P H Y S I C A L R E V I E W V O L U M E 9 9 , N U M B E R 4 A U G U S T 1 5 , 1 9 5 5

Thermal Conductivity of Germanium at Ambient Temperatures* KATHRYN A. MCCARTHY AND STANLEY S. BALLARDI

Tufts College, Medford, Massachusetts (Received March 14, 1955)

The thermal conductivity of high-purity germanium has been measured; it varies approximately linearly from 0.61 watt (cm C0)"1 at 5°C to 0.50 watt (cm C0)"1 at 95°C.

THE thermal conductivity of high-purity ger­manium has been measured through the tem­

perature range 5 to 95°C, employing a technique1

developed especially for use with small samples of poorly conducting materials such as optical crystals. The method is comparative; the thermal conductivity of the "unknown" is measured against a "standard" material of well-established thermal conductivity. In the present measurements, the comparison materials were cast zinc2 and nickel,3 both of high purity, obtained from the New Jersey Zinc Company and the Internationa] Nickel Company, respectively.

The germanium samples were furnished by the Westinghouse Research Laboratories of East Pitts­burgh, Pennsylvania. I t was stated4 that they were cut from an oriented ingot of n-type germanium of resistivity about 40 ohm-cm. Two samples were tested, one of which was a 1-cm cube and the other a parallele­piped with dimensions 1 cmXI cm X 0.5 cm, oriented

. 65

.60

.55

o .50

.45

• 1 1 1

GERMANIUM N-TYPE heat conduction-100axis

^^X Grieco - Montgomery

o \

.155

,143

,131 !

,119

.107 20 40 60

Temperature, °C 80 100

FIG. 1. New thermal conductivity data (plotted as circles) for high-purity n-type germanium. The value previously reported by Grieco and Montgomery is also plotted, as X. Abscissa units are watt (cm C°)_1 on the left, and cal (sec cm C°)_1 on the right.

* Presented at the Berkeley meeting of the American Physical Society, on December 29, 1954 [Phys. Rev. 98, 271 (1955)].

f Present address: Scripps Institution of Oceanography, Uni­versity of California, La Jolla, California.

1 Ballard, McCarthy, and Davis, Rev. Sci. Instr. 21, 905 (1950). 2 National Bureau of Standards, Circular No. 395, 1931, pp.

69-71. 3 E. N. Skinner (private communication). 4 R. E. Davis (private communication).

for heat flow perpendicular to the short side. In both cases the orientation of the samples was such that the heat flow was parallel to a 100 crystal direction.

In Fig. 1, the data are plotted as circles, and a straight line has been drawn through them somewhat arbitrarily. I t is noted that in this temperature range the thermal conductivity decreases with increasing temperature—presumably this trend might be reversed at temperatures approaching the melting point of germanium (960°C) because of the increasing role then played by electron conduction.

The values of thermal conductivity involved in these measurements are at the very top of the range for which the equipment was designed, but it is still felt that the reproducibility of the individual data points is between 5 and 10 percent. The temperature difference across the sample during measurement was about 4°C. Since this is a small value and the variation of thermal con­ductivity with temperature is not great, it appears justifiable to take the average temperature between the two faces of the crystal as the temperature for which data are quoted.

A value of the thermal conductivity of germanium, resistivity 10 ohm-cm, was reported in 1952 by Grieco and Montgomery5; their one data point is plotted in Fig. 1. They stated additionally that the thermal con­ductivity was found to be roughly 20 percent less at 100°C—this would give a point lying somewhat below the extension of our straight-line curve. Their deter­minations were made by a rather similar comparative method, and employed germanium crystals grown at the Bell Telephone Laboratories and apparently of purity not too different from that of our samples. Thus the two sets of data appear to be in substantial agreement.

ACKNOWLEDGMENTS

Appreciation is expressed to our colleague David W. MacLeod for his valuable assistance in the design, fabrication, and maintenance of the equipment, and to the three laboratories that furnished the samples used. The apparatus was constructed with the assistance of a grant received by one of us (SSB) from the Penrose Fund of the American Philosophical Society.

5 A. Grieco and H. C. Montgomery, Phys. Rev. 86, 570 (1952).

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