Evidence of a donor-acceptor type transition in CuGaSe2

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Evidence of a donor-acceptor type transition in CuGaSe2

A. Poure, G. Aguero, G. Masse, J.P. Aicardi

To cite this version:

A. Poure, G. Aguero, G. Masse, J.P. Aicardi. Evidence of a donor-acceptor type transition in CuGaSe2.

Journal de Physique, 1980, 41 (7), pp.707-712. �10.1051/jphys:01980004107070700�. �jpa-00209296�

Evidence of a donor-acceptor type transition in CuGaSe2

A. Poure, ^G. Aguero, ^{G. Masse and J. P. Aicardi}

Laboratoire de Physique ^du Solide, Université de Perpignan,

^de Villeneuve, ⁶⁶⁰²⁵ Perpignan Cedex, ^France (Reçu ^{le 3 octobre} 1979, révisé le 22 janvier, accepté ^{le 28} février 1980)

Résumé.

Nous faisons des mesures de spectroscopie ^résolue

temps (T.R.S.) ^sur

^bande d’émission large

de CuGaSe2, ^{centrée à} 1,59 ^{eV de} largeur ^{40 meV} (à ^la température ^{de l’hélium} liquide). ^Le comportement ^du déclin est mesure à 4 K pour différentes énergies dans la bande d’émission. Nous montrons que les résultats expé-

rimentaux sont

accord

modèle du type donneur-accepteur.

L’étude du déplacement

^T.R.S. permet de déduire par lissage :

2014

la valeur du demi-rayon de Bohr du niveau le moins profond RB

5,6 A (le ^{centre le moins} profond ^{est donc}

à 70 meV

moins);

2014 la probabilité maximum de transition WMAx = 108 s-1;

2014 la valeur de h03BD~

1,53 ^eV.

Les courbes de déclin théorique ^et expérimentale ^sont

^bon accord pour

concentration du porteur majo-

ritaire N

8 1017/cm3.

Abstract.

Measurements of spectrum ^shift

^made by

of time resolved spectroscopy (T.R.S.)

a

broad emission band of CuGaSe2, peaked ^at 1.59 eV with

width of 40 meV (at liquid ^helium temperature).

The behaviour of the decay is measured at 4 K for different emission band energies. ^We will show that the expe- rimental results are in agreement ^with

donor-acceptor ^model.

From the shift of the spectra ^{in T.R.S.}

^{fit :}

2014 the Bohr-half-radius value RB

5.6 Å (the shallowest centre is at least at 70 meV) ;

2014 the maximum radiative transition probability WMAX

¹⁰⁸ s-1;

2014 the value hv~

^{1.53 eV.}

The theoretical and experimental decay

in good agreement ^for

preponderant impurity concentration of N = 8 1017/cm3. By using these various parameters

observe that theoretical and experimental ^T.R.S.

spectra

consistent.

Classification Physics ^Abstracts

78 . 60H

1. Introduction.

CuGaSe2 ^{is a} semi-conductor of the I-III-VI2 type which cristallizes in the chalco-

pyrite system (space group 142d) [1]. Through absorption, electro-reflectance and modulated reflec-

tivity measurements, it has been established that

CuGaSe2 ^{is a direct} gap semi-conductor [2-5].

The temperature dependence ^{of the} gap is given by [6] :

with

Electrical measurements show that the conducti-

vity of this material is hightly influenced by ^the impu-

rities : we can vary the resistivity of this material from 5 x 10- 2 Q cm to 10 MQ cm.

N. Yamamoto gives the value of the _gap according

to the position of the exciton [7] (E,

^{1.711 eV at}

20 K). ^{There is} only ^one paper available ^on the lumi-

nescence of this compound [8]. The results remain of

a qualitative ^{order as} the authors give ^no interpre-

tation of the emission observed.

We have studied the cathodoluminescence of _syn- thetic crystals provided by ^{L. Mandel} (Salford ^Uni- versity). ^{In this} paper, measurements are carried ou

under electron bombardment at liquid ^helium tempe-

rature.

We use a 25 kV electron _gun with an ajustable

electronic density of bombardment (up ^{to 1} mA/mm2).

The electron beam is modulated at the Wehnelt with

an impulsion duration of _{1 lis} at a frequency ^of

10 kHz. The rise and fall time is less than 20 ns.

We use a 7 140 type ^Oriel spectrometer fitted with

a 600 lines/mm grating (Blaze wavelength ^{of 1} Um), ^a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01980004107070700

708

Si ^cathode photomultiplicator ^cooled by ^Peltier

effect. The T.R.S. and lifetime measurements are

performed ^{with a P.A.R. 162} type ^box-car integrator.

The luminescence observed appears like ^a broad band (40 meV wide) peaked ^{at 1.59 eV at} liquid

helium temperature. Experimental methods used for this study ^are time-resolved spectroscopy (T.R.S.)

and luminescence decay..

2. Theoretical notion about donors-acceptors.

F. Williams has already studied and developed ^this

model in the field of semi-conductors and insula- tors [9]. ^D. G. Thomas and J. J. Hopfield [10] ^observe donor-acceptor pairs luminescence in GaP and deve-

lop ^a theory ^on their kinetic of recombination.

The _energy of the photon emitted in a model of the

donor-acceptor-pair type ^is given by the relation :

Eg is the width of the forbidden band, EA ^and ED

the acceptor and donor level depths, e2 j Kg r ^{is the}

Coulombic interaction _energy. The function f(r) ^is

a correction to the Coulombic interaction ; ^{since it} only ^{comes into} effect for _very close-set pairs, ^we

may overlook it. From formula (1) ^{we see that as the}

distance between pairs, r, decreases, ^the energy of the photon emitted increases. As the donor and acceptor ought ^{to be situated at} precise points ^of

the lattice, only certain discrete values of r are allowed and for the smallest of these a sharp ^line spectrum should appear; for greater ^{values a} broad band is to be seen. The transition probability W(r) ^between

the donor and the acceptor, in units of time is for- mulated proportionally ^to the square of the matrix element which brings into effect the overlap integral

of the hydrogenous envelopes FD(r) ^and FA(r) ^{of the}

donors and acceptors :

As the interpair ^distance increases, ^{the transition} probability ought ^{to decrease.} Moreover, ^{when we}

assume that the electron is loosely ^{bound to the} donor, the latter is totally represented by ^a quasi- hydrogen model, the radiative transition probability W(r) ^between associated donor-acceptor pairs ^dis-

tant by ^{r is} given by :

where W MAX ^{is a constant and} RB ^the Bohr-half-radius of the shallowest state.

This equation ^{is correct if we} restrict ourselves to the effective mass approximation. ^{However, it} may be applied ^to deeper levels with a fictitious RB ^where

this approximation ^{is no} longer ^exact.

From the above, this kind of model ought ^{to show}

a spectrum of lines in the high energy field. Yet ^no

observation of such structures has ever been reported

in direct-gap semi-conductors. In this case the emis- sion takes the form of a broad band composed ^of

non-resolved lines stemming from different pairs ^at

different distances.

Time resolved spectroscopy ^{enables us to observe} the spectrum ^at different times after the end of exci- tation. In the donor-acceptor ^{case we observe a shift}

of the emission band towards low energies ^{when t}

increases (t-shift). Indeed, ^most of the close-set pairs,

that is to say those in which the transition probability

is maximal, ^no longer participate in this lumines-

cence. The t-shift is the first criterium used in the

donor-acceptor transition. The second criterium used is that of spectrum ^variation according ^{to excitation} intensity ( j-shift). ^{This is} expressed by ^a shift of the spectrum ^towards high energies ^as the excitation

intensity ^increases.

The study ^of light decay ^{at different} wavelengths

shows a t -" type ^{law. The rate} of decay ^becomes

more rapid ^{when the} energy in the band increases.

3. Experimental ^results.

3. 1 TIME RESOLVED, SPECTROSCOPY.

Figure ¹ represents ^{the lumines-}

cence spectrum ^{at t}

^0. Two emission bands are

observed : one peaked ^{at 1.63} eV, ^{the other at 1.59 eV.}

We choose to study ^{the band} peaked ^{at 1.59 eV.}

At 1.63 eV, the emission has a short lifetime and

disappears rapidly in the T.R.S. spectra.

Fig. ^1.

^Emission spectrum ^{at t = 0} (liquid ^helium temperature).

Figure ² represents ^the time resolved spectra ^at liquid ^helium temperature. ^We observe that the spectrum shifts towards lower energies ^{as the time}

after the excitation increases. There is ^a distortion of the spectrum ^{on the} high energy side and a slight

decrease of the half-width. The total shift of the maximum position is about 30 meV (between ^the

time zero and 100 Us).

Fig. ^2.

Time resolved emission spectra :

0 ;

b -+ t = 800 ns; c -+ t = 2 J1S; d -+ t = 8 J1S; e -+ t = 100 J1S.

3.2 LUMINESCENCE DECAY IN FUNCTION OF THE POSITION IN ENERGY.

We observe the luminescence

decay ^{at different} energies inside the emission band.

Except ^{at the} early time these curves obey ^{a law of}

the form I

t - ", ^{n values are} compiled ^{in table I.}

Table I.

Variation versus E deduced from ^{I= t -}

law.

3.3 DISCUSSION. - The t-shift can be considered

as the characteristic criterium of the pair ^recombina-

tion mechanism.

The total variation (30 meV) of the band position

after the end of the excitation can be attributed in the first approximation ^{to the} difference between the coulombic _energy (e2/Ks ^r) for the close-set pairs

and the pairs ^furthest apart.

In the case of CuGaSe2, the lattice constant is

equal ^{to a}

^{4.614 A.} The static dielectric constant is A% = ^{9. We obtain a} limit of the coulombic _energy for the close-set pairs equal ^{to 300 meV.}

The observed variation indicates a radius of 40 À

for the close-set pairs.

For such a value of the intra-pairs distance, f(r)

can be neglected ⁱⁿ equation (1) [11].

For the study of the emission peaked ^{at 1.59 eV}

we shall use the formula :

We did ^not notice _any shift as a function of exci- tation. Actually, the excitation _range was not suffi- cient to show _any shift.

In conclusion we favour the existence of a donor- acceptor model. The study of the luminescence decay

enables us to confirm this interpretation : the lifetime increases as the _energy decreases.

In the first part, ^we show the total behaviour of

luminescence. In the second part, ^we confirm our

model, by measurement of the fundamental values

(level depth, ^{Bohr radius,} maximum transition pro-

bability).

4. Determnnation of fondamental parameters ^and application ^{to the} stady ^{of total} decay ^of hnminescence and sepctra shapes. 4 , 1 DETERMINATION ^{OF THE}

and spectra shapes. - 4. 1 DETERMINATION ^{OF THE}

MAXIMUM TRANSITION PROBABILITY.

4 .1.1 Theory.

-1n the non-compensated ^{case, the basic} hypothesis

is that depopulation ^{of the centres is} homogeneous

and the time decay ^{of the} zero-phonon ^{line may be}

written in the form :

where K is a constant and Q(t) > ^{is the} average

decay of the neutral donors (acceptors) and Ec ^the

coulombic _energy.

In the compensated ^{case, formula} (3) is still avai- lable in the hypothesis ^that donor-acceptor tunneling

is always slower than the redistribution of the carriers

on the shallowest centres. Therefore the population

of these centres remains homogeneous ^{as in the} previous ^case.

If we derive (3) ^we obtain the Coulomb _energy variation law for the emission peak ^{maximum at a} given ^{time t} [12].

From this we deduoe :

4.1.2 Experimental study.

^{For the} pairs ^fur-

thest apart, the coulombic _energy is approximately

zero. The emission is peaked ^{at :}

We determine this value on the long time T.R.S.

spectrum in the low _energy wing. ^{We calculate}

Table II. - T.R.S. results.

710

Table II gives ^T.R.S. results and enables us to calculate Ee MAX ^for the emission peak ^maximum.

Formula (4) ^can be written in the form :

with x

EcMAX’

By fitting ^{our results to} the last formula we find :

In the hydrogeneous approximation the shallowest level depth would then be : 73 meV.

The results of this fitting ^are given in table III.

Table III.

Peak emission energies ^{versus time} (two parameters fitting).

Without estimating hl’oo ^as previously, ^{we now fit}

our results with the three parameters RB, hi,. ^and WMAX.

Formula (4) ^{becomes :}

where X

ho (peak ^emission energy).

By fitting ^to this formula we find :

The new values of hi,

f(t) calculated with these parameters ^are compiled in table IV.

We deduce for the shallowest level depth : ^{71 meV}

and the value of hl’oo

^{1.53 eV which is} quite ^similar

to the estimation we first made from the low _energy

wing ^{in the} long time T.R.S. spectrum.

So we will now use :

Table IV.

Peak emission energies ^{versus time} (three

parameters fitting).

4. 2 STUDY OF TOTAL LIGHT DECAY. - 4.2 .1

Theory [10].

^Non compensated ^case (lst case) NA > ND,

Q(t) > ^{is the} average probability that the electron is on the donor

where n is the concentration of the preponderant impurity.

The light intensity I(t) ^is given by :

-

Compensated ^case ND

NA.

In this _case, it is more difficult to calculate the

decay. ^{We find} that Q(t) )comp ^is given by :

with

So

and we deduce

with the results obtained ^{in the non} compensated

case, ^{we can} calculate I(T)n.comp x ^6(r) >n.comp ^and

the corresponding t ^{of the} compensated ^case by ^for-

mula

We calculated formulas (6) ^and (8) ^{on a} Mitra 15 CII calculator.

We show the total decay for different values of the

impurity concentration and for the calculated values

RB ^and WmAx in ^{the non} compensated ^case (Fig. 3).

Fig. ^3.

Theoretical total-light-decay

for the values of

WMAX

^{108 s-1 and} RB

^{5.6 A} for several concentrations.

The shape ^{of the curves is} strongly influenced by

the product nRB. Although ^the parameter WMAX

affects the position ^{of the curves, it does not affect}

their shape.

In our case, ^as the function Q(t) > ^{remains cons-}

tant (Q(t) N 1) ^{over the time range involved, the}

curves of the non compensated ^{case are} similar with the compensated ^ones.

, 4.2.2 Experimental results. - Previous calcula- tions are only ^correct if all the pairs involved in the broad band have been initially saturated. In our

experiments this condition has been fulfilled. Figure ⁴ represents ^the luminescence decay ^{in a time} range between 10-’ s and 10-4 s.

The comparison ^between previously ^calculated

Fig. ^4.

Experimental total-light-decay

(points). ^Theore-

tical total-light-decay

^{for n = 8}

1017/CM3 (solid).

curves and the total decay ^{curve obtained} by experi-

ment shows a good agreement ^{in the case of a} dopage

n = 8 x 1017/cm3 .

This value would appear ^to be compatible ^{with the} impurity concentration of that compound.

4.3 STUDY OF SPECTRA EVOLUTION IN FUNCTION OF TIME.

The shape ^{of the} spectrum ^{at different} times, in function of _energy is given by ^formula (3).

From this expression, ^{we can see that the concen-}

tration only intervenes in Q(t) >.

We calculated formula (3) ^at different times.

Results are given ^on figure ^5.

We observe that in the case of close-set pairs (at early times) theoretical spectra follow the experi-

mental curves on the high energy side.

When time increases, ^the spectral ^{shift on the} high

energy side is characteristic of donor-acceptor ^beha-

viour. On the low _energy side the variation between calculated and experimental ^{curves is} important,

even at early ^times.

For long ^times, experiment doesn’t fit at all with

theory, ^{the emission seems} govemed by ^vibration

effects. It would be interesting to correct the theore- tical spectra given by equation (3) with the additional

assumption ^{that the} pairs radiate with a spectral shape given by ^the long ^{time curve} (figure 2 spec- trum e) ^{and to} compare them with the experimental

curves [10].

712

Fig. ^5.

Theoretical

for the spectra assuming ^that

pair

of separation

^radiates only ^{at the} photon energy given by eq. (1) (solid).

t

800 ns ; b - t

2 uS;

^t

8 ps; d --> t

20 _ps;

e - t ⁼

100 _ps. Experimental time resolved

at t

800

((dashed).

5. Conclasion.

This study has enabled us to characterize and to calculate the fundamental _para- meters which intervene in a donor-acceptor ^model

transition. The hypothesis ^is supported by ^time

resolved spectroscopy ^and by ^lifetime decay ^within

the spectrum.

The calculation of the shallowest level depth ^and

recombination probability has enabled us to calculate

decay ^{curves as well as} spectrum evolution in func- tion of time.

A comparison between theoretical and experimen-

tal curves shows that EB, RB ^and W MAX ^{values seem}

correct.

Yamamoto observed [8] ^a donor-acceptor ^emission

at 1.59 eV (110 K). ^{The donor would be a} Se-vacancy,

the acceptor ^a Cu-vacancy. Comparing ^with CuGaS2,

he deduces the acceptor and the donor depths (EA

⁴⁰ meV, ED

⁸⁰ meV) .A

His study ^is only qualitative, he doesn’t confirm the model by any T.R.S. experiment. ^{As far as we}

are concemed, the emission peaked ^{at 1.59 eV is}

observed at helium liquid temperature, ^{at 110 K the} emission cannot be detected _any more. Heat treat- ments on the _as-grown material would enable us to confirm Yamamoto’s hypothesis ^{on the} activator and coactivator.

References

[1] SHAY, J. L. and WERNICK, ^J. H., Ternary chalcopyrite ^Semi-

conductors (Pergamon Press) ^1975.

[2] TELL, ^{B. and} BRlNDENBAUGH, ^P. M., Phys. ^{Rev. 12} (1975) ^3330.

[3] LERNER, ^L. S., ^J. Phys. Chem. Solids 27 (1966) ^1.

[4] ^{BHAR, G. C. and SMITH, R. C.,} Phys. Status Solidi (a) ¹³ (1972) 157.

[5] SHAY, ^J. L., TELL, B., KASPER, ^{H. M. and} SCHIAVONE, L. M., Phys. ^{Rev. 5} (1972) ^5003.

[6] NEUMANN, H., HÖRIG, W., RECCIUS, E., MÜLLER, ^{W. and} KÜHN, G., Solid State Commun. 27 (1978) ^449.

[7] YAMAMOTO, N., HORINAKA, H., OKADA, K. and MIYAUCHI, T., Japan. ^J. Appl. Phys. 16 (1977) ^1817.

[8] SUSAKI, M., MIYAUCHI, T., HORINAKA, ^{H. and} YAMAMOTO, N., Japan. ^J. Appl. Phys. 17 (1978) ^1555.

[9] WILLIAMS, F., Phys. Status Solidi 25 (1968) ^493.

[10] THOMAS, ^D. G., HOPFIELD, ^{J. J. and} AUGUSTINIAK, ^W. M., Phys. ^{Rev. 140} (1965) ^202.

[11] HOPFIELD, J. J., Physics of Semiconductors (Dunod) ^1964.

[12] ^{BAKER, A. T. J., BRYANT, F. J. and HAGSTON, W. E., J.} Phys. ^C.

6 (1973) ^1299.