Four-wave mixing in CdMnTeSe: In crystals

ELSEVIER

Journal

Four-wave B. Koziarska-Glinka”,

of Crystal

Growth

184/185 (1998) 696-700

mixing in CdMnTeSe

:

In crystals

T. Wojtowicza, I. Miotkowskib, J.K. Furdyna”, A. Suchocki”,”

aInstitute of Physics, Polish Academy of Sciences, AL. Lotnikbw 32146, 02-668 Warsaw, Poland b Purdue University, West Lafayette, Indiana 46566, USA ’University of Notre Dame, Notre Dame, Indiana 46556, USA

Abstract It is shown that the four-wave mixing technique can be used as a spectroscopic tool for studying the properties of bistable centers in semiconductors. Two metastable centers with different lattice relaxation energy have been identified in the Cd1 _.Mn,Te, -Se, : In crystal. The power dependence of the FWM signal provides additional support for the “negative-U” model of metastable centers in this material. ‘0 1998 Elsevier Science B.V. All rights reserved. PACS:

74.62.Dh; 61.72.Ji; 42.65.H~

Keywords:

Holography;

Four-wave

mixing; Diluted

magnetic

1. Introduction There has been a sustained interest in bistable centers in semiconductors for many years. The bistable centers are the source of a persistent photoconductivity (PPC) phenomenon in semiconductors, where the exposure of the material to light with photon energy above the photoionization energy threshold at sufficiently low temperatures results in an increase of the carrier concentration that persists for a very long time after the illumination is switched off. The PPC effect is related to the presence of an energy barrier, which separates the deep, localized state of the bistable center from the more

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0022-0248/98/$19.00 ‘c 1998 Elsevier Science B.V. All rights reserved. PII SOO22-0248(97)00553-S

semiconductors;

Metastable

centers

delocalized effective-mass shallow-donor state or band states. The energy barrier arises due to the large relaxation of the lattice (LLR phenomenon). The lattice can undergo rearrangements of various types. It has been established that an interstitialto-substitutional motion of the defect occurs in the case of DX centers in AlGaAs [ 11. Centrosymmetric collapse of the defect neighboring anions is very likely for more ionic CdF2 doped with bistable centers [2,3]. The LLR phenomenon is also responsible for defect bistability in II-VI semiconductors [4]. The value of the energy barrier, that separates the delocalized and localized states, sets the metastability temperature, below which the population of metastable states is persistent. For most of the bistable centers the metastability temperature is below 150 K, except for fairly low, usually CdF2 : Ga. In the latter material the metastability

691

B. Koziarska-Glinka et al. /Journal of Cystal Growth 1841185 (1998) 1596~700

temperature is about 240 K [S]. The localized and delocalized states can have different charge states. The accepted model of the DX-centers in AlGaAs assumes that this center has a negative Hubbard correlation energy, e.g. the localized state captures two electrons, forming a D- state, in contrast to the delocalized one, which is a do state. These states can have also drastically different optical complex polarizabilities due to the differences in the electron-lattice coupling. Therefore, exposure to the light changes not only electrical transport properties of the material but also its absorption coefficient and refractive index. This feature is characteristic of nonlinear optical materials and allows one to use nonlinear optical techniques to study their physical properties. In this paper we present an application of the continuous wave (c.w.) degenerate four-wave mixing (DFWM) technique to study the nature of the metastable centers in Cd, _.Mn,Te, _,Se, : In crystal.

2. Samples and experimental

techniques

The Cdl_,Mn,Tel_,Se, (with x = 0.1 and y = 0.03) crystals were grown by the Bridgman method and they were intentionally doped with indium. They revealed n-type conductivity with room-temperature electron concentration of the order of a few times 1016 cm- 3. The crystals have a direct energy gap of about 1.7 eV [6]. During measurements the crystals were placed in an Oxford CF104 cryostat equipped with a temperature controller. DFWM experiments were performed at a wavelength of 935 nm emitted by a Ti : sapphire C.W. COHERENT model 899 laser. This wavelength coincides with the photoionization spectrum of the localized centers in the crystal. The laser beam was split with a beam splitter into two almost equal intensity “write” beams, which travel equal path lengths before crossing at an angle 0 inside the sample. Their interference forms a sinusoidal pattern that creates a spatial distribution of phototransformed In metastable centers. Due to the difference of the complex dielectric constant when In centers are either in the localized or effective mass states, this population distribution acts as an index-of-refraction grating.

This grating was probed with another beam of the same wavelength as the “write” beams, counterpropagating to one of the “write” beams. The intensity of the “read” beam was always kept below 10% of the intensity of one of the “write” beams in order to minimize the contribution to the FWM signal from the grating formed by the “read” beam with one of the “write” beams and to minimize the grating erasure by the “read’ beam. The scattered beam was detected by a type Sl photomultiplier. The grating scattering efficiency was measured by use of a lock-in technique.

3. Experimental

results and discussion

A strong photomemory effect was observed in magnetization measurements [6] in the sample cut from the same crystal as used in current studies. The magnetization of the crystals increased upon illumination by near-infrared light, which was ascribed to the formation of bound magnetic polarons on shallow centers. The effect was metastable at low temperatures and coincided with the PPC effect simultaneously observed in the sample. The observed results were in agreement with the “negative-u” properties of the In metastable center in CdMnTeSe. Fig. 1 presents the temperature dependence of electrical resistivity of the CdMnTeSe : In sample measured before and after white light illumination for temperatures above

lo-

O.ll~.~'~~~"..'~."~'.'~.~I

0.002

0.01

0.006

0.014

11 T (l/K)

Fig. 1. Temperature dependence Cd0.9Mn0 ITe0,97Se0.03 : In crystal mination at low temperature.

of resistivity of the before (b) and after (a) illu-

698

B. Koziarska-Glinka

et al. J Journal of Crystal Growth 184/185 (1998) 69&700

.

O.lO~

.

I.0

IIT (l/K) Fig. 2. Temperature dependence of the scattering efficiency of : In crystal. a photoionduced grating in Cdo.sMno.,Teo.9,Seo.03 The values of the energy barriers separating metastable and localized states are marked on the graph.

77 K. The illumination, performed at 77 K, was long enough to transform all centers from deep to shallow states. As a result of illumination the sample resistivity strongly decreases. The difference between the resistivity of the sample cooled in darkness and subsequently illuminated reaches about four orders of magnitude below liquid-helium temperature. This difference is smaller at higher temperatures and finally the effect disappears at about 130-140 K. This temperature is defined as a metastability temperature. The PPC effect observed here is a fingerprint of the presence of metastable centers in the material. The scattering efficiency ye of the FWM is described by the Kogelnik formula [7]: y=e

-ad/COsI sin2

XAn d 2 cos c(

+

Aa d sinh’ 4 cos a ’

(1)

where a is the absorption coefficient, Aa and An are the induced changes of the absorption coefficient and the refractive index between peaks and valleys of the grating, respectively, d is the thickness of the hologram and LY. is the Bragg angle. The first term in Eq. (1) describes the contribution to the scattering efficiency from the phase gratings and the second one from the amplitude (absorption) grating. Theoretically, the scattering efficiency from the phase grating could reach lOO%, whereas the maximum scattering efficiency from

the absorption grating cannot exceed 4%. This provides a convenient test for distinguishing the dominating mechanism of grating formation. Fig. 2 shows the DFWM scattering efficiency as a function of temperature. Two peaks of the scattering efficiency are observed at temperatures T1 = 17 K and T2 = 110 K. The absolute value of the scattering efficiency in the peaks reaches 10%. This implies that mainly a phase grating is formed in the crystal and therefore allows one to neglect the contribution of the amplitude grating in the following considerations. The refractive index changes are proportional to the population of the shallow donor or band states. The process of population of the effective mass states under the influence of light can be described by the following rate equation: dN,_ dt

- cN,2 + Zo(N,, - NJ,

(2)

where c is the kinetics parameter, I is the light intensity, g is the photoionization cross section of the deep state and No is the total concentration of the “active” ions. Using this equation we assume that the localized state captures and emits two electrons at the same time since the one-electron localized state of a “negative-U” center is unstable. This is an assumption, which should be well fulfilled at low temperatures at which the measurements were done. We also neglect the thermal emission process from the localized state. It means that the energy barrier for the electron emission from this state is larger than the energy barrier for electron emission from the shallow state. The kinetics parameter, c, is expressed by the formula c(T) = co exp( - AE/kBT). The steady-state following: N

= &a)2 SO

solution

+ 4IoN,,c 2c

(3) of the Eq. (2) is the

- IO (4)

According to the Kogelnik formula (Eq. (1)) the scattering efficiency is approximately proportional to the square of light-induced changes of the refractive index between peaks and valleys of the grating, which, in turn, is proportional to the population of

B. Koziarska-Glinka et al. /Journal oj”Crystal Growth 184118.5 (1998) 696- 700

the delocalized N$

state in the peaks, N$, and valleys,

q x (An)’ 8~ (NrO - NyO)‘.

(5)

In the ideal case, when the intensities of the two “write” beams are exactly equal to each other and provided there is no illumination by incoherent light, the light intensity in the valleys of the grating is zero. In reality, however. there is always some scattered light from the cryostat windows, etc., and the light intensities of the “write” beams are not exactly equal. Therefore, at temperatures below the metastability temperature, the residual light in the valleys of the gratings transforms the bistable centers into the delocalized state. At sufficiently low temperatures the bleaching of absorption of the localized state is complete in the whole illuminated region, provided that illuminaton is long enough. Thus, there is no grating under steady-state conditions. That is the reason why the C.W. scattering efficiency diminishes at low temperatures. At higher temperatures, on the other hand a process of erasure of the grating by thermal emission from the delocalized state takes place. The maximum of the grating efficiency occurs therefore at the temperature for which the rates of thermal and incoherent erasures are equal. For small intensities of light the position of the peak is described by the expression [S]: -AE

T max = kB ln((&

- &)‘~/Noco)

(6)

where AE is the value of the energy barrier separating delocalized and localized state, I, and I, are the light intensities in the peaks and the valleys of the grating, respectively, and kB is the Boltzmann constant. Therefore, by measuring the temperature dependence of the FWM scattering efficiency the value of the energy barrier separating delocalized and localized states can be determined. Thus, the FWM scattering measurements can be viewed as an optical analogue of the classical DLTS technique. The two peaks of the DFWM scattering efficiency observed in our Cd1 _-x Mn,Te, -Sex : In sample are associated with two different bistable centers

699

having different energy barriers separating the metastable state from the ground state. The peak at temperature T2 = 110 K is associated with the center with activation energy of AEB2 = 138 meV. This value has been estimated from the high-temperature slope of the temperature dependence of scattering efficiency (see Fig. 2). This slope is governed by the thermal emission process from the delocalized state. This is an additional, independent method of measuring the energy barrier value. By substituting the rate equation solutions for the peaks and valley of the grating into Eq. (5) one can show that the high-temperature part of the scattering efficiency temperature dependence has a different slope than the low-temperature part. For sufficiently high temperatures the scattering-efficiency is proportional to exp(AE/keT). In contrast to that, the low-temperature part is proportional to exp( -2AE/k,T). This is a direct consequence of the particular form of the rate equation (see Eq. (2)). Another form of the rate equation could result in a different shape of the temperature dependence of the FWM scattering efficiency. The value of the energy barrier obtained with the above method agrees very well with the results of DLTS [9]. Additional support for this value is provided by the temperature dependence of the resistivity (see Fig. 1). The metastability temperature estimated from Fig. 1 is slightly lower than the temperature TZ, for which maximum of the temperature dependence of the FWM scattering efficiency occurs. This behavior is exactly expected from the theory. The second metastable center, associated with the peak of the temperature dependence of the FWM scattering efficiency, which occurs at T1 = 17 K has not been detected in the DLTS experiment. The energy barrier between the delocalized and localized states for this center, estimated from the activation energy of the hightemperature part of the FWM scattering efficiency dependence, is equal to AErr = 12 meV. This value can be slightly affected by the presence of the hightemperature maximum, which overlaps with the low-temperature peak (see Fig. 2). The other consequence of the assumed form of the rate equation is the dependence of the FWM signal on the power of the “write” beams. Nonlinearity of the rate equation results in nonlinear

700

B. Koziarska-Glinka et al. /Journal

dependence of the population of the delocalized states on the power of the light. Therefore, the FWM signal is not proportional to the square of the “write” beam power, as is expected in the case of linear rate equation. The power dependence of the FWM signal in Cd1 _,Mn,Te, _pSeX : In crystal changes with temperature, according to theoretical expectations [7]. This provides an additional support for the “negative-U” model of the bistable centers in this compound [6,9].

of Cystal Growth 1841185 metastability application.

(1998) 696-700

temperature

is required

for practical

Acknowledgements This work was partially supported by Grant 2 P03B 087 09 of the Polish State Committee Scientific Research.

No. for

References 4. Conclusions It has been shown that the four-wave mixing technique may provide important information on the nature of the metastable centers in semiconductors. Two metastable centers with different latticerelaxation energy have been identified in the Cd,_.Mn,Te,_,Se, : In crystal. The values of the energy barrier separating the delocalized and localized states can be estimated from the FWM measurements. The FWM also provides a convenient test to distinguish between the “positive-U” or “negative-U” model of the bistable centers. The Cd, _,Mn,Ter _,Se, : In can be used as a holographic recording material, although a higher

[l] D.J. Chadi, K.J. Chang, Phys. Rev. B 39 (1989) 10063. [2] U. Piekara, J.M. Langer, B. Krukowska-Fulde, Solid State Commun. 23 (1977) 583. [3] J.E. Dmochowski, J.M. Langer, 2. Kalitiski, W. Jantsch, Phys. Rev. Lett. 56 (1986) 1735. [4] D.J. Chadi, C.H. Park, Mater. Sci. Forum 196-201 (1995) 285. [S] A. Suchocki, B. Koziarska, T. Langer, J.M. Langer, Appl. Phys. Lett. 70 (1997) 2934. [6] T. Wojtowicz, S. Kolesnik, I. Miotkowski, J.K. Furdyna, Phys. Rev. Lett. 70 (1993) 2317. [7] H. Kogelnik, Bell System Techn. J. 40 (1969) 2909. [S] B. Koziarska-Glinka, J.M. Langer and A. Suchocki, to be published. [9] T. Wojtowicz. G. Karczewski, N.G. Semaltianos, S. KoleSnik, I. Miotkowski, M. Dobrowolska, J.K. Furdyna, Proc. Int. Conf. on Defects in Semiconductors, Gmunden, 1993, Mater. Sci. Forum, 1433147 (1994) 1203.