NASA Technical Memorandum 102123 

Measurements of Complex Permittivity 

of Microwave Substrates in the 20 

to 300 K Temperature Range 

From 26.5 to 40.0 GHz 

Felix A. Miranda and William L. Gordon 

Case Western Reserve University 

Cleveland, Ohio 

and 

Vernon 0. Heinen, Ben T. Ebihara, 

and Kul B. Bhasin 

Lewis Research Center 

Cleveland, Ohio 

Prepared for the 

1989 Cryogenic Engineering Conference 

sponsored by the University of California, Los Angeles 

. Los Angeles, California, July 24-28, 1989 

fBASA-TH-la2123) tlBASUBEBENTS OF COMPLEX 18 9 -270 38 

PEBHITTIVITY OF MICROWAVE SUBSTRATES I1 THE 

20 TO 300 K TEMPERATURE RANGE FROU 26.5 TO 

i00.Q GHz (NASA. Lewis Besearch Center) Unclas 

10 P CSCL 138 63/31 0224117 
MEASUREMENTS OF COMPLEX PERMITTIVITY OF MICROWAVE SUBSTRATES IN THE 

20 TO 300 K TEMPERATURE RANGE FROM 26.5 TO 40.0 GHz 

Felix A. Miranda and William L. Gordon 

Case Western Reserve University 

Cleveland, Ohio 

Vernon 0. Heinen, Ben T. Ebihara, and Kul B. Bhasin 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 

SUMMARY 

A knowledge of the dielectric properties of microwave substrates at low 

temperatures is useful in the design of superconducting microwave circul ts. 

In this paper, we report the results of a study of the complex permittivity of 

sapphire (Al2O3), magnesium oxide (MgO), silicon oxide (SiOz), lanthanum aluminate (LaA1031, and zirconium oxide (Zr02), in the 20 to 300 K temperature range, 

at frequencies from 26.5 to 40.0 GHz. 

7 M parts of the complex permittivity were obtained from the scattering parameters, 

o which were measured using a HP-8510 automatic network analyzer. For these 

e measurements, the samples were mounted on the cold head of a helium gas closed 

w cycle refrigerator, in a specially designed vacuum chamber. An arrangement of 

wave guides, with mica windows, was used to connect the cool ing system to the 

network analyzer. A decrease in the value of the real part of the complex permittivity of these substrates, with decreasing temperature, was observed. For 

MgO and Al2O3, the decrease from room temperature to 20 K was of 7 and 

15 percent, respectively. 

by 15 percent, and for Si02 by 2 percent, in the above mentioned temperature 

range - 

The values of the real and imaginary 

m 

I 

For LaA103, it decreased by 14 percent, for Zr02 

INTRODUCTION 

The successful applicat on of thin films, made with the new high temperature superconductor oxides, in the development of microwave circuits, rest 

considerably on the dielectr c properties of the different substrates used for 

film deposition. 

strates with low dielectric constant and loss tangent, (ref. 1) If good 

performance from microwave components is expected. 

For microwave applications, it is desirable to have subUntil now, Y-Ba-Cu-0 films deposited on SrTi03, have shown the highest 

quality when compared with films deposited on other substrates. 

due to its extremely temperature dependent dielectric constant, with a value 

for 300 at room temperature, around 1000 at 77 K, and over 18000 at helium temperatures, and its considerably high loss tangent, (ref. 2) its microwave applicability is rather limited. Although other materials as MgO, LaA103, and Zr02 

are now being used as substrates, information about their dielectric properties 

at temperatures below room temperature, and for some of them even at room temperature, is rather scarce. 

Nevertheless, 
In this paper, we report on the measurements of the microwave complex permittivity of MgO, Al2O3, LaA103, Zr02, and Si02, in the 20 to 300 K temperature 

range and as a function of frequency. The measurements were taken following a 

method previously reported by other authors (refa. 3 to 5). This method allows 

the determination of both parts of the complex permittivity in a rather simple 

way, and is very convenient for cases in which a fast determination of the 

dielectric constant of a material is needed. Nevertheless, the method has a 

high uncertainty in the measurement of the imaginary part of the complex permittivity for materials with very low loss tangent. 

ANALYSIS 

In order to determine the value of the real and imaginary parts of the 

complex permittivity for the various substrates under consideration, we have 

followed the method proposed by Nicolson and Ross, (ref. 3) as modified by 

Wier, (ref. 4) and following the implementation suggestions of reference 5. 

an ideal case, consider a piece of material installed in a rectangular wave 

guide with characteristic impedance Zo, as shown in figure 1. 

the scattering parameters, Sll(w) and S21(~), can be related with the 

reflection, r, and transmission, T, coefficients, as follows, 

In 

After solving the corresponding boundary conditions at x = 0 and x = d, 

2 

22 

(1 - r )T 

I-TT 

2 (1 - T )r 

I-TT sll = 22’ s21 = 

The reflection coefficient, when the length of the material is infinite, 

is given by 

z - zo e- 1 

e+ 1 

r=- a z + zo (2) 

Also, the transmission coefficient, when the length of the material is 

finite, is given by, 

T = exp(-jw PE d) = expC(-jw/c) prey dl (3) 

Thus, the reflection and transmission coefficients can be derived by measuring Sll(w) and S21(w>, and in turn they can be used to obtain the value of 

the permi ttivi ty. 

The experimental configuration used for the measurements of the reflection, S11(0>, and transmission, S2l(w>, scattering parameters for the samples 

under consideration, is shown In figure 2. The measurements were made using an 

HP-8510 automatic network analyzer, properly connected by an arrangement of 

Ka-band (26.5 to 40.0 GHz) wave guides, to a cooling system. 

tem consist of a CTI-Cryogenics closed cycle helium refrigerator, associated 

with a Lake Shore Cryotronics temperature controller, model DRC 91C, which 

allows measurements to be taken at the required low temperatures. 

The cooling sys2 
The measurements were performed under vacuum (<lo-3 torr), in an aluminum 

vacuum chamber specifically designed to fit on the top of the external shield 

of the refrigerator and to give access to the set up of wave guides connecting 

the network analyzer with the refrigerator. 

inside the chamber, two mica windows were placed at its ends. The material for 

the windows, was selected due to its very low loss and transparency in this 

frequency range. 

In order to preserve the vacuum 

In order to measure the scattering parameters, the sample was held in a 

sample holder which was suspended between two wave guide flanges, as shown in 

figure 3. The wave guide flanges were in direct contact with a copper plate, 

which in turn was attached to the cold head of the refrigerator. The two supporting wave guides inside the vacuum chamber, were specially designed to be 

used at low temperatures. They are made of stainless steel, a relatively poor 

thermal conductor. A gold plating of their internal surfaces was performed, in 

order to reduced the microwave losses. Finally, in an attempt to reduce the 

errors induced in the measurements, possibly due to linear thermal contractions 

of the wave guides as the temperature decreases, the system was calibrated at 

all the temperatures at which measurements were taken. These calibrations were 

stored, so that they could be recalled to be used in later measurements. 

RESULTS 

The thickness of the substrates used in this study, varies from 0.285 mm 

for MgO, to 1.641 mm for Si02. The thicknesses for the A120 , LaA103, and 

7 and table I show the measurement results for the real part of the complex 

permittivity of the samples, at room temperature and at 20 K. The value for 

the dielectric constant of MgO at room temperature agrees well with values quoted 

by other researchers (refs. 6, 7, 9). For A1203 and Si02, the values of the 

dielectric constant obtained at room temperature, are also in good agreement 

with the values quotedpby Zahopoulos (ref. 8) and Von Hippel (ref. 7) respectively. Although for Zr02 there appear to be no data for comparison in this 

frequency range, the value for its dielectric constant at room temperature is 

consistent with the one reported by Gorshunov, et al., (ref. 9) at frequencies 

within 10’’ to 1012 Hz. In the case of LaA103, the value obtained for its 

dielectric constant at room temperature is not consistent with the value of 

15.3 reported by Simon, et al. (ref. 1). Due to this discrepancy, measurements 

were performed in four different LaA103 samples, each one made from different 

batches, in order to determine if the disagreement was due to intrinsic properties of the sample. 

these measurements was practically the same for all the samples and was consistent with our previously determined value. Nevertheless, since not much 

information for the value of the dielectric constant of this substrate is 

available yet, additional experimental verification wi 11 be appropriate. 

Zr02 samples are 0.496 mm, 0.432 mm, and 0.494 mm respective 7 y. Figures 4 to 

The value of the dielectric constant obtained from 

Table I shows the real and imaginary parts of the complex permittivity, 

For MgO and Al2O3, a decrease of 6 and 14 percent down 

at four different temperatures and at 32.9 GHz. A decrease in the value of the 

real part of the complex permittivity is clearly observed in all the substrates 

under consideration. 

to 70 K, and of 7 and 15 percent down to 20 K respectively, is observed. For 

LaA103 and Zr02, the value of the real part of the complex permittivity is 

lowered by 10 and 13 percent respectively, at temperatures around 70 K, and 

3 
goes down 14 percent for LaA103 and 15 percent for ZrO2, at 20 K. For Si02, 

the dielectric constant is lowered by 1 percent at 70 K and by 2 percent for 

temperatures around 20 K. 

From comparison of the data of table I with that of the references mentioned, it can be seen that there Is relatively good agreement for the real 

part of the complex permittivity but wider variation for the imaginary part. 

For example, a com arison of the value for the loss tangent for MgO at room 

temperature, 8x10-5, obtained from the data in table I, with the value quoted 

by Von Hippel, 3x10-4, reveals a difference of two orders of magnitude. Due 

to this fact, it is very difficult to observe a particular temperature and frequency dependence for this parameter. This is an intrinsic limitation of the 

technique, when applied in the calculation of the imaginary part of the complex 

permittivity for materials of low loss tangent, as mentioned in the 

introduction. 

The frequency of 32.9 GHz was selected for construction of tab 

being typical of the largest variations with temperature. Finally, 

measurements, the statistical error in the real part of the complex 

tivity is 50 

The rea 

02, while the variation in the imaginary part is large 

CONCLUSIONS 

and imaginary parts of the complex perm 

and Si07 have been measured. A decrease 

e I as 

for these 

permitttlvity for MgO, Al2O3, 

LaA103, Zr02 in the value of the real 

part of the complex permittivity, with decreasing temperature, was observed In 

all the substrates. Nevertheless, no considerable change was observed as a 

function of frequency. The results obtained in this study show that, at least 

from the stand point of the dielectric constant, the substrates considered 

appear to be better suited than SrTi03, for use with the new high temperature 

superconductors in microwave applications. 

REFERENCES 

1. Simon, R.W., et al.: Low-Loss Substrate for Epitaxial Growth of HighTemperature Superconductor Thin Films. Appl. Phys. Lett., vol. 53, 

Dec. 26, 1988, pp. 2677-2679. 

2. Padamsee, H., Green, K., Gruschus, J., Kirchgessner, J., Moffat, D., 

Rubin, D.L., Sears, J., Shu, Q.S., Buhrman, R., Lathrop, D., Noh, T.W., 

Russek, S., and Sievers, A.: "Superconductivity and Applications" (To be 

published). 

3. Nicolson, A.M.; and Ross, G.F.: Measurement of the Intrinsic Properties 

of Materials by Time Domain Techniques. IEEE Trans. Instrum. Meas., 

vol. 19, no. 4, Nov. 1970, pp. 377-382. 

4. Weir, W.B.: Automatic Measurement of Complex Dielectric Constant and 

Permeability at Microwave Frequencies. Proc. IEEE, vol. 62, no. 1, Jan. 

1974, pp. 33-36. 

4 
5. Hewlett Packard Product Note No. 8510-3, The Measurement of Both Permlt6. Hossain, M.D.: Microwave Dielectric Properties of Ti4+/Mg0 and Ni*+/MgO. 

tivity and Permeability of Solid Materials. pp. 5954-1535 (1985). 

Appl. Phys. A., vol. 36, no. 1, Jan. 1985, pp. 63-65. 

7. Von Hippel, A.R.: Dielectric Materials and Applications. The MIT Press, 

Cambridge, MA, 1954. 

8. Zahopoulos, C., Kennedy, W.L.; and Sridhar, S.: Performance of a Fully 

Superconducting Microwave Cavity Made of the High Tc Superconductor 

Y1Ba2Cu30. Appl. Phys. Lett., vol. 52, no. 25, June 20, 1988, pp. 2168-2170. 

conductors. Physica C, vol. 153-155, pt. 1, 1988, pp. 667-668. 

9. Gorshunov, B.P., et al.: Submillirnetre Properties of High-Tc SuperTABLE I. - COMPLEX PERMITTIVITY OF MICROWAVE SUBSTRATES AT 32.9 GHz 

[elr = real part of complex permittivity. ellr = imaginary part of 

complex permi ttivi ty.1 

Substrate MgO A1203 LaA103 Zr02 Si02 

300 9.88 0.556 9.51 0.675 21.9 1.70 25.4 1.72 3.82 0.516 

150 9.45 .726 8.52 .925 21.6 1.48 23.6 1.75 3.80 .159 

70 9.26 .351 8.19 .695 19.7 2.98 22.0 2.50 3.78 .688 

20 9.19 .420 8.11 .613 18.8 3.71 21.6 2.23 3.75 .298 

5 
x=o x =d 

FIGURE 1. - WAVEGUIDE WITH FILLED MATERIAL. 

FIGURE 2. - EXPERIMENTAL SETUP. 

ORlCilNAli P?,,GE 

BLACK AND WHITE PHoroQRAP" 

6 
FIGURE 3. - SAMPLE SUSPENSION SETUP. 

nw 

!.x 26.5 28.5 30.5 32.5 34.5 36.5 38.5 40.5 

FREQUENCY. GHz 

FIGURE 4. - MGO SUBSTRATE AT ROOM TEMPERATURE. 

I I I I 

.5 28.5 30.5 32.5 34.5 36.5 38.5 40.5 

FREQUENCY, GHz 

FIGURE 5. - MGO SUBSTRATE AT 20 K. 

7 
J 

dW I I I I I I J oz 26.5 28.5 30.5 32.5 34.5 36.5 38.5 40.5 

FREQUENCY. GHz 

FIGURE 6. - SAPPHIRE SUBSTRATE AT ROOM TEMPERATURE. 

nu 

wn 6 er 26.5 28.5 30.5 32.5 34.5 3E.5 38.5 40.5 

FREQUENCY GHZ 

FIGURE 7. - SAPPHIRE SUBSTRATE AT 20 K. 

8 
1. Report No. 

NASA TM-102123 

7. Author@) 

Felix A. Miranda, William L. Gordon, Vernon 0. Heinen, 

Ben T. Ebihara, and Kul B. Bhasin 

2. Government Accession No. 

- 9. Performing Organization Name and Address 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 44135-3191 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, D.C. 20546-0001 

7. Key Words (Suggested by Author(s)) 

Complex permittivity 

Microwave substrates 

Scattering parameters 

3. Recipient's Catalog No. 

5. Report Date 

6. Performing Organization Code 

18. Distribution Statement 

Unclassified - Unlimited 

Subject Category 

8. Performing Organization Report No. 

E-4903 

3. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of pages 

Unclassified Unclassified 10 

10. Work Unit No. 

506-44-20 

11. Contract or Grant No. 

22. Price' 

A03 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Agency Code 

15. Supplementary Notes 

Prepared for the 1989 Cryogenic Engineering Conference sponsored by the University of California, Los Angeles, 

Los Angeles, California, July 24-28, 1989. Felix A. Miranda and William L. Gordon, Case Western Reserve 

University; Vernon 0. Heinen, Ben T. Ebihara, and Kul B. Bhasin, Lewis Research Center. 

6. Abstract 

A knowledge of the dielectric properties of microwave substrates at low temperatures is useful in the design of 

superconducting microwave circuits. In this paper, we report the results of a study of the complex permittivity of 

sapphire (A1203), magnesium oxide (MgO), silicon oxide (Si02), lanthanum aluminate (LaAIO,), and zirconium 

oxide (Zr02), in the 20 to 300 Kelvin temperature range, at frequencies from 26.5 to 40.0 GHz. The values of 

the real and imaginary parts of the complex permittivity were obtained from the scattering parameters, which were 

measured using a HP-8510 automatic network analyzer. For these measurements, the samples were mounted on 

the cold head of a helium gas closed cycle refrigerator, in a specially designed vacuum chamber. An arrangement 

of wave guides, with mica windows, was used to connect the cooling system to the network analyzer. A decrease 

in the value of the real part of the complex permittivity of these substrates, with decreasing temperature, was 

observed. For MgO and A1203, the decrease from room temperature to 20 K was of 7 and 15 percent, respectively. For LaA103, it decreased by 14 percent, for Zr02 by 15 percent, and for Si02 by 2 percent, in the above 

mentioned temperature range. 

~ ~~~ 

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