J. Phys. D: Appl. Phys.33 (2000) 901–905. Printed in the UK PII: S0022-3727(00)09357-8

Photoreflectance study in the E 1 andE1 + ∆1 transition regions of ZnTe

Akio Kaneta and Sadao Adachi

Department of Electronic Engineering, Faculty of Engineering, Gunma University, Kiryu-shi,Gunma 376-8515, Japan

Received 8 November 1999, in final form 14 February 2000

Abstract. Photoreflectance spectra have been measured to determine theE1 andE1 +11

energies in ZnTe at temperaturesT between 77 and 300 K using an Ar+-ion laser as amodulation light source. The measured photoreflectance spectra can be successfullyexplained by an excitonic line shape. The temperature dependence of theE1 andE1 +11

critical-point parameters (energy, amplitude and broadening parameter) have been analysedusing the Varshni equation and an empirical expression of the Bose–Einstein type.

1. Introduction

Zinc telluride (ZnTe) is a wide-band-gap II–VI semiconduc-tor (Eg ∼ 2.25 eV at 300 K) crystallizing in the cubic, zinc-blende structure. This material is promising for application asa purely green light-emitting diode. Since optical responseis of great importance for many device applications, manyefforts have been made to obtain optical response and, con-sequently, to determine the optical constants of ZnTe [1]. Re-cent spectroellipsometry (SE) studies on ZnTe have proven tobe useful for determining the optical constants and deducingthe critical-point (CP) parameters in this material [2–6].

Modulation spectroscopy is a popular means ofanalysing CP structures in semiconductors [7]. Photore-flectance (PR) is one of a class of electro-modulation tech-niques and is known to be a useful non-destructive andcontactless technique for the characterization of semiconduc-tors and their microstructures. It can yield sharp CP structuresand can also be very sensitive to surfaces or interfaces [8].

Some modulation spectroscopies, such as electrore-flectance (ER) [9, 10], thermoreflectance (TR) [11, 12],wavelength-modulated reflectance [13–16] and wavelength-modulated piezoreflectance (PzR) [17] have been used to in-vestigate the optical properties and CP structures of ZnTe.More recently, Choet al measured PR spectra in theE0-gap region of ZnTe to characterize the surface built-in elec-tric field in the ZnTe/GaAs(100) heterostructure. An Ar+-ion laser was used as the modulation source. They founda remarkable bias illumination effect of the He–Ne laser.This effect is, namely, that the PR intensity under He–Nelaser bias illumination is much stronger than without the biasillumination, and was explained by a competitive process inthe direction of the modulated electric field between the deeptrap levels and the band-to-band transitions. This [18] is theonly paper in which PR measurements have been carried outon ZnTe.

In this paper we measure the PR spectra in theE1 andE1 + 11 transition regions of ZnTe atT between 77 and300 K. The PR spectra were measured using an Ar+-ionlaser as a modulation light source. The obtained spectraare analysed using a standard-critical-point (SCP) line shapemodel [19]. The dependence of the CP energy onT iscommonly described by the empirical equation proposed byVarshni [20]. An alternative approach was suggested by Vinaet al [21], who considered an empirical expression of theBose–Einstein type. TheE1 andE1 + 11 CP parametersagainstT determined for ZnTe are analysed using these twoempirical formulae. This is the first report on the precisedetermination of the temperature dependence of theE1 andE1 +11 energies for ZnTe.

2. Experimental details

The ZnTe single crystal used in this study was grown by theconventional Bridgman method, and was not, intentionally,doped. The crystal was mechanically polished with 0.05µmAl 2O3 powder, followed by chemical polishing with asolution of Br2 in methanol and finally rinsed with deionizedwater [3].

The experimental set-up for PR measurement wasessentially the same as that described in the literature [22].The sample was mounted in a metal, liquid N2 cryostatequipped with quartz glass window. The 488.0 nm line ofan Ar+-ion laser (NEC GLG3110) chopped at 525 Hz wasused as the modulation light. The laser beam intensity wasabout 2 kW cm−2 at the sample position. The probe lightfrom a 150 W xenon lamp was irradiated in near normalon the sample surface. The PR spectra were measured in the3.0–4.8 eV photon-energy range using a grating spectrometer(JASCO CT-25C) and a photomultiplier tube (HamamatsuR375). A cut-off filter, to pass only short wavelengths below400 nm, was used to block the laser light scattered from thesource.

0022-3727/00/080901+05$30.00 © 2000 IOP Publishing Ltd 901

A Kaneta and S Adachi

3. Results and discussion

Modulation spectroscopy, such as PR and ER, measures thechange in the complex dielectric function,ε(E) = ε1(E) +iε2(E). The effect on reflectivityR of the dielectric constantchanges1ε1 and1ε2 induced by an external modulationparameter (M) can be given by [7, 23]

1R

R= α1ε1 + β1ε2 (1)

where the fractional coefficientsα andβ are functions of thephoton energyE = hω and their sign and relative magnitudedetermine the results of analysis in the different spectralregions [7, 23]. The functional form of1ε1 and1ε2 can becalculated provided that the form of perturbation, dielectricfunction and CP type are known.

WhenM does not destroy the translational invariance ofthe crystal, the change inε is given by the first derivative ofthe unperturbed dielectric function:

1ε = ∂ε

∂M1M ≈ ∂ε

∂Eg

dEgdM

1M +∂ε

∂0

d0

dM1M (2)

whereEg and0 are the CP energy and lifetime broadeningparameters. This is the case for TR and PzR.

If the modulating electric fieldM = ξ , as in ER andPR, destroys the translational symmetry, it can be shownthat the low-field modulation spectrum is related to the thirdderivative ofε:

1ε = (h�)3

3E2

d3

dE3(E2ε) (3)

with(h�)3 = e2h2ξ2/8µ (4)

whereµ is the reduced interband effective mass. For amoderate built-in field, the Franz–Keldysh effect dominatesthe ER response in theE0-edge region [7].

Figure 1 shows the TR and PR spectra for ZnTe measuredat T = 300 K. In the TR measurement, temperaturemodulation was achieved by passing a pulsed electric currentat ∼5 Hz (square pulses with a 50% duty cycle) througha Au film heater deposited on a sapphire substrate bysputtering [24]. Also shown in figure 1 is the normal-incidence reflectivity spectrumR for ZnTe calculated fromexperimentalε(E) data using

R = (ε21 + ε2

2)1/2 − [2ε1 + 2(ε2

1 + ε22)

1/2] + 1

(ε21 + ε2

2)1/2 + [2ε1 + 2(ε2

1 + ε22)

1/2] + 1. (5)

The experimentalε(E) data used in equation (5) weredetermined by SE [1, 3].

As seen in figure 1, the dominant peaks in theRspectrum are due to theE1 andE1 +11 transitions. Thesetransitions occur along the〈111〉 direction or at the L pointin the Brillouin zone (E1: 34,5 → 36 or L4,5 → L6;E1 + 11: 36 → 36 or L6 → L6) [1, 3]. The PRtechnique is understood to strongly enhance the changes inreflectivity R. The third-derivative nature represented byequation (3) is the reason why the PR spectrum is sharperand more richly structured than the conventionally measured

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Figure 1. ReflectivityR, TR and PR spectra for ZnTe at 300 K.The normal-incidence reflectivityR is obtained from experimentalSEε(E) data using equation (5).

reflectivity spectrumR or first-derivative spectroscopies,such as TR and PzR.

The PR spectra can be usually analysed using the SCPmodel. This model is simply written as [19]

1R

R= Re

[ p∑j=1

Cjeiθj (E − Egj + i0j )

−nj]

(6)

wherep is the number of the spectral functions to be fittedandC, θ , Eg and0 are, respectively, the amplitude, phaseangle, CP energy and lifetime broadening parameter.n refersto the type of optical transitions in question:n = 2, 2.5and 3 for an excitonic transition, a three-dimensional one-electron transition and a two-dimensional (2D) one-electrontransition, respectively. The phase angleθ accounts forequation (1) as well as for the influence of a non-uniformmodulation field.

Figure 2 shows the PR spectra for ZnTe measured atthree different temperatures,T = 90, 150 and 300 K. The CPstructures observed atE ∼ 3.5 eV (E1) and∼4 eV (E1 +11)are successfully fitted using equation (6) and assuming anexcitonic transition model (n = 2).

Optical spectra at theE1 andE1 +11 regions of someIII–V semiconductors become sharp when the temperature islowered. Such spectral change cannot be explained withinthe framework of the one-electron approximation. This factclearly suggests a contribution of the 2D-excitonic transitionsat theE1 andE1 +11 edges [25]. The excitonic effects areusually stronger in II–VI semiconductors than in III–V ones.Petroff and Balkanski [26] analysed experimentally obtainedreflectivity spectra of some II–VI semiconductors (ZnTe,ZnSe and CdTe) and found, in theE1 andE1 +11 regions, astronger exciton peak with extremely weak one-electron CPstructure for ZnTe and CdTe and a strong exciton peak for

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Photoreflectance study of ZnTe

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Figure 2. PR spectra for ZnTe obtained at three differenttemperatures,T = 90, 150 and 300 K. The full curves representthe best fits of the data to equation (6) assuming an excitonicmodel (n = 2). The vertical arrows indicate the 2D-excitonpositions as evaluated from the SCP analysis.

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Figure 3. Temperature dependence of the 2D-exciton energies(E1 andE1 +11) for ZnTe as evaluated from the SCP analysis(full circles). The open circles represent the literature values. Thebroken and full curves are calculated from equations (7) and (8),respectively. The fit-determined parameters are listed in table 2.

ZnSe only. Our model-dielectric-function analysis on SE-derivedε(E) spectra also indicated the strong 2D-excitoniceffects at theE1 andE1 +11 CPs in these semiconductors[2, 3, 27–29].

Figure 3 plots theE1 andE1 +11 2D-exciton energiesagainstT determined from the SCP fits (full circles). Theopen circles represent the literature values [4, 6, 9, 30–38].

Table 1. Values of theE1 andE1 +11 CP energies for ZnTe. Thetechniques used are defined in the text except, here, A denotesabsorption and R denotes reflectivity.

Temper- CPature(K) E1 (eV) E1 +11 (eV) Technique Reference

20 3.66 4.19 A [31]77 3.71 4.28 R [33]

3.70 4.27 R [35]78 3.64 4.18 A [31]90 3.750 4.320 PR a

3.68 4.25 R [37]100 3.745 4.320 PR a

110 3.740 4.320 PR a

120 3.735 4.310 PR a

130 3.730 4.305 PR a

140 3.725 4.300 PR a

150 3.720 4.290 PR a

180 3.700 4.285 PR a

200 3.57 4.14 A [31]210 3.685 4.270 PR a

240 3.66 4.25 PR a

270 3.64 4.22 PR a

293 3.60 4.17 R [37]3.629 4.221 SE [4]

295 3.58 4.14 R [33]3.52 4.10 A [32]

297 3.52 4.10 A [31]3.64 4.23 ER [9]3.57 4.13 R [30]

300 3.58 4.16 R [35]3.62 4.20 PR a

3.623 4.219 SE [6]3.58 4.18 R [34]3.58 4.16 R [36]3.6 4.15 R [38]

a Present study.

These were determined from the fundamental reflectivity[30, 33–38] or optical absorption measurements [31, 32]. TheER technique was used in [9]; however, no detailed CP fitanalysis was performed. In table 1 we summarize all thesedata.

Traditionally, temperature variation of the band-gapenergies is discussed in terms of Varshni’s formula [20]

Eg(T ) = Eg(0)− αT 2

T + β(7)

whereEg(0) is the band-gap energy atT = 0 K, α is inelectronvolts per kelvin andβ is proportional to the Debyetemperature of the material (in kelvins). The broken curvesin figure 3 show the fitted results of our experimental data toequation (7). The fit-determinedEg(0), α andβ values arelisted in table 2.

Vi na et al [21] proposed a new expression for thetemperature dependence of the band-gap energies by takinginto account the Bose–Einstein occupation factor

Eg(T ) = EB − αB(

1 +2

e2B/T − 1

)(8)

where the parameter2B describes the mean frequencyof the phonons involved andαB is the strength of theelectron–phonon interaction. Vinaet al [21] suggested that

903

A Kaneta and S Adachi

Table 2. Values ofEg(0), α andβ (equation (7)) and those ofEB , αB and2B (equation (8)) for ZnTe (776 T 6 300 K).

Eg(0) α β EB αB 2B

CP (eV) (10−4 eV K−1) (K) (eV) (meV) (K)

E1 3.772 9.50 260± 60 3.859 97.7 260± 20E1 +11 4.345 8.80 260± 60 4.427 91.0 260± 20

Table 3. Values of∂Eg/∂T nearT ∼ 300 K for ZnTe (in10−4 eV K−1).

CP

E1 (eV) E1 +11 (eV) Source

−7.45 −6.90 (9)−7.06 −6.58 (10)−6.5 [16]−5.0 [30]−5.2 −4.1 [32]−6.0 −6.4 [33]−5.9 −5.9 [35]−2.5 −1.4 [39]

this expression is more palatable than equation (7) from thetheoretical point of view [21]. The full curves in figure 3represent the fitted results of the data to equation (8). The fit-determined parametersEB , αB and2B , are listed in table 2.We can conclude in figure 3 that equations (7) and (8) showequally good agreement with the experimental data in thistemperature range. The spin–orbit splitting energy is alsofound to be independent ofT (11 = 0.570 eV).

Differentiating equations (7) and (8) with respect toT ,one obtains

∂Eg(T )

∂T= −α

(2T

T + β− T 2

(T + β)2

)(9)

and∂Eg(T )

∂T= −2αB

2B

T 2

e2B/T

(e2B/T − 1)2. (10)

The temperature coefficients∂Eg/∂T for ZnTe obtainedfrom equations (9) and (10) are listed in table 3, togetherwith those obtained from the literature [16, 30, 32, 33, 35, 39].Our obtained values are found to be slightly larger than theliterature values [16, 30, 32, 33, 35].

We plot, in figure 4, the temperature variations ofCand0 at theE1 andE1 + 11 CPs of ZnTe. The amplitudeparameterC in the zinc-blende-type semiconductors can betheoretically estimated with the following simple expressions[21, 40]:

C(E1) ∝ 44E1 + (11/3)

a0E21

(11a)

C(E1 +11) ∝ 44E1 + (211/3)

a0(E1 +11)2(11b)

wherea0 is the lattice constant in Ångstroms andE1 and11

are in electronvolts. The parameterC is, thus, thought to beof the order of the thermal expansion of the material. Then,it can be safely assumed to be independent ofT . Indeed, thepresent results confirm this simple assumption (see figure 4).

The amplitude ratio can be written, from equation (11),as

C(E1)

C(E1 +11)≈ E1 +11/3

E1 + 211/3

(1 +

211

E1

). (12)

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Figure 4. Temperature dependence of the 2D-exciton amplitude(C) and broadening parameters (0) for ZnTe as evaluated from theSCP analysis. The full curves represents the best-fit result of the0values to equation (13) (see also table 4).

Inserting the E1 and E1 + 11 values (table 1) intoequation (12), we can estimate the amplitude ratio of∼1.25for T ∼ 77–300 K. The experimental data, on the other hand,provided the ratio of∼1.6, independent ofT . The agreementseems to be good in view of the crudeness of the theory used.

The effect of temperature provides not only the shiftof the CP energies, but also the broadening0 of theCP structures. If we grant the electron (exciton)–LO-phonon coupling as the main broadening mechanism, itsparameter value can be described with an expression similarto equation (8) [21]:

0(T ) = 01 +

(00

e20/T − 1

)(13)

where 01 represents the broadening due to temperature-independent mechanisms, such as the Auger process,electron–electron interaction, crystalline imperfections andsurface scattering. This expression ensures a relativelyconstant value of0 from low temperature up to, in manycases, aT ∼ 50–200 K, at which point aT -dependent termin equation (13) becomes discernable, and then increasesnearly proportional toT for high temperature. The fullcurve in figure 4 represents the least-squares fit of the datato equation (13) (see also table 4). For simplicity, we haveforced0 to have the same values between forE1 andE1 +11

CPs.

904

Photoreflectance study of ZnTe

Table 4. Values ofC and0 (equation (13)) for ZnTe betweenT = 77 and 300 K.

0C

CP (×10−6 eV2) 01 (meV) 00 (meV) 20 (K)

E1 8.0 28.0 30.0 260E1 +11 5.0 28.0 30.0 260

4. Conclusions

We have measured the PR spectra in theE1 andE1 + 11

spectral regions (3.0–4.8 eV) of bulk ZnTe single crystalsat temperaturesT = 77–300 K. The measured PR spectrarevealed distinct structures at∼3.7 eV (E1) and∼4.34 eV(E1 + 11). The SCP analysis suggested that the PR lineshape can be successfully explained by the 2D-excitonictransitions over the whole temperature range investigated.The temperature dependence of theE1 andE1 + 11 CPparameters has been determined and numerically analysed.

Acknowledgments

The authors would like to thank Drs T Miyazaki and S Ozakifor their kind advice concerning this work.

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