Fundamental reflectivity spectra of monocrystalline and polycrystalline bulk Cd3As2

~

Solid State Communications, Printed in Great Britain.

Vol.44,No.3, pp.373-377,

1982.

0038-1098/82/390373-05503.00/0 Pergamon Press Ltd.

FUNDAMENTAL REFLECTIVITY SPECTRA OF MONOCRYSTALLINE AND POLYCRYSTALLINE BULKCd3As2 Katarzyna KARNICKA-MOSCICKA § and Andrzej KISIEL

Institute of Physics, Jagellonian University, ul. Reymonta 4, 30-059 Krak6w, Poland and Lidia Zdanowicz

Institute of Solid State Physics, Polish Academy of Science, Zabrze, Poland.

(Received 8 April

Fundamental reflectivity samples of C d ~ s 2 in the The results are compared interpreted on the basis

1982 by C. W. McCombie)

spectra of mono and polycrystalline bulk energy range 0~8 - 5.9 eV are measured. with existing experimental data and are of Lin-Chung model.

Results are compared with available experimental and theoretical data.

Introduction In the recent several years the semiconductor properties of II-V materials have been intensively studied by many authors. The special attention is directed to the most interesting material of the group, cadmium arsenide, Cd3As 2. This degenerate n-type semiconductor is characterized by high mobility of electrons with low effective mass at the same time I. It has also a small inverse energy gap of HgTe type 6. For a proper understanding of Cd3As 2 properties, precise determination of its band structure is essential. The most information about electron structure in the whole Brillouin zone is commonly received by means of analysis of photoemission and fundamental reflectivity spectra. A strong relation between the real structure of a material and its fundamental interhand absorption makes light reflectivity spectra a fruitful genera[ souzce of information about the band structure of semiconductors. The investigations of fundamental absorption by means of reflectivity measurements for energies of incident light higher than the energy gap of Cd3As 2 were carried out for cadmium arsenide in a few cases only 2-5, though the main feature of the Brillouin zone electron band structure in the vicinity of the F point are reasonably well known 6. Nevertheless the band structure of the whole Brillouin zone is not unequivocally defined. Approximate calculations by means of pseudo-potential in the non-relativistic approximation and for the simplified structure of the material have been carried out by Lin-Chung 7. Present communication brings our latest data on fundamental reflectivity spectra, R(E) of mono and polycrystalline bulk Cd3As 2 samples.

Results The measurements were made with Cd3As 2 bulk monocrystalline and polycrystalline samples obtained from the Institute of Solid State Physics, Polish Academy of Science in Zabrze and Institute of Physics of the Technical University in Wroclaw, respectively. Technical details of their preparation from the gaseous phase were given earlierl, 8. The fundamental reflectivity spectra, R(E) were obtained at room temperature in the energy range from 0.8 to 5.9 eV with the aid of a reflectometer described in refs. 9,10. Nearly normal incidence of the electromagnetic beam to a reflecting surface (within 6 deg) was maintained throughout. The fundamental reflectivity spectra for monocrystalline samples were recorded from natural mirror-llke surfaces of a large 'as-grown' monocrystal (referred to later as 'as-grown') and from the surface mechanically and chemically treated as suggested by Tajabor and Lovett II (referred to later as 'polished'). The same preparation of the surface was applied to investigated polycrystalline samples. Typical fundamental reflectivity spectra from two different surfaces of monocrystalline samples are shown in Figure I. Spectrum "i" is obtained from an as-grown surface, "2" from a polished one. The reflectivity spectrum "2" is noticeably weaker and poorer. This can be easily explained in terms of the reflecting surface roughness which effect leads to a significant decrease of intensity and distortion of the reflectivity spectruml2,13. In consequence the information obtained from the as-

On leave at the Laboratoire de Recherches sur les Interactions Gas-Solides: Laboratoire Maurice Letort, Route de Vandoeuvre, 54600 Villers-les-Nancy, France.

373

MONOCRYSTALLINE AND POLYCRYSTALLINE BULK Cd3As 2

374

| ../

I

'-.".,

•°

•

35.

0

25.

0

Vol. 44, No. 3

",...

"4

,,

"..

%.

1

-

",~ • .~:., - •

. ~-~

~'.. .%2 °

15.0

i

i

J

i

i

2.4

1.2

i

3.6

so-,"

.'.;-

•

i

4.8

E [eV]

Figure i Cd3As2:

Fundamental reflectivity spectra R(E) of monocrystalline (I) From as-grown surface;

(2) From mechanically,

chemically treated surface. grown surface is much more valuable and further attention is restricted to spectrum "i" only. R(E) spectra from polished polycrystalline samples showed strong deviations and fluctuations from sample to sample. Similarly to the polished monocrystal, this was caused probably by surface roughness 12 and further analysis was done for the best and strongest spectrum shown in Figure 2, to ensure the smallest contribution of the effect. The optical constants, n(E) and K(E) together with dielectric constants, el(E) and

3 7 .

E2(E) have been evaluated from known R(E). The Kramers-Kronig relations were used for the purpose in a manner suggested hy Ellis and Stevenson 14. The results are shown in Figures 3 and 4. Discussion The transition energies are determined from the maxima positions in R(E) in Figures 1 and 2. Results are tabulated in Table i together with

5

L: .:°*

32.

5

27.

5

-• •~

\ ,~io 22.

"7,:

5

i

1.2

!

i

2.4

i

i

i

3. e

i

4.8

E [eV] Figure 2 Cd3As 2 •

Fundamental reflectivity spectrum of polycrystalline

Vol. 44, No. 3

MONOCRYSTALLINE AND POLYCRYSTALLINE BULK Cd3As 2

I

I

375

I

24.

a.

bl

0

'

'

l

,

,

,

4.8

~"x/"Lx,. \

?,..,

18.0 8.6

=-

\

/ [

12.0

2.4

/

l

/

\""'"'"~-,

i/ 1

/

"\"\ .........

!

/

.0

l;

6.~

/

/

\,

"'--.~\?..\

/

1,2

\

0.0 I

0

I

1 1

I

.5

I

I

3.0

i

4.5

I

0

I

.0

E [eV] Figure 3

I

1.5

I

4.5

E [eV] Optical, n and k, and dielectric, gl and E2, constants

spectra of as-grown monocrystalline Cd3As2, derived from R(E) in Figure I.

I

,

1

a.

,

4.0 ~"'-~_...

. . . . . .

tl

. . . . .

K

,

,

l

r,\

f 2

\

\,,

3.0

\

\

12.0

\

A

\, o

! \

~'"\

ol

'~..j~.~,.

/

\

/\\

8.0

bJ

/

1.0

/

4.0

I .J

k \ \

\

~

\,

\

0.0

J.

""x.

.0 i

o

,

16. O

,~

\

F2.

i

b.

i

.

1.5

i

i

3.0

E [eV] Figure 4

i

i

4.5

i

i

0

i

1.5

i

i

3.0

E [eV] Optical, n and k, and dielectric, E 1 and g2' constants

spectra of polycrystalline Cd3As 2 derived from R(E) in Figure 2.

i

i

4.5

376

MONOCRYSTALLINE

AND POLYCRYSTALLINE

BULK Cd3As 2

Vol. 44, No. 3

Table I: Energy (eV) of the interband transitions observed in the fundamental reflectivity spectra of Cd3As 2 at room temperatures. Present paper

Polycrystal

Monocrystal

0.90

0.90

Sobolev et al. 2

Monocrystal

1.41

1.43

1.71

1.71

1.70

1.89

1.91

1.88

3.63

3.80

3.70

Polycrystal

Zivitz and Aubin and Stevenson 3 Cloutier 4

Monocrystal

1.70

Monocrystal

0.88

O.91

0.6

1.32

1.2

1.41 1.8

1.74 1.95

2.86 3.65

4.5O 5.15

Lin-Chung 7 theory

Monocrystal

1.43 1.70

Bhola 5

5.15

5.6O

data available from the literature 2-5 and the theoretical prediction of Lin-Chung 7. Good agreement between our experimental data and literature ones is noticeable. Furthermore, thanks to a very good extinction at near infrared we have observed for the first time in R(E) spectrum fine details , noticed up to now only in thermomodulation measurements 4'5. The 0.9 eV and 1.4 eV transitions are probably localized in the F point of the Brillouin zone. The direct transitions at very similar energies 0.9 eV and 1.2 - 1.3 eV have been observed earlier in absorption spectra 15 . For 1.8 eV maximum the most probable localisation suggested by the model is direction A. The joint density of states in this direction is high, which is a consequence of nearly parallel alignment of A I and A 3 bands in the vicinity of L point. Proposed localisation is supported by the double peak structure of the maximum observed in R(E) in present studies. This is probably caused by spin-orbit splitting of the higher valence band, A 3. This is not predicted by the Lin-Chung model as it is the non-relativistic approximation and predicts a singluar transition at 1.8 eV, only. One can apply however the empirical "2/3"-rule of Cardona 16 which says that the split for A direction has to be 2/3 of those in F point: A A = 2.AF/3. The rule was successfully applied before to a different set of data for II-Vl and III-V compounds. Comparison between A&read out from our spectra and A_ from literatur~ shows also good agreement speaklng in favour of the nature of a double peak maximum at 1.8 eV. The position of the second main maximum in R(E), and estimated in the present work to be at 3.8 eV is located by the Lin-Chung model in the A direction, too. Saying this we have to keep in mind that such a broad maximum contains usually contributions not only from transitions

3.60

2.30

2.8

3.70

3.8

4.60

4.7

5.16

5.2

5.63

5.8

in singular critical point but from large numbers of them or even from a wide range of the Brillouin zone. A significant contribution to the maximum would come also from transitions in the second type, non-symmetry critical points of Van Hove 17. Spectrum structure related to this type of transition is much more sensitive to any form of perturbation leading to distortion of the bands' parallelness. This in consequence may lead to lowering and shifting of the main maximum. It must be pointed out that the value of 3.8 eV estimated for the position of the maximum in as-grown monocrystals is higher than 3.63 eV of polycrystals or 3.6 - 3.7 eV quoted by other authors. The difference is probably due to the state of the reflecting surface. The surface roughness of the polycrystalline sample and those studied before, can lead to the displacement of the maximum, especially at higher energies, E>2 eV 12. The calculated spectra of n(E), k(E) and gl(E), g2(E) are in good qualitative agreement with previous results of Zivitz 3 which speaks in favour of the applied extrapolation procedure 14 beyond 5 eV for R(E), necessary for KramersKronig integrations. Because of the reflecting surface roughness contribution it is very difficult to put any attention to quantitative comparisons, but higher values of R(E) and furthermore of optical constants in our case point probably to the better quality of the surface of our sample. Surmnarizing, despite the very simplified nature of the Lin-Chung model a reasonably good agreement between our experimental data and theoretical prediction is obtained. Acknowledgements - We wish to thank Professor J. Paw~kowski for making available to us the samples of polycrystalline Cd3As 2, and Dr. Myron Evans for his c o ~ e n t s during the preparation of the manuscript.

Vol. 44, No. 3

377

MONOCRYSTALLINE AND POLYCRYSTALLINE BULK Cd3As 2 References

I.

Wo Zdanowicz and L. Zdanowicz, Annual Review of Material Science, ~, 301 (1975).

2o

W.W. Sobolev and N.N. Sybru, Izviestija ANSSR Neorganiceskije Materialy, ~, 1011 (1966); W.W. Sobolev~ N.N. Sybru and S.D. Shutov, in KHIMIA POLUPROVODNIKOV II-V, Ed. Nauka i Technika, Minsk 1966.

3.

M. Zivitz and JoR. Stevenson, Physical Review, 10_, 3457 (1974); Mo Zivitz~ PhD Thesis, Atlanta University, Atlanta 1974.

4.

M.J. Aubin and J.P. Cloutierj Canadian Journal of Physics,

5.

V.P. Bhola, Physics Status Solidi(a), 4__3, K179 (1976); V~P. Bhola~ Journal of Physics and Chemistry of Solids,

53__., 1642 (1975).

38__, 1237 (1977)~

6.

M.J. Aubin, L.G. Caron and J.P. Jay-Gerin, Physical Review, B15, 8 (1977); J. Bodnar, in PROCEEDINGS III INTERNATIONAL CONFERENCE ON PHYSICS OF NARROW-GAP SEMICONDUCTORS, Ed. PWN, Warszawa 1977; M.J. Gelten~ F.A.P. Blom and J.W.P. Jongeneelen, Solid State Communications, 7_~3, 833, (1980).

7.

P.J. Lin-Chung, Physical Review,

8.

W. Zdanowiez, in FIZYKOCHEMIA

9.

K. Karnicka-Moseicka,

188,

1271 (1969).

CIALA STALEGO,

PhD Thesis,

Ed. PWN, Warszawa

Jagellonian

University,

1967~

Krak6w 1981.

10.

A. Rodzik and A. Kisiel, in preparation.

1|.

N. Tajabor and D.R. Lovett, Physica Status Solidi(b),

|2.

K. Karnicka-Moseicka and A. Kisiel, Surface Science

]3.

E. Czarnecka-Such~ A. Kisiel and J. Szczyrbowski, in PROCEEDINGS VACUUM CONGRESS, Vienna 1977v

14.

W.H. Ellis and J.R. Stevenson, Journal of Applied Physics, 46, 3066 (1975).

15.

L. Zdanowicz and T~ Czapla, Vacuum, 27, 409 (1977).

16.

M. Cardona and D.L. Greenawayp Physical Review,

17.

L. Van Hove, Physical Review,

89___, 1189 (1953).

125,

49, 513 (1972). (1982), in press.

1291 (1962).

VII INTERNATIONAL