Dielectric Function and Interband Transitions in Hg 1-xZn xTe Solid Solutions

(1)

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Dielectric Function and Interband Transitions in Hg 1-xZn xTe Solid Solutions

O. Castaing, J. Benhlal, R. Granger, R. Triboulet

To cite this version:

O. Castaing, J. Benhlal, R. Granger, R. Triboulet. Dielectric Function and Interband Transitions in Hg 1-xZn xTe Solid Solutions. Journal de Physique I, EDP Sciences, 1996, 6 (7), pp.907-923.

�10.1051/jp1:1996106�. �jpa-00247222�

(2)

Dielectric Function and Interband llYansitions in Hgi-xZnxTe Solid Solutions

O.

Castaing (~),

J-T- Benhlal

(~),

R.

Granger (~,*)

^and ^R. ^Triboulet

(~)

(~) Laboratoire de

Physique

des Solides

(**),

I-N-S-A, 35043 Rennes

Cedex,

France

(~)

Laboratoire de

Physique

des Solides

(***), place

A. Briand 92195 Meudon

Cedex,

France

(Received

20 December 1996, received in final form 25 March 1966,

accepted

9

April 1996)

PACS.78.20.-e

Optical properties

of bulk materials and thin films

PACS.71.45.Gm

Exchange,

correlation, dielectric and

magnetic functions, plasmons

PACS.71.20.-b Electron

density

of states and band structure of

crystalline

solids

Abstract. The dielectric function _sr + is, in

Hgi_~Zn~Te

is found, for the first time, at 293 K. It is deduced from

spectroscopic ellipsometry

measurements for the entire composition

range and for

photon energies ranging

from 0.75 eV to 5.7 eV. A detailed

analysis

of the chemical

treatments

leading

to the best surfaces which

correspond

to the

highest

values of _s, at the E2

peak

is

presented.

The

oxydation

of the surface after the last

stripping

is also studied. The

pseudodielectric

function is

analysed

for the critical point model. The variation, with _x of the parameters

describing

the main critical transitions ED, ED +

ho,

El, El + hi and E2 _are

obtained. The results _are discussed in relation to the band structure and to the

properties

of these

compounds.

RAsumA. La fonction

didlectrique

_sr+ is, des solutions solides

Hgi_~Zn~Te

est donn6e, _pour la premiAre

fois,

I 293 K. Ces r6sultats _sent d6duits de _mesures

d'ellipsom6trie spectroscopique

dans tout le domaine de

composition

et pour des

6nergies

de

photon

allant de 0,75 eV I 5,7 eV.

Les traitements

chimiques

permettant d'obtenir les meilleures surfaces

correspondant

_aux plus fortes valeurs de _s, _au

pic

E2 sont

analys6s

_en d6tail. De

mime, l'oxydation

de la surface est suivie _par

ellipsom6trie.

La fonction

pseudodidlectrique

est

analysde

_avec le modAle de

points

critiques. Les variations des

paramAtres

ddfinissant les

principales

transitions ED, ED +

ho,

El, El + hi et E2 sont donndes _en fonction de la

composition

_x. Ces rdsultats sont discutds _en

relation _avec la structure de bande et les

propridtds

de _ces solutions solides.

1. Introduction

Hgi_~ Zn~Te (MZTz)

have been

proposed

as valuable alternative solid solutions to

Hgi_~ Cd~Te

(MCTz)

due _to the

higher

bond

strength

in MZT [1]. Most of the known

experimental

results confirm the better structural

properties

of bulk MZT [2] and its

good

lattice

stability

_near

surfaces

[3].

^The fundamental _gap

Eo,

at 0

K,

varies

strongly

^from -0.3 eV for

HgTe

to 2.4 eV for ZnTe with _a

high bowing parameter

of _at least 0.6 eV

[4, 5].

^This

bowing originates

from

(* ^Author ^for

correspondence (**)

^ERS F0134 CNRS

(***)

LP 1332 CNRS

©

Les

(ditions

_de

_Physique

₁₉₉₆

(3)

two contributions [6]: the first _comes from the lattice constant variation with _x and _can be calculated within the virtual

crystal approximation (VCA)

_[7]. The second contribution _comes from the disorder in the

potential

due to the different _nature of the cations and their deviations in

position

as

compared

to the

perfect sphalerite

structure. These deviations _are

important

in MZT [8] as the lattice

parameter

decreases almost

linearly

with _x from

6.4601

_for

HgTe

to

6.10371

_for ZnTe _[4] when the bond

lengths

Te-Zn and

Te-Hg

remain close to those of the end binairies for _any _x

[9]. Eo

has been thus calculated within the coherent

potential

approximation (CPA) using empirical pseudopotentials [10].

^The

bowing

deduced from this theoretical evaluation is

comparable

to that deduced from

experiment

_[4]. However there _are

no detailed band structure calculations

giving

the different valence and conduction bands in the Brillouin _zone for the ternaries. Besides

Eo,

the

only

known results _on MZT _concern _some

values of the

Ei

transition energy which have been deduced from

electrolyte

electroreflectance

experiments _[11].

Spectroscopic ellipsometry

is _a

powerfull

tool to obtain the dielectric function

e(E)

=

er(E)

₊

iei(E)

variations with

photon

_energy E of _a material and to deduce the parameters

defining

the main interband transitions.

e(E)

has been

given

in MCT

using

^this

technique

for the end binaries and for the

compositions

of technical

importance

_x ₌ 0.20 and _x

= 0.29

[12].

^At the _same time

e(E)

results _were

published

for the entire

composition

_range

_[13] using ^samples

grown

measurements rests _on the

preparation

of the

samples

which must leave _a smooth surface free of contaminants _or

overlayers

of chemical

species,

for instance

oxides,

different from the bulk material. The

amplitude

of the

imaginary part

_e; at the

E2 Peak

is often used _as _a test

of optical

surface

quality

_as the

compounds

considered _are

highly absorbing

in the

corresponding frequency

domain _near 5 eV. There _are

some

discrepancies

about the chemical treatments to be

performed

in order to obtain the best surface _on MCT

(see

Refs.

[10,13]). Sample roughness

at a scale of the _nm remains after the best _processes

[20]

^and

gives

_a

slight

modification in its

sample reflectivity. Quantitative

estimates of this contribution have been

given

in the _case of _very

rough

surfaces

[21]

^however the models have not been

applied

to smoother surfaces which _can be _now measured

by

atomic force

microscopy.

The features

corresponding

to the transitions named

Eo, Eo

+

ho, Ei

and

Ei

+

hi

_are

clearly

identified in MCT

[12,13]

^however the

E2

structure is not _so well

assigned.

It has been described _as _a broad band in

HgTe

and MCT [13] ^and also in ZnTe

[19].

However this band is

clearly

resolved in four

peaks

in reference

[12]

^for

HgTe

and _mercury rich MCT.

Each

peak

is

tentatively assigned

to different transitions in the Brillouin _zone.

This _paper

presents

the first results _on the

optical

_response of _mercury zinc telluride temaries between 0.7 and 5.7 eV. The variation with _z of the

parameters characterizing

the interband transitions _near critical

points

is

given

and discussed. The _paper is written _as follows: _exper- imental details and

particularly

surface

preparation

_are described in Section 2.

Experimental

results _on

e(E),

their third

derivatives,

the

assignment

of the

principal

transitions and the fit to the CP model are

given

in Section 3. The variations of the critical

point

parameters appear in Section 4 with the discussion.

(4)

2.

Experimental

and Surface Treatments

MZT

ingots

have been grown with the

travelling

heater method

(THM) using HgTe

and ZnTe

as source materials and Te _as solvent. The

composition

of the _source

ingot

varies

along

its

axis _so _as to obtain _a

graded composition ingot

after the

growth.

The details _on the

growth

are the _same _as for

graded composition

CdZnTe

ingots

which _are

given

in reference

[22].

^The

only

difference lies in the

temperature

^of ^the ^dissolved zone which is increased from 600 °C at the

beginning (where

a

Hg

rich MZT is

grown)

_to 870 °C at the end

(when

this

part

^is Zn

rich).

The rates of

growth

^and ^of the hot _zone

temperature

increase _are

respectively

2.5 _mm per

day

and 8.4 °C _per

day.

Slices of 2 _mm of thickness _were cut with faces

perpendicular

to the

ingot

axis. An _x

mapping

of each face is obtained in

measuring

the

composition

with _a

microprobe _[23]. Only samples

where the overall deviation of _x _on the entire surface is lower than 0.02 are taken for

ellipsometric

measurements.

Moreover,

the

optical spot

on the

sample

is

placed

in the part of the surface where the

composition gradient

is the lowest. We estimate that the maximum variation of

composition

_on all the

spot

^surface is lower than 0.002 however the values of _x _are

given

with _an

uncertainty

of +0.005. The slices of15 _mm of diameter _are constituted of _a limited number of

crystallites (2

to

6)

with

arbitrary cristallographic

orienta- tions. The boundaries between

crystallites

_were located _so that the

light spot

is

placed

_on _a

single crystalline part. Though

the

crystal

orientation is not

important

in the _e measurements of cubic

crystals,

the chemical reaction _rates and the surface

roughness depend

_on this orienta-

tion. The slices _were first annealed under _a

Hg

overpressure ^to decrease the number of cation vacancies and other defects such _as Te

precipitates [24].

^This ^anneal ^is

performed

at 400 °C with mercury ^at 380 °C for _x < 0.25 and at 500 °C with _mercury at 460 °C for _z _> 0.25.

Finally,

the slices _are

mechanically polished

with alumina

(size grain

0.3 ~tm and 0.04

~tm)

^and then

chemomechanically

etched with

Br2-methanol (Br-MET) 0.5%.

At this

point samples

_are

considered

ready

for the

preparation

of their surface under

ellipsometric

control.

Ellipsometric

measurements _are

performed

with _a

phase

^modulated

spectroscopic ellipsome-

ter UVISEL

(Instrument SA)

at _room

temperature (293 K).

The

ellipsometric

data _are _mea- sured from 0.75 eV to 5.7 eV with _an _energy

spacing

^of10 mev at an incidence of 70°.

The

ellipsometric angles

_~l and A

given

for each

photon

_energy E express the

complex

ratio rp

/r~

=

tg ~lexpiA

where _r~ and rp ^are the

sample

reflectivities when the

polarisation

of the

light

is

perpendicular

and

parallel respectively

to the

plane

of incidence. The value of the

complex

dielectric function

e(E)

of the material is

easily

deduced from ~l and A if _no

overlayer

is considered

(two phase model).

The

highest

value of_ej _at the

E2 Peak

is used _as the test of the

optical quality

^{of the} ^surface.

This _test _can be

performed

_on the

ellipsometer

_as the

sample

is

placed

in _a windowless cell under

flowing

_argon where it _can be

sprayed

with solvents _or reactants. A

great

^number ^of surface _treatments have been tried in

particular

those which have been cited in the literature

as

giving

the best results. We will restrict _our

comparison

to these cited processes. However _we first consider the process which

gives

the best results: after the first

mechanopolishing already

described _a _new _one is

performed

with Br-MET

0.I%, using

electronic

grade

methanol with low water content. The

sample

is

carefully

rinsed in three baths of

methanol,

carried in the last bath to the

ellipsometer

and mounted under the _argon flow in the windowless cell. The value of _ei at the

E2 Peak

is monitored

during

all the

stripping

processes studied. The

highest

value of

ei(E2)

is

reached,

for all

compositions

of

MZT,

after _a last in situ

rinsing

with methanol.

These results _are consistent with those of Vifia et al.

[13]

on MCT and of Sato and Adachi for ZnTe

[19]

^who ûsed âlso ^Br-MET. Ît îs

important

to _use low concentration Br-MET for the last

polishing; however,

there is _no further

improvement

^of

e;(E2)

with concentrations lower than 0.1%. The

ei(E2)

value obtained _on

HgTe [100] (9.8)

is the _same _as the _one found in

(5)

o 250 soo 750 iooo 1250 isoo 1750 2000

t(min)

Fig.

I.

Ellipsometric angle ~

at the

photon

_energy of 5.28 eV _uersus time t for ZnTe and its fit with the relation

~

= r + _u

It

+ _s.

Figure

of reference

[12] (9.62

to the

reading accuracy).

On the other

hand,

_we found _a

slightly higher

value of

e;(E2

for ZnTe

(100) (e; (E2

"

15.8)

than Sato and Adachi

(ei(E2

=

15.2) _[19].

The surface of _mercury rich

samples ix

_<

0.4) degrades

_very

slowly

with time

(time

constant of several

days)

and the decrease in

e;(E2)

remains lower than

5%. However,

the

degradation

rate increases with the Zn content and the time constant goes ^to 4 h for ZnTe _as _can be _seen in

Figure

1. The

ei(E2)

value _can be recovered after _a

long stripping

with electronic

grade

methanol. We have no definite

explanation

of the

degradation

of the surface: the

sample

is

probably

not

fully protected

from the environment in the windowless cell and

gets

^oxidized

by

the air. In the meantime _we establish that the

degradation

increases _as the

rinsing

^{of the}

surface decreases. It is difficult _to

completely

eliminate Br from the surface

by dissolving

in methanol and Br residues _can

help

_a further oxidation of the surface. KCN has been used to neutralise bromine _as I<Br is _very soluble in _water

[25].

^This process

gives

very

good

results _on mercury rich MZT

[26]

as

angle

resolved XPS

spectra

show _a defect free surface without contaminants

apart

from carbon. The neutralization with KCN decreases the amount of

e;(E2) systematically

from

15%

_to _20$lo,

revealing

the _presence of _an

overlayer.

The

depth

of this

layer

is between 2 to 5 _nm and the

layer

is

likely

to

evaporate

ⁱⁿ the ultra

high

_vacuum

chamber of the XPS

apparatus

as the

species composing

this

layer

_are not revealed

by

electron

spectroscopy.

^Anodic oxides have been _grown _on

Hg

rich MZT

samples _[27],

this oxide is then

stripped

with HCI _or acetic acid. After this process

e;(E2)

is

systematically

lower than the best values obtained with the first _process described. After these _processes

ellipsometric

^data

are

modelled

with _an

overlayer

with _a dielectric function that is similar to the _one found _on MCT

[12],

^identified ^to ^be

amorphous

Te. The

attempt

to _use

NaBH4

for

stripping

^residual oxides [28] was unsuccessful. After the surface

degradation

in the windowless

cell,

_a

stripping

with

NaBH4

followed

by

_a methanol

rinsing

_never allows to _recover the

original e;(E2

^whereas

a

methanol rinsing

alone regenerates the surface

completely. e;(E2

_can be

partly improved

_on

(6)

degraded

surfaces after _a

long rinsing (0.5 h)

under

running

deionized water. Water _removes surface oxides like for GaAs

[29],

^however ^the

remaining

dissolved _oxygen in water continues to oxidize MZT. It would be _necessary to _use water with _a _very low concentration of _oxygen _to

reach _a

nearly

oxide free surface

[30].

^Our numerous tests led _us to propose low concentration Br-MET for the

preparation

of MZT

samples

for

ellipsometric

measurements. We have

repeated

this process several times _on the _same

samples

and _we found

reproducible si(E2)

values within the

experimental uncertainty

of the measurements

(0.5%),

if the

steps

of

mechanopolishing

and

rinsing

_are carried out with

rigour.

The

remaining difficulty

is

that,

for _x _>

0.4,

the MZT surface

degrades

too

quickly during

the 20 minutes necessary ^to monitor the

ellipsometric

data between 1.5 eV and 5.7 eV

by steps

of 10 mev. To _pass around this

difficulty,

the

ellipsometric

data _are monitored

during wavelength

scans which _are

sequentially repeated

10 to 15 times

during

the surface

degradation.

The first

scan is started _at the

photon

_energy

E2

for which the final

rinsing gives

the

highest ei(E2)

value. The time of each

~l, A,

E measurement is referred _to the

starting

time of the first _scan.

For each E

value,

_~l and A variations with time

t,

which _are like those

given

in

Figure I,

_can be very well fitted with the

simple

function of time: _r ₊

u/(s

₊

t)

where _r, _u and _s _are the constants for each fit. _r ₊ _u

Is gives

^the value

corresponding

to a non

degraded

surface which is

only

considered here. This method is very time

consumming

^but ^has ^the ^additional

advantage

of _an

averaging procedure

which increases the

signal /noise

ratio of the

ellipsometric

data. The results in the _near infrared

(0.7

_< &&~ < 1.5

eV)

_are obtained in _a

separate

run of _scans _as the measurements in this

spectral

_range need to

change

the

optical

fibers which link the different

optical components

^{of the}

ellipsometer.

The

sample

surface is

processed

_once

again,

in

situ,

on the

ellipsometer

to check that

si(E2)

has reached its

highest

value. Successive

wavelength

scans are

performed

and referred in time _as

previously

described.

3. Dielectric llunction Results and

Analysis

The real and

imaginary parts

^of the

pseudo

dielectric function _e _are deduced from the ~l ^and ^A

values, extrapolated

at t

=

0, using

the two

phase

model [31] ⁱⁿ ^which the surface is considered

perfectly

flat between the bulk of _a

sample

and the

atmosphere.

The real and

imaginary

parts of _e _are shown

respectively

in

Figures

2 and 3

(for clarity, only

5 selected

compositions

_are shown

).

^The ^dielectric ^function is linked _to the band structure of the ternaries which _is similar to that of the end binaries.

Examples

of calculated band structures of the binaries _can be

found,

for

instance,

in references

[10,19].

The main interband transitions _we _are concerned with in the

spectral

_range studied _are:

Eo(r(

_-

rj), Eo

₊

ho (r)

_-

rj), Ei(L(_s

_-

L[)

and

(A(_s

-

A)), Ei

₊

hi (L(

_-

L[)

and

(A(

_-

A[)

and

lastly E2

which is not so

clearly

attributed. Villa et al.

[13] assigned

their broad

E2 Peak

in MCT to transitions in _an extented

region

of the Brillouin _zone _near X and _to other

regions

in the

[100]

^and

[l10]

directions of the

reciprocal

_space.

Experimental

data of Arwin and

Aspnes

_[12] reveal

clearly

four transitions

grouped

in two

pairs

for

HgTe.

These transitions

are shifted towards

higher energies

when x increases and

only

_one _group cad be revealed for CdTe around 5 eV

[12]. They

could be

assigned

,, ZnTe

.. ,

', ',

w~

₆ ^'

HgTe

",,

2

':,

",

-4

2 3 4 5

E (ev~

Fig.

2. Real part ^of ^the ^dielectric ^function uersus

photon

_energy E for several

compositions

of

Hgi_~Zn~Te: (---)

_x

= 0,

(- -)

_x

= 0.216,

(- -)

_x

= 0.484,

(- -)

_~ ₌ 0.814,

(-)

_x ₌ 1.

/~

i i I

I ~ /,-.h

I '..-"

jI

HgTe

I

I ',

I '

.- /

/ '

/

/ / / / /"/

_/

ZnTe

0

1

E(eAo

Fig.

3. The _same _as

Figure

2 for the

imaginary

part of ^the ^dielectric ^function ^of

Hgi_~Zn~Te.

(8)

8000

fi

6 r

)

~ -~

@

,

~w

~ t

~

E~⁺ _A~ ^t

~o

i E~

E~ ⁺ A~

t

2 3 4 5

E(ev~

Fig.

4.

Example

of third derivatives

d~sr/dE~

_and

d~s,/dE~

_uersus

photon

_energy E for ZnTe.

The _arrows indicate the critical

point energies.

at 5.25 eV to transitions _near K in the Brillouin _zone. In their

analysis

of _room

temperature ellipsometric

data of

ZnTe,

Sato and Adachi _seem _to attribute the

pronounced peak

at 5.2 eV to transitions _near X

(Xi

_-

Xj),

however

they

describe its contribution _as due _to _a

damped

oscillator

[19].

The

spectral analysis

of _s follows the usual critical

point (CP) description

where the contribution _near _a threshold _energy

E~

is

given by _[33]

L(E)

₌

A~r/~eJ°~ (E E~

+

in)"

₊

F(E) (1)

where A~ ^is the oscillator

strength,

b~ a

phase angle, r~

_a

phenomenologically

introduced

broadening

_parameter and _n is the order of the transition

in

=

1/2

for _a 3D

transition,

n = 0

(logarithmic)

for _a 2D

transition,

n =

-1/2

for a1D transition and _n

= -1 for _a discrete

exciton). F(E),is

_a

slowly varying

function

coming

from _remote

transitions;

its derivatives _are often assumed to be

negligible.

The fit of the defined parameters is done

simultaneously

_on the third derivatives of _er and _si data which _are

numerically

calculated from the

experimental

data.

Statistical _errors _are low

enough

_on _{~l and} A values

extrapolated

at t

= 0 to obtain

good

results without _any

smoothing procedure.

However it has been _necessary to

apply

_a

slight smoothing

with _an

exponential regression

_[34] to observe

clearly

the weak transitions at

Eo

+

ho

This

smoothing

is

only applied

to the first derivative and

higher

_ones when it appears necessary, but _not _on _the

experimental

_er and _ei, _as this _can lead to

arbitrary

distortions of the line

shapes. Figure

4

gives

_an

example

of

numerically

calculated third

derivatives;

the transition

energies

_are indicated

by

_arrows. The

fitting

of the parameters ^of the CP model defined in

(1)

is

performed

with the

Levenberg-Marquart

method

[35].

For this fit third derivatives of _er and _ei

given by (1)

are also

numerically

calculated and smoothed with the _same

procedure

_as

applied

to calculate the derivatives from

experimental

data _to which

they

_are

compared.

This fit

proposed by

Garland _et al. [36] appears ^to

give

the _most stable and reliable solutions. The

(9)

5.5

4.5

u

0

x

Fig.

5. Critical point

energies

_uersus

composition

_x in

Hgi_~Zn~Te,

_our results for:

(o)

ED, (O) ED + ho, (T7) El,

(0)

El + hi,

(Zi)

E2,

(e)

from

[iii, _(*)

from [12],

(m)

from [13],

(.)

from [19],

(+)

from [37]. ^Full lines

correspond

to the fit with

equation (2),

the dotted _curve is deduced from [4].

Table I. Values

of parameters

_a, b and _c deduced

from

the

fit of

critical

point

_energy variations with

composition

x

using equation (2).

Critical

point

_a b _c _error

-0.146

Eo

0. 1.583

El

2.109 0.sll 1.012 +30

+

hi

2.741 0.656 0.817 +25

4.369 0.428 +30

same level of

smoothing,

when it is

used,

is

applied

for all the fits

corresponding

to the _same critical transition, whatever the

composition

x.

4. Interband Transition Parameters in

HgZnTe

The variations with _x of the transition

energies E~

_are

given

in

Figure 5; they

_are described with

quadratic

laws of the form:

E~(x)

₌ _a + bx ₊

cx~ (2)

The values of _a, b and _c for the different transitions _are

given

ⁱⁿ ^Table I with the

corresponding

uncertainties.

Eo

is

only

determined for _x > 0.48 and the fit of the

quadratic

law _uses the

Eo

value of

HgTe

at _room

temperature

^deduced ^from reference

[37].

^The ^dotted curve in

Figure

5

corresponds

(10)

1.i

i-o

o

~

o

$~

3

~

0 0.1 0.2 0.3 0A 0.5 0.6 0.7 0.8 0.9 1-O

x

Fig.

6. ho

dependence

with

x deduced from

experimental

data for _x > 0.45.

to

Eo

variations obtained from

optical absorption

measurements [4] The

agreement

_appears

good despite

the value of

Eo

chosen for ZnTe in reference _[4] which is too low _as

compared

to

those

given

here

(2.27 eV)

and in the literature

(2.28

eV in Ref. [19]

in

Figure

6.

ho

has the _same

value for ZnTe _as that

already given [19, 38]

^and ^remains constant for _x _> 0.45 with _a _mean value of 0.90 eV. We then consider

ho

_as

independent

of _x for the entire

composition

_range of

MZT,

with

ho

= 0.90 eV. This value is within the domain of

proposed

values for

HgTe

_IO.75

eV, eV],

MCT'S and MZT'S for the low gap

[39, 40],

^with a

preferred

value of

eV;

however it is less than the

experimental

determined value of1.04 eV deduced from electroreflectance

[41]

on

HgTe.

We estimate the

uncertainty

_on

ho

to be +0.07 eV. The fit of the

Eo

+

ho experimental

results is then

performed taking ho

₌ 0.90 eV for

HgTe leading

to

Eo

₊

ho

= 0.75 eV for this

compound.

A first fit of the third derivatives of _e _was

performed separately

_on

El

and

Et

₊

hi

with _a 2D CP line

shape in

= 0 _or

logarithmic

function in

(I)).

The

phase angle

b for

Ei

and

El

+

hi

remains

nearly

constant for _x _up to I with values _near 280° for

El

and 290° for

El

+

hi

These values agree with those found in MCT with _x _< 0.8 [13]

(note

that b

=

31r/2

_{+ q7} where _q7 is the

phase angle

defined in Ref.

[13]).

^On ^the ^other

hand,

the sudden increase of

q7 in Cd rich

MCT is not found in Zn rich MZT. We

verify

that the

analysis

of _e data for CdTe at _room

temperature

obtained

by

_us

gives

_a value of 323° for

b(Ei

_(~7

" 53°

):

_as ⁱⁿ reference

[13],

^such

b values _are attributed to many

body

effects

[13,14,42].

The fits of the third derivatives of _e have thus been

performed

for the binaries

ZnTe,

CdTe and

HgTe, using

_a 2D line

shape

(Y1 ⁼

0)

on the _one hand and with _an excitonic line

shape in

=

-I)

on the other hand. Moreover the derivatives of

experimental

data _are fitted

simultaneously

(11)

fi

u

/

~

?~

~

$

~#4

fi3 ,

~w

fi3

t

~i

~

~i

~E,

3A 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4A 4.5

E jelo

Fig.

7.

Comparison

of third derivatives of

experimental

_s with two models of line

shape

for ZnTe

between El and El + Ail

(-)

2D line

shape, (- -)

exciton line

shape, (D),

and

(il) numerically

calculated third derivatives of _sr and _s,.

for

El

and

Ei

₊

hi

transitions _as _was done for GaAs

[42]. Despite

the

comparatively large hi

value in MZT which is about 3 times that of GaAs where

hi

^~ 224 mev

[42]

^{the fit} ^is

severely improved

when

considering Ei

and

Ei

+

hi together.

In

particular

this simultaneous fit _removes the differences between calculated and

experimental

values in the

wings

of the _curves _as _can be _seen in

Figure

7 for ZnTe. In these fits all the

parameters

^defined

by equation (I)

for

Et

and

Ei

₊

hi

_are taken free except n = 0. The _same fits _are then

applied taking

_n ₌

-1,

^which characterizes excitonic transitions

[14, 33].

The results with both

types

^of line

shape (2D

and

exciton) performed

_on

El

and

Ei

₊

hi

transitions _are

given

in

Figure

7 for ZnTe. The values of the

parameters

^for ^both ^line

shapes

_are

presented

in Table II for the three binaries

already

cited. We _see in

Figure

7

that,

for

ZnTe,

the difference between the best fits

given by

the two models is

clearly

lower than the

experimental

uncertainties

except

ⁱⁿ the low

frequency wing

of the

El peak

where the exciton model

gives

_a

sligthly

better fit. On the other

hand,

the 2D line

shape

leads _to _a

sligthtly

better fit for

HgTe

in this low

frequency region.

We

verify

also for the second derivatives of _sr and _e; that the difference between both line

shapes

remains inside the

experimental

uncertainties except ⁱⁿ the low energy side of

El

where this difference is

slightly higher

and with the _same conclusions _on the fits for ZnTe and

HgTe just given

^before. ^Table II shows that b increases

monotonically

in the ordered _sequence of the

binary compounds HgTe,

ZnTe and CdTe

using

both

types

^{of line}

shapes.

The

broadening parameters

deduced from the fit with the 2D line

shape

_are indeed

systematically

lower than those deduced from the fit with the excitonic line

shape. However,

the differences in the

energies El

and

Ei

+

hi

using

both line

shapes

remain inside the _error

margins

due _to

experimental

uncertainties. We will

give

the results for the

Et

and

Et

+

hi

transitions in MZT

using only

the 2D CP line

shape.

This line

shape

fit _appears to be

slightly

better in the

Hg

rich side of

compositions,

the

broadening parameters

are lower and the results _can be

compared

with those obtained for

(12)

Table II. Values

of

the

parameters entering equation (1) for Et

and

El

₊

hi

transitions in

HgTe,

ZnTe and CdTe

after

the

fit

with _a 2D CP line

shape

and _an excitonic line

shape.

2.109+0.002 3.636+0.001 3.351+0.002

bEi (degree)

280 + 2 304 + 1.5 304 + 2

rEi (eV)

0.078 + 0.002 0.041 + 0.001 0.066 + 0.001

3.09 + 0.ll 4.44 + 0.ll 3.38 + 0.10

El

+

hi

2. +

bEi+~i (degree)

284 + 7 311 + 3.3 325 + 5

rEi

_+~i

(eV)

0.128 + 0.005 0.078 + 0.003 0.099 + 0.003

3.79 + 0.13 3.14 + 0.18 2.15 + 0.10

Exciton

=

El

2.106 + 0.003 3.629 + 0.001 3.351 + 0.005

bEi (degree)

192 + 3 203 + 1 215 + 2

rEi (eV)

'0.123 + 0.003 0.085 + 0.001 0.l13 + 0.001

3.26 + 0.12 6.74 + 0.06 4.04 + 0.07

+ + 0.010 4.221 + 0.002 0.004

bEi+~i (degree)

190 + 10 219 + 2 225 + 4

rEi+~i (eV)

0.174 + 0.009 0.138 + 0.002 0.164 + 0.004

AEI+~i

Figure

8

Parameters associated with the

E2

transition _are deduced from the fit with _a 2D line

shape

which describes better the dielectric _response if several transitions _occur _near the _same energy

[13,14]. E2

variations with

composition

show _an

upward bowing

with _a

relatively high

_c value

(cf.

Tab.

I).

_c is found low and

negative

in MCT

[13]

^and very small in CdZnTe

[47]

^however ^the

assignation

of their transitions is not in

agreement

^with ^other data. The Lorentzian

broadening

parameter,

given

in

Figure 9,

has _an

unexpected dependence

_on _x,

reaching

a minimum around

x =

0.65,

the _same behaviour of

r(E2

is also found in MCT

[13].

^The ^value ^of

r(E2

for

HgTe

is

slightly higher

than that of reference

[13]

^but agrees with that

given

for ZnTe

[19].

^The

phase angle

b

(not shown) varies,

almost

linearly

with _x from 240° for

HgTe

to 280° for ZnTe.

5. Discussion

The results of _a CPA calculation at 0 K for the fundamental _gap of MZT'S have been

given,

for _x _< 0.5 in

Figure

2 of reference

[10].

^These

results,

fitted with

equation (2)

^and

taking

Eo (0 K)

= 2.37 eV for ZnTe

[10], give

c = 0.74 eV. This _c value _compares

favourably

with the

(13)

m

$~

"

h ~

$'

o

o o

. °

~ o

o ~ ~

w

0 0.1 0.2 0.3 0A 0.5 0.6 0.7 0.8 0.9 1.0

x

Fig.

8.

Broadening

parameter _uersus

composition

in

Hgi_~Zn~Te: (o) r(Eo), (D), r(Eo

+

ho),

(T7)

r(Ei ), (0) r(Ei

+ hi

), (Zi) r(E2), (m)

from [13],

(.)

from [53], ^full ^libes

correspond

to

quadratic

fits of the data.

0.

o o

$l

_o _o

* 0.65

o

° ° °

~- m

~

o

0 0.1 0.2 0.3 0A 0.5 0.6 0.7 0.8 0.9 1-O

x

Fig.

10. Variations with _x of the difference d between experimental El + hi values and the values obtained with _a linear

interpolation

of El + hi between values of

HgTe

and ZnTe. The

curve represents

the best fit to _a third order

polynomial.

experimental

_one of 0.72 eV which is deduced here. This indicates that the CPA calculation

can take

properly

into account

potential

disorder with _a

strong

^bimodal distribution of bond

lengths.

The

phase angle

^b ⁱⁿ

(1)

is 90° for _x

= 0.45

corresponding

to a 3D CP of

Mo type [14].

It increases almost

linearly

with _z to reach _a value of155° for _x

= 1. This b variation is due to the

increase,

with _x of the excitonic contribution at the

Eo

transition

[14,42] although

^this

contribution appears weak at 300 K in the

optical absorption

of ZnTe

[48].

^The

broadening parameters

^of

Eo

and

Eo

+

ho

_are _very _near,

they

remain in the range of values found in other solid solutions

[46].

^The ^main contribution to the r's _comes from

phonons _[41],

however their low value is indicative of the overall

good quality

of the MZT

crystals.

No

bowing

is found for

ho,

this is also the _case in other solid solutions

[46]. ho

has been

theoretically

calculated for both end binaries and values calculated for

HgTe (1.07 eV)

and ZnTe

(1.02 eV)

are very close when

they

_are obtained with the _same method

[49].

El

values deduced from electroreflectance measurements in MZT

[11],

are

placed

in

Figure

5.

They

_are in overall

agreement

with those

given

here. However _no detailed information is

given

on the line

shape analysis

and _on the

composition homogeneity

of the

samples.

The

bowing parameters

of

Ei

and

Ei

+

hi

_are

greater

than for

Eo

_as _more states are mixed and

damped by

the disorder

potential

at this

point

of lower

symmetry

in the Brillouin _zone

[50].

^The difference d between the actual

El

+

hi

threshold and the value obtained

by

the

interpolation

of

El

+

hi

between

HgTe

and ZnTe is drawn in

Figure

¹⁰ as a function of _x. The maximum of d is

slightly higher

in MZT than in

MCT,

this maximum is reached _near _x

= 0.55 in MZT

whereas it is reached _near _x

= 0.75 for MCT

(see Fig.

8 of Ref. [13]

).

^The

dependence

of d with _x is _more

asymmetrical

in MCT than in MZT. In MCT the bond

lengths Hg-Te

and

Cd-Te _are

nearly

the _same and have _a small variation with _x. In MZT the

Zn-Te and Hg-Te

bond

lengths

^remain ^those ^of ^the ^binaries _[9] ^when ^the ^lattice

parameter

decreases

linearly

(15)

with _x [4]

leading

to a

strong

bimodal distribution of bond

lengths.

The

asymmetry

ⁱⁿ

d(x)

for MCT has been

tentatively

linked _to the

large

increase of the

broadening

of electronic states of the conduction band when _x goes to 1

[13].

^This ^increase ⁱⁿ state

broadening

is evidenced in the CPA calculation of Haas et al.

[50]

^for ^the ^electronic ^structure ^of ^MCT'S. ^We ^must ^take

into account

that,

in

MZT,

the difference in

pseudopotentials

of cation _atoms is

higher

and

also the static

displacements

of all the atoms from the ideal

positions

in the Bravais lattice

[8].

This leads _us to

expect

^for an even more

asymmetrical

variation of

d(x)

in MZT than when the

contrary

^is ^found.

Clustering [51, 52]

^and

probably

also

ordering

_on

show

that,

in MCT with _x _ci

0.7,

the

probability

of

finding

the local

arrangement (cluster) Cd3Hg

around _a Te _atom is less than its

probability corresponding

to _a

perfectly

random

alloy.

On the

contrary

the

probability

of

finding

the _ar-

rangement Cd4

around _a Te atom is in _excess of that for the

perfectly

random _case

[51].

^This

distribution of clusters could

explain

the maximum of d and the r's _near _x

= 0.7. The _same

calculations of cluster

energies

in MZT lead to _a more

symmetric

situation in the

probabilities

of each

type

^of cluster [51] ^which ^will ^lead ^to ^d ^and ^r's ^maxima near x = 0.5. Other calculations

give

_a

slightly asymmetric probability

distribution of clusters in MZT

[52]

^which may be consistent with the maximum of d _near _x

= 0.55. In the _case of MCT

however,

the _same calculation shows _a _more

symmetric

distribution of clusters [52] which could not

explain

the

asymmetric

behaviour of

d, r(Ei)

and

r(Ei

+

hi ).

The

phase angle

b in

equation (I)

with _n

= 0

(2D

^line

shape)

is

plotted

in

Figure

11 for the

Ei

and

Ei

+

hi

transitions. b values for ZnTe have been also deduced from

ellipsometric

data

using

the _same critical

point

model which is fitted with _n

= 0 _on the second derivatives of

e

[53]. b(Ei)

and

b(Ei

₊

hi

values _are

slightly

lower than _ours

(see Fig. 11).

^This ^difference

is

mainly

due to the

separate

fit around

Ei

_on the _one hand and around

Ei

+

hi

_on the other

hand;

it

explains

the not very

good

fit in the

wings

of

d~ei /dE2

in reference

[53]. Although

the results _on b _are

relatively scattered,

no

noteworthy

variation _can be deduced from

Figure

11 outside _a monotonous increase of b between

HgTe

and ZnTe values which _are not far from

one another. b values different from _a

multiple integer of1r/2 correspond

to excitonic effects

leading

to a mixture of critical transitions

[14, 54].

^The

good

fit with _a 2D line

shape

with b

near 270° would lead _us to

expect

to transitions between

nearly

uncorrelated electronic states at a saddle

point.

However _we have _seen that the fit of the _e data with _an excitonic line

shape

is as

good

_as with _a 2D _one

(slightly

better for ZnTe and

slightly

_worse for

HgTe).

With this excitonic

fit, b(Ei

for

HgTe

^{is 12°} above _1r and deviates off to a

slight

extent from this _1r value when

going

to ZnTe. The corrections _to the excitonic Lorentzian model due to

many-particle

contributions

[14, 55, 56]

remain weak and _are taken

properly

into account, at 293

K, through

the

phase angle

b. Both line

shapes (2D

and

excitonic)

_can describe the

Ei

and

El

+

hi

CP in MZT at 293 K. This situation is

probably

the _same _as in GaAs where the excitonic line

shape

goes

progressively

to the 2D _one _near 293 K

[42].

^The

high

excitonic contribution at

Ei

has been

recognized

at low

temperature

and first described in the effective _mass

approximation

with _an exciton

binding

_energy of 0.16 eV

[57].

^The

high

value of the exciton energy ^at

Ei places

ZnTe at the _upper

right

of the classification table

given by Lautenshlager

et al.

[58]

with Znse and CdTe

corresponding

to _an excitonic line

shape

at

Ei

for all

temperatures.

Our results lead _us to

place

ZnTe rather at the

boundary

^between 2D and excitonic line

shapes.

The main

problem

_comes from

HgTe

for which the

phase angle

b remains _near that of ZnTe whereas its exciton

binding

_energy at

Ei

~

i

o ~

o o

kf

~s ^~ °

4f _o

240

0 0.1 0.2 0.3 0A 0.5 0.6 0.7 0.8 0.9 1.0

x

Fig.

II. Variations with _x of the

phase angle

0 for transitions at El

(empty circles)

and El + hi

(empty squares); (.), (m)

from [13],

(e), (l§)

from [53].

at

decreasing temperatures, currently undertaken,

will

give

_an _answer to this

question.

The

problem

_seems also the _same in MCT since the simultaneous fit _at

El

and

Ei

+

hi

with both the 2D and excitonic line

shapes

leads to

b(Ei

and

b(Ei

₊

hi

values for CdTe which _are _a

little

higher

than those of ZnTe

(cf.

Tab.

II).

The Lorentzian

broadening parameter dependence

_on

composition

of the

E2

transition appears unrealistic

(see Fig. 9).

The

assignment

of the

E2

band in II-VI

compounds

is not

completely

clear

[12,18,19]

and several transitions have been

proposed

to contribute to the dielectric function. Various

dependences,

with _x, of the energy and of the other

parameters

^for each of these transitions could

explain

the behaviour of

r(E2

and the

strong bowing

of

E2 (13].

Low

temperature experiments

would allow to

separate

the different transitions involved in this energy domain. However the

parameters characterizing

the

E2

transition _are deduced from

measurements

performed

at

energies

where the

compounds

_are _very

absorbing

and the contri-

bution of the surface becomes _more

important [13].

The surface

rugosity

can

by

itself

modify

the line

shape

_near _a critical

point. Changes

in the chemical

properties

of the MZT surface have been discussed in Section 2. These

changes

with time _are related to surface

rugosity

^and

reconstructions. The

Hg-Te

bond _energy is increased when

Hg

is substituted

by

Zn

[1, 59]

and leads to _a lower

segregation

of

Hg

in the

vicinity

of the surface. Theoretical estimates show that the

stoichiometry

is

preserved

at the second atomic

layer

under the MZT surface

[60].

However the electron _wave functions must vanish outside the semiconductor surface _so that the dielectric _response of the surface

region

^is ^different ^from the bulk

[61]. Moreover,

surface

rugosity

or surface reconstructions may introduce electronic _states in the

vicinity

of

E2. Ellip-

sometric measurements

performed

under well controlled

atmospheres

_may

lead

_to

enlightening

answers to this