Transport mechanisms in MoTe2-x single crystals

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Transport mechanisms in MoTe2-x single crystals

A. Bonnet, A. Conan, Y. Tregouet, M. Zoaeter, M. Morsli

To cite this version:

A. Bonnet, A. Conan, Y. Tregouet, M. Zoaeter, M. Morsli. Transport mechanisms in MoTe2-x single

crystals. Journal de Physique I, EDP Sciences, 1991, 1 (5), pp.779-787. �10.1051/jp1:1991169�. �jpa-

00246370�

classification Physics Abstracts

72.20D 72.20P 71.25R 71.30

Transport ^mechanisms in MoTe~_~ single crystals

A. Bonnet (~), ^{A. Conan}

('),

Y.

Tregouet ('),

M. Zoaeter (2) ^{and M.} Morsli

f) (')

Laboratoire de

Physique

Cristalline, I-P-C-M-, 2 _rue de la Houssinidre, 44072 Nantes Cedex 03, France

(2) Laboratoire de

Physique

des Matdriaux et

Composants

de

l'Electronique,

Facultd des Sciences et des

Techniques,

Universitd de Nantes, 2 _rue de la Houssinidre, 44072 Nantes Cedex 03, France

(Received

4 October J990, revised J4

January

J99J,

accepted 25January J99J)

Rksumk. Los _mesures des coefficients de transport

(conductivitd dlectrique, pouvoir thermodlectrique,

effet Hall ont dtd effectudes _{sur des} monocristaux de

MoTe~_~ (x

=

0,040 et

0,045)

dans _{une gamme} dtendue de

tempdrature.

Les rdsultats

expdrimentaux

sont

interprdtds

_sur

la base d'un moddle de semi-conducteur

compensd

de type p fi niveaux

dlargis d'origine

lacunaire.

A basse

tempdrature,

les mdcanismes de conduction sont

principalement gouvemds

_par des _sauts activds

thermiquement

des porteurs ^dans le niveau accepteur

dlargi.

A

plus

haute

tempdrature,

la

contribution des dtats dtendus doit dtre

prise

_en compte.

MoTej,~w

et

MoTej,~ss prdsentent

_un comportement de type

quasi mdtallique

associd h la ddlocalisation dlevde des dtats

dlectroniques

dans les niveaux

dlargis.

Abstlract. Transport coefficient measurements (electrical conductivity, therrnoelectric power, Hall effect) have been

performed

_on

single crystals

of MoTe~_~ (x= 0.040 and 0.045).

Experimental

results _are

interpreted

_on the basis of _a

compensated

p-type semiconductor model where donor and acceptor lacunar levels broaden in two energy bands. At low temperatures, the

conduction mechanisms _are

mainly

governed

by

_a thermal

hopping

of carriers in these bands. At

higher

temperatures, the contribution of the extended states must be taken into account.

MoTei.9w

et

MoTei

9ss exhibit _a

quasi

metallic behaviour which reflects the

high

delocalization of the electronic states in the broadened levels.

1. Introduction.

The

crystalline

semiconductor

MoTe2 belongs

to the

large family

of

layer-like compounds (MX2 type)

whose

crystal

structure results from the

stacking

of sheets of

hexagonally packed

atoms in the sequence

Te-Mo-Te,

Te-Mo-Te. As _a consequence,

they

_can be used

successfully

in intercalation

chemistry [1, 4].

The

particular photoelectrochemical properties

of transition metal

dichalcogenides

enable _a

large variety

of _new

applications

to be

explored.

One of the

important advantages

associated with these materials _over other

chalcogenides

and III-V semiconductors is that for the former _case the

photogenerated

holes

belong

to _a

non-bonding

d-orbital state and hence cannot

participate

in corrosion reactions

[5, 6].

^In order to

study

the

780 JOURNAL DE PHYSIQUE I M 5

electrical

properties

of the

subsequent compounds,

the behaviour of the

transport

coefficients electrical

conductivity,

thermoelectric _power, Hall effect of the host

compound

in _a wide

temperature

range is of

great

^interest.

In _a recent paper

[7],

measurements of the electrical

conductivity

wand thermoelectric power S have been

performed

_on

MOTe~

~

(x

=

0.01 and

0.015) prepared by

_a based Te flux method

[8]. Experimental

results have been

interpreted

_on the basis of _a

compensated

_p-type

semiconductor model. For the

compound

which

presents

^the

larger departure

from

stoichiometry (x

=

0.015),

it has been shown that the donor and

acceptor

^{levels broaden in}

two _narrow energy bands _:

at low

temperatures,

^conduction mechanisms _are

mainly govemed by

thermal

hopping

of small

polarons

in these

bands,

at

higher temperatures,

^the contribution of the extended _states must be taken into account.

Then,

it seemed to _us

interesting

to undertake _a continuation of these studies in other

compounds

for which the Te content is smaller and the band structure model would be built in

a continuous _way.

In order to do _so, the electrical

conductivity

and the thermoelectric _power of

MOTe~_~ crystals (x

=

0.04 and

0.045)

_were measured within _a

large

_range of temperatures

(7T650K).

It is observed that

MoTej_~~o

and

MoTej_~55 compounds

exhibit

quasi~metallic

behaviour

(«

= 5 Q~ ^' cm~ ^' and S

=

30

~V/K

at _room

temperature). Then,

it is

clearly put

ⁱⁿ evidence that the

increasing departure

from

stoichiometry

favours the delocalization of the states in the _narrow bands which

originate

from the donor and acceptor levels. These bands

participate

to the conduction in the form of

phonon

assisted

hopping

between nearest

neighbours.

2.

Experimental

results.

Non-stoichiometric

MoTej_~~o

^and

MoTej_~55 crystals

have been obtained

by decreasing,

in _a controlled way, the Te content in

MoTe2 compounds.

The determination of the

composition

value 2 _x is in average within _an accuracy of about I fb.

It must be noticed that

X-ray

diffraction pattems,

performed

in _a Guinier

chamber,

_are

practically unperturbed by

the Te decrease.

The electrical

conductivity

_« and the thermoelectric _power

(T.E.P.)

S of

MoTej,~~o

and

MoTej_~55 crystals

have been measured between 77 and 700 K in the

hexagonal planes.

Several

experimental

measurements have been

performed

_on each

sample.

A

good reproducibility

is obtained and

experimental

data _are

always

within the _error bars determined for each

technique, I.e.,

=

2 9b for

conductivity

and

= 5 9b for T.E.P.

[9].

The

experimental

varitations of In _«

(Q~

^' _cm~

')

and S

(~V/K)

_versus

10~/T

_are

plotted

in

figures

I and 2 for

MoTej,~~o

^and

MoTej,~55.

The electrical

conductivity

^{is found} to be of the order of 9.4 Q~ _cm~ ^'

(7.4

Q~ ^' cm~

')

_at

liquid nitrogen

temperature. ^{It decreases}

slowly

down to a minimum 4.2

Q~'cm~' (3.3 Q~' cm~')

which is reached at about 500K. For

higher temperatures,

^{the intrinsic}

regime

_occurs and _« increases

rapidly.

In this

temperature

_range, a thermal activation energy of 0.4 eV _can be evaluated.

The behaviour of the T.E.P. coefficient

S,

which is

positive

_over the whole

temperature

range

investigated,

is _very characteristic and different from that observed _on

MoTe~ [10]

^and

MoTej_~~ [7].

At low temperatures, ^S

slightly

increases from

approximately

_zero to 25

~V/K (45 ~V/K)

at 250 K.

Then,

it has _a

relatively

small variation up ^to 350 K. At

higher

temperatures, ^S

drops drastically

down _to 7

~V/K (25 ~V/K)

at 670 K. These

variations,

~JE _SJ

~Q

~

a

>

1

ig. I. -

xperimental

ariations

are

as

full _lines.

t

~

0.4

>

8

8

1

, 1

T

are _drawn

as

hich

ontributions to

phenomena.

All

these results

are

lose

to

what

is

_observed in

MOTe~_~ _in powder _form [I1].

782 JOURNAL DE PHYSIQUE I M 5

The _room temperature ^{value of the Hall} coefficient

R~

which has been obtained

by

d.c.

Hall coefficient measurements is

positive

and

nearly equal

to

0.scm~/C

for the two

compounds.

This value has to be

compared

with that obtained in stoichiometric

MoTe~

(=

400

cm~/C), MoTej

~~j

(

= 240

cm~/C)

and

MoTej

~g5

(=

10.5

cm~/C).

3. Theoredcal

approach.

The

experimental

results

reported

here _can be well fitted

using

_a

slightly

modified model derived from that

developed

for

MoTej_~g5

ⁱⁿ

[7].

^The semiconductor is

compensated

and the

random

potential

due _to

charged

_acceptors and donors induces _a

broadening

of the

corresponding

levels

E~

and

E~

into _narrow bands. As _a consequence, these bands

participate

to the conduction

through

thermal activated

hopping

mechanisms.

Hopping

conduction _can be written in the

general

form

[12, 13]

:

«~=

«oexp(-2aR-pW)

where _a is the

damping

factor of the _wave

function,

R is the

hopping

distance between nearest

neighbours,

W is the

hopping

_energy and

p

stands for

I/kT.

In order ot make _a

comparison possible,

it must be recalled that _a thermal

hopping

of small

polarons

has been assumed to take

place

in

MoTej,~g5 _[7]

_{: as a} consequence, a

polaron

term

W~(T)

and _a disorder term

JJ§

_were included in W.

On the

contrary,

^{the electric} states _are

quite

delocalized for

MoTej,~~o

and

MoTej,~55

and the

hopping

_energy has been taken

equal

to W~ ^{which is}

T-independent [12, 13].

The

conductivity

_«~ due to

hopping

between nearest

neighbours

sites is therefore written _:

~2

p

"H ~ ~

$

^{~~~ ~~}

~~~~ ~ ~~

where _v is a

jump frequency

add _c is the relative

quantity

of

particles

for which

hopping

_can

occur :

c =

(ND N] )/ND

_or N j

/N~

W~ represents

_any energy difference which

might

exist between the initial and final sites due to variations in the local

arrangements

of ions. The term _v is assumed to

obey

the law _:

I~

~

~Ph

~/2

d

where I is the transfer

integral

between sites

separated by

R and v~~ is ^a

phonon frequency.

In this _case, where the kinetic energy of the carriers is

negligible,

the

thermopower

is

given by

the well~known Heikes formula

[14]

_:

S=kleIn (~).

At low

temperatures,

the conduction mechanisms _are

mainly governed by

the thermal

hopping

in the _narrow band

E~.

At

higher temperatures,

^the contribution of the extended

states must be taken into _account. Holes _are excited in the valence band where

they

_are

expected

to interact with both ionized

impurities

add

long wavelength

acoustic

phonons.

At much

higher temperatures,

^{the main} contribution to conduction mechanisms is that of excited

electrons in the conduction band where

they

interact with acoustical vibration modes.

The associated electrical

conductivity

and thermoelectric _{power are}

expressed

_as follows

jn ^-3/2

NI~

_jn 3/2

~~

~~~~

1~0

~~

~~~~

~I

_1~0

~~'' ~

~'(P

_{f + Pi}

I

= pep

~

"

nepn

^l~

~~'~

~ ~o

~

^{= nep} ~

~

~

(fl (EF Ey)

₊

2j

'

~

e

~~ ~~F Ey)

₊ 4

' ~~ ~~c ^EF)

+

2)

where _{n, p,}

N~

₌

N(

₊

Nfi

_are the concentrations in

electrons,

holes and ionized

impurities.

The

f

and I indices _are related to the collision mechanisms with the lattice and with the ionized

impurities respectively

whereas the 0 index denotes _room temperature.

On the whole

temperature

range

investigated,

the electrical

conductivity

is therefore the summation of the

following

terms

W=Wy,I+W#+Wi+W~

and S

=

«4 54

₊

«4 Sk

_{+ On}

_Sn

₊

^~~ II _{1/~ /«}

RH

can be calculated in the

following approximation [15]

which is usable close to _room

temperature

:

R~

m

(«~ _p~

_{«~ p}

~)/«~.

As shown in

figures

I and

2,

_a

good agreement

is obtained between

experimental

and theoretical results for both

conductivity

and T-E-P-

The contribution of electrons and holes to the

conductivity

and T-E-P- _are

represented

in

figures 3a,

b et

4a,

b.

It is shown that

hopping

conduction in the broadened

acceptor

^{level is the main}

contribution to the

conductivity

below 500 K. At

higher temperatures,

^{conduction of holes in} the valence band must be taken into account. On the contrary, the main contribution to the T.E.P. _comes from holes in the valence band in the whole temperature range

investigated,

whereas that of the donor level becomes

significant

_on T-E-P- above 250 K.

The Hall coefficient value at _room

temperature

leads to _an

equivalent density

of states in the valence band

Ny~

=

6 _x 10~~

cm~~

_{at 300 K in}

_{MoTej_~~o} (I

_x

10'~ cm~~

_in

MoTej_~55).

The values of the

physical

parameters which

give

the best fit to the

experimental

_{curves are} listed in table1.

4. Discussion.

Comparison

can be made with the results which have been obtained _on

MoTe~ [8], MoTej

~~j and

MoTej_~g5 [7].

^It appears that the concentration of the donor and

acceptor

^sites increases _as the Te content decreases in the

compound. Moreover,

the

N~/N~ compensation

remains close to 0.5.

Obviously,

the

origin

of the donor and acceptor levels is

lacunary.

The

random

potential

of donor and acceptor

charged

centers induces _a

broadening

^{of the}

corresponding EA

and

E~

levels into _narrow bands which

participate

in the conduction

by

thermally

activated

hopping

between nearest

neighbours.

784 JOURNAL DE

PHYSIQUE

I M 5

o

a

~ ~' 5 ~'

ldlT

(a)

(b)

Fig.

3. Electrical

conductivity

contributions: a)

MoTei9w, b) MoTei.9ss.

1) «,

2)

«1~,

3) al, ₄₎

at,, 5) _«~.

~

_~

m

~

©3

~

io

i

(a) b)

Fig.

4.

~i~il~, 5) ~n/~.

Table I.

MoTej,~w MoTej_~~~

A

(ev~

0.66 5.4 _x 10-4 T 0.60 5.4 _x

10~4

T

Nv~ (cm~~)

6 _x

10'7

_x

10'8

Nc~ (cm~~)

_{3 x}

10'8

3 _x

10'8

E~ Ey (mev)

5 4

N~ (cm~~)

6.7 _x 10'8 6.7 _x

10'8

ED EA (mev)

130 135

N~ (cm~

~) 3.3 _x

10'8

3.3 _x

10'8

pf (cm ~/V/s)

60 60

pi _{(cm ~/V/s)}

_{15 10}

p

f _{(cm ~/V/s)}

_{426 426}

i§j _(mev)

_{5.5 4.5}

Wfl (mev)

^{5.5 4.5}

p( (cm~/V/s)

7.5 6

p

f _{(cm ~/V Is)}

_{10 7}

The acceptor broadened level is found _to be very close to the valence band

m

5 mev to be

compared

with the values

130,

60 and 28 mev obtained

respectively

on

MoTe~, MoTej_wj

and

MoTej_~g5).

This result is not

unexpected

and is characteristic of the increase of the

macroscopic

static dielectric constant with the

stoichiometry

deviation. An

approximate

value has been found for s~

by

the

capacitive

method at _room

temperature (s~

=

45).

Moreover,

the energy difference

EA Ey

varies _as the effective _mass of the

density

of states

m~

of the holes in the valence band which _can be deduced from the

equivalent density

of _states

Nv~ (respectively

6 _x

10'~

_and

10'8

_cm~ ~ for

MoTej_~w

and

MoTej_~55)

:

m~

is found to be

equal

to

0.08m~

in

MoTej,~w

and

0.12m~

in

MoTej_~55

to be

compared

with the

respective

values 0.55 m~ in

MoTe~, 0.52m~

in

MoTej_~~j

and 0.28 m~ in

MoTej_~g5.

This modification of the curvature of the valence band _can be attributed to the

increasing

interaction between the valence band and the broadened

acceptor

^level

E~

with the

decreasing

_energy difference

E~ Ey.

Furthermore,

the decrease of the energy gap

width,

I.e.

respectively

0.66 and 0.60 eV at 0 K to be

compared

with the values 0.98

[8],

0.99 and 0.83 eV

[7], clearly _puts

in evidence _a

softening

of valence

bondings.

It must be noticed

that,

in _a first

approach,

the small

polaron

model

proposed

in

MoTej_~g5

^{has been tested in order the}

interpret

the results obtained _on

MoTej_~~o

^and

MoTej_~55.

The fit

yielded

to _a value of the transfer

integral

I which did not

satisfy

the criteria

of

validity

of the small

polaron

model _: the calculated

polaron

radius

r~ (r~

=

RI/W~)

_was

found to be of the _same order _as the intersite _{distance R.}

In

fact,

the electronic states in the broadened levels

E~

and

E~

_are much

highly

delocalized and the electrical

conductivity

has been assumed to follow the classical Mott law

[12]

for the

high

temperature range.

In order to estimate the aR term, _an

approximate

value of the intersite distance can be obtained from the site concentration

(

= 40

A).

If _we put v~~ =

10'~ _Hz,

_the

hopping mobility

values

(

= 7

cm~/Vs)

allow _us to calculate _a value of _a R

nearly equal

to 0.9. This value _as well

as the

hopping

_{energy ones}

(=

5

mev~

_are consistent with the assumed

type

of conduction.

786 JOURNAL DE PHYSIQUE I M 5

At

least,

it appears that

MoTej_~55

^which

presents

the

larger departure

from

stoichiometry

exhibits values of electrical

conductivity

lower than that observed _on

MoTej_~~o

whereas its T-E-P- value at _room

temperature

^is 60 9b

higher.

These results have to be

compared

with those obtained _on

MoTe~

~

in

powder

form

[9]

and

on

MoTe~_~~n type single crystals doped

with bromine

[16]: transport

coefficients

(«, S,

Hall

effect,

thermal

conductivity)

variations _versus Te

depletion

_{present an}

optimum

at

x =

0.04 for which _a

quasi-metallic

behaviour is observed. An ordered defect structure for this

particular departure

from

stoichiometry

_may

explain

this fact _: it must be noticed that _a careful

study

of the

crystalline

structure allows _us to prove the

possible

theoretical existence of _an ordered structure of lacunar sites in Te at x = 0.04.

5. Conclusion.

In this paper we have

clearly given

evidence of the role

played by

an

increasing departure

from

stoichiometry

in

MoTe~_~ single crystals

:

electronic states in the acceptor and donor broadened levels become _more and _more delocalized. Conduction

hopping

mechanisms take

place

in these bands with _a

significantly

small

hopping

_energy for _x close to 0.04 _;

the decrease

(by

a factor of _more than 10

relatively

to the stoichiometric

compound)

of the

equivalent density

of states in the valence band has to be associated with deformations of the

crystalline

structure which affect the extension of the valence orbitals. However these

deformations _are too weak to affect

X-ray

diffraction measurements ;

the decrease of the gap width indicates _a

softening

of the valence

bondings

the

departure

from

stoichiometry

_appears to be crucial at _x

= 0.04 _: the

quasi~metallic

behaviour is the _most

significant

_on

MoTej_~~o

which may exhibit _a

partially

ordered defect structure.

The electrons

participate only

at

high temperatures,

_so the electron

mobility

and the

equivalent density

of states in the conduction band _are very little

dependent

_upon the

E~

and

E~

bands and have been assumed to be constant and

equal

to those determined for _n~

type MoTe2 single crystals [16].

The lattice

mobility

values calculated at 300 K _are found to be lower

(by

_a factor

nearly equal

to

10)

than those observed _on

MoTe2

^{this result} seems to suggest some

dependence

of the

phononic

spectrum of the

crystal

_upon the Te content decrease.

On the other

hand,

the decrease of the

impurity mobility namely

reflects the

increasing

concentration of ionized sites

Ni

and

N[.

Moreover,

it _must be noticed that

exponents

in mobilities _as well _as kinetic terms in the thermoelectric power are

practically

similar to their theoretical values.

For the theoretical

fitting,

the activation

energies

which have been found _are those which

can be

directly

deduced from the

experimental

curves. The

room-temperature

^Hall coefficient and electrical

conductivity

have been used to scale the carrier concentrations and

mobilities, respectively.

Then

only

the

mobility

and concentration ratios have been

directly

deduced from the fit.

To

conclude,

_{we can}

emphasize

the

good

agreement ^between

experimental

and theoretical results _{over a} wide

temperature

range, without

using

_any

asymptotic

behaviour for the

calculation of the carrier densities. This confirms the

validity

of the

simple

model which has been retained.

References

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chemistry, Physica

MB

(1980)

89.

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6

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214.

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Energy

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