Radiative recombination of donor-acceptor pairs in ZnTe

SoLid 6tare Co~amunications, Vol. 38, pp. 1289-1292. Pergamon Press Ltd. 1981. Printed in Great Britain.

0038-1098/81/241289-04502.00/0

RADIATIVE RECOMBINATION OF DONOR-ACCEPTeR PAIRS IN ZnTe S. Nakashima Department of Applied Physics, Osaka University, Suita, Osaka 565, Japan and A. Nakamura Institute for Solid State Physics, University of Tokyo, Minatoku, Tokyo 106, Japan

(Received 28 January 1981 by Y. Toyozawa) Lifetime of the first excited state of donor-accepter pairs has been measured in ZnTe as a function of the donor-accepter distance. The measured lifetime for the radiative recombinations of donor-accepter pairs agrees well with the calculated one in which the central cell correction for the ls state of the accepters is taken into account. It has been found that the lifetime depends on the impurity concentration. The concentration dependence is discussed in connection with the non-exponential decay of the luminescence observed for more distant donor-accepter pairs. 1. INTRODUCTION RADIATIVE LIFETIME of the donor-accepter ( D - A ) pairs in semiconductors relates closely with the spatial extent of their electronic wavefunctions and spatial distribution of the pairs. Although the luminescence spectra of the D - A pairs have been studied in detail by many researchers, few experiments have been done conceming the dependence of the radiative lifetime on the D - A pair separation. Recent theoretical works [ 1,2] on the shallow accepters and the experimental determination of their excited state energies for ZnTe by electronic Raman scattering [3] and selective photoluminescence [4, 5] measurements allowed us to obtain detailed information about the energy structure of the accepter levels. On the basis of these investigations, we have examined the dependence of the radiative lifetime of D - A pairs on the accepter binding-energy and impurity concentration in ZnTe. Crystals containing three different accepters have been studied. Radiative lifetimes have been calculated for these donor-accepter pairs as a function of the donor-accepter pair distance, where we have used the variational wavefunction of the accepters for which the central cell correction is taken into account. We have compared the experimental results with the calculation. 2. EXPERIMENTAL RESULTS Crystals of ZnTe used in this experiment were grown from melt containing excess Te. These are the samples from the same ingot used earlier [3, 4]. The experiments were performed on several samples which in

all cases were immersed in liquid helium during the experiment. Luminescence was excited with a dye laser (coumarin 485) pumped by a nitrogen laser whose peak power was about I MW. The D - A pair luminescence was analyzed by a 0.75 m Spex monochromator and the decay curves of the luminescence were measured by a box-car integrator. The decay curves have been measured for Li, P and As doped ZnTe as a function of energies of D - A pair luminescence. The energies of the exciting laser were chosen so that there could be observed the sharp selective emission lines whose energy the spectrometer was set at. The decay curves are not exponential over wide range measured, as was noticed by other workers. While the deviation from a single exponential curve is dominant for more distant pairs, the curves can be approximately fitted to an exponential function in the first decay stage for close pairs. The decay curves were exponential over a decade of intensity for the D - A pairs with distances shorter than about 100 A. The decay time was defined only for the pairs for which its decay curve could be approximated by an exponential function at least for the time down to i/e of the maximum intensity. Figure 1 shows experimental decay time of ZnTe : Li as a function of the D - A pair distance R, which is calculated from the following relation between emitted photon hoe and R, e2 h w e = EG - - (ED + EA) + - - .

1289

eR

(1)

1290

DONOR-ACCEPTOR PAIRS IN ZnTe

Vol. 38, No. 12 Z rite : As

ZnTe : L i U

4.2K

".2K

/

In

~0 ~

vi~6

I.lJ

tO NA~SxlO :6 cm"] I->-

>< L) Lid Q

N~ ~Sx lOCr¢m 3

< {..)

,DO

O

NA ~ I x I01"~cr'n"3

0 000

~°

Id7

ld7

50

100

D-A

lds . 5O

150

k

D-A

Here, E c is the band-gap energy, ED and Ea are the donor and acceptor binding energies, respectively, and e is the static dielectric constant. The decay time increases with increasing D---A pair distance R. Of the three acceptors, the decay time for arsenic acceptors is longest at the same distance. The decay time is much affected by the impurity concentration. Its concentration dependence has been examined for ZnTe : As and the results are shown in Fig. 2. As the impurity concentration is increased, the decay time decreases. This concentration effect is prominent for more separated pairs and hence the slope of the r - R curve is less steep for the sample with higher impurity concentration. The higher the concentration is, the shorter the D - A distance is at which the nonexponential behavior appears in the initial stage of the decay. Hence the definite decay time was obtained only for D--A pairs with shorter distances in the sample with high impurity concentration.

4e:Z~e

where h~o, is the photon energy, n is the refractive

(2)

h

I

150 DISTANCE R (,h,)

index, Mev is the matrix element of momentum operator between the conduction band and the valence band. I(R) is the overlap integral between the envelope functions of donor and acceptor states: I(R) = f g,~(r)~,~(r -- R) e .

(3)

The general wavefunction for the acceptor ls state can be written as ~ , ( r ) = fo(r)lL = O, J = ~, F = ~, Fz) + go(r)lL = 2, J = ~, F = ], Fz >,

(4)

and fo(r) and go(r) are solutions of the equations (27a) of [1 ]. As the exact solutions are not available, approximate wave-functions are calculated by the variational method [7]. We use the following variational functions,

C,I

:o(r) = A , -ka,I

go(r) = A a ~

Adams and Landsberg [6] gave the formula for the radiative recombination time of D - A pairs as follows:

I

Fig. 2. The decay time as a function of the D-A distance in arsenic doped ZnTe is shown for three different acceptor concentrations. The solid line indicates the calculated curve.

4 3. ANALYSIS AND DISCUSSION

m~hcanlM~1212(R),

L,

100

DISTANCE R ( A )

Fig. I. Decay time of the D - A pair as a function of the donor-acceptor separation in lithium doped ZnTe with the impurity concentration of 5 x 1016cm -3. The solid line indicates the curve calculated from equations (8) and (9).

r(R) -l -

Z

UJ ra

exp (-- r/as), [1y/2

exp (-- r/3aD).

(5) (6)

\aDl

The two equivalent Bohr radii a, and a D are introduced as independent variational parameters. A, and Aa are the normalized admixture coefficients of the different envelope states. The parameter a, and a D are determined so that the binding energy E(1S) for the ground state is

Vol. 38, No. 12"

DONOR-ACCEPTOR PAIRS IN ZnTe

maximized by variation. The variational energy is obtained as a function of the spherical parameter ta. The result is in agreement with the result of Balderesch and Lipari [2] within 5% for/a < 0.7. The experimental value of ~ is 0.613, which was determined by analysis of the electronic Raman scattering and infrared absorption spectra of the shallow acceptors in ZnTe [3]. We obtain IAa/Asl 2 = 0.185 for this value. The Bohr radii as and a D corresponding to/a = 0.613 are 13.25 and 3.26 A, respectively, where we take the effective Bohr radius a = 21.9 A, [8]. When the Bohr radius of the donor Is-state, ae and the D - A distance R is greater than the effective Bohr radius of the acceptor, the exponential function of integrand in equation (3) is approximated as follows exp ( - - l lr -- R,) - exp ( l ( z --R)) ,

(7)

where the acceptor site is at the origin and the donor site has the Cartesian coordinates (0, 0, R). The overlap integral is easily calculated by use of equations (4)-(7). In the calculation we use a function 6/15rr(3 cos20 -- 1) as the angular part of d-like function in equation (4) for simplicity, though the function derived group theoretically should be used. The calculation showed that the contribution of the d-like function to the integral ID is less than that of the s-like function 1s and does not exceed twenty percent o f I s. Hence we neglect the contribution of the d-like function here. The result has, in this case, the same form as that derived by other authors [9, I0], r(R) - t =

rot exp (---~e:)

m2h2ca [Mev[2 {A s " ~ =8aan 7"0' - 4e2h~en ~ a , ) 2 }2,

(8)

(9)

where a = a e / a s . * In ZnTe the central cell correction to the acceptor 1S state is large: the ratio of central cell correction AE to EM is 0.2 (Li) ~ 0.4(As), where EM is the binding energy of the ground state calculated in the effective mass approximation. No appropriate theory to obtain the corrected wavefunction is available when the central cell correction is so large. In the calculation o f / , equation (3) we have chosen the wavefunction for which its form is retained and the Bohr radius is corrected. The corrected Bohr radius of the s-like wavefunction, a, is derived by assuming that the Bohr radius is inversely proportional to the binding energy of acceptors, i.e. a =/]E,~1. The proportionality constant 13is determined so that the binding energy obtained from the variational method (EM = 51.5 me'v) gives the effective Bohr radius of the s-like function (13.25 A.). The momentum matrix

1291

element Mev is evaluated from the formula by Adams and Landsberg, which gives [Meol2 = m x 2.84 eV. In Figs. 1 and 2 experimental decay time is compared with the calculated one by use of the corrected Bohr radii determined by this method: Parameters used in the calculation are listed in Table 1. Good agreement between observed and calculated values is obtained for the Li acceptor. As shown in Fig. 2, a reasonable agreement is found between the experiment and the calculation for the sample with low As-acceptor concentration, though the experimental values deviate slightly from the calculated curve for large distances. This deviation would indicate that the concentration effect on the decay process still exists in this sample. In view of the fact that the agreement between the experiment and the calculation for the acceptor for which large central cell correction is necessary, we can say that our correction of the Bohr radius and the neglect of the d-like part of the acceptor wavefunction are reasonable for the acceptors with A E / E M < 0.4. Non-exponential feature of the D - A luminescence has been recognized so far by many researchers. Thomas e t al. [9] explained that the pairs are not isolated and the non-exponential decay occurs owing to the parallel paths of the recombination from minority center to other surrounding majority centers which are randomly located. However, our results could not be well fitted by the decay curves calculated from their model. Recently Golka [1 I] proposed a model to explain the non-exponential decay: The energy of the d o n o r acceptor pairs is influenced by the interaction with the neighbouring majority impurities. The energy shift arising from this interaction depends much on the configuration of these impurity complexes. Accordingly one cannot see one to one correspondence between the D - A distance R and the emitted photon energy. As there are various impurity complexes in the crystal and we observe the sum of the emitted light from these complexes, non-exponential feature of decay kinetics will be observed at certain emitted photon energy. The rapid decay component from the impurity complexes will give rise to small decay times at a given emission energy compared to that of the isolated D - A pairs. The probability of finding such impurity complexes will be higher for highly doped samples. When the D - A distance is comparable to or larger than the average inter-impurity distance, number of the pairs will be influenced by surrounding majority impurities. This means that the contribution from the impurity complexes is dominant for the decay process at the lower energies of the D - A pair emission. These considerations are in line with our results on the concentration dependence of the decay time for ZnTe : As, although the mechanism proposed by Thomas et at [9] is not completely ruled out.

1292

DONOR-ACCEPTOR PAIRS IN ZnTe

VoL 38, No. I2_

Table 1. Parameters used in the calculation o f the li[etimes o f the first excited state o f donor-aeeeptor pairs Acceptor

E, (meV)

Corrected Bohr radius as (A)

Binding e n e r ~ Es

Bohr radius ae = eZ/2eE~

a

58.5 60.2 73.5

11.6 11.2 9.2

18.4 18.4 18.5

39.7 39.7 39.4

0.292 0.29 0.233

Binding energy ZnTe : Li ZnTe : P ZnTe : As

Donor

= asia e

Effective mass values of the acceptor binding energy and Bohr radius a s are 51 meV and 13.25 A, respectively, n = 2.7. Another possible mechanism that reduces the measured decay times would be the existence of other competing decay channels, e.g. retrap of electrons (holes) by deep levels and non radiative decay process. The decay time constant resulting from the nonradiative process has been introduced by Kamiya and Wagner to explain the deviation of the experimental value from the calculation for the D - A recombination in GaAs at longer D - A distance [I 2]. For phosphorus doped samples, the experimental decay time showed a close agreement with the calculation for the pairs with distance less than 110 A. The decay time for the impurity concentration of ~ 5 × 1016cm -3 was slightly larger than that of ~ I0 ~ cm-3. However the marked difference in the decay time as in the As doped samples was not found for these two sampies. This result suggests that the deviation of the decay time from the calculated one as was found in d o n o r phosphorus acceptor pairs with R > 110 A is predominantly due to the existence of other unknown decay channels in these samples. The experimental decay times were almost independent of excitation processes. The same decay time was obtained within experimental errors for the selective excitation of {D(ls)A(2s)} and {D(2s)A(1 s)} states and also non-selective excitation by the light with aboveband-gap energy. This result indicates that the lifetime for the transition from the excited state to the ground state within donors or acceptors is shorter than that for the first excited state of D - A pairs, {D(ls)A(ls)}. This conclusion is consistent with the recent observation of the saturation of the D - A pair emission under the selective excitation at the high intensity levels [ 13]. In summary the calculated decay times for the D - A pair recombination agree with the measured values. In the calculation we use a variational function of the acceptor 1S-state, for which the central cell correction is

taken into account. As the calculated decay times are quite sensitive to the spatial extent of the wavefunction, i.e. the Bohr radii, decay time measurements will be useful to obtain inforamtion about the wavefunction of shallow impurities.

Acknowledgement - The authors express their sincere thanks to Professor S. Shionoya and A. Mitsuishi for their support and encouragement during the course of this work. The Kurata foundation is gratefully acknowledged for its grant to one (S.N.) of the authors. We wish to thank Mr. K. Yamashita for calculating the variational wavefunction. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

A. Baldereschi & N.O. IApari, Phys. Rev. B8, 2697 (1973). A. Baldereschi & N.O. Lipari, Phys. Rev. B9, 1525 (1974). S. Nakashima, T. Hattori, P.E. Simmonds & E. Amzallag, Phys. Rev. BI9, 3045 (1979). S. Nakashima, T. Hattori & Y. Yamaguchi, Solid State Cornmun. 25, 137 (1978); S. Nakashima & Y. Yamaguchi, J. Appl. Phys. 50, 4958 (1979). H. Venghaus, P.J. Dean, P.E. Simmonds & J.C. Pfister, Z. Physik B30, 125 (1978). M.J. Adams & P.T. Landsberg, Gallium Arsenide Lasers (Edited by C.H. Gooch), p. 5. WileyInterscience, London (1969). M. Sondergeld, Phys. Status Solidi [b) 81,253 (1977). S. Nakashima & K. Yamashita (to be published). D.G. Thomas, J.J. Hopfield & W.M. Augustiniak, Phys. Rev. 140, A202 (1965). R. Dingle, Phys. Rev. 184,788 (1969). J. Golka, Solid State Commun. 28, 401 (1978). T. Kamiya & E. Wagner, J. Appl. Phys. 47, 3219 (1976). S. Nakashima & A. Nakamura, Proc. 15th In t. Conf. Phys. Semicond. Kyoto 1980, J. Phy~ Soc. Japan 49 (1980) Suppl. A, p. 193.