Sensors and Actuators A 108 (2003) 55–58

Study on piezoresistive effect of diamond films under magnetic field

W.L. Wanga,b,∗, K.J. Liaoa,b, C.G. Hua, S.X. Wanga,b, C.Y. Konga, H.Y. Liaob

a Department of Applied Physics, Chongqing University, Chongqing 400044, Chinab Key Lab of the Education Ministry for Photoelectric Technology and System, Chongqing University, Chongqing 400044, China

Received 29 July 2002; received in revised form 7 July 2003; accepted 10 July 2003

Abstract

The piezoresistive effect of P-type diamond films was investigated under magnetic field. The diamond films in these studies weresynthesized by microwave plasma chemical vapor deposition. The experimental results have shown that the change in the resistance wasabout 12.0% without magnetic field when microstrain was 100 at room temperature, but decreased by 9.5% under the magnetic field of3 T at tensile stress. The origin of the piezoresistive effect in P-type diamond films can be explained by the strain-induced valence bandsplit-off and the magnetoresistive effect in the films that was caused by additional hole movement in a magnetic field.© 2003 Elsevier B.V. All rights reserved.

Keywords: Piezoresistive effect; Diamond films; Magnetoresistive effect; CVD

1. Introduction

Owing to outstanding physical and chemical properties,diamond thin films prepared by chemical vapor deposition(CVD) have attracted enormous interest in the last decade,and have been extensively used in tools in thermal andoptical applications[1–4]. The doped diamond films canbe used in active semiconductor elements for high-power,high-temperature and high-frequency electronic devicesbecause of their high hole mobility, wide gap and highbreakdown voltage. Recently, it was found that both theP-type single and polycrystalline diamond films have avery significant piezoresistive effect; the gauge factor ofheteroepitaxial diamond films at room temperature can begreater than 1000 at 100 microstrain, which is much largerthan for metals (2–12), silicon (5–175), and organometal-lic crystals (100–500)[5,6]. It suggested that with theunique combination of mechanical, electronic, thermal, andchemical properties, there is a tremendous potential fordiamond piezoresistive sensors with a performance signif-icantly better than that of similar Si or SiC, especially inchemically harsh, strong radiation, and high-temperatureenvironments.

In present paper, we investigated the piezoresistive prop-erties of CVD P-type diamond thin films under magnetic

∗ Corresponding author. Tel.:+86-23-65-103-490;fax: +86-23-65-106-704.E-mail address: wanluw@cqu.edu.cn (W.L. Wang).

field. The origin of the piezoresistive effect in P-type dia-mond was theoretically explained by valence band split-offmodel.

2. Experimental details

The diamond films in this study were synthesized by mi-crowave plasma CVD[7]. Mirror-polished P-type Si(1 0 0)was used as substrate. The substrate with a total area of10 × 10 mm2 were ultrasonically cleaned in acetone for10 min and subsequently in methanol for 10 min. After ashort rinse in methanol, the substrate was placed into the de-position chamber. The reactive gases were a mixture of H2and CH4. The total pressure was 18 mbar, and flow rate was300 sccm. The substrate temperature was about 850◦C. Themicrowave power and frequency were 800 W and 2.45 GHz,respectively.

The silicon substrate was firstly treated with hydrogenplasma for 20 min, then CH4 was fed into the chamber, andCH4 concentration in H2 was approximately 2%. A biasvoltage of−250 V, relative to the microwave plasma, wasapplied to the substrate for 20 min. The bias current wasabout 110 mA. After nucleation step, the bias voltage wasturned off, but all other deposition conditions remained un-charged except for CH4/H2 of 0.5% and substrate temper-ature of 750◦C. The growth time was 12 h, which resultedin a film thickness of 6�m. It was confirmed that the filmsobtained were the heteroepitaxial diamond films by X-raydiffraction, Raman spectra and SEM[8,9]. The diamond

0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.sna.2003.07.004

56 W.L. Wang et al. / Sensors and Actuators A 108 (2003) 55–58

diamond filmselectrode

gauge pressure compressor

Ar

Fig. 1. Measurement system for the piezoresistive effect of diamond films.

films were boron-doped by the cold implanted and rapid an-nealing technique[10].

The strain gauge of diamond films were prepared byetching the boron-doped diamond layers on the undopeddiamond films using an oxygen plasma in a reactive ion inetching system at 200 W and 38 mTorr. The strain gauge was550�m wide and 100�m long. A diaphragm structure witha diameter of 3 mm and a thickness of 100�m was obtainedby removed silicon substrate. Four parallel strain gauges onthe diaphragm were set in a sealed test vessel to measure thepiezoresistive effect. Ar gas was introduced into the vessel,and a tensile stress was created by Ar pressure on the dia-mond films. The magnetic field perpendicular to the currentflow direction was applied to the samples as shown inFig. 1.

3. Results and discussion

Fig. 2 shows the relationship between resistance change(�R/R0) and strain at room temperature without magneticfield. R andR0 are the resistances at strainsε and 0, respec-tively, and�R = R − R0. The directions of strain and re-sistance measurement were the same. The intrinsic strain ofdiamond films was neglected. The gauge factor fromFig. 1for the heteroepitaxial diamond films was found to be 1200at 100 microstrain.

Fig. 2. The relationship between the resistance change (�R/R0) and thestrain without magnetic field at room temperature.

Fig. 3. Changes in resistance under tensile strain: (a) with and (b) withoutmagnetic field at room temperature.

Fig. 3 shows the resistance change (�R/R0) with tensilestrain with and without the magnetic field at room tem-perature. FromFig. 2, it can be seen that the change inthe resistance of diamond films was about 12.0% withoutthe magnetic field when the microstrain was 100, whereas�R/R0 was found to be 9.5% at 100 microstrain under themagnetic field of 3 T. The origin of the piezoresistive effectin P-type diamond films can be explained in terms of thestrain-induced valence band split-off and the magnetoresis-tive effect in the films, which is caused by additional holemovement in a magnetic field[11]. Based on this model, theratio of the hole densities between light-hole, split-off, andheavy-hole bands are expressed as

Tensile:

P12(�ε) = P1

P2=

(m∗

1

m∗2

)3/2

exp

(−�ε

KT

)(1)

P32(�) = P3

P2=

(m∗

3

m∗2

)exp

(− �

KT

)(2)

Compressive:

P12(�ε) = P1

P2=

(m∗

1

m∗2

)3/2

exp

(�ε

KT

)(3)

P32(�) = P3

P2=

(m∗

3

m∗2

)exp

(− �

KT

)(4)

where Pi and mi (i = 1, 2, 3) are the hole density andeffective-mass of the light-hole band, heavy-hole band, re-spectively.� is the energy level interval between heavy-holeand split-off band and�ε is the interval between light-holeand heavy hole band to shift upward and downward underuniaxial compressive and tensile stress. Considering a stripdiamond films with thicknessd under an electric field�E, amagnetic field�B and a uniaxial stress, the Boltzmann equa-tion in the relaxation time approximation can be written as

�v · ∇f − e

h( �E + �v× �B) · ∇�kf = f − f0

τ(5)

W.L. Wang et al. / Sensors and Actuators A 108 (2003) 55–58 57

in which �vis the velocity of the hole,f andf0 are the distri-bution and equilibrium distribution function, andτ the re-laxation time.

The general solution ofEq. (5) is given by

f = f0 − �v · �D∂f0

∂ε

[1 + F(�v)exp

(− z

τvz

)](6)

or

f − f0 =[

eτA( �E · �v)(1 + ω2τ2A2)

+ eωτ2A2(�B× �E) · �vB(1 + ω2τ2A2)

]∂f0

∂ε(7)

Then, current density�J and conductivityσij are as follows

�J = 2e

(2π)2

∫�v(f − f0)d

3k = 2e2

(2π)3

∫�v

×[

τA�v(1 + ω2τ2A2)

+ ωτ2A2(�v× �B)B(1 + ω2τ2A2)

]�E∂f0

∂εd3k (8)

σij = 2e2

(2π)3

∫ [τAvivj

1 + ω2τ2A2+ ωτ2vi(�v× �B)jB(1 + ω2τ2A2)

]∂f0

∂εd3k

(9)

For a single valence band, the Maxwell–Boltzmann statis-tics and spherical energy band surface were assumed. Theconductivity components of the stripe samples fromEq. (9)can be written as the function of magnetic fieldBr and en-ergy level interval�ε of the valence band split-off causedby uniaxial stress,

σxx(γ,�ε) = p(�ε)eµLϕ(κ)K(γ) (10)

σXY(γ,�ε) = −12

√πP(�ε)eµLγ

1/2η(κ)L(λ) (11)

where

K(γ) =∫ ∞

0

α3e−α(α+ β)

(α2 + β2)+ γα3dα

L(γ) = 2√π

∫ ∞

0

α9/2e−α

(α2 + β2)+ γα3dα

γ = 9π

16(µLB)

2

ϕ(κ) = 1 − 3

8κ(1 − S)

and

η(κ) = 1 − 9

16κ(1 − S)

(1 + S

3

)

in which α = (Ev − ε)/KT, µL is the mobility of hole,βa slowly varying function of energy.κ = d/λ, λ the meanfree path,S the coefficient of surface scattering. Considering

a parallel connection model for light-hole (1), heavy-hole(2), and split-off (3) bands, the resistivity of the films isexpressed as

ρ(γ,�ε) = Sxx(γ,�ε)

S2xx(γ,�ε)+ S2

xy(γ,�ε)(12)

where

Sxx(γ,�ε) = σxx(1)+ σxx(2)+ σxx(3) (13)

Sxy(γ,�ε) = σxy(1)+ σxy(2)+ σxy(3) (14)

when a uniaxial stress was applied to the samples, thepiezoresistive effect of diamond films in magnetic field isgiven by

�ρ(γ,�ε)

ρ(γ,0)= Sxx(γ,�ε)

Sxx(γ,0)

S2xx(γ,0)+ S2

xy(γ,0)

S2xx(γ,0)+ S2

xy(γ,�ε)− 1

= A(γ,�ε)

A(γ,0)

A2(γ,0)+ πγ2B2(γ,0)/4

A2(γ,�ε)+ πγ2B2(γ,�ε)/4− 1

(15)

where

A(γ,�ε)= P12(�ε)

(µL1

µL2

)ϕ(k1)K(γ1)+ ϕ(k2)K(γ2)

+P32(�ε)

(µL3

µL2

)ϕ(k3)K(γ3)

B(γ,�ε)=[P12(�ε)

(µL1

µL2

)2

η(k1)L(γ1)+ η(k2)L(γ2)

+P32(�ε)

(µL3

µL2

)2

η(k3)L(γ3)

]2

Fig. 4shows the calculation results of piezoresistive effectin diamond films under a uniaxial stress, which led to aenergy level split-off (�ε) between the light-hole band andthe heavy-hole band. FromFig. 4, it can be seen that the

Fig. 4. Variation of the resistance as a function of energy level split-offbetween light-hole and heavy-hole bands under a uniaxial tensile stress:(a) with and (b) without magnetic field.

58 W.L. Wang et al. / Sensors and Actuators A 108 (2003) 55–58

change in the resistivity of the films is 0.114 and 0.091without and with magnetic field for tensile stress when |�ε|is about 0.6 × 10−3 eV. On comparingFig. 3 with Fig. 4,it was found that the relative changes in resistance under100 microstrain are similar to that when |�ε| is about 0.6×10−3 eV. This implied that the change of split-off band wasabout 0.6 × 10−3 eV at 100 microstrain.

4. Conclusion

The experimental results have shown that the piezore-sistive effect in P-type diamond films was degraded bymagnetic field. The origin of the piezoresistive effect inmagnetic field is due to the strain-induced valence bandsplit-off and magnetoresistive effect. The theoretical cal-culation is in good agreement with experimental data. Thepiezoresistive effect of diamond films as a sensor has sig-nificant applications in high-temperature, strong radiationand chemically harsh environments.

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China under grant No. 199904016 and No.50005027.

References

[1] W. Zhu, B.R. Stoner, B.E. Williams, J.T. Glass, Proc. IEEE 79 (1991)621.

[2] F.A.M. Kock, J.M. Garguilo, R.F. Nemanich, Diamond Relat. Mater.10 (9/10) (2001) 1714.

[3] M. Thumm, Diamond Relat. Mater. 10 (9/10) (2001) 1692.[4] K.V. Ravi, A. Joshi, Appl. Phys. Lett. 58 (1991) 246.[5] W.L. Wang, K.J. Liao, B. Feng, G. Sanchez, M.C. Polo, J. Esteve,

Diamond Relat. Mater. 7 (1998) 528.[6] L. Fang, W.L. Wang, P.D. Ding, K.J. Liao, J. Wang, J. Appl. Phys.

86 (9) (1999) 5158.[7] W.L. Wang, X. Jiang, K. Taube, C.-P. Klages, J. Appl. Phys. 82 (2)

(1997) 729.[8] X. Jiang, C.-P. Klages, R. Zachai, M. Hartweg, H.-J. Fusser, Appl.

Phys. Lett. 62 (1993) 3438.[9] W.L. Wang, K.J. Liao, B. Feng, Z. Zhang, Chin. Phys. Lett. 15 (6)

(1998) 460.[10] F. Fontaine, C. Vzan-Saguy, B. Rhilosph, R. Kalish, Appl. Phys.

Lett. 68 (1996) 2264.[11] C.Y. Kong, W.L. Wang, K.J. Liao, S.X. Wang, L. Fang, Y. Ma, J.

Appl. Phys 15 (5) (2002) 3044.