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Electrooptic effect and dielectric properties of cadmium-mercury-thiocyanate crystals
Volume 34A, number 7
PHYSICS
LETTERS
References
all the others. This will have a strong effect on experiments designed to measure the lateral mobility of electrons on the surface. In a field, the whole crystal should move as a unit as suggested by K0l.m [51. Finally, a distribution of free electrons separated from their corresponding positive charges may be produced in a solid by means of a field electrode. In analogy with the present experiment, conditions for crystallization of such electrons may eventually be found.
[l] E. Wigner, Trans. Far. Sot. 34 (1938) 678.
[2] P. Nozi&res and D. Pines, Phys. Rev. 111 (1958) 442. [3] W. J. Carr, Phys. Rev. 122 (1961) 1437. [4] H. M. Van Horn, Phys. Rev. 157 (1967) 342. [5] W.Kohn, Phys. Rev. Letters 19 (1967) 789. [6] F. W. dewette, Phys. Rev. 135A (1964) 287. [7] N. F. Mott and E. A. Davis, Phil. Mag. 17 (1968) 1269. [8] A. Bagchi, Phys. Rev. 178 (1969) 707. [9] R. Bogdanovic, Phys. Stat. Sol. 22 (1967) 603. [lo] D. Pines, Elementary Excitations in Solids (W. A. Benjamin, Inc. , New York, 1963), Chap. 3. [ll] R. Williams, R. S. Crandall and A. Willis, Phys. Rev. Letters 26 (1971) 7. [12] M. W. Cole and M. H. Cohen, Phys. Rev. Letters 23 (1969) 1238. [13] M. W. Cole, Phys. Rev. 2B (1970) 4239.
We are indebted to Jules Levine for acquainting us with the concept of crystallized electron systems and their possible relation to our experi mental system. **
ELECTROOPTIC
EFFECT
AND
19 April 1971
***
DIELECTRIC
CADMIUM-MERCURY-THIOCYANATE
PROPERTIES
OF
CRYSTALS
U. Von HUNDELSHAUSEN Research
Laboratories
of Siemens AG, Munich, Gennany
Received 13 March 1971
The electrooptic half-wave field-distance product of Cd [Hg (SCN)4] single crystals, belonging to the tetragonal crystal class I 4, has been measured. The low electrooptic coefficient 113 in comparison with the high d31-coefficient for SHG can be explained by the Miller-rule.
Cd [Hg (SCN)4] crystals belong to the tetragonal symmetry class I 4. They have been grown in our laboratories in sizes of several millimeters [ 11. Stlirmer and Deserno [l] showed that the SHG-coefficient is comparable to that of LiNbO3. So it was of great interest for technical applications to know its electrooptic and dielectric properties. The nonvanishing electrooptic coefficients in crystal class I Y are: rl3 = +33, r41 = Y53, r51 = -r43 and ?$3 [3]. The equation of the indicatrix for an applied electrical field EQ can be written as: (*+~13E3)x. ++j ne
+(-$-‘13E3)4 + 2re3 E3XlX2 = 1
(1)
The half -wave field-distance product [Es I] &/2 for light propagation in xl- or x3-direction is:
The measurements of the transverse electrooptic effect have been achieved by placing the crystal between crossed polarizers and analyz ing the amplitude modulation of light by means of a photomultiplier. Because the crystals were of small size, only several millimeters, we could not achieve full modulation without electrical breakdown. Therefore the light intensity, transmitted by the modulation device, was adjusted to be $(Zmaz + Zmin) by means of optical bias, where Zmax and Zmin are the light intensities at the on- and off-position of the light modulator. The half-wave field-distance product and the electrooptic coefficient were derived
405
Volume 34A, number ‘7
PHYSICS
from the measurement of the change of the light intensity AZ with applied voltage Air at the bias point. The maximum voltage that could be applied was 1.2 kV. The voltage at the crystal varied periodically in a saw-tooth shape at a frequency of 6 Hz. The driving voltage of the crystal and the output of the multiplier were displayed at an oscilloscope. Measurements have been effected at two different wavelengths, 6320 w and 4760 A. By changing the applied voltage as AV, the intensity changes by an amount AZ. As Z rr sin2 $Aq? it follows at the chosen optical bias: Z
Zmax -Zmin
(3)
= sin$Aq,
if Acp is the phase retardation induced by the voltage AV. The result for the half-wave fielddistance product is:
The measured half -wave fiel!-distance product was (11.8*3) kV at h = 476OA or (15.6*4) kV at x = 6328& This leads with (2) to an electrooptic coefficient: ~13 = (5.3 f 1.4) x lo-l2
m/V .
On the background of Robinson’s theory [3] the small electrooptic effect in comparison with the high SHG-coefficient can be explained by the low value of E in agreement with Miller’s rule [4]. Since d13 = x1.x2.x3.A13 and using the notation of Robinson d13 = r13*n4/8n, we calculate from the electrooptic measurement of ~13 the Miller-index Al3: A13 =A31 = (4.1+1.6) x 1O-6 =. esu This value is in satisfying agreement with the value of Sttirmer and Deserno [l] for SHG, which is in the notation used by Robinson 2.8 x 10-6 cm/esu, and with the mean value of 3 x 10m6 cm/esu for most materials. Measurements of the other electrooptic coefficients will be performed as soon as crystals of larger sizes will be available. I wish to acknowledge Professor Stiirmer for leaving the crystals, Mr. Winzer, Mr. Oberbather and Mr. Rauscher for polishing them and Dr. Graf for helpful discussions.
References -111 _ W. StUrmer and U. Deserno, Phvs. _ Letters 32A (1970)
No change in ~13 with the wavelength could be observed within the experimental error. The dielectric constant ~3 was measured with an error of 10%. Its value decreases from 6.5 at 1 kHz to 5 at 30 MHz, tan 6 at 30 MHz is 1eSS than 0.03.
406
19 April 1971
LETTERS
539.
[2] J. F. Nye, Physical properties of crystals (Oxford, Clarendon Press, 1969). [3] F. N. H. Robinson, Bell Syst. Techn. J. 46 (1967) 913. [4] R. C. Miller, Appl. Phys. Letters 5 (1964) 17.
PHYSICS
LETTERS
References
all the others. This will have a strong effect on experiments designed to measure the lateral mobility of electrons on the surface. In a field, the whole crystal should move as a unit as suggested by K0l.m [51. Finally, a distribution of free electrons separated from their corresponding positive charges may be produced in a solid by means of a field electrode. In analogy with the present experiment, conditions for crystallization of such electrons may eventually be found.
[l] E. Wigner, Trans. Far. Sot. 34 (1938) 678.
[2] P. Nozi&res and D. Pines, Phys. Rev. 111 (1958) 442. [3] W. J. Carr, Phys. Rev. 122 (1961) 1437. [4] H. M. Van Horn, Phys. Rev. 157 (1967) 342. [5] W.Kohn, Phys. Rev. Letters 19 (1967) 789. [6] F. W. dewette, Phys. Rev. 135A (1964) 287. [7] N. F. Mott and E. A. Davis, Phil. Mag. 17 (1968) 1269. [8] A. Bagchi, Phys. Rev. 178 (1969) 707. [9] R. Bogdanovic, Phys. Stat. Sol. 22 (1967) 603. [lo] D. Pines, Elementary Excitations in Solids (W. A. Benjamin, Inc. , New York, 1963), Chap. 3. [ll] R. Williams, R. S. Crandall and A. Willis, Phys. Rev. Letters 26 (1971) 7. [12] M. W. Cole and M. H. Cohen, Phys. Rev. Letters 23 (1969) 1238. [13] M. W. Cole, Phys. Rev. 2B (1970) 4239.
We are indebted to Jules Levine for acquainting us with the concept of crystallized electron systems and their possible relation to our experi mental system. **
ELECTROOPTIC
EFFECT
AND
19 April 1971
***
DIELECTRIC
CADMIUM-MERCURY-THIOCYANATE
PROPERTIES
OF
CRYSTALS
U. Von HUNDELSHAUSEN Research
Laboratories
of Siemens AG, Munich, Gennany
Received 13 March 1971
The electrooptic half-wave field-distance product of Cd [Hg (SCN)4] single crystals, belonging to the tetragonal crystal class I 4, has been measured. The low electrooptic coefficient 113 in comparison with the high d31-coefficient for SHG can be explained by the Miller-rule.
Cd [Hg (SCN)4] crystals belong to the tetragonal symmetry class I 4. They have been grown in our laboratories in sizes of several millimeters [ 11. Stlirmer and Deserno [l] showed that the SHG-coefficient is comparable to that of LiNbO3. So it was of great interest for technical applications to know its electrooptic and dielectric properties. The nonvanishing electrooptic coefficients in crystal class I Y are: rl3 = +33, r41 = Y53, r51 = -r43 and ?$3 [3]. The equation of the indicatrix for an applied electrical field EQ can be written as: (*+~13E3)x. ++j ne
+(-$-‘13E3)4 + 2re3 E3XlX2 = 1
(1)
The half -wave field-distance product [Es I] &/2 for light propagation in xl- or x3-direction is:
The measurements of the transverse electrooptic effect have been achieved by placing the crystal between crossed polarizers and analyz ing the amplitude modulation of light by means of a photomultiplier. Because the crystals were of small size, only several millimeters, we could not achieve full modulation without electrical breakdown. Therefore the light intensity, transmitted by the modulation device, was adjusted to be $(Zmaz + Zmin) by means of optical bias, where Zmax and Zmin are the light intensities at the on- and off-position of the light modulator. The half-wave field-distance product and the electrooptic coefficient were derived
405
Volume 34A, number ‘7
PHYSICS
from the measurement of the change of the light intensity AZ with applied voltage Air at the bias point. The maximum voltage that could be applied was 1.2 kV. The voltage at the crystal varied periodically in a saw-tooth shape at a frequency of 6 Hz. The driving voltage of the crystal and the output of the multiplier were displayed at an oscilloscope. Measurements have been effected at two different wavelengths, 6320 w and 4760 A. By changing the applied voltage as AV, the intensity changes by an amount AZ. As Z rr sin2 $Aq? it follows at the chosen optical bias: Z
Zmax -Zmin
(3)
= sin$Aq,
if Acp is the phase retardation induced by the voltage AV. The result for the half-wave fielddistance product is:
The measured half -wave fiel!-distance product was (11.8*3) kV at h = 476OA or (15.6*4) kV at x = 6328& This leads with (2) to an electrooptic coefficient: ~13 = (5.3 f 1.4) x lo-l2
m/V .
On the background of Robinson’s theory [3] the small electrooptic effect in comparison with the high SHG-coefficient can be explained by the low value of E in agreement with Miller’s rule [4]. Since d13 = x1.x2.x3.A13 and using the notation of Robinson d13 = r13*n4/8n, we calculate from the electrooptic measurement of ~13 the Miller-index Al3: A13 =A31 = (4.1+1.6) x 1O-6 =. esu This value is in satisfying agreement with the value of Sttirmer and Deserno [l] for SHG, which is in the notation used by Robinson 2.8 x 10-6 cm/esu, and with the mean value of 3 x 10m6 cm/esu for most materials. Measurements of the other electrooptic coefficients will be performed as soon as crystals of larger sizes will be available. I wish to acknowledge Professor Stiirmer for leaving the crystals, Mr. Winzer, Mr. Oberbather and Mr. Rauscher for polishing them and Dr. Graf for helpful discussions.
References -111 _ W. StUrmer and U. Deserno, Phvs. _ Letters 32A (1970)
No change in ~13 with the wavelength could be observed within the experimental error. The dielectric constant ~3 was measured with an error of 10%. Its value decreases from 6.5 at 1 kHz to 5 at 30 MHz, tan 6 at 30 MHz is 1eSS than 0.03.
406
19 April 1971
LETTERS
539.
[2] J. F. Nye, Physical properties of crystals (Oxford, Clarendon Press, 1969). [3] F. N. H. Robinson, Bell Syst. Techn. J. 46 (1967) 913. [4] R. C. Miller, Appl. Phys. Letters 5 (1964) 17.