Electromodulation spectroscopy of excitons in simple cubic TlCl and TlBr

Physics and Astronomy Publications

Physics and Astronomy

3-1979

Electromodulation spectroscopy of excitons in

simple cubic TlCl and TlBr

John Frederick McClelland

Iowa State University

David W. Lynch

Iowa State University

, [email protected]

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Electromodulation spectroscopy of excitons in simple cubic TlCl and TlBr

Abstract

Transmission and electromodulated transmission spectra have been measured in the direct Wannier exciton

region for TlCl and TlBr. The spectra were obtained at a sample temperature between 5 and 6 K for a range of

applíed electric fields. The data have been reduced to obtain the electric-field-induced changes in the dielectric

function and compared in detail to the calculations of Blossey. The experimental results support the trends

predicted by the calculations.

Keywords

Ames Laboratory, Wannier, dielectric function

Disciplines

Atomic, Molecular and Optical Physics | Condensed Matter Physics | Optics | Physics

Comments

This article is from

Physical Review B

19 (1979): 3244, doi:

10.1103/PhysRevB.19.3244

. Posted with

permission.

PH Y

SICAI,

RE

VIE% 8

VOI,IJMK

19,

15

MARCH l

979

Electromodulation

spectroscopy

of

excitons

in simple

cubic

TlCl

and

TlBr

J. F.

MeClelland and D.

%.

Lynch

Ames

I.

aboratory-USDOE and Department ofPhysics, Iowa State.Uniuersity, Ames, Iowa 50011

(Received=10 October 1978)

Transmission and electromodulated transmission spectra have been measured in the direct Wannier exciton region for Tlcland T18r.The spectra were obtained at a sample temperature between 5and 6Kfor a range

ofapplied electric fields. The data have been reduced to obtain the electric-field-induced changes in the dielectric function and compared indetail tothe calculations ofBlossey. The experimental results support the trends predicted by the calculations.

I. INTROI)UCTION

Certain features observed in the optical spectra ofsome crystalline insulators and semiconductors provided an early indication of.inadequacies in

s~mple band theory. The Frenkel excxton model'

was successful in explaining rionband features

which had been observed xn alkali halide spectra.

.'

Later Wannier excitons' were postulated, prior

to the experimental work.

'

Subsequently optical

measurements on Ge' were interpreted on the

basis of.Wannier excitons in the important work

by Elliott.

'

Much of the electronic structure not

encompassed by band theory has now been clarified for high dielectric constant solids by adding energy

levels associated with Wannier exciton states and

altering nearby band

states.

However, efforts

to make detailed quantitative comparisons between

the results of calculations based on the Wannier

model and experimental measurements often have

been djLfficult because the hydrogenic energy levels

ofthe ideal Wannier exciton

are

nearly always

significantly perturbed by interactions with the

crystal.

This results in a shifting and broadening of exciton energy levels and often additional states

which are outside the scope of the simple Wannier

model.

Modulation _{spectroscopic} techniques' ean be

used for quantitative studies ofboth exciton states

and band structures. They provide sharper

deriv-ative

spectra,

usually as a function of an external

perturbation applied to the sample. The sharper spectra may al.}owa more quantitative

test

of the

exciton model than would be afforded by the

unmod-ulated

spectra;

however, one

is

then testing the

exciton model's ability to predict spectral changes

as a function ofan applied perturbation rather than

directly testing the unperturbed model.

.

Electric

and magnetic field modulation are most appropriate for Wannier exciton studies because

they cause a direct perturbation to the exciton

Hamiltonian. The most detailed calculations for

comparison with experimental results have been

done for

electr

jefjeld modulatjon8 io and a nu ber of experimental comparisons have been made.

"'

"~ _{Definitive comparisons}

between

ex-periment and theory have been difficult due to a

scarcity

of solids having ideal Wannier exciton

states with low broadening, difficulties with both

sample preparation and modulation, and the

com-plexity Of data reduction to _{enable comparison} with

theory in terms of the field-induced changes in the complex dielectric function.

Progress

is reported in this work toward a

mor'e quantitative _comparison of experimental

re-sults with the detailed electroabsorption

calcula-tions ofBlossey.

'

"

Section IIof this paper will

include a discussion ofthe thallium halide samples used in the investigation and a description of the

exper imental rneasur ement system. Data-reduc-.

tion methods

are

covered in

Sec. III.

Results of

the measurements are presented in

Sec.

IV,

fol-lowed _by the comparison ofresults to

Blossey's

calculations in

Sec.

V. Finally, aconclusion is

given in

Sec.

IV.

II. SAMPLESAND EXPERIMENTAL APPARATUS

Thin-film simple-cubic samples of T1Cl and

TlBr

were prepared for the exciton

electromodu-lation studies in the region ofthe lowest-energy

direct interband transition at the

J

point in the

Brillouin zone.

"+

The electrotransmission

mea-surements were not extended to the indirect

band-gap region because the excitons associated with

this region do not fit the assumptions of Blossey's

theory and substantially thicker samples would have been

r

equired than are appropr iate for the

direct-transition region. The influence ofthe in-direct transitions was, however, present in the

direct exciton electromodulation measurements

through photocarriers associated in part with the

indirect transitions which complicated establishing

ELECTROMODULATION

SPECTROSCOPY

OF

EXCITONS

iN. .

.

This aspect will be addressed in more detail in

Sec.

IV,

TlCl and

TlBr are

good candidates for Wannier

exciton studies because they have very high

di-electric

constants, '4

37.

6 and

35.1,

respectively.

The exciton Bohr radius to lattice constant

ratios"

for TlC1 and

TlBr

are 20 and 15, while the

exci-ton binding

energies" are

11.

7 and

9.

8 meV,

re-spectively, The

direct

excitons have anumber of associated energy states which

are

outside the

scope of the simple Wannier exciton model. These states have been attributed to inter- and

intra-valley scattering of

excitons"

and to phonon

side-bands.

"'"

These

"extra"

states,

however, have not caused serious interference to observations ofthe hydrogenic exciton levels as demonstrated in remarkable detail by spectroscopic

measure-ments"

using aperturbing magnetic field.

The magnetic field measurements were made

possible by asample preparation

method"'"

which allowed thin-film samples to be cooled to

helium temperature to reduce thermal broadening

without inducing strain in the film due to the usual

thermal expansion mismatch between a thin film

and its substrate. Samples prepared by this meth-od consist of athin film evaporated on a very

thin methacrylate membrane. The membrane

is

supported by a frame cut from a single crystal of

the compound being evaporated, thus providing a

close match in thermal expansion coefficients

be-tween the film and substrate. This method was initially tried for the electromodulation

measure-'ments conducted in this study but proved

imprac-tical

due to a coupling effect, which does not occur

with a magnetic field, between the membrane-supported thin-film sample and the modulating

electric

field.

"

The coupling was due to spatially inhomogeneous regions in the

electric

fjeld which

drew the dielectric film toward higher-field regions, thereby inducing a strain modulation in the sample. This resulted in amodulated

trans-mission spectrum containing components due to both

electric

and strain modulation which could

not easily be separated for comparison to theory. To control the strain modulation problem,

samples"

were evaporated on methacrylate-membrane-covered solid

CsI

substrates which

have an expansion

coefficient"

close to those of

the thallium

halides"

being studied. The mem-brane prevented diffusion' between the film and

substrate and provided a slip plane to relieve strain in the film. The strain

relief

was, however,

not complete and these samples had ahigher level

of

static

strain"

than was associated with the

frame-supported membrane configuration. The substrates were mounted between

Teflon-insulated plates which formed a capacitor sample

WAVELFNGTH SIGNAL LIGHT

SOURCE

Lt('HT I

MONO-BEAM

g

CHROMATOR CHOPPER

SERVOED

~

LAMP POWER

QUARTZ _SAMPLE TRANSMISSON

PLATE SIGNAL

~PHOTOMULTIPLIERS

2

CHOPPER DRIVE AND

REFERENCE

SIGNAL

SOURCE

LAMP CONTROL

FEED

BACK SIGNAL

HIGH VOI TAGE SUPPLIES

LAMP SERVO CIRCUIT

,AND POWER SUPPLY REFERENCE

SIGNAL

WA VE LEN GTH ENCODER

LOCK-IN AMPLIF IER

FIG.

1.

Blockdiagram ofthe experimental

measure-ment system as operated fortransmission

measure-ments.

mount" attached to the cold finger of

a cryostat.

The Teflon prevented injection luminescence and

provided padding during cool down. The

evapora-tion was done in situ at a

rate

of 4.

0-6.

0nm/min

in avacuum in the low 10

'-

to high 10

'-Torr

range with the substrate at room temperature.

The quartz evaporation boat was charged with

single-crystal chips ofTlCl or

TlBr

from the

Harshaw Chemical Company. The boat could be

translated in vacuum between a position adjacent

to a quartz crystal thickness monitor, where the

evaporation

rate

was established, and a position

infront ofthesubstrate. Film thicknesses were in

the

50-70-nm

range and were checked by

inter-ferrometric

measurements on films deposited simultaneously on a glass slide mounted adjacent

to the sample substrate. The low thickness limit

was imposed by a thin-film disorder problem often found in sir@pie-cubic thallium halide films

below 50-.nm thickness. The upper limit was

set,

as a result of experience, to reduce photocarrier effects which interfere with the

electric

field

modulation.

"

The experimental measurement

system"

en-abled the determination ofthe transmission Tand the electromodulated transmission bT/T

spectra

ofsamples near helium temperature. Figure 1

shows a block diagram of the system as operated

for transmission measurements. The light beam

originates at a quartz halogen l,amp, in the upper

left-hand corner of

Fig.

1, and is focused on the

entrance

slit

of a McPherson model 218

mono-chromator after being chopped

for

synchronous

detection. After passing through the

monochroma-tor

the beam has abandpass of

0.

08-0.

16nm or

approximately

0.

7-1.

4meV, and

is

focused on the

J.

F.

NIcCLELLAND AND

D.

W. LYNCH 19 to amonitoring photomultiplier. This detector is

part of afeedback loop which maintains an

approxi-mately constant beam intensity on the sample by

automatically adjusting the lamp power during

wavelength scans.

"

The photomultiplier,

position-ed after the sample, provides a signal

proportion-al to the transmitted light intensity which is

pro-cessed

by a lock-in amplifier and plotted by a

re-corder synchronized to the wavelength scan by an

encoder. Scans were also taken with the sample removed from the beam to provide a correction

curve forthe servo system due tosmall differences

in the optical paths and detector responses. The

wavelength was calibrated with Qsram line source

lamps.

The bT/T operating mode is shown in the block

diagram in

Fig. 2.

In this mode the beam intensity was neither chopped nor servoed prior to reaching

the sample. A unipolar 50%duty-cycle

square-wave voltage of up to 10kV was applied at 200

Hz to the sample by capacitor plates with a spacing

of

1.

8 mm. The

electric

field modulation resulted

in a transmission modulation at wavelengths where

field-sensitive exciton features

exist.

In these

regions there was a corresponding accomponent

added to the dc transmission signal from the

photo-multipler. The ac photomultiplier signal was

ap-proximately proportional to

hT/T

when a servo system, as shown in

Fig.

2, automatically main-tained the dc photomultiplier signal at a constant value by adjusting the voltage applied

across

the

photomultiplier.

"

A lock-in amplifier processed

the ac signal which was plotted with the dc signal on a chart

recorder.

III. DATAREDUCTION METHODS

bT

1BT

1 BT

T (hv,g)=

—

TBn an(hv,'g)+

—

TBk

ah(hv, g)

and

n6(hv, g)=

—

B8_{sn(hv, g)}+

—

BL9ah(hv, g)

Bg ' Bk (2)

for by& and Ak, the field-induced changes in the real and imaginary parts of the index of

refrac-tion, respectively. AT/T and 1/T were provided

by the experimental measurements.

~6,

the

electric-field-induced change in the transmission

phase shift, was calculated with the

Kramers-Kronig expression,

a9(hv,

g)

=-

hv in[1 +6 T/T(hv„g)]d(hvo)

(hv,

)'

—(hv)'

The limits ofintegration spanned the direct

band-gap exciton region since contributions fromother regions are expected to be negligible. Equation (3) was derived from the Kramers-Kronig phase shift formula" and the integration was performed

by computer. The partial derivative expressions

were derived from standard thin-film formulas.

"

The 6&,and Ae, spectra were calculated from The T(hv, g) and hT/T(hv, g)

spectra

were

re-duced to the electric-field-induced changes in

the real and imaginary parts ofthe dielectric

function, b,

e,

(hv, g) and b,

_e,

(hv,

g),

respectively.

The symbols hv and

$

represent the photon energy

and applied

electric

field amplitude, respectively.

Data reduction to obtain Ae, and Ae, spectra

re-quired solving simultaneous equations given by

WAVELENGTH SIGNAL ELECTRIC FIELD

CAPACITOR SAMPLE

PHOTOMULTIPLIER

AC AND CONSTANT SERVOED Ii DCSIGNALS

PM HIGH VOLTAGE

LIGHT SOURCE

LIGHT MONO-BEAM CHROMATOR

HIGH VOLTAGE SQUAREWAVE SIGNAL

I

HIGH VOLTAGE SQUAREWAVE GENERATOR AND REFERENCE

SIGNAL SOURCE

CONSTANT DC

SIGNAL SERVO SYSTEM REFERENCESIG~

WAVE FORM MONITOR

OSCILLOSCOPE

LOCK-IN OUTPUT

«ACSIGNAL

LOCK-IN AMPLIF IER

CON STANT

DCSIGNAL

J

WAVE LENGTH ENCODER

CHART

RECORDER

FIG.2. Blockdiagram ofthe experimental

measure-ment system as operated for electromodulated

trans-mission measurements.

and

~~,

=_{2k~~+ 2n~k,}

which are derived from the usual expressions

re-lating the index of refraction and dielectric

func-tion. Both these equations and the partial

deriva-tive expressions require

spectra

of

z

and kfor

the thallium halides, the methacrylate membrane,

and

CsI.

The latter two were obtained from a mea-surement" and the literature,

"

respectively. The

n and k data used for the thalium halides were

values measured by Bachrach'4 which were

adjust-ed to account for ahigher level of static strain in the samples used in this study. The adjusted values were obtained by programming acomputer to search over ranges near the literature values

to locate n and kvalues which produced a

19

ELECTROMODULATION

SPECTROSCOPY

OF

EXCITONS

IN. .

.

the experimental measurement. This procedure

resulted in multiple solutions and final values of

z

and k were determined by starting at low photon

energy where k

=0

and n. is known, and working

graphically to higher photon energy, using

require-ments of continuity ofn and P

pairs,

the known

general functional form for yg and k in this region,

and calculations to check the. agreement between

calculated and measured transmission. The values

ofn and kfinally obtained gave calculated

trans-mission

spectra

which reproduced the experimental

spectra

for both T1C1and

TlBr.

IV. EXPERIMENTAL RESULTS

Spectra of.

hT/T,

Ae„and

Ae, are presented in

this section at two applied field strengths

for

T1C1

and

T18r.

The unmodulated

spectra are

included

in each figure for comparison. The primary

fea-tures of these

spectra

and others taken on the

same samples at different applied fields are com-pared to the results of

Blossey's

calculations in

Sec.

V.

The Tand AT/T spectra are shown in

Figs.

3

and 4for TlCl and

TlBr,

reSpeetiveely, at sample

temperatures between 5 and 6 K. The locations

of the yg

=1,

2, and

~

hydrogenic energy

states

are

marked, with

~

denoting the

series

limit atthe conduction-band edge. The n=2position was

lo-cated in Fig, 3 by calculating the energy spacing

from the ~

=1

peak using the reported exciton

binding

energy"

and the hydrogenic model. The

energies of other .expected spectral features were plotted relative to the n

=1

peak using energy spacings from

Ref. 16.

The primed features

cor-respond to splittings of the hydrogenic levels

0.

6-0.5—

04—

O.i—

0.

0-—

I I I I I I I I I I

TIBr(sc)

JB

g

—

TRANSMISSION

6.0kV

p ----xIO

'

—_7.2 —_6.4

O

56

Z.' CO (A (f)

40

(f) 5.2 CL 24 I.6 o. ~-2

I I I I I I I I I I

2.98 5.00 3.02 5.04 5.06

PHOTON ENERGY (eV)

FIG.4. Tlar transmission (dashed line) and electro-modulated transmission spectra attwo applied voltages.

-O.

I-—_0.8

caused by the

inter-

and intravalley scattering perturbation.

"

The n and Psymbols denote the locations of the phonon sideband

features.

"'6

The

spectra

for T1Brdo not show as much resolved structure due to three

factors:

the lower exeiton

binding energy and splitting

charaeteristie

of

TlBr,

the greater thermal broadening caused by alower

Debye temperature, and the higher applied fields.

Figures 5 and 6 show the _q, and Ae,

spectra

for

TlC1 and

TlBr,

respectively, which were

calcula-ted from the spectra shown in

Figs.

3 and 4. The main effect of the

electric

field, as seen in the

~q,

spectra,

is

abroadening and attenuation of the

major positive and negative &,peaks below the

direct band-gap corresponding to g=

~

while

os-cillations appear in the 6&,

spectra

above the

bandgap, as predicted by theory 8-io

The e, and

~q,

spectra

are

shown in

Figs.

7 and 8for T1C1and

T1Br,

respectively. The Ae,

spec-I I I I I I I I T I

0.8— a

I I I I I I I I I I I I I I

04—

ooI-x I—

L

04--0.

8-I.0—

0,5— 0.0— L-0.5— —I.O— c) ON .56 .48 40o .32K&

(/)

a

.I6fl=

.08 .00

l.2— 0.8

—-AJ

o 04

x 0.

0---—_0.4

0.0

O

x -04 L

—_0.8

I

2

I.5IIV

TICI(sc)

.0kv

a 20.0

—I6.0

I2.0

8.0

4.0 0.0

—_4.0 —_8.0

I I I. I I I I I I I I I

3;36 3.38 3.40 3,42 3.44 3.46. 3.48 3.50

PHOTON ENERGY (eV)

FIG.

3.

TlCl transmission (dotted line) and

electro-modulated transmission spectra at two applied voltages..

I I I I I I I I I 1 l I I I I

3.38 3.40 3.42 3.44 3.46 3.48 3.50

PHOTON ENERGY (eV)

FIG.5. Ee&spectra (solid lines) and e&spectrum

(dotted 1ine)ofTICI. The marked photon energy

J.

F.

McCLELLA1VD AND

D.

W. LYNCH 19

8.0— I I I I I I

—16.0

2.

0-0.0

-2.

0--4.0—

.0kv

TIBr (sc)

—_12.0

8.0

4.0

0.0

—_-4.0

l

I 1

(I —_-8.0

80 . I I I t

298 3.00 3.02 3.04 3.06

PHOTON ENERGY {eV}

FK".6. Ae~spectra (solid and dotted lines) and e&

spectrum (dashed line) ofTlBr. The marked photon

energy locations coincide with those in Fig.

4.

1.0.— 9.5

kV--0.0—

6.0kv

~

-30-C]

-_4.0—

-_5.0—

-_6.0—

-_7.0—

298

Il 'lI

ll

(I a

TIBr(sc)

I

0

I P

/

IM I I I I I I I

3.00 3.02 3.04 3.06

PHOTON ENERGY (eV)

—_18.0 —

16.0 —_14.0

—_12.0

—_{10.0 ep} —_8.0 —₆₀

—₄₀ —_2.0 0.0

FIG.8. 4e2(solid and dotted lines) and e&spectra

forTlBr.

tra

also show the peak broadening and attenuation

effect of the field below n

=~

and the higher photon

energy oscillations. A small amount of peak shifting ofuncertain orgin occurs in the

hc,

spec-tra

relative to the

aT/T

spectra for features

as-sociated with the hydrogenic exciton

states.

In

all

cases

these shifts

are

small fractions of the

linewidths ofthe unmodulated

spectra.

The photon

energy locations labeled in

Figs,

7and 8coincide

with those in

Figs.

3 and

4.

V. COMPARISON OF EXPERIMENTAL RESULTS TO CALCULATIONS

A detailed comparison is made in this section

between the measurements and

Blossey's

calcula-tions for the primary spectral features as a

func-tion ofthe applied

electric

field modulation ampli-tude. The primary

spectral

features, as designa-ted in

Ref. 9,

are shown in

Fig.

9.

A spectral broadening parameter,

'

I' =0.

2A,

was selected on the basis of acomparison between

calculated and measured line shapes for

unmodu-lated

spectra.

8

is

the exciton binding energy.

This

is

a larger value than the sample

tempera-ture would have indicated due to the broadening of

the

spectra

by strain.

The

first

comparison of experimental spectral features to theory is shown in a

6

e, plot ofthe

zero-crossing

separation

hZ,

/R vs

g/g,

shown

in the upper left-hand corner oi

Fig. 10.

AZ,/R

is defined in

Fig. 9,

g

is

the

electric

field

calcula-ted from the applied voltage and plate separation,

and

_g,

is the exciton ionization fief.d' defined as

the exciton binding energy divided by the product ofthe exciton Bohr radius and the electronic

1.2

0.8

O 04 L

0.0

-_0.4

CO

21 I

1.5kv

T t T t

I —20.0

I6.0 I2.0

8.0

0.0

hl

6E,

PHOTON ENE RGY

CI

0.4

0.0

-0.4

C&

~-0.8

L

- 1.2

TICl (sc)

h,

Pj-IPTQN ENc Ri-y

I I I I j I I I I I I I j I I

3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.50

PHOTON ENERGY (eV)

FIG.

7.

4E'

2(solid lines) and e2(dotted line) spectra

for T1C1.

FIG.

9.

Primary electromodulation spectral features

19 ,

ELECTROMODULATION

SPECTROSCOPY

OF

EXCITONS

IN. . .

3249

0

_Ip—

0

0

CU

LLJ

m=0.

67

.

.

-l

TICI.

~

6.

0

V TIBr

60kV

m=0.

₅₀

CU

6e(

TIBr

.

TICI

0 'ha

Ip Ip~

Ipo Io~ I

0~

E.

/6,

(calculated from voltage)

IO i

pl

I I I I I I I

0

E,/E.

_,

(Effective)

Ip—

~

T

IBr

IO'-00 o

~ TIBr

.

TICI

E./E& (Effective)

Ipo O-l

E/E,

(Effective)

FIG.10. Experimental zero-crossing separations for the Dc~ and Ae2 spectra plotted as afunction o'f_applied

effec-tive field, asdescribed in the text. The ordinate labels are defined in Fig.9, .The solid and dashed lines are plotted

from Blossey's calculations (Ref. 9).

charge. The _gl values were calculated

for

TlCl

and T1Brfrom the exciton parameters given in

Ref. 16.

The dashed line has been fit to the points

calculated by

Blossey'

and denoted by squares in

Fig. 10.

The experimental curves are low in both

magnitude and slope until the square-wave voltage

amplitude reaches the 6-kV region. The slopes

then become approximately equal to those predicted

by theory. The most likely cause for the

discrep-ancy between theory and experiment appears .to be

alowering of the field sensed by the excitons due

to the presence of

photocarriers.

This cause

is

suggested both by electroreflection measurements"

on T1C1and

TlBr

by other workers and by

obser-vations made during the measurements reported

here which can be explained on the basis of

photo-carriers.

'.

"'

_{Since quantitative photocarrier}

mea-surements were- not possible during this study, no

detailed explanation could be definitely established for the role of

photocarriers.

To provide the

most useful comparison of experimental results

to theory, effective fields sensed by the exciton

were calibrated

for

each applied voltage by using the experimental b,

E,

/R values and the theoretical

curve in the b,_e, plot ofn,

E,

/It vs g/gz. The

ef-fective field values were read from the

abscissa

and used for the other plots in

Figs.

10and

11.

Figure 10 shows the other b,&,and hq,

zero-crossing separation plots using the effective-field values. The various

zero-crossing

separations

plotted on the ordinates of the graphs

are

defined

in

Fig.

9, The plots show reasonably good

agree-ment with theory in the high-field regions where

the calculated results

are

represented by the solid

lines.

Blossey's

results did not extend to the

low-field region of the plots, Ifthe calculated lines

are

extended linearly to the low-field region the experimental points are too low relative to the

theoretical extrapolation. This could be due to the

effects of photocarriers,

inter-

and intravalley

J.

F.

MCCLELLAND AND

D.

%.

LYNCH

3250

IOI-PEAK

kEIGkT

CALIBRATION

Io—

1 T I I I I I

.

TIBr

.

TICI

dd

0 0

100

IOI

IO', J I J I

Io

E,/E,

& (Effective)

I

Io

E,/E:, (Effective)

0

.

TIBr

TICI

I I

IP IP

E,

_/E,

(Effective)

TIBr

TICI

I I

Io

_,

Io

F/E,

(Effective)

0 0 0

Io Io ip2

Io

Io—

I I OI &eI

0 0

I I I I I i

0 0 0

0 6

0

Og

TIBr

TICI

TIBr

* _TICI

IP J L I I I

~

t t I

Ip0

E/F

&

(Ef

fective)

Io

IO I

.

IO'

F /E& (Effective)

IOI

ofh, vs

g/g,

(effective) in the upper left-hand

corner of Fig. 11was used to scale the

experi-mental peak heights. The curve

is

shown with a

dashed region extended with a drafting curve to

allow scaling of the lower-field data. The h, peak heights ofboth AE'y and

he,

are too high relative

where the applied field

is

less

dominant.

Figure 11shows the 6&,and 6&,experimental peak heights plotted on the ordinates as a function

ofthe effective field. The various peak heights, denoted by the letter h with different subscripts,

are

defined in

Fig.

9.

The calculated Ae, curve

F)G.gl. Experimental peak heights for the 6&fand &e2 spectra plotted as afunction ofapplied effective field, as

described in the text. The ordinate labels are defined in Fig.

9.

The solid lines are.plotted from Blossey's calculations

19

E

LECT ROMODU LAT ION

SPECTROSCOPY

0

F

EXCITO

NS

IN.

.

.

3251

to theory. The other experimental peak heights

are

reasonably well clustered around the calcula;— ted curves.

VI. CONCLUSIONS

This study is the most comprehensive effort

reported to date to compare Wannier exciton

elec-tromodulation calculations to experimental results

in terms of the electric-field-induced changes in the dielectric function.

Earlier

efforts have

gen-erally involved

less

resolved structure and

neg-lected to obtain results in terms of the dielectric

function for comparison to theory.

The measurements reported here are comprom-ised,

as

most previous investigations have been,

by nonintrinsic broadening mechanisms and by

difficulties in applying awell-defined

electric

field

modulation, apparently due, in this

case,

to the

presence of photocarriers. The measurements do

support the general trends predicted by

Blossey's

calculations, regardless of these experimental

problems. The study also indicates some ofthe

problems which should be addressed in planning

improved measurements.

ACKNOWLEDGMENTS

%e

would like to acknowledge the assistance

ofDr.

T.

Pinter in the computer program coding

and Dr.

C.

Culp in the design of the high-voltage

square-wave generator. Thanks are due to

Dr.

D.

Blossey and Dr. H. Bachrach for providing

ex-panded plots ofgraphs. This work was supported

by the U.

S.

Department of Energy, Office of

Basic

Energy

Sciences,

Materials

Sciences

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