Volume 43A, number 3 PHYSICS LETTERS 12 March 1973

INFRARED CYCLOTRON RESONANCES IN InSb AT MEGAGAUSS MAGNETIC FIELDS

J.A. DAVIS and F. HERLACH* Department of Physcs, Illinois Institute of Technology, Chicago, Ill. 60616, USA

Received 26 January 1973

Cyclotron resonance was studied in reflection in InSb at room temperature using pulsed magnetic fields of up to 1.4 MC and laser-obtained wavelengths of 10.6 and 5.56 ~1. At 10.6 r~, four resonances were found while one resonance was found at 5.56 cc.

Cyclotron resonance has been studied in reflection at room temperature in InSb using pulsed magnetic field of up to 1.4 MC and laser-obtained wavelengths of 10.6 and 5.56 cc. Previously cyclotron resonance in the infrared was observed by Lax et al. [ I] in InSb with magnetic fields up to 300 kG. We have extended those measurements to higher magnetic fields and higher optical frequenties. Using 10.6 p light, four resonances were found indicative of transitions between different nonequally spaced Landau levels while a single resonance was found with the 5.56 cc light.

A CO, laser provided light at a wavelength of 10.6 I-( and yielded about 15 watts in a TEM,, mode. The light was reflected off the sample and focused on a Ge : Au detector which was operated with a time constant of 30 nsec. The detector signal was amplified

and recorded simultaneously with a number of dual

beam oscilloscopes. Changes of 1% in reflectivity were

detectable with this system. Electrical shielding of the detector was very critical in the vicinity of the high- voltage high-current discharge. To avoid heating of

the sample, the laser beam was chopped by a rotating aluminum disc. The approximate pulse length was 400 pet with a repetition rate of 60 Hz.

The magnetic field was fired at the peak of the optical pulse using a capacitor-discharge megagauss generator which had been developed for an experiment at the Stanford Linear Accelarator [2]. The basic data for the capacitor bank are: 20 kV, 60 kJ, 12 nH and 2 mA. The waveform of the magnetic field is a strongly damped sine wave with a quarter period of 2 p sec. This time scale cannot be extended because of coil disintegration. Coils were made of 2 mm thick copper

* Now at the University Leuven, Belgium

sheet in two sizes: “larger” 10 mm i.d., 10 mm long (highest field 1.2 MG) and “medium”, 5.5 mm i.d., 8.5 mm long (highest field 1.6 MG). At discharge voltages above 12 kV, it was found that the coils emit a radiation which had a stronger effect on the detector than the reflected laser light and completely wiped out the useful detector signal. This spurious radiation was, after the electrical noise, the most troublesome pro- blem in these experiments. It was solved by coating and completely wrapping the coils with opaque insulat- ing materials. At the highest fields, this effect was still

critical because the coils moved with a speed of the order km/set, with seemed to result in an occasional

rupture of the opaque light shield.

The samples were obtained from Monsanto Corpora- tion and had l-l - 1 orientations. In n-InSb had a car- rier concentration of 2.1 X 1016/cm3 and a mobility of 1.14 X 105cm2/Vs at 77°K. The samples were polished and mounted on phenolic sample holders in the midplane of the coils. To measure the magnetic field, a single turn loop was moulded in epoxy close to the rear surface of the sample. Each probe was individually calibrated with a precision of 1% in a sta- billized RF field. The probe voltage was integrated by a RC-combination with a time constant of 200 psec and photographed on the same oscilloscopes as the optical signals.

The instrumentation was tested and calibrated with the known InSb resonance [l] which was confirmed at 270 kG for both the leading and trailing edge of the magnetic field waveform. In addition to this, additional resonances were found at 390 f 35 kG, 617 + 33 kG, and 788 + 27 kG. These resonances were much broader and the ratio of their amplitudes to the lower field resonance varied strongly from experiment to experi-

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Volume 43A, number 3 PHYSICS LETTERS 12 March 1973

ment. It appears that this effect depends on the preparation of the sample surface.

The laser was later converted to room-temperature operation using CO gas to obtain the 5.56 ~1 wavelength in order to shift the resonance to higher fiels. The power obtained was 1 watt in a TEM,, mode which was sufficient for the experiment due to the increased

detector sensitivity at this wavelength. A very faint resonance was detected at 785 + 15 kG.

The magnetic field dependence of the effective

mass, as indicated by the resonance at 270 kG using 10.6 /J light and at 785 kG using 5.56 /.L light, as well as the additional structure found in the former case, can be interpreted in terms of the non-parabolicities in the conduction band as established by Kane [3]. As discussed by Lax [4], the energy levels for the non- parabolic conduction band in the presence of a mag- netic field can be written as

where we have included spin and taken k = 0. The pos- sible cyclotron resonance frequencies will correspond to transitions with An = 1 and with the spin remaining constant. Here, Eg is the energy gap (0.18 ev), geff is

the effective g factor (- 74), and wc = eH/m; c is the cyclotron frequency with rn; the effective mass

(0.0125 m) at the bottom of the band. The fields at which cyclotron resonance should

result were calculated using eq. (1) and

(2) forthetransitions(O++l+),(O-+l-),(1++2t) and (1 - + 2 -). The calculated fields for 10.6 I-( radiation are 270 kG, 425 kG, 600 kG and 750 kG respectively. For 5.56 /.f radiation, the (0 + + 1 t) transition should occur at a field of 860 kG. The agreement between theory and experiment is quite good in view of the extremely large fields involved and the fact that the theory neglects the interaction of bands other than the valence bands.

We would like to thank R. Schmidt and E. Petit for their help in the experiments. Helpful discussion with Dr. H. Spector regarding the theoretical aspects of the work are also gratefully acknowledged. A grant from the Research Corporation provided support for this experiment.

References

[ 1 ] R.J. Keyes, S. Zwerdling, S. Foner, H.H. Kolm and B. Lax, Phys. Rev. 103 (1956) 825.

[ 21 F. Herlach, R. McBroom, T. Erber, J. Murray and R. Gearhart, IEEE Trans. Nucl. SC., NS-18.

[3] E.O. Kane, J. Phys. Chem. Solids 1 (1957) 249. [4] B. Lax and J.G. Mavroides, Solid state physics, eds.

F. Seitz and D. Trumbull, (Academic Press, Inc., New York, 1960) Vol. 11.

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