AT'L INST. OF STAND & TECH R.I.C.

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NIST

PUBLICATIONS

mistUnited States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1512

Dielectric and Magnetic Properties

of Printed Wiring Boards and

Other Substrate Materials

James Baker-Jarvis

Bill Riddle

Michael D. Janezic

! QC

[ 100 1

.U5753 1

NO. 1512 1

1999 1

A/AS T Technical Note 1512

Dielectric and Magnetic Properties

of Printed Wiring Boards and

Other Substrate Materials

James Baker-Jarvis

Bill Riddle

Michael D. Janezic

Radio-Frequency Technology Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

March 1999

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1512, X pages (March 1999)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1999

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Contents

1 Introduction 2

2 Properties of Printed Wiring Board Materials 2

2.1 Overview of PWB Technology 2

2.2 Materials Used in PWB and Substrate Applications 6

2.3 Thermal Properties 12

2.4 Electric Properties of Surface-Cladding Material 15

2.5 Transmission-Line Parameters for Circuit-Board Applications 17

3 Dielectric Measurements 19

3.1 Overview of the Measurement Problem 19

3.2 Measurements of Thin Materials 19

3.2.1 Measurement Methods 19

3.2.2 Reentrant Cavity 20

3.2.3 TEoi Split-Cavity Resonators for Thin Dielectrics 21

3.2.4 Cavity Resonators for Thin Dielectrics 22

3.2.5 TEoi Split-Post Dielectric and Magnetic Resonators 22

3.2.6 Courtney Technique 24

3.2.7 Full-Sheet Resonance Method for Thin Sheets 24

3.2.8 Whispering-Gallery and Fabry-Perot Resonators 28

3.2.9 Transmission-Line Techniques 30

3.2.10 Coaxial Apertures 32

3.2.11 Capacitive Techniques 34

4 Measurements 36

5 Elevated Temperature Measurements 51

6 Conclusion 60

7 References 64

in

Dielectric and Magnetic Properties

of Printed Wiring Boards and

Other Substrate Materials

James Baker-Jarvis* Bill Riddle * and Michael D. Janezic *

National Institute of Standards and Technology

325 Broadway, Boulder CO 80303-3328

This is an overview of dielectric and magnetic material measurements on printed wiring

board and substrate materials. The most commonly used methods are presented. We

begin with an overview of pertinent properties of circuit-board and substrate materials. We overview cavity and dielectric resonators, reentrant cavity, full-sheet resonance,

coaxial probe, stripline, and capacitive methods. The frequency range of applicability

and typical uncertainties associated with the methods are summarized. It is found

that the reentrant cavity is useful for both loss and dielectric constant determination

for materials of thickness greater than one-half millimeter. It is concluded that the

full-sheet resonance technique is useful for the determination of the real part of the

permittivity of clad substrates, but not for the loss measurement. Dielectric resonator

techniques achieve the greatest sensitivity for both permittivity and loss. However,

many printed wiring board materials are too lossy to achieve a resonance. We also present measurements of many substrate materials.

Key words: dielectric constant; dielectric resonator; full-sheet resonance; loss factor; microwave measurements; permeability; permittivity measurement; printed wiring

board; resonance; stripline; substrate

'Radio- Frequency Technology Division, MS 813.01, email:jjarvis@boulder. nist.gov
1. Introduction

This report is an overview of the dielectric and magnetic properties of substrates and

printed wiring board (PWB) materials. The goal of this report is to present relevant

information on material properties and measurements for thin materials.

As electrical components are miniaturized, needs for accurate low-loss dielectric measurements on thin materials increases. There is a need for measurement metrology that

supports the development of novel thin materials. Accurate measurement of complex permittivity and permeability are needed for circuit design, minimization of crosstalk, and

characterization of propagation speed. As a consequence it is important to understand the

related radio-frequency concepts and the limitations of the various measurement methods.

In Section 2 we overview the important fundamental concepts in circuit-board applications.

This includes the types of materials and laminates commonly used and the definitions of

important electrical and thermal properties. We also provide an overview of the relevant

concepts of transmission-fine theory. In Section 3 we review the various permittivity methods for thin materials. In Section 4 we present measurements of substrate and circuit-board

materials. In Section 5 we present a technique for elevated temperature measurements and

measurement results for a number of commonly used materials.

2. Properties of Printed Wiring Board Materials

2.1. Overview of PWB Technology

New packaging technology requires low dielectric constant materials, interconnections made

of high-conductivity metals, and high wiring density [1-9]. The use of fine-line signal con- ductors requires thinner, possibly laminated, low dielectric constant printed wiring board,

thin films, and substrate materials. Monolithic integrated circuit applications require semiconducting substrate materials for active device operation.

The permittivity is written as e = [e'r — je"] eo- The real part of the relative permittivity

e'r

is a measure of the phase change as a signal propagates through a material. The

imaginary part of the permittivity e" is related to attenuation of the signal and includes

both dielectric and d.c.-conductivity losses. Generally the loss in a material is expressed

e" in terms of the loss tangent, tan 8 = •$-. Dielectrics with low loss reduce attenuation and

heating in circuits. In microelectronic applications the lower the dielectric constant, the
lower the propagation delay. This is manifest in the equation for propagation delay which

is approximated by

td =

l^SK, (2.i) c where c is speed of light, / is line length, and /j,'r

is the relative permeability given by

fi = yuo[/4 — j/i"}. Forming patterns or multilayers can decrease propagation delay by

decreasing the signal path length. Propagation delay can also be decreased by lowering

the dielectric constant; however, shortening the signal path increases wiring density and

therefore increases cross-talk between elements. Low dielectric constant and anisotropy can

decrease the signal cross-talk between conductors by decreasing the capacitive coupling.

High dielectric constant materials also have a niche in microelectronic applications.

At low frequencies, well-characterized, high dielectric constant materials are used to keep

dimensions of circuits small. This can be understood by considering how the TEM mode

wavelength in a material A is related to the permittivity and frequency /,

JVer/4

Compact antenna arrays require high-dielectric constant substrates for maintaining phase

shifts between elements. High dielectric constant materials include aluminum nitride, silicon carbide, polycrystalline alumina, monocrystalline materials such as quartz, sapphire,

lanthanum aluminate, ferromagnetic materials, titanates, and gallium arsenide [1]. Tunable or frequency-agile ferroelectric and ferrite materials in bulk or thin-film form

are being used for device design and consequently a need for unbiased and biased dielectric

and magnetic measurements. In ferroelectric materials the permittivity is a function of the

applied bias field. In ferromagnetics or ferrimagnetics the permeability can be a function of

the applied magnetic field. Permittivity tuning by applied voltage requires strong electric

fields, so usually ferroelectric materials are used as thin-films. Ferroelectric materials such

as barium-strontium titanate can be tuned by bias fields since the Curie temperature

is close to room temperature. Domains consisting of electric dipoles are formed from

strong dipole-dipole interactions. Ferroelectric material losses are affected strongly by

temperature. The loss tangent of ferroelectrics increases approximately with temperature

as T

2

. Applications include phase shifters for antenna arrays. The loss in these materials

is minimized by adding manganese to the solid. The most commonly used ferroelectric

material is barium-strontium titanate. High-temperature performance of dielectric and

ferromagnetic materials is also important for high-power systems.
Field orientation is important for measurements of anisotropic materials. The characterization of anisotropic materials generally requires two techniques, one for the component

of permittivity perpendicular to the plane of the sample and one for in-plane permittivity.

Measurement fixtures in which the electromagnetic fields are tangential to the airmaterial interfaces, such as in TEoi cavities and dielectric resonators, generally yield more

accurate results than fixtures where the fields are normal to the interface. Unfortunately,

for many applications it is not always possible or preferable to measure in-plane field

orientations. For example, circuit boards and printed wiring boards operate with the

electric field primarily normal to the plane of the sheet and therefore this component

of the permittivity is of primary interest. However, measurements with the electric field perpendicular to the sample face may suffer from consequences of air-gap depolarization. In such cases the air-gap must be either accepted, mitigated by metalization of sample surfaces

or application of conductive pastes, or corrections made by numerical techniques [4,5].

For resonant measurements the permittivity or permeability is determined from measurements of the resonance frequency and quality factor (Q). The quality factor of a res- onator decreases as frequency increases. This is a consequence of increasing loss as a

function of frequency. In low-loss materials the permittivity is nearly constant over the

microwave band. Magnetic materials are low loss above gyromagnetic resonance. In ferrite

materials the permeability is a tensor for a bias field in the z direction is

I U JK \

(*= A«o -jk n (2.3)

V

fiz J

Since ferrites and garnets have magnetic-spin domains it is not possible to completely

demagnetize a specimen. In the demagnetized state the permeability measurement yields

\iz

. The gyromagnetic ratio and resonant (Larmor) frequency are related by 75 = —u)q/{hqHq) — 1.759 x 1011 m2 /Wb-s. As a magnetic field is applied to a specimen it reaches a level where all spins are aligned in the field. This is called saturation. The saturation magnetization Ms in ferrites is typically 0.03 T to 0.5 T. Below saturation ferrites are lossy,

and as a consequence devices are usually operated at frequencies above saturation. The

saturation field is strongly temperature dependent. Resonant systems with loss require a complex resonance frequency uoq — ujq + jctco. a is related to the linewidth, AH by

AH - 2otu)/(fj,o~fg

) = Au)o/([io~/g

). Linewidth is a measure of the sharpness of the res-
Table 2.1. Summary of substrate properties and applications.

Property Advantages Desired range

Minimize cross talk

Decreased propagation delay

Smaller circuits

Generate phase changes

Less heat generated

Less signal attenuation.

Less substrate fracturing

Less impedance change with temperature

High thermal conductance Cooler operation k > 30 (W/m°C)

Low dielectric constant

High dielectric constant

Low loss

Low thermal expansion

4 w 2 - 4

4 w 10 - 500

tan <J < 5 x 10~ 4

a < lO-^C-1

)

onance curve for the loss part of the magnetic susceptibility as a function of bias field

strength.

Other important properties of printed wiring board and substrate materials include low

loss, high thermal conductance, low thermal expansion, and high interfacial adhesion to metal surfaces or other films (see tables 2.1 and 2.2). Cost is a crucial for the widespread

acceptance of a specific material. Epoxy-glass is the least expensive material and as a con- sequence holds a large market share. In increasing order of cost are epoxy-glass, polyimide,

Table 2.2. General properties of classes of PWB materials.

Class Range of permittivity Range of loss TCE Adhesion

Plastics 2- 5 0.0001 - 0.01 poor poor-good

Plastic/ Ceramic composites 3- 50 0.0001 - 0.01 good poor-good

Glasses 6- 12 0.00005 - 0.01 good good

Ceramics 10 - 500 0.00005 - 0.01 good good

Ceramic/Glass composites (i- 100 0.00005- 0.01 good good
Figure 2.1. Typical reinforcing patterns used in PWB materials [10].

polyimide-quartz, and Teflon 1

.

2.2. Materials Used in PWB and Substrate Applications

Printed wiring board and substrate materials are usually composite materials and may

be anisotropic. The composites usually consist of a mixture of plastics and ceramics,

together with reinforcing materials. Usually plastics are reinforced with glass fibers or impregnated with glass or ceramics. Typical reinforcing materials used are paper fabric, woven glass cloth, random fiberglass fibers, and aramid fiber cloth (see figures 2.1 and 2.2).

The fabric and fiber weaving has some variability due to manufacturing limitations which

translates into a variability in permittivity. Polymer resins are classified into thermoplastics

or thermosets. Thermoplastics, for example polyethylene or Rexolite, soften when heated.

Thermosets such as epoxies and phenolics do not melt when heated. Epoxies are polyethers

and have good chemical resistance and adhesive properties. Common resins for low-cost

laminates are phenolics. Phenolics, such as Bakelite, are thermosetting plastics. When heat

and pressure are applied in the moulding process, thermosetting plastics react to form a

Specific materials that are commonly used are mentioned. This does not imply any endorsement by

the National Institute of Standards and Technology.

(»
1.20

1.15

"§ 1.10

1.05

Woven PTFE/Glass

Fiber PTFE/Glass

2.20 2.30 2.40 2.50

fc

r

Figure 2.2. The degree of anisotropy in permittivity calculated from the ratio of normal

to in-plane dielectric constant plotted against bulk dielectric constant [11].
4.8 -i 4.6 - 4.4 - 4.2 - 4.0 - 3.8 - 3.6 - 3.4 -20 30

—i

40 —i50 60 70 80

Resin (%)

Figure 2.3. Dielectric constant in FR4 material as a function of the percent of resin content

by weight [10].

1 / PTFE /

1 Ceramic Filler /f

Glass-Microfiber Copper

Reinforcement Cladding

Figure 2.4. PTFE composite.
Copper

Laminate

Conductor

Figure 2.5. Geometry of metal-clad substrates.

Material # 1

Materia] #2

HI tfKBl

Metal Core llll

Copper

'foil

Figure 2.6. Dual material structure.
cross-linked structure. This structure yields excellent dimensional and thermal stability

and superior load-bearing capability at low to high temperatures. Phenolic resins are products of the condensation reaction of phenol and formaldehyde. Other polymers used

in PWB materials are polyimides, cyanate ester, bismalimide triazine (BT), fluropolymers,

and polysulfone. Polyimides, bismalimide triazine, and cyanate ester can withstand higher

temperatures than other polymers. Fluropolymers and polysulfone have low dielectric

loss. Polymers may be crystalline, amorphous, or a combination. Dielectric properties as

functions of both frequency and temperature of many commonly used organic materials

are summarized in [12]. Many PWB's are laminates. Examples of laminates are fiberglass-epoxy composites

(FR4), high-temperature fiberglass-epoxy composites (FR5), bismalimide triazine-epoxy,

cyanate ester, arimid-epoxy, polyimide-glass, and polyimide-quartz [13] (see figures 2.1

through 2.6).

Low-dielectric constant materials include bulk plastics such as polytetrafluoroethylene

(PTFE), cross-linked polystyrene (CPS), fiberglass, polyimides, fluropolymers, and composites made from fiberglass, fused silica, ceramics, aerogels, and foams. Plastics have low

permittivities, but large expansion coefficients and low mechanical strength. Properties of

plastic materials are summarized in table 2.3. Low-dielectric properties can be achieved by

introducing porosity, use of low-dielectric constant materials, or by forming hollow stripline

ceramic structures [14]. Recently, more complex low dielectric constant polymers such as

polyquiolines and benzocyclobutenes have been developed.

Properties of some commonly used ceramics are summarized in table 2.4. Many ceramics such as alumina, aluminum nitride and silicon carbides have good thermal conductance,

small expansion coefficient, and high dielectric constant. The ceramics beryllium oxide,

aluminum nitride, and silicon nitride have higher dielectric constant than most organic materials and good mechanical strength [15, 16]. The loss tangent for many ceramic materials

and some plastics obey a linear dependence with frequency / of the form tan 5 = af + 6, where a is usually a positive number.

Sapphire, rutile, silicon, and quartz are anisotropic. Sapphire has a high thermal conductivity and very low dielectric loss. Sapphire and quartz are both brittle and difficult

to drill and cut. Glasses such as fused silica and borosilicate have low loss and medium

values of dielectric constants. Rutile has a very high dielectric constant and medium loss.

Recently it has been shown that Ba(Mg1/2 W1/2 )03 [17] and Mg^b^Ta^^Os [18] have

10
Table 2.3. Plastic substrates [1]. Material 4 tan 8 Machinability Range of Anisotropy

or composite temperatures (°C)

PTFE 2.06 0.0002 Poor -20 to 200 no PTFE/Fiberglass 2.25 0.0010 Good -20 to 200 yes

PTFE/Quartz 2.50 0.0005 Excellent -20 to 200 yes

PTFE/Ceramic 10.0 0.0010 Excellent -20 to 200 yes

CPS 2.54 0.0004 Good -20 to 100 no

CPS/Fiberglass 2.70 0.0010 Good -20 to 100 yes

CPS/Quartz 2.70 0.0005 Good -20 to 100 yes

Polyolefin 2.30 0.0005 Poor -20 to 100 no

Polyimide 3.50 0.0010 Good -20 to 200 no

high-dielectric constant, low loss, and low coefficient of thermal expansion. Zirconium ti- tanate with added ZnO, Y2O3, or CuO has been shown to have low expansion coefficient,

high dielectric constant and low loss [19]. Another well-studied high-dielectric constant

ceramic is Ba(Znj

/

3 Ta2 /3)03. The presence of tantalum increases loss. It has been found

that if this material is doped with BaZrOs, the domain boundaries are stabilized and losses

decrease [20]. A novel high-permittivity material AgNbi-^TazOa with dielectric constant

in the 300 to 400 range with losses on the order of tan S ~ 1 x 10 -3 has been developed [21,22]. Semiconducting materials such as silicon and gallium arsenide are also used

as substrates. Silicon is very lossy at low frequencies, whereas gallium arsenide is low loss

over the microwave band.

Examples of dielectric resonators used in the wireless industry as shown in figure 2.7

are made of low-loss, temperature stable, high-dielectric constant materials. The requirements for dielectric resonators are summarized in table 2.5. Dielectric resonators are used

as oscillators, filters for rejection of unwanted frequencies, and combiners. Materials com- monly used for high-Q resonators include alumina, sapphire, and titanate compounds. The

relevant properties of dielectric resonators are summarized in table 2.5. Magnetic substrates include garnets and ferrites. Loss-loss magnetic materials axe used

in isolators and circulators. A commonly use magnetic substrate is yttrium-iron garnet

11
Table 2.4. Ceramic substrates [ll. Material Machinability Range of Anisotropy

or composite temperatures ( C)

Alumina Excellent -200 to 300 yes

Sapphire Good -200 to 300 no

Fused silica Excellent -200 to 500 no

Rutile Excellent -200 to 500 yes

Beryllium oxide Excellent -100 to 300 no Aluminum nitride Excellent -200 to 300 no

Borosilicate / Alumina Excellent -200 to 500 yes

Table 2.5. Summary of important properties for dielectric resonators.

Property Advantages

High-dielectric constant

Low loss Low-thermal expansion

High-thermal conductance

Miniaturization

Large Q, close channel spacing

Frequency stability

Cooler operation

(YIG).

2.3. Thermal Properties

The two thermal properties relevant to substrates are coefficient of thermal conductivity

(k) and thermal expansion coefficient (TCE) . The thermal coefficient of expansion qTce is

defined as

cktce = 77^. ( 2 -4) LAT"

where L is material thickness and AL is the change in thickness as temperature changes

by AT. Coefficients of thermal expansion are given for a number of materials in table 2.6

[1,16,23,25]. Most materials have positive coefficients of expansion. There are exceptions

such as rutile that has a negative TCE. Materials with negative TCE's can be combined

12
Table 2.6. Thermal coefficients of expansion (TCE).

Material a xlO6 (°C- ! ) Material a xl0f; ( C~ l ) ABS plastic 71 lanthanum aluminate 9

acetal 85 lithium niobate 15 -L, 4.1 || acrylic 68 magnesium oxide (MGO) [1] 8

alumina [1] 6.7 neodymium gallate 9

aluminum [1] 24 nylon 90.7

aluminum nitride [1] 4.6 PMMA 68

aluminum oxide [1] 2.6 polycarbonate 66

aluminum titanate 0.4 polyethylene (high density) 129

aramid/epoxy [10] 6-9 polyimide [23] 40

beryllium oxide [1] 8.5 polyimide/glass [1] 14-15

bismalimide triazine/epoxy [10] 15-17 polyimide/quartz [10] 6-8

borosilicate glass [23] 3.1 polypropylene [24] 86

calcium oxide 14.8 quartz [1] 11.2 copper [1] 17 Rexolite [6] 70

cordierite [1] 1.0 rutile [1] 70

cyanate ester [10] 13 sapphire [1] 5.3 diamond [1] 1.02 silicon [1] 3

epoxy [24] 54 silicon carbide [1] 3.7 FR-4 [1] 17-18 spinel [1] 6.6 FR-5 [1] 17-18 strontium titanate 9 fused quartz 0.5 strontium lanthanum aluminate 7 [6] fused SiC>2 0.5 strontium lanthanum gallate 10 [6] fused silica [1] 0.5 Teflon [6] 140

gallium arsenide [6] 5.7 tridymite [1] 17.5 gallium gadolinium garnet 8 zirconia oxide 9.2 germanium 6.1 Zr-Sn titanate [1] -6.9 kovar 5

13
Coaxial resonator

Dielectric

resonator

Figure 2.7. Dielectric resonators.

with materials with positive TCE's to produce a material with a small composite TCE.

Plastics have large TCE and low glass transition temperatures Tg (see table 2.7).

The temperature coefficient of permittivity is denned as

1 Ae'r

el AT (2.5)

r€ is usually expressed in parts in 106

[26]. When measuring permittivity as a function of

temperature it is important to first correct for thermal expansion and then use eq (2.5) to

calculate r£. The effects of temperature on permittivity has two origins. One is thermal

expansion which is due to lattice size changes and the other is the change of polarizability

with temperature.

A commonly used method of quantifying the effects of temperature on resonance fre- quency is the temperature coefficient of resonance frequency

A/ 1 Tf

(2.6)

/ AT

The thermal coefficients of expansion for composites can be calculated by mixture

formulas such as

14

(2.7)
Table 2.7. Glass transition temperature [10]. Material Tg (°C)

Polyimide/ Quartz 250

Cyanate ester 250

Polyimide/Glass 250

Teflon 200

BT/Epoxy 190

FR5 170

Rexolite 120

FR4 130

where ki, a.i, and Vi are the bulk modulus, coefficient of expansion, and volume fraction

of the ith phase [27]. The effective dielectric constant of a mixture of constituents with

permittivity eri can be approximated by

€r{eff) ~ l — _ y^ Vi(eri ~ 1) , , 1^ ( e

. + 2e )' [ } r{eff) i V e" + Zt"i

In addition to thermal expansion there is the problem of thermal warping of circuit

boards. Warping or camber is a result of differential thermal expansion. A measure of

camber can be estimated by

AW aw LAT

L ~ d

' { yj

where AW^ is the height of the warp of the material from a plane surface, aw is coefficient

of thermal bending, L is the length of material, and d is thickness [28].

2.4. Electric Properties of Surface- Cladding Material

Clad materials can have appreciable surface roughness. In order to promote adhesion, the

copper foil that is applied to the PWB material has a roughened surface. Surface roughness

affects measured capacitance. The effect of surface roughness on the loss tangent is small

at low frequencies; however, above 1 GHz the resistance of rough copper increases over

15
CD

60

-J

50 -

40 -

E 30 H o

E

o

20

10

50 100 150

Copper thickness (nm|

200

Figure 2.8. Copper thickness versus resistance [10].

16
Table 2.8. Conductivities of metals.

Material Conductivity, a Skin depth at (10 GHz)

xl07 (S/m) xl0-7 (m)

6.60

8.26

6.42

7.85

17.0

12.70

19.0

that of smooth copper [2]. Fields may penetrate thin metal cladding (see figure 2.8). The

skin depth is related to the conductivity a by

1

Cu 5.80

Al 3.72

Ag 6.17

Au 4.10

In 0.87

70-30 brass 1.57

Typical solder 0.71

The surface resistivity is

(2.10)

(2.11) a

Electrical conductances of commonly used metals are given in table 2.8.

2.5. Transmission-Line Parameters for Circuit-Board Applications

Important properties of transmission lines in PWB applications are attenuation, loss,

phase, impedance, and propagation delay. The propagation constant is given in terms

of distributed-circuit parameters

7 = a + j(3 = y/iRs + jcjL)(G + juC) « juisfZcJl + -^ + -^, (2.12)

where C,G,L are measured distributed circuit parameters. In eq (2.12) we neglected the

term containing CG and Rs — Rd.c. + Ra.c.\/7\ Rs is total surface resistance, Rd.c. and Ra. c . are the resistances at d.c. and a.c, and / is frequency. For TEM waves the attenuation can be separated into conductor and dielectric components

Rs W VoUr Jl 2Z 2 V e e'

T

17
11 r

5LUQ

o

i—

•<occ

DIELECTRIC CONSTANT

Figure 2.9. Propagation delay versus dielectric constant for many materials [23].

where Zq is the characteristic impedance of the line, and //o is the permeability of free

space.

The characteristic impedance is

Rs + jtoL _ L . Rs j. ,,

The loss tangent is tan 8 = G/{2nfC). The propagation delay in a lossless line is

td — Y

^r^^vac)

(2.14)

(2.15)

where L and Cvac are the inductance and vacuum capacitance of the line. The propagation delay increases as the square root of the dielectric constant [23]. In figure 2.9 the

propagation delay is plotted against the dielectric constant.

18
Table 3.1. Measurement parameters.

Component of permittivity (in-plane or normal)

Frequency

Loss measurement

Specimen thickness

Temperature

3. Dielectric Measurements

3.1. Overview of the Measurement Problem

No single technique can characterize all materials over all frequencies. Each frequency band

and loss regime requires a different method. Thin materials present a unique measurement

challenge since thickness is the dominant source of uncertainty for many measurements.

Dielectric properties depend on frequency, homogeneity, anisotropy, temperature, surface

roughness, and in the case of ferroelectrics, applied d.c. bias field [2]. Dielectric materials

may be isotropic or anisotropic, epitaxial or amorphous, clad or unclad. Anisotropy is

usually a result of weaving fiber in the material. In table 3.1 some of the various parameters pertaining to permittivity measurements are summarized. The measurement of thin

materials presents a special challenge in that uncertainties in thickness of the specimen

translates into uncertainty in the permittivity.

3.2. Measurements of Thin Materials

3.2.1. Measurement Methods

In this section we will overview the most commonly used thin material measurement techniques. We will discuss and compare the strengths and weaknesses of each technique.

We will also compare the techniques in light of destructive versus nondestructive measurements. For each technique, we either overview the theory or we refer to published

work [29]. We will indicate which fixtures can be used for obtaining permittivity normal

or in the plane of the sample. We also will give an uncertainty range for each fixture. We

do not consider thin films since this is an extensive area in and of itself. For thin films we

19
Sample

Figure 3.1. Schematic cross section of the reentrant cavity. The coaxial line inner and

outer diameters are 2r\ and 2r2, and specimen diameter is 2rs as indicated. The cavity

height is L.

refer the interested reader to recent references [30,31].

3.2.2. Reentrant Cavity

Resonant measurement methods are the most accurate ways of obtaining dielectric constant

and loss tangent. Most resonant techniques yield permittivity in the plane of the sample.

The resonant reentrant cavity is an exception in that it yields the permittivity component

normal to the face of the material at radio frequencies. The reentrant cavity is useful

because it is possible to accurately measure materials at frequencies from 100 MHz to 1 GHz.

The reentrant cavity depicted in figure 3.1 consists of a coaxial line or other transmission

line with a gap in the inner electrode. The specimen is inserted into this gap. The cavity is then resonated and the capacitance of the gap produces a frequency shift. If the specimen

20
gap region is at the very top or bottom of the cavity then the system is called a singly

reentrant cavity, whereas, if the sample gap is in the middle of the cavity it is called a

doubly reentrant cavity. The loss tangent is determined from quality-factor measurements

with and without specimen in place. Typical uncertainties for a well-characterized system

for low to medium permittivity are Ae'r — ±1%, A tan S — ±0.0005.

Two approaches have been used for modeling the reentrant cavity. The first is a lumpedcircuit approximation [32,33]. The other approach is a rigorous mode-matching technique

[34-36] . The full-field model is given in reference [34]

3.2.3. TEoi Split-Cavity Resonators for Thin Dielectrics

Unclad thin materials can be measured nondestructively using a split-TEon cavity res- onator as depicted in figure 3.2 [37-39]. This dielectric-resonator technique allows rapid

measurement at X-band frequencies for thin, low-loss materials. This type of resonator

has the electric field in the plane of the sample. The thin material is placed between the

sections and a resonant mode is excited. Generally the cavity is operated such that the

TEoi<5 mode propagates in the specimen and is evanescent outside the specimen. These

cavities can be constructed in various sizes to allow operation at frequencies from 8 to 20

GHz. Typical uncertainties are Ae'r = ±0.2% and A tan 5 = ±5 x 10 -5. The theory for

Split Cavity

Sample

Figure 3.2. TEqi split-cavity dielectric resonator for thin sheets.

21
this fixture is summarized in references [37,38]. Details of the full-mode model are given

in reference [40] . The full-mode model includes the effects of the fringing fields at the gap

in the cavity.

3.2.4. Cavity Resonators for Thin Dielectrics

Cavities have also been used for thin materials. The most common cavity is the TEoi

resonator [41]. In this case the permittivity in the plane of the specimen is measured. The

TMom cavity is also commonly used. In this cavity there is a strong Ez component of

the electric field at the center. If a specimen is placed near the center then it is possible

to measure the Ez component of the permittivity [42] . Either rod or bulk specimens can be used. TMmnO cavities have been used to measure the components of the permeability

tensor. In these measurements a thin rod specimen is inserted in a hole at the center of

the cavity [43]. A rod specimen has an advantage of less demagnetization.

3.2.5. TEoi Split-Post Dielectric and Magnetic Resonators

The split-post dielectric and magnetic resonator techniques are methods for measurement

of thin materials (see figures 3.3 and 3.4) [44-46]. In the split-post method a thin material

or film is inserted between two fixed dielectric resonators. The posts which support the

resonators have low dielectric constant and low loss. The resonance frequency and quality

factor of the posts are influenced by the presence of the specimen. Split dielectric res- onators were developed by DelaBalle [47,48], Maj [46], and Nishikawa et al. [45]. There

are many variations of this technique reported in the literature. Some fixtures have the

specimen extending to the back wall of the cavity. The lowest-loss technique is when the

dielectric resonators are supported by low dielectric constant posts. This configuration has

the advantage of reduced wall loss. Nishikawa et al. [45] used the finite element method

to analyze this fixture. Various techniques have been employed for this purpose: finite

difference , mode-matching, and finite-element methods. The geometry of a split dielectric

resonator fixture used in our measurements is shown in figure 3.3. Such a resonator operates with the TEoi<5 mode which has only an azimuthal electric field component so that

the electric field remains continuous on the dielectric interfaces. This minimizes air gap

systematic uncertainties. The resonator measures the permittivity component in the plane

of the specimen. A useful feature of the split-post resonator is that it can be designed

to operate in the low gigahertz region. We have successfully used dielectric resonators

22
Dielectric Resonator Past

Copper

Sample

Figure 3.3. Schematic diagram of a split dielectric resonator fixture.

operating from 1.5 to 12 GHz. Loop coupling is used in these dielectric resonators. Thin magnetic materials can be measured with the split-post magnetic resonator technique. This fixture consists of a dielectric post above a ground plane. The ground plane

induces a region of strong magnetic field. The thin magnetic material is inserted between

the posts and resonance frequency and quality factors are measured.

The main source of uncertainty in the real part of the complex permittivity of the splitpost resonator, as with the split-cavity resonator measurement, is from the uncertainty in

the thickness of the specimen. The relative uncertainty of the real part of the permittivity

is primarily due to thickness uncertainty. We have found the following equation for a specimen of thickness h is useful to estimate uncertainties

Ad Ah

! h

(3.1)

Typical uncertainties in the split-post resonator of the real part of permittivity are Ae'r =

±1%. Dielectric loss tangent uncertainty depends on other factors such as the accuracy

with which the quality-factor can be measured. For properly chosen specimen thickness, it

is usually possible to resolve dielectric loss tangents to approximately ±5xl0-5

for qualityfactor measurements made with accuracies of 1

23
Sample^ -

Figure 3.4. Schematic diagram of a split magnetic resonator fixture.

3.2.6. Courtney Technique

The Courtney fixture can be used to measure the dielectric properties of materials at

gighertz frequencies [26,49-54]. In this technique the TE015 mode is used to determine

dielectric properties. Low-loss, high dielectric constant sleeves are used to lower the res- onance frequency, thereby increasing the frequency coverage. Two measurements are re- quired to get both the permittivity and permeability of a material. First the material may

be measured without an applied magnetic field and then the Courtney fixture can be placed

between the poles of a magnetic so that the permeability can also be measured. In figure

3.6 we show a Courtney fixture with a specimen and sleeve resonator. Measurements on

garnets are given in figure 3.5 [49]. These measurements were made using both a TEon

resonator with sleeves and a coaxial transmission-line technique.

3.2.7. Full-Sheet Resonance Method for Thin Sheets

The full-sheet resonance technique is used to determine the permittivity of clad circuit

and printed wiring board materials (see figure 3.7) [55-57]. It is a nondestructive test and measures the bulk property of a substrate. The frequency of measurement is limited

by the specimen dimensions since the method uses one-half wavelength resonances. The

24
103

102

=£ 101

10°

10-

i E

::

'

:

l

Tti

4—

M

'Ml'.' .1 M 1 1 li 1 - RA. k-A/m- Pa.V/ fSarnot . Mm -149 kA/nrr Y flannel

s

N-- .

... :\_ "ft—I"

' v T[ I

[

| :::s;1 "•

H

'

\

i

i _. .

. 1 UIOIOCuk, noauiiaiui

J \ 'III

L/dld

Coaxial T ransmission Line Data^5 -Z=: : f

/ 7l :

:

0.001 0.01 0.1 1 Frequency (GHz)

10 100

0.001 0.01 0.1 1 Frequency (GHz)

Figure 3.5. Measurements on demagnetized garnets [49].

25
Side View

Sleeve

Sample

Top View

Figure 3.6. Courtney fixture with dielectric sleeve.

specimen is usually open at the sides; however some researchers measure with the sides

closed. The open edges make the electrical length of the specimen slightly longer than the

actual physical dimensions. The permittivity is measured by transmission and reflection

coefficients of test signals introduced by coupling to coaxial feeds. This causes the cladded

structure to resonate at integral multiples of one-half wavelength in the specimen. Higher

modes can also be used to extend the frequency coverage. The main difficulty in this

technique is mode identification and degeneracy. The full-sheet resonance method is limited

in its ability to determine the loss factor since the surface area of the metal cladding is

large relative to the volume of the specimen.

The relative permittivity is obtained from the resonant frequencies of a cavity. The

resonance condition for TEmn modes is

2/,

mV

a) (3.2)

where c is speed of light, and a and b are cross sectional dimensions, m and n are mode

26
Coaxial Couplers

Figure 3.7. Full-sheet resonance technique

numbers, and fmn are the resonant frequencies. Note that the equation does not depend

on specimen thickness. This lack of sensitivity to thickness has an advantage over other

techniques.

The measured resonant frequencies calculated from eq (3.2) differ from the theoretical

frequencies because of the open edges, conductivity of the plates, and radiation losses. The

very low measured quality factors in this technique produce frequency-pulling that must

be taken into account. Mode interference can also be a problem. Generally, better mode

separation is possible if the specimen is rectangular rather than square.

Collins derived an expression that accounts for frequency pulling due to finite wall

conductivity

fl = fuljl+-k- (3.3)

Br

Qc GrQr

where // and fu\ refer to loaded and unloaded resonant frequency. Qr is the radiation

quality factor, and Yr — Gr + jBr is the open-side aperture impedance [55].

27
Coupling Loops

« Post

Figure 3.8. Whispering gallery mode resonator. The specimen is in form of a disk.

The quality factors of cavity, radiation, and coupling ports Qc, Qr, and Qe are related

to the loaded Qi

(3.4)

1 i i i Qc Qr Qe Qo

where n is the cavity coupling coefficient.

The real part of the permittivity is also affected by the open sides of the specimen.

A correction for open sides can be made in terms of the capacitance of the plates C and

fringing capacitance Cf.

The relative permittivity with end correction is obtained from the resonant frequencies

of a cavity. The resonance condition is

, c + cf C + Cf

/e'r 2/„

(-) +(t) (3.5)

3.2.8. Whispering-Gallery and Fabry-Perot Resonators

Low-loss dielectric and magnetic materials can be measured in the microwave frequency

range by use of whispering-gallery modes as shown in figure 3.8 [58-61]. Whispering-gallery

modes have been used in measurements of both the real part of the permittivity and loss

tangent. Highly accurate dielectric loss measurements can be made using this technique.

In this dielectric-resonator technique the specimen is usually supported from the bottom

28
Coupling Aperture

Minor

Sample

I:::::

- :::::::::::::::::::::::::::::::::::: jlllf JBII

Mirror

Figure 3.9. Fabry-Perot resonator.

with a dielectric rod. The support rod does not influence the measurement because the

modes do not penetrate appreciably into the specimen [47,57,62-66]. Measurements using

whispering-gallery modes on low-loss materials are advantageous since conductor loss can be made very small.

Open resonators have been used for measuring low-loss materials in the millimeter range

in the configuration shown in figure 3.9 [67-71]. Open Fabry-Perot resonators consist of two

separated mirrors with a coupling aperture on one of the mirrors. In the confocal setup

both mirrors are concave, whereas in the semi-confocal arrangement one of the mirrors

is flat and the other is concave. The concave feature of the mirror minimizes radiation

leakage from the open sides of the resonator and focuses the beam onto a smaller area

of the specimen under test, thereby minimizing specimen edge diffraction effects. FabryPerot resonators have large quality factors and are useful for measurements on thin, low-loss

materials. Since they are open structures they suffer from radiation leakage. The tensor

permittivity values can be obtained by measuring at different angles of incidence. The

metal in the mirrors limits the accuracy of the loss measurement. Thin substrate materials can be measured with this technique by positioning the specimen on the flat mirror.

29
Copper

Figure 3.10. Stripline resonator [11].

3.2.9. Transmission-Line Techniques

Various transmission-line techniques have been used for nondestructive substrate property

determination [41,72-78]. These techniques can be broadly grouped under resonant or nonresonant techniques. In many applications transmission lines have open surfaces. Open

structures can radiate and have a more complicated field structure [3,79-93]. Conductors

may be deposited directly on wiring boards or substrates to form transmission lines, or

alternately, the conductor on a PWB board may be etched or routed into a test fixture.

PWB materials are thin and usually clad by copper, making measurements with closed

waveguide or coaxial transmission lines difficult. Also, many substrates and printed wiring

board materials are laminated so the required component of permittivity is normal to the

sample face. Transmission-line techniques are useful in PWB applications since the electric

field has predominately the right orientation.

The permittivity of a substrate or substrate-thin film composite can be obtained by

forming either a stripline from clad substrate (see figure 3.10), microstrip (see figure 3.11),

or coplanar fixtures (see figure 3.12), and then either resonating the system or looking at

the combined transmission and reflection response. Usually an effective dielectric constant

eefj is defined in the numerical modeling which includes the effects of the fields in the

30
Ground Plane

Figure 3.11. Micro-strip.

air region surrounding the transmission line. As a result the effective dielectric constant

depends on the fields in the specimen and the fringing fields. Theoretical models are usually

available that extract the material permittivity from the effective dielectric constant.

Striplines have been used both in resonant and nonresonant modes of operation. A

commonly use technique is the stripline-card method. In this technique a stripline is etched into a corner of a large sheet of PWB material. The stripline is then resonated and

thereby an estimate of the permittivity is obtained. In another approach the specimen

sheet and copper conductors are stacked and then pressure is applied to form a stripline

resonator [10]. In stripline we have a quasi-TEM mode and the fixture resonates at frequencies corre- sponding to integral multiples of one-half wavelength. The real part of the permittivity for

stripline is given by nc

2fr {L+AL).

where n is the number of half wavelengths, c is speed of light, L is the physical length of

transmission line, AL is a length extension due to fringing fields, and fr is the resonance

frequency. The loss tangent is calculated from

tan S

1 _L_ ^unl Qr (3.7)

31
Sample

Ground Plane

Figure 3.12. Coplanar waveguide fixture.

Qunl is the quality factor not including coupling port losses, but includes losses due to

dielectric and metal; Qc is the quality factor of the coupling probes [90,94].

A rectangular waveguide measurement technique is shown in figure 3.13 [78]. In this

method a specimen is inserted through a slot in the transmission line. The specimen is

positioned parallel to the waveguide walls to minimize air-gap depolarization since the

electric field is parallel to the sample face. A slight loss of electromagnetic energy occurs due to the presence of the slot.

3.2.10. Coaxial Apertures

Open-ended coaxial lines and waveguides [95,96] have been used for years as nondestructive

testing tools. In the open-ended coaxial or waveguide measurement the probe is pressed

against a specimen and the reflection coefficient is measured and used to determine the

permittivity. Coaxial probes have also been used for elevated temperature measurements

of solids and liquids [97]. The technique has been popular and studied extensively. Although nondestructive, the method has definite limitations. The method is sensitive to air

gaps since the probe has both Ez and Ep electric field components. At low frequencies

there is little field interaction with the material. Since the coaxial probe has electric field components in both axial and radial directions, the measurement contains components of

32
Figure 3.13. Waveguide substrate tester.

both the axial and radial permittivities. The open-ended waveguide technique has the

advantage of a tangential electric field at the probe end, thus minimizing the effect of an

air-gap. In process control, for example, in thickness testing, a noncontacting probe may

be required [97-104]. For this reason it is important to have a model of a coaxial probe

which includes lift-off [101], or inclusion of an air gap between sample and probe as shown

in figure 3.14. The coaxial probe operates at such a frequency where only the fundamental

TEM mode propagates in the coaxial line. Evanescent TMon modes are also assumed to

exist in the coaxial line near the probe end. In the coaxial line and the material under

test, the magnetic field is assumed to be azimuthally symmetric. Therefore only the H^

component needs to be calculated.

Two coaxial probes can be used to form a two-port test device. In this type of fixture33
(1)

ground plane

Mro (-ro alr gaP (2)

specimen (3)

termination (4)

jl=L + d

Figure 3.14. The open-ended coaxial probe over a specimen with an air gap between

specimen and probe.

a specimen is inserted between the probes and both reflection and transmission data is obtained and inverted for permittivity. The full-mode model is given in reference [34]. The analytical solution follows the same line of reasoning used in the full-mode single

coaxial-probe problem. Experimental results indicate that the coaxial probe is useful for broadband material measurements on thin materials as shown in figures 4.1 and 4.2. Uncertainties in open-ended coaxial measurements include calibration, dimensional,

and scattering parameter measurement uncertainties.

The coaxial probe has the advantage of nondestructive testing capability, but the uncertainties are larger than for resonant techniques.

3.2.11. Capacitive Techniques

Capacitance techniques are important at frequencies in the range of 1000 Hz to 100

MHz [105-109]. In these techniques the electric fields are nearly normal to the sample

plane. The difficulties with these measurements pertain to air-gap depolarization, elec- trode polarization, and minimizing the effects of the fringing field. An air gap at the

sample-capacitor interface will yield a low value for the real part of the permittivity. The

fringe field is usually partially eliminated by measuring the capacitance with and without

specimen and subtracting the results. Guards also can protect from fringing fields. At very

low frequencies, for conducting materials, electrode polarization is possible. Two-fluid ca^

pacitor measurements are frequently used on printed wiring board materials [110]. The

technique has the advantage that the material thickness does not enter the calculation.

The capacitance is measured in air and then in a fluid, with and without specimen. The

34
Permittivity Measurement of Epoxy Substrate

w

3.U 1 1 1 1 1 1 | 1 1 1 | 1

T

A

•

1 | I I I | I

Split-Post Resonator

Reentrant Cavity

Full-Sheet Resonance

One-Port Coaxial Probe

4.5 -

- -

-

r

4.0

1

II

' 1

» 1 r <

" » 1, -

-- -

7 S 1 •

i 1 1 1 1 1 1 1 1 1 1 i 1 i i i 1 i 12 3 4 5

Frequency (GHz)

Figure 4.1. Real part of the permittivity from measurements of FR4 material using a

coaxial probe compared to measurements made by reentrant cavity, split-post resonator,

and full-sheet resonance techniques.

equations are then solved for the permittivity. The fluids used in the method, such as

n-heptane, must have very low loss and be well characterized.

4. Measurements

In figures 4.1 and 4.2 coaxial probe measurements are compared to reentrant cavity and

full-sheet resonance results. Measurement results for different materials using a split-dielectric resonator operating

at a frequency of approximately 5.6 GHz are shown in tables 4.1 through 4.5 [111]. In

table 4.1 three different aluminas from three different manufacturers are given, notice the

variation in results. Measurement results for stacked or layered dielectrics are almost in35
Permittivity Measurement of Epoxy Substrate

0.3

0.2 -

1

to

-

-0.1

-0.2

"l—i—i—

|—i—i—i—

|—i—i—i—

|—i—i—i—

|—i—i—i—|—

r

i i

A Split-Post Resonator

Reentrant Cavity • One-Port Coaxial Probe

j L i i i i i i i i i i i i i i i i

Frequency (GHz)

Figure 4.2. Imaginary part of the permittivity from measurements of a FR4 material using a coaxial probe compared to measurements made by reentrant cavity, split-post resonator,

and full-sheet resonance techniques.

36
Table 4.1. Split-dielectric resonator results on low-loss materials [48].

Material f(MHz) Q h(mm) e'r tan 8 (x 104

) a£; A tan 8 (xlO4) Empty 5608.45 9335

Teflon 5587.07 9040 0.620 2.04 2.7 ±0.03 ±1.0

A12 3 5559.31 9639 0.842 9.95 0.4 ±0.03 ±0.5

A12 3 5321.06 9115 0.999 9.75 1.0 ±0.06 ±0.5

A12 3 5406.28 8081 0.740 9.23 2.7 ±0.06 ±0.5

dependent of the number of layers (see table 4.3). Since the field is in the plane of the

sample the split dielectric resonator method is not sensitive to the presence of air gaps

between stacked films. Since the electric field for the mode of operation has a component

only in the plane of the substrate under test, dielectric properties in the plane are determined. Some dielectric substrates may exhibit uniaxial anisotropy. Therefore additional

measurements in the direction perpendicular to the substrate are necessary to characterize

fully the dielectric properties. Measurement of the component of permittivity normal to the sample plane can be accomplished using the reentrant cavity technique.

In table 4.5 measurements on PWB materials are displayed. A set of measurements

using FSR on a number of modes is shown in tables 4.6 and 4.7 and compared with

measurements on reentrant cavity [55]. The circle fit procedure is yields a more accurate

quality factor and is summarized in [55]. Tables 4.8 to 4.14 report measurements of many

materials often used for substrates. The results are presented as data on substrate materials

from reference [111]. Figure 4.3 and 4.4 are plots of the permittivity of high-resistivity

gallium arsenide as a function of frequency. These measurements were made by X-band

cavity. Tables 4.15 through 4.17 and figures 4.5 through 4.12 tabulate measurements of a number of ceramics, plastics, and PWB laminate materials made by other researchers.

37
Table 4.2. Results from split-dielectric resonators operating unloaded at 10.35 and 12.8

GHz [48].

Material f(MHz) Q h(mm) 4 tan 5 (xlO4

) Ae'r Atan 5 (xlO4

) Empty 10375.1 8944

A12 3 (Vistal) 9570.2 9740 0.848 10.03 0.245 ±0.05 ±0.5

Rexolite 10214 7666 0.98 2.53 4.16 ±0.02 ±1

GaAs 9719.5 7134 0.51 12.9 2.75 ±0.02 ±1

Teflon 10304 8709 0.625 2.05 1.61 ±0.03 ±1

Empty 12818 5513

Teflon 12727 5416 0.62 2.034 1.94 ±0.05 ±1

LaSrAlOs 11319 5081 0.50 23.22 1.78 ±0.07 ±1

A12 3 11955 5560 0.70 9.94 1.18 ±0.05 ±0.5

Table 4.3. Split dielectric resonator results on 1 mm thick stacked polymer films of the same material [48].

f(MHz) Q h(mm) e'r tan 5 (xlO4

) Ae'r Atan 5 (xlO4) # Films

5608.59 9400 empty

5601.11 8000 0.100 3.19 49 ±0.05 ±4 1 5593.54 6890 0.201 3.20 50 ±0.05 ±3 2 5586.08 6080 0.303 3.20 50 ±0.04 ±2 3

5578.67 5480 0.406 3.20 49 ±0.04 ±1 4

5571.28 4480 0.511 3.19 49 ±0.03 ±1 5 5563.96 4970 0.616 3.18 50 ±0.03 ±1 6

38
Table 4.4. Measurement results of polymer films from split- dielectric resonators operating

unloaded at 1.46 and 2.05 GHz [48].

Material f(MHz) Q h(mm) e'r tan 5 (x 104

) Ae'r A tan 5 (xlO4

) Empty 2055.37 14392

film 2046.00 2020.7 0.96 3.34 324 ±0.02 ±50

Empty 1460.62 16028

film 1455.27 2487.6 0.96 3.34 323 ±0.02 ±50

Table 4.5. Split dielectric resonator results on printed wiring board materials [48]

Specimen f (MHz) Q h (mm) 4 tan 5 (xlO4

) Ae'r A tan 8 (xlO4

) 5608.71 8515 ±0.02 ±4

1 5584.71 2823 0.402 2.77 177 ±0.02 ±4

2 5585.05 2829 0.412 2.71 176 ±0.02 ±4

3 5584.66 2828 0.402 2.78 176 ±0.02 ±4

4 5584.66 2818 0.399 2.79 177 ±0.02 ±4

5 5585.21 2825 0.405 2.73 178 ±0.02 ±4

6 5582.34 5561 0.393 3.28 46.5 ±0.02 ±1

7 5579.97 5413 0.380 3.25 45.9 ±0.02 ±1

8 5579.41 5346 0.380 3.29 46.8 ±0.02 ±1

Table 4.6. FSR measurement on 0.38 mm thick panel. The reentrant cavity result was 4 = 2.45, ±2% at 440 MHz.

TE Mode f (MHz) 7r Circle fit FSR Uncertainty

01 310 2.476 2.488 ±0.007

10 439 2.466 2.478 ±0.009

11 539 2.459 2.449 ±0.017

02 621 2.474 2.478 ±0.011

22 1080 2.462

39
Table 4.7. FSR measurement on 1.41 mm thick panel. The reentrant cavity result was

e'r

== 4.22, ±1% at 568 MHz. Open-ended coaxial probe yielded e'r = 4.23 ±5% at 580

MHz.

TE Mode f (MHz) e'r Circle fit FSR Uncertainty

01 234 4.059 4.184 ±0.060

10 333 4.092 4.158 ±0.080

11 405 4.001 4.185 ±0.128

02 473 4.084 4.118 ±0.096

12 578 4.019 4.140 ±0.080

Table 4.8. Glass specimens. The standard uncertainties (RSS) are as follows: parallel-plate

dielectric resonator: Ue

> = 0.5%, Uta,n8 — 2xl0-5

, split-cavity: U€

> = 1%, Utain s = lxlO-4

, TEoi cavity resonator: Ue

> = 1%, Utan § = 1 x 10-4

, Fabry-Perot resonator: e

> = ±2%,

Ut&nS = 2 x 10~4

, reentrant cavity: e

> = ±1%, Ut!m 5 = 2 x 10-4

.

Material Value Parallel plate Split cavity 60 mm TEoi Split post Reentrant

Corning

7980

34604

f(GHz)

e' tan£

5.07

3.84

6.85 x 10-5

8.85

3.827

11.9 x 10-5

9.64

3.84

1.40 x 10-4

2.03

3.84

4.40 x 10- 5 Corning

7980

34605

f(GHz)

e' tang

5.07

3.844

6.8 x 10~5

8.82

3.822

11.7 x 10~5

9.63

3.843

1.4 x 10-4

2.03

3.838

3.1 x 10-5 Corning

7980

34606

f(GHz)

e' tan 5

5.26

3.844

6.90 x 10~5

8.86

3.825

1.80 x 10-4

9.64

3.826

1.5 x 10-4

2.03

3.84

4.9 x 10~5 Corning

7940

44608

f(GHz)

e' tan 5

4.89

3.847

6.83 x 10~ 5

8.86

3.825

11.6 x 10-5

9.64

3.826

1.4 x 10-4

2.03

3.839

3.6 x 10~5 Corning

H. Bussey

1723 (1959)

f(GHz)

e' tan^

9

6.20

5.36 x 10-3

1 6.21

3.2 x 10-3

40
Table 4.9. Plastic specimens of polytetrafluoroethylene (PTFE), cross-linked polystyrene

(CPS), fluoroethylenepropylene (FEP), polymethylmethacrylate (PMMA), and nylon. The

standard uncertainties (RSS) are as follows: parallel-plate dielectric resonator: Ue

> — 0.5%,

TEqi cavity resonator: U€

> — 1%, t/tan<5 = 1 X 10-4

^tan<5 : 2 x 10- , reentrant cavity:

%>, Utlm 6 2 x 10"

Material Value Parallel plate 60 mm TEoi Reentrant cavity

FEP f (GHz)

e' tan 5

6.59

2.064

7.04 x 10~4

9.837

2.025

3.12 x 10-4 PTFE f (GHz)

e' tan 5

9.93

2.05

2.0 x 10-4

9.816

2.055

2.1 x 10-4

1.082

2.06

3. x 10-4 CPS f (GHz)

e' tan 8

5.7 2.542

5.1 x 10-4

9.982

2.533

4.2 x 10-4

1.032

2.56

7 x 10-4 Nylon f (GHz)

d

tan 5

4.75

3.08

8.4 x 10-3

9.742

3.01

7.1 x 10-3 PMMA f (GHz)

e' tan 5

5.721

2.634

7.2 x 10-3

9.813

2.626

4.4 x 10-3

41
Table 4.10. Cubic single crystals. The standard uncertainties (RSS) are as follows: parallelplate dielectric resonator: IV = O.o^c. L"tan(5 = 2xl0_o

. whispering gallery Mode resonator:

Ue

> = 0.1%, 1'ta.nS — - x 10 . Anisotropic materials were measured either by two dominant modes (TEom and HEm) using the parallel plate rod resonator or two families of

whispering gallery modes.

Material Value Parallel Plate

LaA103 freq. (GHz) 18.38

(cubic) e 23.99

tan 5 1.0 x lO" 5 NdGa03 f (GHz) 18.49

(cubic) e' 21.82

tan 5 1.07 x lO"4 Zirconia f (GHz) 4.30

(cubic) e

1 27.8

tan 5 3.28 x 10~3 GGG f (GHz) 15.7

(cubic) e' 12.43

tan 8 2.64 x lO"3 SrTiOs f (GHz) 7.20

(cubic) e' 310

tan 5 4.01 x 10-4

MgO f (GHz) 17.46

(cubic) e' 9.70

tan 5 2.5 x lO-6

42
Table 4.11. Noncubic single crystals. The standard uncertainties (RSS) are as follows:

parallel-plate dielectric resonator: £/«=/ = 0.5%, UtaLn $ = 2 x 10 -5

, whispering gallery Mode

resonator: U€

> = 0.1%, Uta.nS = 2 x 10

-5

. Anisotropic materials were measured either by

two dominant modes (TEom and HEni) using the parallel plate rod resonator or two

families of whispering gallery modes.

Material Value Parallel plate Whispering gallery

A12 3 f (GHz) 10.0 12.4

|| c-axis e' 11.58 11.58

(sapphire) tan S 2 x lO"5 5. x 10~6 A12 3 f (GHz) 12.4

_l_ c-axis e' 9.40

(sapphire) tan S 2 x lO -5

7. x 10~6 LiNbOs f (GHz) 10.19

|| c-axis e' tan 5

32.97

8. x 10~ 5 LiNb03 f (GHz) 11.56

_]_ c-axis

tan 5

42.34

8.4 x lO"5 Quartz f (GHz) 7.75

'

_l_ c-axis

tan 8

4.59

1.5 x lO"5 Quartz f (GHz) 9.03

|| c-axis t' tand

4.443

1.3 x 10~5 Ti02 f (GHz) 4.2

|| c-axis e' 163.7

tan 5 1 x lO"4 Ti02 f (GHz) 4.2

_L c-axis e' 85.6

tan 5 8 x lO"5

43
Table 4.12. Low-medium dielectric constant ceramic specimens. The standard uncertainties (RSS) are as follows: parallel-plate dielectric resonator: U€

i = 0.5%, Utim 6 = 2 x 10 -5

, TEoi cavity resonator: Ue

> = 1%, Uta. n 6 = 1 x 10-4

, whispering gallery mode resonator: Ue

> = 0.1%, Ut&nS = ±2 x 10-5

.

Material Value Parallel Plate 60 mm Cavity Whispering Gallery

Ceramic f (GHz) 3.675 9.76

4 e' 4.704 4.686

tan 5 6.8 x 10-4 5.80 x 10-4 Ceramic f (GHz) 3.17 9.74

6 e' 6.592 6.592

tan S 4.58 x 10~ 4 5.30 x 10-4 Ceramic f (GHz) 2.713 9.74

9 e' 9.808 9.73

tan 5 2.55 x 10~4 2.50 x 10-4 Alumina f (GHz) 3.27 9.53 9.528

(1986) e' 10.04 10.02 9.98

tan 5 3.9 x 10~5 3.38 x 10- 5 3.2 x 10-5 Alumina f (GHz) 9.00

(1996) e' tan 5

9.992

1.30 x 10~3

44
Table 4.13. High-dielectric constant ceramic specimens. The standard uncertainties (RSS)

are as follows: parallel-plate dielectric resonator: Ut

i — 0.5%, Ut a.nS = 2 x IO

-5

, TEoi cavity

resonator: Ue

> = 1%, £/tan <5 = 1 x IO

-4

, whispering gallery mode resonator: U€

> — 0.1%,

C/tan <5 =±2x IO"5

Material Value Parallel plate 60 mm cavity Whispering gallery

Ceramic f (GHz) 1.987 9.72 9.577

13 e' 13.51 13.55 13.54

tan 5 1.07 x IO"4 1.10 x IO"4 1.01 x IO"4 Ceramic f (GHz) 1.834 9.71 9.692

16 e' 16.60 16.64 16.66

tan 5 2.43 x IO

-5

0.4 x IO

-4

5.70 x IO"5 Ceramic f (GHz) 1,617 9.70

20 e' 20.77 20.80

tan 5 8.4 x IO

-5

2.00 x IO"4 Ceramic f (GHz) 1.328 9.44 6.023

31 e' 30.96 31.03 30.99

tan 5 2.4 x IO" 5 5.0 x IO"5 4.9 x IO" 5 Ceramic f (GHz) 1.200 9.46 5.460

35 e' 35.15 35.19 35.14

tan 5 4.8 x IO

-5

1.6 x IO

-4

1.18 x IO

-4

Ceramic f (GHz) 1.116 9.46 4.812

36 e' 36.55 36.56 36.55

tan 8 3.3 x IO" 5 1.2 x IO

-4

8.8 x IO- 5 Ceramic f (GHz) 1.109 9.73

38 e' 38.65 38.77

tan 5 5.8 x IO" 5 3.0 x IO"4 Ceramic f (GHz) 2.83

78 e' tan 678.29

3.1 x IO"4 Ceramic f (GHz) 0.855 9.44 4.448

79 e' 79.27 79.29 79.11

tan 5 1.63 x IO"4 7.8 x IO"4 4.40 x IO

-4

45
12.97

12.96 -

12.95

c

1 12.94 1

r

12.93

12.92

12.91

i*V

?

A- Start I- Middle -Q- Terminus ^-a^

lii-it r

»*-**

*w4.

*- .-i-A-il

, i . ,

i , i , , . , i

8 8.5 9 9.5 10 10.5 11 11.5 12

Frequency (GHz)

Figure 4.3. Measurement of the real part of the permittivity of gallium arsenide using an X-band cavity [112]. Start, middle, and terminus refer to different specimens taken from

the same boule.

tan 5 x 10

3

8 8.5 9 9.5 10 10.5 11 11.5 12

Frequency (GHz)

Figure 4.4. Measurement of the loss tangent of gallium arsenide using an X-band cavity

[112].

46
Table 4.14. 1964 round-robin measurements compared with current measurements. The

round-robin results from 1964 are given below [113,114]. The standard uncertainties (RSS)

are as follows: parallel-plate dielectric resonator: U€

> — 0.5%, £/tan<5 = 2 x 10-4

, TEoi cavity

resonator: Ue

> = 1%, Uta. n s = 1 X 10

-4

.

Material Value NBS(1964) Parallel Plate TEoi (50 mm) TEoi (60 mm)

1723 Glass f (GHz) 9 10

(1964 RR) e' 6.20 6.26

tan 5 5.3 x 10-3 4.8 x 10~3 1723 Glass f (GHz) 9 9.58 10

(1972 RR) e' 6.155 6.16 6.146

tan 5 4.7 x 10~3 4.9 x 10~3 4.7 x lO-3 7940 Glass f (GHz) 9 9 10 9.82

(1972 RR) e' 3.826 3.822 3.828 3.829

tan 5 1.2 x 10~4 1.4 x 10-4 1.03 x 10- 4 1.2 x 10~4

47
Table 4.15. Additional dielectric measurements on ceramics and crystals.

Material Crystal f (GHz) e'r tan 5

Aluminum nitride [115]

Barium borate

Beryllium oxide [115]

Boron nitride [115]

Calcium carbonate [115]

Calcium fluoride [115]

Germanium [115]

Lithium niobate [115]

Neodymium gallate [115]

Nickel oxide [115]

Silicon nitride [115]

Potassium bromide [115]

Silicon [115]

Silicon carbide [23] Sodium chloride [115]

Strontium lanthanum aluminate [115]

Strontium lanthanum gallate [115]

Topaz [115]

Yttrium iron garnet [115]

Yttrium oxide [115]

Zinc oxide [115]

No 8.5 8.5 0.0030

Yes 0.001 4.6 0.0005

Yes 8.5 6.86 0.0003

No 5.0 4.30 0.0002

Yes 0.0001 8.5 0.0004

Yes 1 6.3 0.0006

Yes 10 16.6

Yes 10 29

Yes 10 20 0.0030

No 1 7.5 0.0001

No 8.5 5.5 0.0036

Yes 10 4.9

Yes 14 12 0.0090

No 10 47 0.0010

Yes 0.001 5.7 0.0001

Yes 10 17 0.0008

Yes 10 22 0.0001

Yes 0.01 6.5 0.0001

Yes 10 14.9 0.0001

No 0.001 11.3 0.0006

No 0.01 8.3 0.0300

48
Table 4.16. Additional dielectric measurements made on plastics.

Material f (GHz) 4 tan 5

PMMA [115] 3.0 2.61 0.0057

Nylon [115] 3.0 2.84 0.0117

Polyethylene [115] 3.0 2.26 0.0003

Styrofoam [115] 3.0 1.03 0.0002

Polyimide [23] 0.001 3.50 0.0003

Polysulfone [116] 1.0 3.02 0.0090

Polyolefin [116] 1.0 2.75 0.0200

49
Table 4.17. Dielectric measurements of PWB composites.

Material range of e'r FR-4 [10] 4.2-5.0

FR-5 (high temp) [10] 4.3-4.6

BT/epoxy [10] 4.0-4.2

Cyanate ester [10] 3.5-3.7

Arimid/epoxy [10] 3.7-3.9

Polyimide/glass [10] 3.9-4.2

Polyimide/quartz [10] 3.4-3.5

5. Elevated Temperature Measurements

Many substrate and PWB materials vary with temperature. In this section we will describe a system for making elevated temperature measurements; we also present permittivity

measurements as a function of temperature for a number of substrate materials. We use a

TEoi<5 dielectric resonator as shown in figure 5.1 for these measurements. The specimen is supported by a low-loss dielectric rod in order to minimize wall losses. The temperature

system as shown in figure 5.2 is an environmental chamber that operates from -80 °C to 300

°C. We use cavities, transmission lines, and reentrant cavities in the chamber. The chamber

has access holes on the sides for insertion of coaxial feeds for the cavities or transmission

lines. The chamber can also be purged with nitrogen gas to reduce oxidation and water

vapor.

Measurements of some common low dielectric constant materials are given in figures

5.3 to 5.8.

50
Frequency (Hz)

Figure 4.5. Measurements on the real part of the permittivity for MgO [115].

10-1

10*

10"3

in" 1 1 1 mill 1

i i i mill i inn

-a-298K

-1-473K

-0-673K

II

l i mill i i i mill i I nil 10

2 103 io4 io5 io6 10

7 io

{ 9 10 10 10 Frequency (Hz)

Figure 4.6. Measurements on the loss tangent part for MgO [115].

51
3.95

-Q 9- -a-a

3.85

3 fl I I

I I ""'I I I I ""'I I I

I

'

I 23456789'""I 1 "'I '' 10 11 10 10 10 10 10 10 10 10 10 10 Frequency (Hz)

Figure 4.7. Measurements on the real part of the permittivity for Si02 as a function of

temperature [115].

tan 8

298 K

373 K

473 K -Q-673K

Frequency (Hz)

Figure 4.8. Measurements on the loss tangent part for Si02 as a function of temperature

[115].

52
10 10 Frequency (Hz)

Figure 4.9. Measurements on the real part of the permittivity for rutile with electric field perpendicular to axis as a function of temperature [115].

1: 10 10 10 Frequency (Hz)10 10

Figure 4.10. Measurements on the loss tangent part for rutile with electric field perpendicular to axis as a function of temperature 115 .

53
10 10 Frequency (Hz)

Figure 4.11. Measurements on the real part of the permittivity for silicon nitride as a

function of temperature [115].

ii 10

10 10 Frequency (Hz)

Figure 4.12. Measurements on the loss tangent part for silicon nitride as a function of

temperature [115].

54
D<

///////////////

//

^MeU

D

Sample-^

II

1

h

r 1

B/ Dielectric

Support

j

//////, ///////

[=>c

Figure 5.1. TEoia resonator for elevated temperature measurements.

55
Plug

7 mm to 14 mm

Adapter

(2ea.)-ESIPlugs ^^p

14 MM AIR LINE AND ADAPTER IN CHAMBER

Inner Dimensions

30 cm wide x 40 cm deep x 50 cm high Outer Dimensions

49 cm wide x 75 cm deep x 75 cm high Top & Side Port are 10 cm diameter

Thermocouple

* Thermocouple.

wires^ m

Stainless Steel

Air Lines Adapter

pea.)

i ii iiiiiiii

iiiiiiiii

i

iii

i iiiiiiii

i a

- 15 cmPlugs are to allow the use of 14 & 79 mm coaxial lines

Plug

Inert Gas Port

Length of Adapter is 20 cm

Figure 5.2. Environmental chamber for elevated temperature measurements.

56
e;

2.08

2.06

2.04

2.02

2.00 :

1.98 ;

1.96 -

1.94

:<

1 1 1 1 1 1

i i i i i i — i i i i i i

| ! , -

( i

-

1 T

1 1 1 1 1 1 — 1 1 1 1 1 1

1 1 1 1 1 1

.

.

i

i

) \

i n i t

i i i i

i l l i

i i i i

1

I

'" i i i i

>: : :

i i i i r"

i i i i i i

1

' ' A ' ' r i 1 1* t

i i i i i

T

|

'

,

.

,

,

!

i i i -i i j i\

i i i i i i

i i i i i i —

i i i i 1 i i i i 1 i i i i 1 i i i i 1 i i i i 1 i i i i 1 i i

9

20 40 60 80 100 120 140 160

Temperature, °C

Figure 5.3. Real part of the permittivity of Teflon as a function of temperature.

57
tan 5x10

3.80

3.60 -

3.40 --

3.20 -

3.00

2.80

2.60

2.40

2.20

2.00

M=ffl i i i i R> i

i i i i i i

i . i i i i i

1 J 1 1 1 ^ +

i i i i j i

i i i i i i

i i i i i i $""• :

: : :

;

i

l l l l J i

I I I I I I

I I I I I I

20 40 60 80 100 120 140 160

Temperature, °C

Figure 5.4. Loss tangent of Teflon as a function of temperature.

58
2.55

2.54 -

£r

1 2.53 -

2.52 -

0 : t i : : : : —|

! i ! , ! 1 T

i ;

i i i i i

: : 1 : k': 1 :____:

: : : ~1

f j| :

2.51 20 40 60 80 100 120 140 160

Temperature, °C

Figure 5.5. Real part of the permittivity of Rexolite as a function of temperature.

6. Conclusion

Each technique we have reviewed has a niche in the frequency band, field behavior, and

loss characteristics of printed wiring board and substrate materials. One technique alone is not sufficient to characterize materials over all of the necessary parameters. Measurements

of substrate materials present a metrological challenge because of uncertainty in thickness

and anisotropy. Typical PWB materials have a thickness of between 0.2 to 3 mm. Large

uncertainties of thin materials are caused by large thickness uncertainties. Measurement

with this type of field orientation can suffer from the effects of air gap.

The reentrant cavity, stripline, and full-sheet resonance techniques are useful for mea59
7.00

6.80

6.60

6.40

6.20

tan 6 x 10

4 e.oo

5.80

5.60

5.40 F

5.20

5.00 20

:'C

i i i —i

1

i i i i i

i i i i i

i i i j _ _ i }

:

i

> :

:

:

i J

' 4

:

1 1 Ji-i 4 -t -

: <

+ —

>

: 9 :

: : : j . :<> :

i i i i i

i i i i 1 i i i i 1 i i i i 1 i i i i 1 i i i i 1 i 1 1 1 1 1 1 1

1

60 80 100 120 140 160

Temperature, °C

Figure 5.6. Loss tangent of Rexolite as a function of temperature.

Table 5.1. Dielectric measurement categories compared.

Technique Field Advantages Disadvantages Ae'r A tan 5r Full-sheet resonance TE10 < Poor e'; ±2

Transmission-line TEM,TEio Broadband Machining of specimen ±5% ±0.01

Capacitor Capacitor Normal E-field Air gap ±1% ±10~4

Cavity- TEoi Very Accurate Narrow band ±0.2% ±5 x 10" 5

Cavity TM0m. <, Air gap ±0.5% ±5 x 10~4

Dielectric resonator TEoi Very Accurate Low-loss region ±0.2 ±5 x 10" 5

Open-ended probe TEM, TMoi Nondestructive Contact problem ±10% ±0.02

Fabry-Perot Quasi-TEM High frequency Low-loss materials ±2% ±0.0005

60
E/

10.16

10.14

10.12

10.10

10.08

10.06

10.04

10.02

10.00

9.98

:

-:—:

;------y----i T---!--f

-

1- i ' -• i-0 t

i

;

i : j' § : :

| | L.| -j 4 4.

I I Q I —f- I I

I ill I I i

• - - - ' ~r ~ ~ r "i " " "i "

' "i" "7"

i l iii ; i i i i

i i i i -I—J---W-"! ; " '

;

:A....^.J>._; ; .; \

;

20 40 60 80 100 120 140 160

Temperature, °C

Figure 5.7. Real part of the permittivity of alumina as a function of temperature.

Table 5.2. Magnetic measurement methods compared.

Technique Field Advantages Disadvantages Ae'r A tan Sr Transmission-line TEM,TEio Broadband Machining of specimen ±2% ±0.01

Cavity- TEon Very accurate Low loss ±0.5% ±5 x 10" 4

Cavity TMno Vrz Low loss ±0.5% ±5 x 10^

Dielectric resonator TEon Very accurate Low loss ±0.5% ±5 x 10

-4

Whispering-gallery Hybrid Very accurate High frequency ±1 ±5 x 10~6

Courtney TEoi Very accurate Use sleeves ±1 ±5 x 10_i

61
tan 5x10

0.4U

5.20

5.00

4.80

4.60

4.40

4.20

4.00

3.80

i en

1 1 1

1 1

1 1 : 4

J ^t

''

a :

i 1

i i i

- / i

< I i < i

i i i 9 !__ __ 1 __

T

_

i i i i i i i i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 40 60 80 100 120 140 160

Temperature, °C

Figure 5.8. Loss tangent of alumina as a function of temperature.

62
surement of the component of permittivity normal to the sample face. The reentrant cavity

technique has difficulty with specimens thinner than 0.5 mm; however, it yields a good measurement of loss. TMom cavities yield a measurement with the electric field normal to the

specimen face. These cavities can measure over a frequency band of 1 to 10 GHz by using

higher modes. The stripline technique has the advantage of easily accommodating PWB

materials. It gives reasonable estimates for the real part of the permittivity and borderline

estimates for the imaginary part of the permittivity. Many of the important features of

the most important measurement techniques are summarized in tables 5.1 and 5.2. The

split-cavity and split-post resonators are useful for obtaining in-plane permittivity and

loss. Whispering-gallery modes are very sensitive to loss. Fabry-Perot resonators are useful at high frequencies. The coaxial probe techniques are useful in obtaining permittivity

of isotropic materials with medium accuracy.

The full characterization of thin, anisotropic materials generally requires two techniques, one for the component of permittivity normal to specimen face and one for in-plane

permittivity. However, the loss measurement is not affected as much as the real part of

the permittivity by anisotropy and a single measurement often suffices. Therefore for the

normal-field measurement, resonant transmission- line methods can be used. However the

loss could be obtained by more accurate in- plane techniques such as TEq\ resonators. Magnetic substrate measurement requires a strong magnetic field. Magnetic materials can be measured by a split-post magnetic resonator, TMno [43] or TEon cavities,

whispering-gallery modes, or TEon cavities or dielectric resonators (see table 5.2).

We would like to thank J. Krupka and R. Geyer for measurement assistance. Also Brad

Givot for reviewing the report.

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