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Internal friction measurements in Boron-doped single-crystal silicon
Volume 85A, number 1
PHYSICS LETTERS
7 September 1981
INTERNAL FRICTION MEASUREMENTS IN BORON-DOPED SINGLE-CRYSTAL SILICON C.C. LAM and D.H. DOUGLASS Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
Received 6 February 1981
Internal friction measurements, Q~’,of a boron-doped single crystal of silicon at a frequency ~ = 2ir X 29.2 kHz showed: (1) results in agreement with the Akhieser mechanismabove 100 K; and (2) Q~~ ~ at temperatures below 10 K.
We have been studying large semiconductor single crystals as a possible gravitational wave detector [1]. One of the important desirable properties is a high mechanical quality factor Q. The inverse quality factor Q—1, which is called the internal friction, is a direct measure of the dominant mechanism of the attenuation
of sound. We will discuss some of the internal friction measurements and their interpretation in this paper. The sample is a single crystal of silicon which was manufactured by Monsanto by the zero dislocation Czochralski process in the form of a cylinder (diameter 3.8 cm, length 15.2 cm), with the [111] axis parallel to the cylinder axis. The crystal is boron doped,with a resistivity of 18 ~ cm at room temperature. The first longitudinal frequency is 29.2 kHz. In order to minimize coupling to the crystal, the
crystal was suspended by a 0.1 mm tungsten wire around its center. The crystal and the whole detection assembly were placed in vacuum 1 chamber which can measurements on be to 1 .2 K.byThe Q thecooled crystaldown are described McGuigan et al. [2]. The data in fig. I are plotted as ~.,—‘Q—1 and show a number of prominent features. Above 100 K, our measurements (solid dots) are compared to ultrasonic attenuation a measurements by Mason and Bateman [31at 480 MHz in pure silicon. The relation between Q1 and a is 1
SILICON SINGLE CRYSTAL (Boron doped)
I I
I
_L
-
:
W
IO~~-
3RD HARMONIC ~
—
1T
IO’~
-
I
•
I
I 0
00
000
TEMPERATURE (K) .
-i
Fig. plot of (wQ) as a function of temperature for the first 1. andA third harmonic.
sets of data are in excellent agreement with each other. Mason and Bateman explained show that by their can be satisfactorily themeasurements thermal phonon theory ofAkhieser [4]. Thus we have observed the Akhieser mechanism. This is the first time that it has been observed by internal friction. Since this is a fundamental process no values of internal friction less than those reported here can be achieved. Below 100 K our results deviate from those of Mason and Bateman. This is caused by some other mechanism which is dominant in this temperature
=
(2V 5/w)a(neper/cm)
(cgs)
where V~is the velocity of sound in the medium and w 1 that is the angular frequency. We computed the Q their measurements of a imply (solid squares). The two
region.
At aboutcaused 30 K by we found an absorption peak which is possibly the activation of the boron acceptors.
41
Volume 85A, number 1
PHYSICS LETTERS
At low temperatures (below 10K) the internal friction is proportional to frequency and inversely proportional to temperature. We propose the following explanation: The ground state of shallow acceptors, boron in this case, in cubic semiconductors is four fold degenerate which can be partially removed into two doublets by strains inside the crystal. This strain can be produced by the randomly distributed local electric fields such as those due to disolocations. Anderson et al. [5] have considered the case of absorption of acoustic energy by a two-level system. They found an ultrasonic attenuation proportional to w2/T (or 1/Q ~ w/T) for the case 11w small compared to kT. This is what we have found. The proportionality constant,
42
7 September 1981
which is a function of neutral acceptor concentration and the distribution of energy level splitting, is being studied. References [11 D.H. Douglass and V.B. Bradinsky, in: General relativity. eds. S.W. Hawking and W. Israel (Cambridge U.P., 1979) p. 90. [2] D.F. McGuigan eta!. J. Low Temp. Phys. 30(1978)621.
[31W.P. Mason and T.B. Bateman, J. Acoust. Soc. Am. 36 (1964) 644. [4] Akhieser, J. Phys. USSR (1939) 277. [5] P.W. Anderson, B.L. Halperin and C.M. Varma, Phios. Mag. 25 (1972) 1.
PHYSICS LETTERS
7 September 1981
INTERNAL FRICTION MEASUREMENTS IN BORON-DOPED SINGLE-CRYSTAL SILICON C.C. LAM and D.H. DOUGLASS Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
Received 6 February 1981
Internal friction measurements, Q~’,of a boron-doped single crystal of silicon at a frequency ~ = 2ir X 29.2 kHz showed: (1) results in agreement with the Akhieser mechanismabove 100 K; and (2) Q~~ ~ at temperatures below 10 K.
We have been studying large semiconductor single crystals as a possible gravitational wave detector [1]. One of the important desirable properties is a high mechanical quality factor Q. The inverse quality factor Q—1, which is called the internal friction, is a direct measure of the dominant mechanism of the attenuation
of sound. We will discuss some of the internal friction measurements and their interpretation in this paper. The sample is a single crystal of silicon which was manufactured by Monsanto by the zero dislocation Czochralski process in the form of a cylinder (diameter 3.8 cm, length 15.2 cm), with the [111] axis parallel to the cylinder axis. The crystal is boron doped,with a resistivity of 18 ~ cm at room temperature. The first longitudinal frequency is 29.2 kHz. In order to minimize coupling to the crystal, the
crystal was suspended by a 0.1 mm tungsten wire around its center. The crystal and the whole detection assembly were placed in vacuum 1 chamber which can measurements on be to 1 .2 K.byThe Q thecooled crystaldown are described McGuigan et al. [2]. The data in fig. I are plotted as ~.,—‘Q—1 and show a number of prominent features. Above 100 K, our measurements (solid dots) are compared to ultrasonic attenuation a measurements by Mason and Bateman [31at 480 MHz in pure silicon. The relation between Q1 and a is 1
SILICON SINGLE CRYSTAL (Boron doped)
I I
I
_L
-
:
W
IO~~-
3RD HARMONIC ~
—
1T
IO’~
-
I
•
I
I 0
00
000
TEMPERATURE (K) .
-i
Fig. plot of (wQ) as a function of temperature for the first 1. andA third harmonic.
sets of data are in excellent agreement with each other. Mason and Bateman explained show that by their can be satisfactorily themeasurements thermal phonon theory ofAkhieser [4]. Thus we have observed the Akhieser mechanism. This is the first time that it has been observed by internal friction. Since this is a fundamental process no values of internal friction less than those reported here can be achieved. Below 100 K our results deviate from those of Mason and Bateman. This is caused by some other mechanism which is dominant in this temperature
=
(2V 5/w)a(neper/cm)
(cgs)
where V~is the velocity of sound in the medium and w 1 that is the angular frequency. We computed the Q their measurements of a imply (solid squares). The two
region.
At aboutcaused 30 K by we found an absorption peak which is possibly the activation of the boron acceptors.
41
Volume 85A, number 1
PHYSICS LETTERS
At low temperatures (below 10K) the internal friction is proportional to frequency and inversely proportional to temperature. We propose the following explanation: The ground state of shallow acceptors, boron in this case, in cubic semiconductors is four fold degenerate which can be partially removed into two doublets by strains inside the crystal. This strain can be produced by the randomly distributed local electric fields such as those due to disolocations. Anderson et al. [5] have considered the case of absorption of acoustic energy by a two-level system. They found an ultrasonic attenuation proportional to w2/T (or 1/Q ~ w/T) for the case 11w small compared to kT. This is what we have found. The proportionality constant,
42
7 September 1981
which is a function of neutral acceptor concentration and the distribution of energy level splitting, is being studied. References [11 D.H. Douglass and V.B. Bradinsky, in: General relativity. eds. S.W. Hawking and W. Israel (Cambridge U.P., 1979) p. 90. [2] D.F. McGuigan eta!. J. Low Temp. Phys. 30(1978)621.
[31W.P. Mason and T.B. Bateman, J. Acoust. Soc. Am. 36 (1964) 644. [4] Akhieser, J. Phys. USSR (1939) 277. [5] P.W. Anderson, B.L. Halperin and C.M. Varma, Phios. Mag. 25 (1972) 1.