V. A. TYACAI et al.: Electroreflectanoe of InN Semimetallic Thin Films 589

phys. stat. sol. (b) 103, 589 (1981)

Subject classification: 14.3.1 and 20.1; 22.2

Institute of Semiconductors, Academy of Sciences of the Ukrainian SBR, Kiev1)

Electroreflectance of InN Semimetallic Thin Films BY V. A. TYAGAI~, 0. V. SNITKO, A. M. EVSTIGNEEV, and' A. N. KRASIEO

Plasma electroreflectance spectra (1.2 to 2.2 eV) and the bias dependence of capacitance are presented for InN semimetallic (N z 3 x 1020 cm-3) thin films. The interference patterns in the electroreflectanoe spectra are analysed and grouped into two types according to the form of the electroreflectance undulations. From capacitance measurements the Fermi energy is determined to EF = (0.4 f 0.1) eV. The contribution of Friedel oscillations to the capacitance is also discussed.

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1. Introduction

I n a normal semiconductor, the electroreflectance (ER) effect usually appears to be due to the modulation of the combined density of states [l]. For metals, on the other hand, previous ER measurements [2] have indicated a significant contribution from the modulation of the electron plasma parameters caused by the penetration of the external electric field into the metal. However, in metals the plasma contribution to the ER is small. I n some instances, it is also obscured by the field-modulated specific ionic absorption a t t,he metal-electrolyte interface [3]. Because of these difficulties, it seems worthwhile to extend the plasma ER measurements to semimetals and heavily doped semiconductors. Such measurements were first reported in a paper by Zook [a] in which the plasma ER of SrTiO, was observed.

It is the objective of this paper to discuss the results of a series of experiments designed to observe the plasma ER in InN thin films. Relatively little data are avail- able on the optical properties of this 111-V compound semiconductor which is character- ized by a band gap of about 2.05 eV and a nearly metallic electron concentration of No = 3 x 102O cm-,. A second motivation for the present work is t o understand and categorize the interference patterns that are observed in the ER spectra of thin films.

2. Experimental

The samples used in the experiments were hexagonal polycrystalline InN films with a carrier concentration No = (2.5 to 3.3) x 1020 cm-, and a mobility p = 20 cm2/Vs, deposited onto fused-quartz substrates by means of reactive cathode sputtering similar to that described in [5 ] . As shown in a separate paper [GI, the high-frequency dielectric constant for InN E~ = n: = 9.3, the extinction coefficient x = 0.05 to 0.1

1) Prosp. Nauki 115,252 028 Kiev 28, USSR.

590 V. A. TYAGAI, 0. V. SNITKO, A. M. EVSTIGNEEV, and A. N. KRASIKO

(in the spectral range A = 0.8 t o 1.0 pm), and the optical effective mass for electrons m&t = O.llm,. The film thicknesses were obtained from multiple-beam interference fringe measurements and ranged from 0.3 to = 2 pm. The ER measurements were made by the electrolyte method in a quartz electrolytic cell containing a 1 NKC1 aqueous solution. For contacts, InGa eutectic insulated from the electrolyte by a purified paraffin layer was deposited on the film surface, apart from the surface being studied. The capacitance measurements were done with a bridge in the same electrolytic cell. They revealed the existence of an appreciable dispersion in the com- ponents of the film impedance for f >. 10 kHz which were recognized as being due to the surface distribution of the film resistance. This may be overcome by using elec- trodes in the form of a narrow rectangle (1 to 2 mm wide, 10 to 20 mm long) with electrical contacts attached to the long sides. At any rate, for such a geometry the dispersion was scarcely noticeable in the frequency range f = 5 to 100 kHz.

3. Results and Discussion 3.1 Capacitance measurements

I n order to derive the space-charge layer (SCL) width as well as some other surface parameters needed to quantify the ER data, it is of interest first to discuss the C-U curves of the semimetallic films studied. Typical data are illustrated in Fig. 1 where it is seen that a straight line can be drawn through the points. The capacitance decreases as the sample becomes more and more positively charged. This behaviour is qualitative- ly similar to what has been known for the Schottky depletion layer at the surface of an n-type semiconductor, but the capacitance per unit area in our case is about the same in magnitude as that of the Helmholtz layer (C, = 20 to 40 pF/cm2 for metals). The effective width of the SCL as evaluated in the approximation C I , , ~ < C, is d’ = ~ / 4 n C iz 10 d.

For further analysis we make use of the well-known one-dimensional screening theory of Thomas and Fermi. If we assume no thermal smearing in the electron distri- bution function (EF > kT), it is easy to show that with an accuracy to the second order in U .

Fig. 1

lo-’ 100 10’ 10‘ Y-

Fig. 2

Fig. 1. Measured C-U curve for InN films. Modulation frequency f = 30 kHz

Fig. 2. Quantum correction to the capacitance versu8 y = h ~ / 2 k ~

Electroreflectance of InN Semimetallic Thin Films 591

where CTF = &/4nLTF, LTF = I/dF/6nN,e2 is the Thomas-Permi screening length, m& the density of states mass, and U - Uo the band bending inside the semimetal. Assuming a parabolic band, one may then evaluate the Fermi energy from the slope of the line in Fig. 1 giving

I n this way we obtain EF = (0.4 &- 0.1) eV for No = 3 x 1020 ~ m - ~ . One comment about the validity of the Thomas-Permi screening theory is important.

In assuming that i t is appropriate, we assume that the contribution from quantum effects is negligible. Otherwise, the SCL width may be significantly increased owing both to the reduction in the electron density near the surface as well as t o the oscillat- ory behaviour in the plasma screening due to the finite Fermi sphere radius (Friedel oscillations [7]). These oscillations can occur if 2kFLTF < 1, i.e. if the de Broglie wavelength of the electrons a t the Fermi surface is long compared to the screening length. The contribution of the Friedel oscillations to the capacitance can be calculated theoretically using the wave-vector-dependent dielectric function

where e0 is the static dielectric function of InN, A T F = L& x = q / 2 k , , and kF = = ( 3 ~ 2 N , ) ~ / 3 is the Fermi wave number. Neglecting the “tail” in the electron density outside the semimetal one obtains that in the near proximity of the flat band the con- tribution of the Friedel oscillations to the capacitance is given by

00

1 *a&;: 0) , (4)

CTF - 0

Cqllant co --

dq q2&TF(q)

0

where &TF(q) = &,(I + &/q2) and Cquant is the capacitance of a semimetal including the Priedel oscillations. Fig. 2 presents numerical results for CTF/Cquant plotted against y = &F/2kF. As one can see, for typical InN parameters (kF = 2 x lO’cm-l, LTF = 7 A, y ;2: 0.3) the quantum correction for the Friedel oscillations is within 6%.

3.2 Electroreflectance measurements

As shown in Fig. 3, in typical ER spectra of thin InN films oscillatory patterns are observed which correlate with those in the “static” reflection spectra. The important conclusion to be drawn from the inspection of Fig. 3 is that the ER spectra obtained may be classified into two categories according to the form of the ER undulations: (i) ER spectra with relatively symmetric unipolar peaks occurring practically a t the same energies as those in the “static” reflection spectra (Fig. 3a) ; (ii) ER spectra with asymmetric alternating-sign peaks occurring a t a different set of energies than those of reflection. Note that in this case the peaks in R usually appear to be very close to the ER zeroes (Fig. 3b).

The effect of interference on plasma ER spectra has been first demonstrated by Zook [4] who has explained this as a result of an additional reflection of light from the back side of a Schottky depletion layer. This situation, however, is not expected to occur

V. A. TYACAI, 0. V. SNITKO, A. M. EVSTIGNEEV. and A. N. KRAYIKO 592

- t ’ Y 9 * o 2

-z

-7 1

0

-1

b

1 1 1

22 26 2.0 hwlelll-

0.2

%

0.1

I I I I I 22 23 14 25

hwfeW- Fig. 3 Fig. 4

Fig. 3. Measured ER spectra for InN films. a) Film thickness d = 1.6 pm, electron concentrat,ion No = 2.6 x 1020 bias voltage U = -0.3 V, modulation AU = 100 mV, b) d =-- 0.3 pm, hi, = 3.3 x 1020 ~ m - ~ , U = -0.2 V, AU = 100 mV. Arrows in the figure represent the position of the interference peaks in the reflection spectra

Fig. 4. a) Spectral dependence of the reflectance of InN films compared with the b) to e) cal- culated logarithmic derivatives of the reflectance. Film thickness d = 1.7 pm. The values of n and x are 3.05 and 0.0706, respectively, and were chosen to fit the reflectance curve (solid line) to the experiment (circles)

in the present case since the criterion for such an interference is not fulfilled due to the small value of the screening length. Since the period of oscillations appears to be a func- tion of the total film thickness rather than of the SCL width, we may conclude that the undulations in Fig. 3 arise from the electromodulated interference in multiple reflection in the film. The phenomenological treatments of the modulated multibeam interference [8 to 111 are usually based on the general theory of the propagation of light in layered inhomogeneous media [12]. According to this theory the relative modu- lation of the reflectivity of a thin absorbing film is given by

where rl = [(nl - ,n)2 + x 2 ] / [ ( n , + n)2 + x 21 and pl = arctan2x nl/(n2 + x 2 - n f ) are the Fresnel coefficient and the phase shift for the reflection at the electrolyte-InN interface, respectively, n, is the refractive index for the electrolyte and rp = 2nnd/A the phase shift for the transmission of light through the film. In Fig. 4 the spectral

Electroreflectance of InN Semimetallic Thin Films 593

dependences of logarithmic derivatives of reflectivity are shown which were computed using the formulas given in [la]. Because of the relatively small photon energy range involved in the ER measurements, in calculating the derivatives we have assumed the values of n and x to be constant. They are derived from a fit of the theoretical curve R(Aco) to the experimental one and given in the figure caption. We note that both the electromodulation of the reflectivity at the electrolyte-film interface and the electro- absorption of light in the film lead to interference patterns similar to those of Fig. 3a, whereas the modulation of the phase parameters allows one to explain the interference undulations shown in Fig. 3 b. However, the electroabsorption effect may practically be ruled out as the SCL width is very small. For the same reason, the phase shift modu- lation for the transmission of light through the film may be neglected as well. Thus, we conclude that the interference patterns in the ER spectra obtained in the present measurements are caused by the modulation of reflectivity and/or of the phase shift for the reflection a t the electrolyte-film interface. For these mechanisms, the ER is given by

where (x and /3 are the Seraphin coefficients for an electrolyte-semi-infinite film interface [l],

W

(7) A&* = - 7 Aa(x) exp (T)dx 4niiix

0

is the effective change of the dielectric function including the averaging over the SCL 11131, AE(x) its local change, and ii = n + i x . Note that in the case of InN films deposit- ed onto a quartz substrate, the interference enhancement of the ER ( a h Rli3 In r?)max= = 2.8.

We next consider the question of the origin of the electro-optic modulation. An important feature is that this is non-resonant in the spectral range hm < 1.8 eV. Since such a behaviour is characteristic of plasma ER for energies tzw > Amp, the latter assignment seems natural, Then, in the classical Drude approximation, the change of the local dielectric function due to the modulation of the plasma frequency is

Further, making use of the standard approximation for the electron concentration profile,

where A N , = C AV/eLTF is the surface modulation of N , and assuming that spectral range for which an intensive interference structure exists, one obtains

AR R AP, 9 -=---

where ;I, = Znc/wp. For typical InN parameters given above and for modulation AU = 100 mV, the contribution of the modulation in r, t o ER is ( A R l R ) , = 1.4 to 4.8 x

An unusual feature of our ER spectra is the small contribution from the interband transitions to ER. Many of the samples show no structure in the ER spectra in the

This estimation agrees quite well with the experiment (Pig. 3a).

594 V. A. TYAGAI e t al. : Electroreflectance of InN Semimetallic Thin Films

t - 0 - s 2 z

- I

-2

Fig. 5. Measured ER spectrum of InN films (d = 1.7 pm, No = 3.3 x 1020 ~ r n - ~ ) demonstrating the ab- sence of E R structure associated with the Franz- Keldysh effect. Bias voltage U = -0.4 V, modulation A U = 700 mV -

- I I I

spectral range from 2.0 to 2.2 eV (see Fig. 5) in which the optical absorption edge occurs. For these samples the appearance of the interband absorption manifests itself only in a progressive damping of the interference oscillations in the ER spectrum. I n several of our films, however, we have succeeded in obtaining a small ER signal associated with the Franz-Keldysh effect and observed in the form of an inflection or a broadened peak on the high-energy side of the interference structure in the EB spectrum. These data yield a threshold energy E, = 1.9 to 2.0 eV and a broadening parameter r of 0.15 to 0.20 eV, values which are in good agreement with those obtained from the absorption measurements [GI.

References

[l] B. 0. SERAPHIN, in: Semiconductors and Semimetals, Vol. 9, Ed. R. K. WILLARDSON and A. C.

[2] J. FEINLEIB, Phys. Rev. Letters 16, 1200 (1966). [3] J. D. E. MCINTYRE, Surface Sci. 37, 658 (1973). [4] J. D. ZOOR, Phys. Rev. Letters 20, 849 (1968). [5] K. OSAMURA, S. NAKA, and Y. MURAKAMI, J. appl. Phys. 46, 3432 (1975). [6] V. A. TYAGAI, A. M. EVSTIGNEEV, A. N. KRASIKO, A. F. ANDREEVA, and V. YA. MALAKHOV,

[7] J. M. ZIMAN, Principles of the Theory of Solids, Cambridge University Press, Cambridge

[8] E. SCHMIDT, J. appl. Phys. 40, 2671 (1969). [9] D. E. ASPNES, J. Opt. SOC. Amer. 63, 1380 (1973).

[lo] V. K. SUBASHIEV, Surface Sci. 37, 947 (1973). [ I l l M. J. GELTEN and J. H. P. CASTELIJNS, phys. stat. sol. (b) 49, K5 (1972). 1121 M. BORN and E. WOLF, Principles of Optics, Pergamon Press, Oxford/London/Edingurgh/

[13] D. E. ASPNES and A. FROVA, Solid State Commun. 7, 155 (1969).

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(Received Xeptember 15, 1980)