TRANSPORT PROPERTIES OF CdIn2S4 AND CdIn2(1-x) Cr2xS4 SINGLE CRYSTALS

HAL Id: jpa-00216285

https://hal.archives-ouvertes.fr/jpa-00216285

Submitted on 1 Jan 1975

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

TRANSPORT PROPERTIES OF CdIn2S4 AND CdIn2(1-x) Cr2xS4 SINGLE CRYSTALS

S. Endo, T. Irie

To cite this version:

S. Endo, T. Irie. TRANSPORT PROPERTIES OF CdIn2S4 AND CdIn2(1-x) Cr2xS4 SINGLE CRYSTALS. Journal de Physique Colloques, 1975, 36 (C3), pp.C3-77-C3-81.

�10.1051/jphyscol:1975315�. �jpa-00216285�

JOURNAL DE PHYSIQUE

Colloque C3, supplkment au no 9, Tome 36, Septembre 1975, page C3-77

TRANSPORT PROPERTIES OF CdIn,S4 AND CdIn,,,-,, Cr2,S, SINGLE CRYSTALS

S. E N D 0 a n d T. IRlE

Department of Electrical Engineering

Faculty of Engineering, Science University of Tokyo, Shinjuku-ku, Tokyo, J a p a n

Rkum6. ^-

Plusieurs propriktes de transport ont ete etudiees sur des monocristaux de Cdln2S4 de differentes compositions stcechiometriques. La rksistivite electrique a tempkrature ambiante recouvre le domaine de 10-3 B 104 0-cm en correspondance avec l'excts de soufre. Le coeficient de Hall se situe dans le domaine de 10-

¹ a

106 cmS/C. Tous les khantillons sont de type n.

A

partir des mesures 6lectriques, Ie gap

ⁱⁱ

0 K se situe 2,2 eV. La variation thermique de la mobilite de Hall et le signe du coefficient de Nernst indiquent que la diffusion des porteurs est prin- cipalement due aux phonons acoustiques du rkseau et aux impuretes ioniskes respectivement dans le domainc dc haute et basse temperature. L'anisotropie de la magnetorCsistance a Cte CtudiCe. On suggkre que les minima de la bande de conduction sont situes en des points le long des directions

(100)

dans l'espace des

k. La

masse effective de la densit6 d'etat des electrons a 6tC determinee comme etant 0,19

^m0

A partir de mesures de Seebeck et de Hall. La conductivite a

CtC

mesurke de 4 B 300 K et analyske par le formalisme de Callaway.

Des etudes de transport ont egalement et6 effectukes sur C d I n ~ c I - ~ , C ~ Z ~ S ~ pour 0

< ^X

0,02.

On a trouvk que les atomes de Cr substitues A In donnent lieu A un niveau accepteur profond a 0,7 eV en dessous de la bande de conduction. Les ions de substitution provoquent des diffusions de phonons rksonnantes aux environs de 2,5 et 30 K.

Abstract.

-

Several transport properties have been studied on CdInzS4 single crystals with different degree of deviation from stoichiometry. The electrical resistivity at room temperature spreads from an order of 10-3 Q-cm to 104 Q-cm corresponding to the degree of excess sulphur. The Hall coefficient also spreads from an order of 10-1 m 3 / C to 106 cm3/C. All the samples exhibited n-type conduction.

The energy gap at 0 K was determined from the electrical measurements to be 2.2 eV. The tempe- rature dependence of the Hall mobility and the sign of the Nernst coefficient indicate that the scatter- ing of carriers are mainly due to the acoustic mode of lattice vibrations and the ionized impurities in the high and low temperature range, respectively. The anisotropy of the magnetoresistance effect was studied. It is suggested that the minima of the conduction band are located at points along the [l001 directions in k space. The density-of-states effective mass of electrons was determined to be 0.19

m0

from the Seebeck and the Hall measurements. The thermal conductivity was measured from 4 K to 300 K and analysed by Callaway's formalism.

Transport studies were also made on CdInz11-~)Cr2~S4 for 0

C X S

0.02. It was found that the Cr atoms substituted for In atoms produced a deep acceptor level a t 0.7 eV below the conduction band.

The substituted Cr ions cause resonance type phonon scatterings at about 2.5 K and about 30 K

Introduction. - The ternary compound Cdln2S4 is a photosensitive semiconductor crystallizing in a cubic spinel structure. Its optical properties have been studied by several workers. However, a difficulty of growing the large and homogeneous single crystal had been preventing them from a detailed investigation of the transport properties until recent years. Recently, we have succeeded in growing large a n d homogeneous single crystals of CdIn,S4 with different degree of deviation from stoichiometry a n d have made prelimi- nary study o n the transport properties [l], [2], [3]. T h e work presented here is the result of more detailed measurements of the transport properties of CdIn2S4 single crystals than have been madc previously. Etrect of C r ions substituted f o r In ions in Cdln,S, o n the transport properties will also be presented. Such a

study will provide a foundation for the study of the ferromagnetic semiconducting spinel.

I . Experimental procedure.

-

Stoichiometric amounts of the components with o r without excess sulphur were sealed into a n evacuated quartz tube and heated t o about 500 OC a t a rate of 50 OC per day. After the tube was held a t this temperature for a b o u t one week, the temperature was again raised t o a b o u t 1 250 OC a t the same rate a s before a n d maintained for one day. T h e n the tube was cooled down to room temperature a s the same rate a s that for heating. Oriented crystals were grown from the ingots by the horizontal o r vertical Bridgman process. Single crystals a s large a s a b o u t 150 mm

X 4 mm X

l 0 mm were obtained. X-ray diffraction analysis revealed the spinel structure having

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975315

C3-78 S. E N D 0 AND T. IRIE

the lattice constant in accordance with the published

data. The crystal grows preferentially in the [l 1 l ] or the [l 101 direction. The Cr-doped samples were cut out of the single crystals grown from the melts having compo- sition of CdIn,( ,-,, Cr,,S4 with

X =

0.000 4

-

0.02.

The solid solubility was confirmed by X-ray analysis in the compositional range studied. The susceptibility and the paramagnetic resonance measurements provided evidence that chromium substituted for indium in the lattice.

Electrical and thermal measurements were made by the conventional mcthod using a potentiometer or a vibrating reed electrometer.

2.

Experimental results and analysis. --

2.1 ELEC-

TRICAL

PROPERTIES.

-

2 . 1 . l CdIn2S4.

-

The electri- cal resistivity p and the Hall coefficient R, are plotted against the reciprocal temperature in figure 1 and figure 2, respectively for a series of samples having different compositions. The samples cut from a crystal grown from a melt with stoichiometric composition are designated as ST-1 and that from a melt with excess sulphur as ES-l, where 1 is a sample number. I t can be seen that the electrical resistivity at room tempera- ture spreads from an order of 10-3 R-cm to 1O4 SZ-cm corresponding to the degree of excess sulphur. The Hall

/ ES-I

/O /O

ES-5

/OH

m.

.'.

^m--.*

-

^{ES - 6}

ST- 3

ST- I

FIG. 1.

-

Electrical resistivity of CdIn2.54 single crystals as a function of inverse absolute temperature.

FIG. 2. - Hall coefficient of Cdln2S4 single crystals as a func- tion of inverse absolute tempcrature.

coefficient also spreads from an order of 10-I cm3/C to 106 cm3/C. As the sulphur excess in the melt is increased the electrical resistivity and the Hall coelli- cient increase. The sign of

RH

is negative for all the samples in the temperature range studied. From a slope of the resistivity curve in the temperature range which can be regarded as an intrinsic region, the energy gap at 0 K was determined as 2.2 eV.

Figure 3 gives the temperature variation of the Hall mobility

p,.

In the high temperature range

p,

varies as T - 3 1 2 indicating that the scattering is mainly due to the acoustic mode of latticc vibrations. In the low tempe- rature range

p,,

is nearly constant for ST-samples, while it increases with the rise of the temperature for ES- samples. These results indicate that the ionized impu- rity scattering is predominant in this temperature range for all the samples. In order to confirm these conclu- sions the Nernst coefficient was measured in the tempe- rature range between 80 K and 700 K. It was found that the Nernst coefficient was negative in the low temperature range and positive in the high temperature range. These results are consistent with the mobility data. From an analysis of the mobility data at low temperature using the Brooks-Herring's formalism [4],

[ 5 ] ,

the density of the ionized impurities was found to be the order of 10t9 cm-3 for the all samples. This fact indicates that the high-resistive samples are highly compensated by acceptors.

In order to obtain some information about the band

structure of CdIn2S,, angular dependence of the

TRANSPORT PROPERTIES O F CdInzS4 AND C ~ I ~ Z ( I - ~ ) C ~ Z ~ S ~ SLNGLE CRYSTALS C3-79

6

30 50 100

m

^{500 IOOO}

TEMPERATURE

(

K )

-

-

_{ST- I}

-

^{= v v v v}

v v \

M -rr..,

ST-2 v$

M

+ +++ ^{r ,}

- ++

⁺⁺

€S -7++ c

-

M ti

-

-

.

m ^{' = A} ' = A

- ES-6

E S - 4

. A A . " A

- _{. o O U}

:.

^AA

ES-5'=

-

_{AES -3}

-

-

1 1 1 1 1 1 1 I I 1 1 1 1 1 1

FIG. 3. - Hall mobility of Cdln2S4 singlc crystals as a function of absolute temperature.

magnetoresistance relative to the direction of the magnetic ficld on the oricnted samples was measured at 300 K. The magnetoresistance

Aplp

was confirmed to be proportional to thc square of the magnetic field intensity. Angular dependence of

Aplp

are shown in figurc

30

and b for the current directions of the [ l 101 and the [001 1, respectively. From an analysis using a phenomenological theory developed by Seitz [6], it is suggested that the minima of the conduction band are located at points along the [l001 directions in k space.

The Seebeck coeficient was also measured between

100

K and 700 K and combined with the Hall data, thc density-of-states effective mass was determined to be 0.19

m,,

where

m,

is the mass of electron in free space.

2

ST- I

0 0 ⁹⁰ l80

FIELD DIRECTIONLdeqrees) FIELD DIRECTION(deqrees)

FIG. 4. - Weak-ficld rnagnetorcsistance at 300 K as a function of magnetic field orientation. ^{( U )} Sample current in the [l101 direction and the rnagnctic field is rotated in the (110) and the (001) _plane. (b) Sample current in the [001] direction and the

magnetic field is rotated in the (170) plane.

2 . 1 . 2 CdTn,(, -,,Cr,,S,. - CdIn2(, -,,Cr2,S4 is a system of solid solutions between CdIn,S, and CdCr2S4 which is known as a ferromagnetic semi- conducting spinel. Electrical measurements were made on the samples of

^X =

0.002 and 0.01. Composition and specification of the samples are summarized in table I. The samples RS-1 and 2 are the as-grown samples and RS-3 - 6 are the annealed ones. Figures 5 and 6 show

p

and R,, respectively as a function of

Sample Composition

x

-

-

RS- l 0.01

RS-2 0.0 I

RS-3 0.01

Specification - as-grown as-grown

RS-2 annealed at 300 OC for 1 hour

RS-3 annealed at 500 OC for 48 hours

annealed at 300 OC for 1 hour

RS-5 annealed at 500 OC for 54 hours

FIG. 5. -Electrical resistivity of CdTn2(1-~) C r ~ r S 4 single crystals as a function of inverse absolute ternpcrature. Cornpo- sitions and specifications are givcn in table I. Dashed lines are

the data for CdIn2S4.

C3-80 S. E N D 0 A N D T. IRIE

to0

I , - . _ _ _ _ _ _ _ - , - - -

- - _ - - - _

^-

- - _ - _ _ - - - - - - - - -

- - -

- - -

^{S T - I}

- - - - - 1

S T - 2

FIG. 6.

-

Hall coefficient of C d I n ~ ( l - ~ )

c~2~s.1

single crystals as a function of inverse absolute temperature. Con~positions and specifications are given in table I. Dashed lines are the data

for CdInsS4.

of the Hall curve in the high temperature range exhibits an activation energy of about 0.7 eV which is not observed in pure CdIn2S, and remain invaried for annealing. It may be said that chromium substituted for indium in CdIn2S4 lattice acts as a deep acceptor the level of which lies about 0.7 eV below the conduc- tion band. Figure 7 shows the Hall mobility as a func- tion of temperature. Comparing with the result of the undoped samples which is shown in figure 3, it can be said that chromium ions have pronounced effects on the mobility such as lowering the absolute value and increasing the temperature variation at low tempera- tures.

2 . 2 THERMAL

CONDUCTIVITY. -

The thermal conductivity of CdIn2S4 was measured from 4 K to 300 K and plotted in figure 8 as a function of the tempe- rature. The sample used is ES-l. The electronic part of the thermal conductivity can be neglected in the tempe- rature range studied. The solid line in the figure repre- sents Callaway's equation [7],

k

^BolT X4 ^,X

K =

--(c)3 _{2 z 2 v h} 5

_o ^i-

( e " - ~ ) ~ ^{- d x , (I)} inverse absolute temperature for a series of the Cr- with

8, =

200 K,

doped samples. For comparison, the data of undoped

A =

l

^X

10-43 s 3 , B

=

9

X

10-l8 s . d e g - l , crystals are also shown in the figure by dashed lines.

It can be seen that both p and R, of Cdln2S4 are b

=

4 0 K and t)/L

=

8

^X

106 S - ' . considerably increased by doping of chromium. A slope

- -

ST-I

----

p

- - - ---- .\ \

^\

-

p

- - -

- :o

-

RS-6 +*

-

0

RS-2

RS-5s ooooo

8 00

- 0 0 0 o@

-

-

RS-38 8

O R S - I

- 0

-

Q

I 1 1 1 1 1 1 1 1 1 1 1 1 1 1

FIG. 8. - Lattice thermal conductivity as a function of absolute temper.ature for sample ES-I. The solid line is a fit of Callaway's

equation to the data.

-

^{10 L}

by 2 n, 0, the Debye temperature,

W

the phonon

FIG. 7. - Hall mobility of C d I n z ( ~ - ~ ) CrzZS4 single crystals

as a function of absolute temperature. Compositions and speci-

angular frequency and L is the characteristic length of

fications are given in table I. Dashed lines are the data for

the sample. The values of the Parameters A , B and b are

Cdln~S4.

reasonable from a physical point of view. A large value

-

C A L C U L A T E D

E

0,

2

30 50 00 m 500

- -

:

1000

In eq. ( 1 ) and (2) k is the Boltzmann constant, v the

S *

TEMPERATURE ( K )

average sound velocity, h the Planck constant divided

-

- ^€S-I

'Oo

' 0 0

O

\

I l l l l l l L

I l0 100 1000

TEMPERATURE

(K)

B

0 '0

\

Toa,

I 1 1 1 1 1 1 1

loo- k

- ^oO

>

^-

F -

U -

3 - D Z

16'

-I Q

3

IY W l- I

=

- -

-

-

-

102

^{l 1 1 1 1 1 1 1}

TRANSPORT PROPERTIES O F CdJ.nzS4 A N D CdIn2cl-z,Cr2zS4 SINGLE CRYSTALS

of v / L compared with the value deduced from the sample dimension which is about 8

^X

105

^{S - '}

may be due to existence of internal boundaries in the sample.

I 3 10 30 100 300 000

TEMPERATURE ( K

FIG. 9. - Lattice thermal conductivity as a function of absolute temperature for C d l n n ( ~ - . ~ ) CrzzS4 with X =- 0.000 4, 0.0008

and 0.02.

Figure 9 shows the lattice thermal conductivity of CdIn2(,-,,Cr2,S4 as a function of temperature for

X =

0.000 4, 0.000 8 and 0.02. For comparison the result for CdTn2S4 is also shown in the figure by dashed line. It can be seen that an addition of chromium substituted for indium has a pronounced effect on the lattice thermal conductivity. The additional thermal resistivity defined by

is plotted in figure 10 as a function of temperature, where

K

and

^{U ,}

are the measured lattice thermal conductivities of the Cr doped and the undoped crystals, respectively. It is apparent that resonance type phonon scatterings take place at tempcratures of about 2.5 K and about 30 K. Generally, the phonon fre- quency

^o

at which thc spectral distribution of the heat current has its maximum is given by

ho =

3.8

kT.

Hence the resonance wave numbers of the phonons for the two peaks in figure 10 are about 6.6 and 80 cm-'.

These phonon energies may correspond to the separa- tion between the encrgy levels of the d-shell electrons of Cr ions in the crystalline host [8], [9],

[10].

FIG. 10. - Additional thermal resistivity W defined by eq. (3)

as a function of absolute temperature for C d l n 2 ( 1 - ~ , C T ~ ~ S ~ with X L 0.000 4, 0.000 8 and 0.02.

3.

Conclusions. -

The temperature variation of the electrical resistivity of CdIn2S, single crystals in the intrinsic range shows that the energy gap at 0 K is 2.2 eV. The anisotropy of the. magnetoresistance effect indicates that minima of the conduction band are located at points along the [l001 directions in k space.

The density-of-states effective mass for the conduc- tion band is 0.19 m,.

The carrier scatterings are mainly due to the acoustic mode of lattice vibrations and the ionized impurities in the high and the low temperature range, respectively.

The chromium substituted for indium in CdIn,S4 acts as deep acceptor the level of which lies 0.7 eV below the conduction band and has a pronounced effect on the carrier scatterings.

The lattice thermal conductivity of CdIn2S4 single crystal in the temperature range from 4 K to 300 K can be satisfactorily explained by the Callaway's theory.

The chromium ions substituted for indium ions in CdIn2S4 lattice produce additional phonon scatterings of resonance type. This may be caused by the phonon assisted transitions between energy levels of the d-shell electrons.

Acknowledgments. -

The authors would like to thank Prof. Kimura and Mr. Kobayashi of Tokai Uni- versity for performing the paramagnetic resonance study on our samples of Cdln2,,-,,Cr2,S,. They are also much indebted to Mr. Ueno for help with the experiments.

References

[ l ] SUDO, I., E ~ n o , S., IRIE, T. and NAKANISHI, H., J. Phys. [6] SEITZ, F., Phys. Rev. 79 (1950) 372.

Soc. Japan 31 (1971) 949. [7] CALLAWAY, J., Phys. Rev. 113 (1959) 1046.

[2] ENDO, S., SUDO, 1. and IRIE, T.3 J . P ~ J ' s . Soc. 29 [g] SLACK, G . A. and GALGINAITIS, S., P / ~ ) J s . Rev. 133 (1964)

519.

.

[3] ENDO, S. and IRIE, T., J. Phys. SOC. Japan 36 (1974) 1210. ^{A L35.}

141 BROOKS, H., Adv. Electron. Phys. 7 (1955) 156. [g] CHALLIS, L. J., MACCONACHIT., M. A. and WILLIAMS, D. J., [5] BEER, A. C., In Solid State Ph~lsics-S~ipplement, Edited by Proc. R . Soc. A 308 (1968) 355.

Seitz F . and Turnbull D. (Academic Press Inc., New [l01 MORTON, 1. P, and Lliwts, M. F., Phys. Rev. 3 (1971)

York) 1963, Vol. 4, p. 1 1 l ff. 552.