Fundamental insight on developing low dielectric constant polyimides

J.O. Simpson*, A.K. St.Clair

NASA Langley Research Center, Hampton, VA 23681-0001, USA

Abstract

Thermally stable, durable, insulative polyimides are in great demand for the fabrication of microelectronic devices. In this investigationdielectric and optical properties have been studied for several series of aromatic polyimides. The effect of polarizability, fluorine content,and free volume on dielectric constant was examined. In general, minimizing polarizability, maximizing free volume and fluorination alllowered dielectric constants in the polyimides studied. Published by Elsevier Science S.A.

Keywords:Low dielectric constant; Polyimides; Optical properties; Microelectronic devices

1. Introduction

High performance polyimides are widely used in themicroelectronics industry. Of utmost importance for thesemicroelectronics applications is that the polyimide have alow dielectric constant. In electronics packaging, lowdielectric materials minimize crosstalk and maximize signalpropagation speed in devices. Hence, the development ofpolyimides with increasingly lower dielectric constants hasbeen the focus of several recent investigations [1–5].

Among the strategies used to lower dielectric constants inpolyimides are: (1) incorporating diamine and dianhydridereactants which minimize polarizability; (2) incorporatingdiamine and dianhydride reactants which impart a highdegree of free volume; and (3) incorporating fluorineatoms into the molecular structure of the polyimide [6].We have synthesized and characterized several series ofaromatic polyimides to examine the effect of polarizability,free volume, and fluorine content on the dielectric proper-ties of polyimides. The fundamental insight gained fromthese studies, and others, is reported herein.

2. Background

2.1. Polarizability

Dielectric constants of polyimides, in general, are knownto decrease gradually with increasing frequency. For exam-

ple, Kapton H film (25.4mm) has a dielectric constant ofapproximately 3.5 at 1 kHz and 3.3 at 10 MHz [7]. Thisvariation in dielectric constant is attributed to the frequencydependence of the polarization mechanisms which comprisethe dielectric constant. The magnitude of the dielectric con-stant is dependent upon the ability of the polarizable units ina polymer to orient fast enough to keep up with the oscilla-tions of an alternating electric field. As shown in Fig. 1, thepolarizable units are electronic, atomic and dipolar. At opti-cal frequencies (1014 Hz), only the lowest mass species,electrons, are efficiently polarized. At lower frequencies,atomic polarization of heavier, more slowly moving nucleialso contribute to the dielectric constant. Atomic polariza-tion of induced dipoles such as a carbonyl group can occurin the infrared (1012 Hz) or lower frequency regimes. Dipolepolarization is the redistribution of charge when a group ofatoms with a permanent dipole align in response to theelectric field. In the solid state, alignment of permanentdipoles requires considerably more time than electronic oratomic polarization, occurring at microwave (109 Hz) orlower frequencies.

The polarizability (a) of each species is generally addi-tive, (i.e. a = aelectronic + aatomic + adipolar) and can be com-bined with the Clausius–Mossotti relationship to estimatethe contribution of each polarization mode to the dielectricconstant (e) as shown in Eq. (1) [11].

e = eelectronic + eatomic + edipolar (1)

At optical frequencies, where only electronic polarizationoccurs, the dielectric constant,e∞, is related to the refractiveindex, nref, by Maxwell’s identity.

Thin Solid Films 308–309 (1997) 480–485

0040-6090/97/$17.00 Published by Elsevier Science S.A.PII S0040-6090(97)00481-1

* Corresponding author.

e∞ = (nref)2 (2)

A comparison of thee∞ and the dielectric constant mea-sured at frequencies lower than optical frequency can leadto a basic understanding of the influence of molecular struc-ture on dielectric properties in polyimides.

2.2. Free volume

A correlation of high free volume and low dielectric con-stant has been previously reported for polyimides [8–10]. Inthese investigations positron lifetime spectroscopy andgroup additivity methods were used to quantify free volumefractions. The introduction of free volume in a polymerdecreases the number of polarizable groups per unit volumeresulting in lower values foreatomic andedipolar. The additionof pendant groups, flexible bridging units, and bulky groupswhich limit chain packing density have all been used toenhance free volume in polyimides and are used in thisstudy to examine their effect on dielectric constant.

2.3. Fluorine content

Although incorporation of fluorine into polyimides hasbeen shown to lower dielectric constants, indiscriminatefluorine substitution may actually yield an undesired effect.Hougham et al. have shown that non-symmetric substitutionof fluorine for hydrogen increases the average magnitude ofthe dielectric constant by approximately 0.05 per substitutedring [11]. Symmetric substitution of fluorine does notincrease the net dipole moment of the polymer and hence,does not increase the dielectric constant. In fact, in the samestudy Hougham et al. have shown that the dielectric constantdecreases with symmetric fluorine substitution by a combi-nation of lower electronic polarizability and larger free

volume. In this study, symmetric and non-symmetric fluori-nated groups are used to elucidate the influence of fluorinecontent on dielectric constant.

3. Experimental

Chemical repeat units of the aromatic diamine and dia-nhydride monomers used to prepare the polymers of thisinvestigation are shown in the accompanying tables. Pyro-mellitic dianhydride (PMDA), 3,3′, 4,4′-benzophenone tet-racarboxylic dianhydride (BTDA), and 2,2-bis(3,4-di-carboxyphenyl)hexafluoropropane dianhydride (6FDA),4,4′-oxydianiline (4,4′-ODA), 3,3′-diaminodiphenylsulfone(DDS02) and 1,3-bis(aminophenoxy)benzene (APB) wereobtained from commercial sources. The other monomerswere experimental materials obtained as follows: 4,4′-oxdiphthalic anhydride (ODPA) and 1,4-bis(3,4-dicarboxy-phenoxy)benzene dianhydride (HQDEA) from OccidentalChemical Corporation; 4,4′-bis(3,4-dicarboxyphenoxy)di-phenyl sulfide dianhydride (BDSDA), an experimentalmaterial from General Electric Corporate R and D Center;3,3′-oxydianiline (3,3′-ODA) and 2,2-bis[4(3-aminophe-noxy)phenyl]hexafluoropropane (3-BDAF) from MitsuiToatsu, Inc.; 2,2-bis[4(4-aminophenoxy)phenyl]hexafluoro-propane (4-BDAF) from Ethyl Corporation and 2,2-bis(4-aminophenyl)hexafluoropropane (4,4′-6F) from HoechstCelanese.

Polyamic acid precursor solutions were prepared by mix-ing equimolar portions of diamine and dianhydride at roomtemperature at 15% solids by weight in dimethylacetamidefor 8–24 h. Polymer films were prepared by casting thepolyamic acid solutions onto glass plates in an encloseddust-free chamber at 10% RH. Polyamic acid films wereconverted to polyimide by heating 1 h each at 100°, 200°,and 300°C in forced air.

Dielectric measurements were performed on 1 mm (25.4mm) thick polyimide films by two methods. The GHz dielec-tric constant measurements were obtained using a HewlettPackard 8510 Automated Network Analyzer over a fre-quency range of 8–12 GHz. The films were desiccated over-night prior to measurement and were run at roomtemperature at 25–35% RH. The reported dielectric con-stants are quoted at 10 GHz and are accurate to±0.03.The MHz dielectric constant measurements were obtainedusing a fixed gap parallel plate capacitor consisting of2 × 2.54 cm2 aluminum plates mounted on glass plates. Aspacer was used to obtain a capacitor with a fixed gap spa-cing no more than 20mm greater than the sample thickness.Using the impedance measurements, with and without thefilm, and the film thickness, the dielectric constant of thesample was calculated at 1 MHz with an accuracy of±0.12.

Refractive index measurements were obtained at ambienttemperature by the Becke Line method [12] using a polar-izing microscope and standard immersion liquids obtainedfrom R.P. Cargille Labs.

Fig. 1. Polarization phenomena which influence the dielectric constant.

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4. Results and discussion

4.1. Polarizability

Table 1 lists the measured dielectric constants ande∞ ascalculated from the refractive indices. The optical frequencydielectric constant values are equal within experimentalaccuracy to the dielectric constants measured at 10 GHzexcept for the polyimide which contains BTDA. TheBTDA dianhydride contains the polar carbonyl linkagewhich contributes to the large difference betweene∞ ande

(@10 GHz). While the –CF3 pendant groups in 6FDA+ 4-BDAF combine to give a net resultant dipole, the polariza-tion of this dipole is essentially frozen out at 10 GHz.

Dielectric constants measured at 10 GHz and 1 MHz areplotted against the optical frequency dielectric constant inFig. 2. Substantial increases in the dielectric constant areobserved as the measurement frequency is decreased from10 GHz to 1 MHz. This increase is attributed to the polar-ization of induced and permanent dipoles as the time scaleof the dielectric constant measurement is extended. As illu-strated in Fig. 1, dipole alignment which is not detectable at10 GHz adds to the dielectric response at 1 MHz.

4.2. Free volume

The introduction of free volume in aromatic polyimidescan be accomplished by using reactants which result in

inefficient chain packing in the solid state. Among the meth-ods for achieving decreased chain packing density are incor-porating substituents witho- and m-linkages along thepolymer backbone; incorporating flexible bridging units inthe backbone; and adding pendant groups along the polymerbackbone. Table 2 presents dielectric constant measure-ments for a series of oxydialine (ODA) containing polymersin which thep- and m-isomers, 4,4′-ODA and 3,3′-ODA,

Table 1

Chemical repeat unit and dielectric properties for 4-BDAF containing polyimides

Dianhydride Structure (Ar) nref e∞ e (GHz) e (MHz)

BDSDA 1.64 2.69 2.69 3.08

BTDA 1.62 2.62 2.74 3.03

ODPA 1.62 2.62 2.68 3.08

PMDA 1.62 2.62 2.63 2.93

6FDA 1.58 2.50 2.50 2.77

Fig. 2. Dielectric constants for 4-BDAF containing polyimides measured atthree frequencies.

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Table 2

Dielectric properties of ODA containing polyimides

Polymer Dianhydride (R) Diamine (Ar) e (10 GHz)

PMDA + 4,4′-ODA (Kapton) 3.22

PMDA + 3,3′-ODA 2.84

BTDA + 4,4′-ODA 3.15

BTDA + 3,3′-ODA 3.09

ODPA + 4,4′-ODA 3.07

ODPA + 3,3′-ODA 2.99

HQDEA + 4,4′-ODA 3.02

HQDEA + 4,4′-ODA 2.88

BDSDA + 4,4′-ODA 2.97

BDSDA + 3,3′-ODA 2.95

6FDA + 4,4′-ODA 2.79

6FDA + 3,3′-ODA 2.73

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have been systematically varied to illustrate the effect ofincorporating ‘kinks’ in the polymer backbone on thedielectric constant. In each casem-isomerism lowers thedielectric constant as compared to the corresponding poly-mers withp-isomerism.

A large reduction in dielectric constant is observed withthe use of the 6FDA dianhydride. The 6FDA+ 3,3′-ODApolymer has a large free volume due to the pendant –CF3

groups and them-catenation of the diamine.Free volume fractions have been quantified for three of

the polymers studied by positron lifetime spectroscopy asdescribed by Eftekhari et al. [13]. As shown in Table 3, thefree volume fraction is larger for ODPA+ 3,3′-ODA thanODPA + 4,4-ODA. The ‘kink’ in the 3,3′-ODA diamineinhibits close packing of the polymer chains resulting in alarger free volume. Likewise, the incorporation of bulkytrifluoromethyl pendant groups in the 6FDA dianhydridesterically hinders packing and enlarges the free volume in6FDA relative to the ether linkage in ODPA. Increased freevolume correlates with decreased dielectric constants forthese polymers.

4.3. Fluorine content

Dielectric constant as a function of fluorine content isshown by the filled circle symbols (X) in Fig. 3 for thepolyimides listed in Table 1. The dielectric constantdecreases almost linearly with increasing wt% fluorine.The exception to this trend is for BTDA+ BDAF polyimidefor which the dielectric constant is slightly higher due to thepolarization of the carbonyl group. The dielectric constant isminimized for 6FDA+ 4-BDAF in which both the dianhy-dride and diamine portions of the polymer contain trifluor-omethyl groups. Fluorine substitution lowers the dielectric

Table 3

Free volume fractions for polyimides

Polyimide Dielectric constant(10 GHz)

Free volumefraction (%)

ODPA + 4,4′-ODA 3.07 0.58ODPA + 3,3′-ODA 2.99 0.626FDA + 3,3′-ODA 2.73 1.34

Fig. 3. Dielectric constant as a function of fluorine content. Polyimideswhich contain 4-BDAF diamine as shown in Table 1 (X). Polyimideswhich contain 6FDA dianhydride as shown in Table 4 (B).

Table 4

Chemical repeat unit, dielectric constant and fluorine content for 6FDA containing polyimides

Diamine Structure (Ar) e(10 GHz) Wt% fluorine

DABTF 2.58 29

DASP 2.51 33

3-BDAF 2.40 25

4,4′6F 2.39 31

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constant by a combination of mechanisms. The incorpora-tion of the bulky –CF3 group prohibits close packing of thepolymer chains and reduces interchain charge transfer of thehighly polar dianhydride groups [14]. In addition, the largefluorine atoms increase the free volume fraction in the poly-mer essentially reducing the number of polarizable groupsin a unit volume. Fluorine substitution also lowers the elec-tronic polarization in the polymer due to the large electro-negativity of the C–F bond.

The two trifluoromethyl groups in these polymers resultin a net dipole which can produce dipole polarization ifenough molecular mobility exists. However, for the mea-surement conditions, (i.e. room temperature and high fre-quency), the effect of polarization associated with thisdipole on the dielectric constant is not as pronounced as itis for polymers that contain a single, non-symmetric polargroup. Non-symmetric substitution of fluorine did notnecessarily result in a lowering of the dielectric constantwith increasing fluorine content. As shown in Table 4, theDABTF and DASP diamines contain a single trifluoro-methyl and pentafluorosulfanyl group, respectively,whereas the 3-BDAF and 4,4′6F diamines contain two tri-fluoromethyl groups. The synthesis of the DABTF andDASP containing polyimides is described elsewhere[15,16]. The filled square symbols (B) in Fig. 3 illustratethe effect of wt% fluorine on dielectric constant for thesepolyimides. The non-symmetric fluorinated diamines bothyield polyimides with higher dielectric constants than thosecontaining symmetric trifluoromethyl groups. This is possi-bly due to the large dipole moments of the C–F and S–Fbonds. Each of the polymers with dielectric constants wellabove the linear fit in Fig. 3 (BTDA, DABTF, and DASP)contain asymmetric polarizable groups. Even though the6FDA + DASP polyimide has the highest fluorine content,its dielectric constant is not the lowest. It is important tonote that

5. Conclusions

In this investigation we report structure/property data onthe effect of polarizability, free volume and fluorine contenton dielectric constants for several aromatic polyimides. Thistype of analysis is crucial for making further improvementsin the development of insulative polymers. Minimizingpolarizability, maximizing free volume and fluorinationall lowered dielectric constants in the polyimides studied.

Polarizability is the primary variable influencing dielectricconstants whereas free volume and fluorine content are sec-ondary variables which can alter a polymer’s polarizability.Enhanced free volume lowers polarization by decreasing thenumber of polarizable groups per unit volume. Fluorinationincreases free volume, lowers electronic polarization andcan either increase or have no effect on dipole polarizationdepending on whether the fluorination is asymmetric orsymmetric.

Acknowledgements

The authors gratefully acknowledge the technical supportof Mr Mason Proctor and Mr Burt Emerson of NASA Lang-ley Research Center for polyimide film synthesis and mea-surement of dielectric properties.

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