.

The value of 5 found for this ratio is in agreement with

results obtained with other synthetic metals for which the

transport mode is also the variable-range hopping. At this

stage, we should mention that our experimental method,

in which we record the Rc±L variations for a ®lm squeezed

between a plane and a ball carefully polished, could repre-

sent an alternative to the high pressure vessel method

habitually used to study the in¯uence of the pressure on

Table 5

Metals relative concentrations at the surface of the samples

Heat-treatment [Ni]% [Fe]%

Raw ±a ±

5508C ± ±

5758C 0.5 ±

6008C 10 5

6508C 10 5

7008C 10 5

a Not detected.


the conductivity of ®lms. For the 5758C samples, the contact

resistance are scattered (from 0.06 to 100 O under 50 gf at

258C). The samples annealed at this temperature seem to be

covered with a very thin poorly conducting non-adherent

layer, revealed by a home-made technique involving an

AFM with a conducting tip. For Tmax � 600�C, the contact

resistances are very low (a few mO) and due only to the

constrictions in the metallic electrodes. This is proved

by the temperature and load curves: Rc±Tcont, and Rc±L.

Unfortunately, it is not possible by our method to

determine the conductivity of the ®lms, which should

be high enough. Surface analyses performed on these

®lms reveal the presence of large amounts of nickel and

iron, probably partly responsible for their good electrical

behavior.

Acknowledgements

Part of this work has been realized in the Laboratory of

Electrochemistry headed by Christophe Bureau (Commis-

sariat aÁ l'EÂ nergie Atomique, Service de Recherche sur les

Surfaces et l'Irradiation de la MatieÁre) with the great help of

Pascal Viel.

Appendix A. Derivation of the Rfilm � F(L) law whenthe resistivity and thickness are pressure dependent

We consider an organic conducting ®lm with a free

thickness e0 and a resistivity r0. When the ®lm is subjected

to a pressure p, we assume that the variations of e and 1/rmay be described by ®rst order expansions

e � e0�1ÿ ap� (A.1)

1

r� 1� bp

r0

(A.2)

Eq. (A.1) is simply an expression of Hooke's law. The

pertinence of Eq. (A.2) is supported by the fact that a

parabolic expansion of the conductivity has been found

satisfactory to describe the behavior of doped polypyrrole

[27]. Here, for simplicity, we stop the expansion at the first

order.

When the ®lm lying on the plane substrate is pressed

against the sphere considered in Section 4.1, it is subjected

to a pressure p(r) inside the contact disc of radius a.

Although, not used in this simple model, the formula giving

p(r) is

p�r� � 3L

2pa21ÿ r2

a2

� �1=2

� Pmax 1ÿ r2

a2

� �1=2

(A.3)

where L is the load. In this work, Pmax � 750 MPa when

L � 1 N.

Denoting by V the voltage drop between the metallic

electrodes (the sphere and the plane), the current density

flowing through the film is

j�r� � V

er� V�1� bp�

e0r0�1ÿ ap� (A.4)

Assuming ap ! 1, Eq. (A.4) may be approximated by

j�r� � V

e0r0

�1� �a� b�p� (A.5)

Eq. (A.5) is indeed a first order expansion of j as a function

of p.

The current I ¯owing through the organic conducting disc

is given by

I � 2pZ a

0

j�r�r dr � pa2V

e0r0

� �a� b�Ve0r0

2pZ a

0

p�r�r dr

� pa2V

e0r0

� �a� b�Ve0r0

L (A.6)

Then, from Eq. (2), we have a � kL1=3 with

k � �3R=4E��1=3. So as I � V=Rfilm, we have

1

Rfilm

� pk2

e0r0

L2=3 � a� be0r0

L (A.7)

Finally, Rfilm may be expressed simply as

Rfilm � 1

AL� BL2=3(A.8)

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Influence of temperature and pressure on the static contact resistance of vacuum heat-treated...

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