Cyclotron resonance study of the conduction band in GaP

PhystcallTB&ll8B (1983)66-68 North-HollandPubhshmsCompany

66

CYCLOTRON RESONANCE STUDY OF THE CONDUCTION BAND IN GaP

Noboru Miura, Giyuu Kido, Michinobu Suekane and Soshin Chikazumi

Institute for Solid State Physics, University of Tokyo, Roppongl, Minato-ku, Tokyo, Japan Far-infrared cyclotron resonance was observed in n-type CaP at high magnetic fields in the megagauss range. For magnetic fields parallel to the axls~ the second absorption peak was observed at i00 T in addition to the first peak at 23 T for a wavelength of 119 pm. The apparent cyclotron masses of electrons were thus determined to be m* t = 0.254 + 0.004 me and m*~ = 4.8 -+ 0.5 mo at 119 pm. At 337 pm, on the other band, a broad absorption band was observed around 42 T besides the first peak at 8.0T.

i.

INTRODUCTION

The conduction band edge of GaP is known to have a "camel's back" structure.(1) From the analysis of the indirect exclton spectra, the depth of the "camel's back" has been evaluated as 3-4 meV. (2-4) The cyclotron resonance experiment for GaP can be done only in high magnetic flelds because of the low mobillty of electrons. The transverse effective mass of electrons, m* t was determined to be 0.25 mo by the cyclotron resonance for the magnetic field H parallel to the <100> axls.(5,6) As for the longitudinal effective mass m*~, there have been no direct measurements so far. For H # <100>, the second absorption peak associated with the mass m~*~m* t has not been observed at 337 ~m in magnetic fields up to 30 T. Therefore Leotin et el. concluded that the mass anlsotropy factor K*=m*~/m* t should be larger than 14 at 337 pm.(5) From the angular dependence of the cyclotron resonance field, the apparent longitudinal mass m*~ was estimated at wavelengths of 337 pm and 119 pm. (5-7) However, because of the large error bars of the experimental points, it was difficult to obtain a conclusive result on m*~. Moreover, on the basis of the "camelts back" structure~ the analysis of the angular dependence of the resonance field requires a complex calculation of the Landau levels. The purpose of the present paper is to obtain the longitudinal mass m*~ directly from the far-lnfrared cyclotron resonance in a configuration H ~<100> using pulsed high magnetic fields up to 140 T.

2.

EXPERIMENTAL

Pulsed high magnetic flelds in the megagauss range were produced by the electromagnetic flux compression method.(8) Non-destructlve pulsed fields up to 40 T were also produced by using conventional pulse magnets consisting of wirewound coils. The flelds were applied in the direction. The far-infrared radiation was obtained by employing an H20 laser for A=II9 ~m and an HCN laser for A=337 ~m. The lasers were operated in a pulse mode. The measurement was

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carried out with left-handed clrcularly polarized (l.c.p.), rlght-handed circularly polarized (r.c.p.), linearly polarlzed (1.p.) or unpolarized (u.p.) radiation. The transmitted radiation by the sample was detected by the photoconductivity of Ga-doped Ge and GaAs. The transient slgnals were recorded employing transient recorders with digital memories. The magnetic fleld was measured by a plck-up probe, and callbrated by the ESR in ruby, whose absorption peaks are very sharp as is shown in Fig. i. The samples of n-type GaP were cut both from a bulk crystal wafer of 300 ~m thick and a S-doped epltaxlal crystal of 98 pm thick. The carrier concentration of the crystals was 0.8 - 1.2 × 1017 cm -3 for the bulk crystal and 2 - 20 x 1017 cm -3 for the epltaxlal crystal. The temperature of the samples was controlled in the range between 80 - 152 K in order to

I

i

I

r

I

A= 337 p.m T=80

K

-r-

Ruby

-

H//c

z O St ¢n z n., I-

H / I <100> GaP

t

I i I J I 10 20 30 MAGNETIC FIELD

H #<100>

I

(T

I 40

)

Figure 1 : Experimental recordings of ESR in ruby (H H c) and the cyclotron resonance of n-Si and n-GaP (H H) at a wavelength of 337 pm. T=80 K.

N Mtura et aL / Conduction band m GaP

o b t a i n b o t h enough m o b i l i t y and c a r r i e r tration. 3.

concen-

RESULTS AND DISCUSSION

An experimental recording obtained in a nondestructive field for a wavelength of 337 pm is shown in Figure I. In thls figure, the result on n-type Si which has also conduction band minima near X-polnt is shown for comparison. In contrast to the case of SI, only a single absorption peak was observed in GaP at 8.01 T from which m* t was obtained as 0.252 mo. No other absorption is seen up to 37 T. Figure 2 shows the absorption spectra at 337 ~m observed in higher fields up to ii0 T. As for the first peak, only the tail of the peak is seen in this figure, because merely the data above about I0 T were recorded in the transient recorder. After the first peak, the transmission stayed almost constant up to 40 T, but started to increase above 40 T. Any other absorption peaks were not discernible up to ii0 T. There was not a signlflcant difference between the data for u.p. and l.c.p, radiations. For the fleld direction 5 ° off the axis, the absorption appeared to become slightly more prominent at a lower fleld. The absorption around 40 T is very weak

I

I

I

I

GaP

I

I

I

I

I

<100>

A = 3

3

I

I

I

u.p,

67

and broad. However, subtracting the effect of the first peak, we found that the absorption band is centered at 42±5 T. If we can regard this absorption band as the second absorption peak associated with ~ w h l c h we are seeking, the apparent longltudlnal mass m*~ is estlmated to be 6.9±1.7 mo at 337 ~m. Figure 3 shows the cyclotron resouanceabsorptlon spectra at 119 pm. For l.c.p, and l.p. radiations, the first absorption peak was observed at 23 T, as in the previous measurement.(6) The transverse effective mass m* t is confirmed to be 0.254 mo. In addition to the first one, the second absorption peak appeared at 100 T. From this peak position, the apparent longitudinal effective mass was determined to be m*~=4.8±0.5 mo. From the half width of the absorption peaks, the value of ~c z was estimated to be 2.9 for the peak at 23 T and 4.2 for the peak at 100 T. For r.c.p., the first absorption peak was not observed, whereas the second peak was observed with almost the same magnitude as for l.c.p. This is a characteristic feature of the cyclotron resonance in a highly anlsotroplc band. Table 1 lists the determined values of the apparent cyclotron masses of electrons in GaP by the present experiment. For ~=337 ~m, the uncertainty is very large because of the broadness of the second absorption. However, we can see that the anisotropy factor K*=m*~/m*t appears to be larger at a photon energy of ~u=3.68 meV than at ~w=i0.45 meV, while the difference in m*t is very small between the two photon

~

I

I

GaP

I

f

I

I

I

I

1

i

I

I

I

I

I

HII

•x = 119 #.m

Z

0 IE

Z 0

I/] Z .(

f~

IE

I.p.

I,.-

u') Z

I-I

I

I

I

l

I

I

I.I

I

I

r.c.p.

I

50 100 MAGNETIC FIELD (T)

Figure 2 : Transmission vs. ~agnetlc fleld for a wavelength of 337 pm. u.p. and l.c.p. stand for the unpolarlzed and left-handed circularly polarized radiation, respectively The bottom trace was obtained for a magnetlc fleld 5 ° off the the axis. The sslples were epitaxlal crystal. T - 80 - 100 K.

I 0

i I I I I I

K I ] I I I I I

50 100 MAGNETIC FIELD

150 (T)

etgure 3 : C y c l o t r o n r e s o n a n c e a b s o r p t i o n J p e c t r a i n n-CaP f o r H//<100> a t a w a v e l e n g t h o f I19 ~m. 1 . c . p . , 1 . p . and r . c . p , d e n o t e the light-handed circularly polarized, linearly p o l a r i z e d and r i l h t - h a n d e d c i r c u l a r l y p o l a r i z e d radiation, reapeetively. The s a m p l e s were b u l k crystal. T - 106 - 152 K,

68

N M~ura et al / Conductmn band m GaP

Table Wavelength (~m)

i.

Apparent

Photon Energy ~ = (meV)

337

3.68

119

10.45

H 1 and H 2 are

cyclotron

HI (T)

the magnetic

fields

/~-m-/--t/m0

m*f/m 0

K*

42±5

0.252±0.003

1.32±0.16

6.9±1.7

28±7

100±5

0.254±0.004

1.11±0.06

4.8±0.5

19±2

of

According to Lawaetz's model(l), the energy dispersion of the conduction band edge of GaP is given by

[

A

4~.k22

(2)2+~ ~°11/2'

in G a P

m*t/m 0

energies. This finding cannot be explained by the usual type of non-parabollcity, but by the non-parabolicity taking into account the effect of the "camel's back" structure.

.,K21.2 ..,g2~2 E(k)= 2mr +2m~ ~'~-

of e l e c t r o n s

H2 (T)

8.01±0.10 22.9±0.3

masses

(1)

where k . and kll are respectively the components of the k-vector perpendicular and parallel to the axis, A is the energy gap between the X 1 and X 3 bands, and A 0 is an energy parameter representing the magnitude of the k-llnear term. When A
the

first

and

the

second

absorption

peaks

corresponding to different transitions which occur at slightly different fields with each other. However, on the assumption of the 0++i assignment, the calculation of the transition probability predicts that for ~ = 3 . 6 8 meV, a much larger absorption should be observed near 80-90 T corresponding to other transitions such as i++i - or 0-+1 + . As is shown in Figure 2, any absorption peak was not observed above 42 T for • ~ = 3.6+8 meV. Therfore, we have to exclude the 0 +i- transition as a possible origin of the second absorption peak. It is also likely that the second absorption peak arises from the transition 0++0 -. However, with this assignment, we have to assume smaller values of AE and m~ in order to explain the values of m* Z in Table I. More details of the analysis of these parameters will be reported elsewhere. REFERENCES [i] P. Lawaetz, Solid State Commun. 16 (1975) 65. [2] M. Altarelli, R. A. 8abatini and N. O. Lipari, Solid State Commun. 25 (1978) ii01. [3] G. F. Glinskii, A. A. Kopylov and A. N. Pikhtin, Solid State Co=~nun. 30 (1979) 631. [4] R. G. Humphreys, U. RDssler and M. Cardona, Phys. Rev. B 18 (1978) 5590. [5] J. Leotin, J. C. Ousset, R. Barbaste, S. Askenazy, M. S. Skolnick, R. A. Stradling and G. Poibland, Solid State Commun. 16 (1975) 363. [6] K. Suzuki and N. Miura, Solid State Commun. 18 (1976) 233. [7] G. Kido, N. Miura, H. Katayama and S. Chikazumz, in S. Chikazumi and N. Miura (eds.), Physics in High Magnetic Fields, (Springer-Verlag, 1981) pp. 64. [8] N. Miura, G. Kido, M. Akihiro and S. Chikazumi, J. Magn. Magn. Mater. Ii (1979) 275. [9] K. Nakao, T. Doi and H. Kamimura, J. Phys. Soc. Jpn. 30 (1971) 1400. [i0] A. Onion, Phys. Rev. B 4 (1971) 4449.