exact determination of the real substrate temperature and film thickness in vacuum epitaxial growth...

Vacuum/volume 46/number l/pages 69 to 76/1995

Pergamon 0042-207X(94)E0019-U

Elsevier Science Ltd Printed in Great Britain

0042-207x/95 $9.50+.00

Exact determination of the real substrate temperature and film thickness in vacuum epitaxial growth systems by visible laser interferometry H Sitter, Research Institute for Optoelectronics, Altenbergerstrafie 69, A-4040 Linz, Austria

and

G J Glanner, Johannes Kepler University Linz, lnstitut fijr Experimental Physik, Linz, Austria

and

M A Herman,* Institute of Vacuum Technology, PL-00-24 1 Warsaw, Poland

received 19 January 1994

A concise description of the application of laser interferometric thermometry (LIT) for exact calibration of the process manipulator thermocouple and, thus, for exact determination of the real substrate temperature in a MBE system is presented. A He-Ne laser visible 0.6328 pm light has been used as a probe, and a GaP plane- parallel wafer polished on both sides to an optical finish served as a calibration standard. The behaviour of the substrate temperature in dynamic thermal conditions has been tested experimentally with LIT and a long delay time has been found when the substrate temperature approaches an intended value at cooling or heating processes, after the heating block temperature of the manipulator has been changed. Finally, the experimental procedures of in situ determination of the growing film thicknesses with visible laser interferometry during MBE growth processes have been described for two cases, concerning films completely transparent to the laser light used and films only partly transparent to this light.

1. Introduction

In modern technological systems for molecular beam epitaxy (MBE), ref (l), hot wall beam epitaxy (HWBE), ref (2), or ionised cluster beam deposition (ICBD), ref (3), the substrate wafer is mounted on a specially designed substrate holder. In the simplest case this is a MO block of diameter equal or greater than 25 mm, about 1 mm thick. This substrate holder may be positioned, by using the substrate transfer system, on the heating block of the process manipulator in the deposition chamber, or may be removed from the growth environment to the load-lock chamber and eventually out to the atmosphere. The major requirement for the production of uniform and reproducible thin film structures in vacuum epitaxial growth systems is that the temperature across the substrate is uniform and that it is exactly determined and controlled during the growth process.

Usually, the substrate temperature measurement is achieved using a thermocouple, either in contact with the substrate holder, or carefully positioned in a black-body enclosure situated behind

*Also at: Institute of Physics, Polish Academy of Sciences, PL-02-668, Warsaw, Poland.

the holder. This method suffers, however, from the unavoidable

presence of considerable temperature gradients in the ‘substrate holder heating block of the manipulator thermocouple’ (SHT)

system. These gradients may cause differences as large as 50- 100°C between the real substrate temperature and the thermocouple (as measured) temperature at substrate temperatures of 400&6OO”C, depending on the geometry of the SHT system4.‘.

Therefore, calibration of the thermocouple (as-measured) temperature in relation to the real substrate temperature is indis-

pensable for gaining a correct growth process control feasibility. An infrared pyrometer may be used for direct measurement of

the substrate temperature by viewing the substrate through a viewport, thus allowing calibration of the manipulator ther-

mocouple. However, when there are light reflections from the substrate surface originating from a light source on the same side of the surface as the pyrometer, then the substrate temperature cannot be reliably measured with a pyrometer ; this happens, for example, during MBE growth when an effusion cell of the MBE system is open (the glowing crucible of the cell is the light source). In order to avoid this difficulty we have used laser interferometric thermometry (LIT), refs (5%8), for exact calibration of the manipulator thermocouple and, thus, for exact determination of

69

H Sitter et al: Vacuum epitaxial growth systems

the real substrate temperature in our MBE system. We have used a He-Ne laser visible 0.6328 pm light as a probe and a GaP plane-parallel wafer, 290 pm thick, polished on both sides to an optical finish, as a calibration standard; this considerably simplifies the experimental implementation in comparison to the case of infrared LIT used in silicon UHVH technology’.

In this paper we present a concise description of the performed calibration procedure, starting this with a short introduction to the theoretical foundations. After having calibrated the thermocouple (as-measured) temperature in relation to the real sub-

strate temperature, we have performed a set of measurements concerning the behaviour of the substrate temperature in

dynamic thermal conditions, i.e. when heating up or cooling down the substrate holder. The numerical results of these measurements are presented and discussed. Despite the fact that these numerical data bear no general meaning, as related to a definite geometry of the SHT system in our MBE deposition chamber, we consider them worth publishing. The behaviour tendency of the substrate temperature in the dynamic thermal conditions shown in our experiments is quite general. In any arbitrary technological growth or processing operation performed after changing the intended temperature of the substrate wafer one should exactly determine the real instant substrate

temperature, which even at unexpected long time intervals may differ considerably from the intended temperature. Finally, we describe our experiments in the application of the visible laser interferometry (VLI) for in situ determination of thicknesses of the epilayers of II-VI wide-gap semiconductor compounds grown in our MBE system.

2. General description and theoretical foundations of the LIT technique

The LIT technique is based on precise interferometric measurement of small changes in the optical pathlength within a wafer (usually plane-parallel, polished on both sides to an optical finish) as its temperature changes’. When this technique is applied to semiconductors, an important simplification may be introduced

which is justified by the characteristic feature of these materials, namely, a much greater sensitivity to temperature of the refractive indices n than of the thickness d of the substrate wafers or grown thin films (the temperature coefficients /& = (An/AT)/n,, z 10m4- lo-’ Km’, while PC, = (Ad/AT)/d,, z lO-5-1O-o K-‘, respectively’). Consequently, one may ignore the influence of the thermal dependence of d on the optical pathlength in the first approximation of the evaluations required in this technique.

Using LIT, laser light of wavelength i which is mostly transparent to the substrate (deposited film) illuminates the substrate (film) at a small incidence angle c(, (z 1 ‘). Combination of light reflecting from the top surface of the substrate (film) with the light transmitted through the substrate (film) and reflected off the polished back side of the substrate (the film-substrate interface) causes a so called multiple beam interference”. The intensity of reflected light oscillates in a periodic fashion with increasing temperature as the optical pathlength within the substrate (film) increases because of the increase in IZ and d. One full cycle in the observed reflection-interference oscillations, i.e. in the ‘inter-

ferogram”‘, corresponds to an increase (decrease) in the optical

pathlength of 42~1 at normal incidence.

It should be emphasised that the ‘interferograms’ of the LIT technique need to be calibrated in temperature values, which means that a separate calibration procedure is required through

which the sequential maxima (minima) numbers of the oscillations become ascribed to exactly determined temperatures of the wafer. Once calibrated for a given material, wafer thickness and wavelength, the oscillation curves of the wafer may be used as an absolute temperature standard in any environment. For typical semiconductor wafer thicknesses of 0.2-0.7 mm a full cycle is observed every 2-6°C ref (7). The LIT technique has a precision of f 0.5”C and an accuracy of k 2°C ref (6).

Let us consider a plane-parallel wafer of medium (r) sandwiched between two media (i) and (s) with different refractive indices n, and IZ,~ (Figure 1). Let the electromagnetic wave of

the laser incident on this wafer from the side of medium (i) be represented by an electric field plane wave E(r,t) = E,exp [i(wt-

kr)] with w = 2rf, k = 27-m/&, E,, r and t having the definitions

of angular frequency, wave number, electric field amplitude, spa- tial co-ordinate and time, respectively. Here, n,,fand i., have the usual meanings, namely, refractive index, frequency and wavelength in vacuum. When crossing an interface, e.g. the (i)-(r) interface, this wave will be divided into the reflected wave R,,E

and the transmitted wave T,,E. The reflection and transmission coefficients may be evaluated from Fresnel formulae” :

R, = [sin (CI, - ai)]/[ sin (x1 + cc,)] and (1)

Ti, = [2 sin a,cos a,]/[sin (M, +tiJ], (2)

where s(, and tl, are the incidence and the refraction angles, respectively (Figure 1). Using Snell’s law, n, sin c(, = n, sin a,, one may then write the formulae in the form :

R,, = (nl -n,)/(n, +nr) and (3)

Ti, = 2n,/(n,+n,). (4)

The total intensity of the reflected light incident onto the lens, shown in Figure 1, may be evaluated by summing up the intensities of the constituent beams reflected up and down at surfaces of the water. The general formula

the

\ Rt E, interference pattern

Figure 1. Schematic illustration of the reflection of a laser light wave in a plane-parallel wafer of medium (r) sandwiched between two media (i) and (s) with refractive indices different from n,. The multiple-beam interference pattern is formed in the focus plane of the lens.

H Sitter et a/: Vacuum epitaxial growth systems

R,E = R,,E+ 7;,R,T,,Eexp (ik,2dcosa,)

+TirR,R,,Rr,,T,,Eexp(ik,4dcoscr,)+. (5)

indicates that for each constituent beam of the reflected light the variable part of the phase of the wave E, differs from that of the preceding beam by an amount A, which corresponds to a double transversal of the wafer. Considering the geometry of the ‘wafer- light beams’ system shown in Figure 1 and using Snell’s law one

may calculate that

A = 2 k,dcos ct, = (4rc/&)nr dcos a, (6)

Assuming now, for simplicity, that n,, = nR one may use R,, = R,,, which considerably simplifies equation (5). For p constituent beams of the reflected light

R, = R,, + T,, TriR,i exp (iA) ( 1 + R?! exp (iA)

+ . . . + Rr,2(P-2) exp Lib-WI}. Summing up the geometrical progression one obtains :

(7)

R, = Ri, + TirTriR,, exp (iA)(l- R,z,‘p-‘)

x exp [i(p- l)A]}/[l - R;;exp (iA)],

which takes in the limit of p + cc the form” :

(8)

R, = -R,,[l-(R~i+Tj~Tr,)exp(iA)]/[l-R~exp(iA)].

(9)

Taking into account that the intensity of light is given by the squared absolute value of the amplitude of the light wave, one obtains for the total intensity of the reflected light

IR = (RJXR,E)*

= [2R,,*(l -cos A)EE*]/[l+ RFi4 -2R,,2 cos A], (10)

where the asterisk denotes a conjugate complex quantity. Equation (10) is known in the literature as Airy’s formula for

multiple-beam interference”. It may be written in the simple

form :

IR = C(l -cos A), (11)

when (R,4 - 2R,2, cos A) will be neglected in comparison to one in the denominator; this is justified by the fact that the reflection coefficient is by definition smaller than one. The constant C is

real and it depends on the reflection coefficient R,, of the considered plane-parallel wafer and the intensity of the incident light. One may now conclude that the total intensity of the light reflected from the wafer is a cosine function of the thickness and the refractive index of the wafer and, thus, of the temperature of the wafer. ZR = max if A = 2n(m+ l/2), while IR = min if A = 2nm, where m is an integer. It should be pointed out that

this general conclusion is also valid for the case when n, # n, which has been confirmed by many experimental result?‘.

3. Calibration procedure of the GaP wafer ‘interferograms’

As already mentioned in Section 2, the ‘interferograms’ of the semiconductor wafer used as temperature monitor need to be calibrated in temperature values. In order to get reliable values of the temperatures ascribed to the sequential maxima (minima)

numbers of the ‘interferogram’ oscillations, the calibration procedure should be performed in thermal steady-state conditions. Under these we understand conditions at which temperature

changes occurring during heating-up or cooling-down processes in the calibration procedure are so slow that no changes in the ‘interferograms’ can be recorded when the temperature scan is interrupted. Such conditions have been assured in the calibration system used in our calibration procedure of the GaP wafer ‘inter-

ferograms’. The set-up of the system is shown schematically in Figure 2.

The GaP wafer is placed in a specially designed sample holder made of copper. A uniform temperature distribution over the whole wafer and the measuring thermocouple is ensured by the construction of the holder and Cu-tube in the furnace (Figure 2). The thermocouple is dipped in a heat conducting Ga-In mixture which is in direct contacts with the bottom surface of the wafer. The upper surface of the wafer is in contact with the holder lid which has an opening, 3.8 mm in diameter, in its central part allowing the incidence on and reflection from the wafer surface

of the laser light. During the calibration procedure, the sample holder is pos-

itioned in the central part of the furnace, 630 mm long, in the

quartz-glass tube which is surrounded in its middle part by an additional Cu-tube, as shown in Figure 2(b) ; this ensures a homo- geneous temperature distribution over the whole length of the sample holder.

In the quartz-glass tube a vacuum of about lo-’ mbar is generated by an external pumping unit, what protects the GaP wafer upper surface from being contaminated by a gas layer which could eventually influence the optical properties of the wafer during the calibration procedure. The He-Ne laser light of 0.6326 mm wavelength enters the quartz-glass tube through a vacuum tight viewport with a quartz-glass window. After being reflected from the GaP wafer, the laser light coming out through the viewport is directed by a simple optical system on the Si photodiode placed in a dark housing [Figure 2(a)]. The electrical

current generated by the photodiode, when illuminated by the reflected laser beam, and the thermoelectric voltage from the thermocouple, indicating the temperature of the GaP wafer, are simultaneously recorded by a 2-channel X-Y plotter. Thus, a temperature calibration curve for the oscillations is plotted over the ‘interferogram’ curve. In that way, each maximum could be attributed to a certain temperature. An exemplary diagram of the two overlapping curves measured whilst cooling-down the furnace (and thus the GaP wafer) with a rate of 1.7”C mini’ is shown in Figure 3(a). The calibration curve plotted according to

the numerical data given in Table 1 is shown in Figure 3(b).

4. Calibration of the manipulator thermocouple in the MBE deposition chamber

Depending on the geometry of the SHT system in a definite deposition chamber, the temperature of the substrate wafer, indicated by the manipulator thermocouple differs more or less from the real temperature of the substrate wafer’. Therefore, having calibrated the GaP wafer ‘interferogram’ as a temperature monitor, we used this GaP wafer and the VLI technique for calibration of the manipulator thermocouple in our MBE deposition chamber. The GaP wafer fixed to the substrate holder has been positioned on the manipulator heating block, as shown in the inset of Figure 4(b), and then heated-up in a vacuum of lo-’ mbar to 400°C according to the indications of the thermocouple. After I h

71


) Thermocouple, 1 c \ , 160

Thermocouole

with GaP wafer

HeNe- LASER .6326 pm

MIRROR /

vacuum pump temperature measuremenf unh

lb)

Figure 2. Set-up of the system used for calibration of the GaP wafer ‘interferograms’ (a) and schematic illustration of the construction of the furnace and the sample holder of the system (b).

from the moment the thermocouple indication became constant at a level of 4OO”C, we found also that the ‘interferogram’ curve of the GaP wafer remained unchanged. Thus, we could conclude

72

10 20 30 Time [min]

Figure 3. Example of an ‘interferogram’ of the GaP wafer with the overlapping temperature calibration curve, recorded during cooling down of the wafer from 160°C to 120°C with a rate equal to 1.7 C mini’ (a) and the complete temperature calibration curve (b) plotted according to the numerical data given in Table 1.

40 60 80 100 120

number of maxima

that the sample holder exhibited a constant temperature too. Subsequently, we started a slow cooling down process according to the program shown in Figure 4(a). This program, with cooling rates of 1 ‘C mini’ and O.YC min-‘, ensured thermal steady-

state conditions in the SHT system, which has been confirmed

experimentally. When the cooling process was interrupted for 10

min at 3OO’C, no changes in the ‘interferogram’ were observed in that time interval.

During the programmed cooling down process the thermocouple indications (the as-measured temperatures) and the

reflected laser light intensity oscillations (the GaP wafer ‘interferogram’) were simultaneously recorded by a 2-channel X-Y

plotter. The real substrate wafer temperatures could then be determined from the ‘interferogram’ maxima by assuming that the final temperature of the cooling process, i.e. 25 ‘C (the room temperature), indicated by the thermocouple was equal to the real substrate wafer (the GaP wafer) temperature. Counting back the interference maxima, starting with number 1 for the temperature 27’C (according to the GaP wafer calibration data given

in Table 1) and comparing these ‘interference maxima GaP wafer temperatures’ with the recorded indications of the thermocouple, the calibration data for the thermocouple may be evaluated. These numerical data are also given in Table 1, while the thermocouple calibration curve is shown in Figure 4(b).


Table 1. The sequential numbers of the ‘interferogram’ maxima and the real wafer temperature (r,) together with the thermocouple temperature (T,J of the substrate heater

Max # Q(“C) T&C) Max # TX’C) T,,(“C) Max # TXC) T&C)

1 27.0 27.5 10 65.2 83 60 255.8 336.0 2 31.7 33.2 20 107.2 142.5 70 290.5 376.0 3 35.5 39.0 30 146.0 191.0 75 307.4 400 4 40.0 45.7 40 183.6 242.0 90 357.6 - 5 44.0 51.3 50 220.9 289.0 103 398.5 -

5. Substrate temperature in dynamic thermal conditions

After the calibration procedures described in Sections 3 and 4

were been completed, we performed a set of experiments concerning the thermal behaviour of our process manipulator in dynamic conditions, i.e. when temperature changes are generated

with fairty high heating or cooling rates. We have chosen temperature changes simiiar to those which occur in real epitaxial growth processes of the wide-gap II-VI compounds usually performed in our MBE machine, Again using the VLI technique, we

(a)

G 0 ,i,

0 120 240 360 480

time [min]

500 6 e

$ 400

z c 2 300 z?

$ g 200 r z

3 z 100 .- f = 0

0 100 200 300

lb) Substrate wafer temperature [“Cl

Figure 4. The cooling down program of the heating block of the manipulator (according to the thermocouple indications) which ensures thermal steady-state conditions during the catibration procedure (a) and the manipulator the~ocouple calibration curve (b). The geometry of the SHT system is shown schematically in the inset.

have gained interesting experimental results for the same SHT

geometry shown in Figure 4(b). Figure 5(a) shows the manipulator heating block temperature

rising-up program, according to the thermocouple indications. During programmed heating and subsequent free cooling

processes, the real GaP (substrates wafer temperatures were evaluated from the measured GaP ‘interferograms’. The relations between the thermocouple temperatures and the real substrate (Gap) wafer temperatures found in our experiments indicate the thermal behaviour of the process manipulator in dynamic conditions. They are plotted in Figure 5(b) together with the calibration curve obtained at thermal steady-state conditions

Ia)

400

300

100

0 60 120 180 240 300 360

time [min]

- calibration curve

- heating and cooling curve

04 I I ! t , I -

(b)

0 lcla 200 300 400

substrate temperature PC]

Figure 5. Manipulator heating block temperature rising-up program, according to the thermocouple indications (a) and the real (Gap wafer sampIe holder) temperatures measured by VLI thermometry (b). The calibration curve concerns thermal steady-state conditions [this curve is also shown in Figure 4(b)]. The numbers in the curves of (a) and (b) indicate the corresponding changes in the heating rate.

73


z 3501 ’ J

150 s ’ ’ I 20 0 60 &jO 100

I ; time [min] ; I I I

500 I ! i 1

I I I

I ( a I I I I

I b

I I

I I

I I

I I

I I 0 t j

0 20 40 60 60 100

Time [min]

Figure 6. Changes of the substrate holder temperature after the thermocouple showed a constant temperature of 4OOT after a rapid heating (a) or 250°C after a rapid cooling process (b).

[this curve is also shown in Figure 4(b)]. One may recognise considerable differences in the manipulator behaviour in dynamic

thermal conditions, in comparison to the thermal steady-state conditions.

These differences become larger when the heating or cooling

rates are increased. Figure 6 shows the thermal behaviour of the manipulator substrate holder (substrate wafer) temperature after the intended temperature of 400°C has been reached, according to the thermocouple indications, when fairly short heating and cooling processes were performed (see the lower part of Figure 6). At constant thermocouple temperatures the real substrate wafer temperature still changed. After the thermocouple indication had been stabilised at a level of 4OO”C, a rising-up rate of the substrate temperature of about 12.3LC min-’ within the next 20 min, decreasing then at 70 min to about 4.5-C h-‘, was measured by VLI thermometry. Subsequently, the heating block was cooled down with the same rate of 20-C min-‘, according to the indications of the thermocouple, while simultaneously recording the real substrate temperature determined by VLI. Again a considerable delay between the thermocouple and substrate temperatures was found (see the upper part of Figure 6).

6. In situ measurement of the film thickness

Taking into consideration equations (6) and (11) one may conclude that when the growth temperature in a thin film deposition process is known and well stabilised, the thickness of the film may be determined in this process by the laser interferometry technique in situ. The ‘interferograms’ are in this case caused by

74

the change in thickness of the film and the relevant formula for the film thickness takes the form :

d = (m&)/(2n, cos cc,). (12)

If the laser light incidence angle is small and the refraction angle z, is also small, the formula becomes :

d = (mi,)/(2n,) (13)

It is evident that the thickness period of the ‘interferogram’ curve

oscillations is given by :

Adp = &/(2nl). (14)

The thickness of the growing film may be determined in situ when the refractive index n, of the material of the film is known for the growth temperature T,. This value of n, can be evaluated by counting m on the ‘interferogram’ curve during the growth at r, and then measuring ex situ (after the growth is finished) the thickness of the film grown. Having once evaluated the refractive

index at T,, one may determine in situ the thickness of each film grown next from the same material when grown at T,.

The described evaluation procedure is fairly simple only for films transparent to the laser light. Then the refractive index, n, is a real number and the influence of the substrate wafer basic optical constants (the real and the imaginary parts of the complex refractive index) on the intensity IR of the reflected light results

only in a constant decrease of the amplitude of the ‘interferogram’ oscillations. In such a case equation (11) changes and may be written in the form :

IR = C, +C,cosA, (15)

where C, and Cz depend on the mutual relations between n, and n,, the refractive indices of the film and the substrate wafer (Fig-

ure 1). Applying VLI to our MBE growth system we have determined the refractive indices of the two II-VI wide-gap

semiconductor compounds ZnTe and cubic MnTe, both being transparent to the visible He-Ne 0.6328 pm laser light. Having got the values’

~1, (286CC)ZnTe = 2.51 andn,(286”C),,,,,,,,, = 3.26,

we could measure in situ the film thicknesses of these materials during the MBE growth on GaAs (100) substrates (not transparent to the laser light) at 286°C. We found the thickness period Ad, of the ‘interferogram’ curve oscillations as being equal to 126.1 nm and 97.1 nm, for ZnTe and MnTe respectively. Thus we could estimate the precision of the thickness measurements for these two materials. Assuming that it is determined by a quarter of the Ad, value, we obtain 31.5 and 24.3 nm for ZnTe and MnTe, respectively.

Let us now consider the problem of in situ determination by VLI of the film thickness when the film is only partly transparent to the laser light. In this case, we have to determine the intensity ZR of the light reflected from a bi-layer system comprising of a film of thickness d and a complex refractive index N, = n, + ik,

and a GaAs substrate of complex refractive index N, = n2 + ikz. Such a case has been analysed by Farrel et al” in the example of AlGaAs grown on GaAs by MO MBE. It has been shown, that the intensity I, oscillates again with a thickness period Ad, depending only on the real part of the refractive index of the film (equation (14)), however, the amplitude of the oscillations of the film growth decrease in time due to absorption in the overlayer.

H Sirrer et al: Vacuum epitaxial growth systems

The light absorption and, thus, the amplitude decrease rate of the damped oscillations of the ‘interferogram’ curve is governed by the extinction coefficient k, of the grown film.

In our experiments concerning the case considered, we have grown, by MBE at T, = 286°C a CdTe film on a GaAs (100) substrate. Using VLI during the growth we have recorded damped oscillations of the reflected light intensity. Counting then the total number of the oscillation maxima and measuring ex situ the thickness of the grown film, we can determine the real part

of the refractive index of CdTe at the growth temperature to be equal to n,(286C)cdTe = 2.86. This value agrees well with the experimental data of the literature”. The precision of the film thickness measurement in this case (defined again as a quarter of the Ad, value) was, thus, equal to 27.9 nm.

7. Conclusions

We have described in detail the experimental procedure concerning application of the VLI thermometry to exact calibration, at thermal steady-state conditions, of the process manipulator thermocouple and, thus, to exact determination of the real sub-

strate temperature in our MBE growth system. After having calibrated the thermocouple in relation to the real substrate temperature, we have tested experimentally the behaviour of the substrate temperature in dynamic thermal conditions, i.e. when the manipulator heating block was heated up or cooled down at fairly high rates. We have found, that in dynamic thermal conditions, the substrate wafer temperature changes essentially in comparison to the case of thermal steady-state conditions. The differences became larger for increased heating or cooling rates. Also, long time delays have been found when the substrate wafer temperature approached an intended value, at cooling or heating processes, after the heating block temperature was changed. The time delay was measured from the moment when the heating block reached this intended value. Finally, we have described procedures of in situ determination of the growing film thicknesses

when applying the VLI technique during MBE. Two cases, concerning films completely transparent to the used laser light and films only partly transparent to this light, have been considered.

The VLI technique may, however, also be applied for the evaluation of the basic optical constants of thin films in growth conditions, e.g. at elevated temperatures in high or ultra-high vacuum environments5. The real part of the refractive index may be evaluated by measuring e3c situ the film thickness and counting the number of maxima in the ‘interferogram’ curves recorded during the growth process performed at a constant, well stabilised temperature. This procedure may be applied in both cases, for the completely transparent and the partly transparent films.

In order to determine the extinction coefficient, the sequential amplitudes of the damped oscillations of the recorded ‘interferogram’ curve have to be evaluated. In this case, in equation (5), the terms with exponential functions are multiplied by real exponential damping coefficients (as a result of the fact that in the wave numbers complex refractive indices occur). Consequently, equations (11) and (15) giving the intensities ZR of the laser light reflected from the film also have to be changed to their relevant forms.

Let us consider for simplicity the first approximation, when in equation (5) only two terms occur and CI, = c(, z 0. Then one gets :

R,E = R,,E+T,,R,T,;~~~ (ik,n,2d)exp(-k,k,2d), (16)

where k, = 27c/ A0 is the wave number in vacuum. The intensity of light reflected from the films is, thus, given by :

1~ = (&E)(M)* = C, + C2 exp (- k,k, 24 exp (jr),

(17)

with C, and C, being real and the oscillations of the ‘interferogram’ curve being described by the phase angle I. The constant C, gives the intensity of the reflected light for an infinitely thick film, when no more oscillations of the light intensity can be recorded, while the constant Cz gives the maximal amplitude of the oscillations counted from the intensity level C,.

Calculating now the normalised amplitudes of the ‘interferogram’ curve for the m,-th maximum, namely :

ZRO(m,) = [IR(mj) - C,]/C, = exp (- k,k, 2dm,), (18)

where the film thickness dm, is given, according to equation (14),

by m,n,2rc/l,, one may recognize that the extinction coefficient can be evaluated from :

k, = {[lnZ,“(m,)-lnIR”(mi)]n,}/[2rr(m,-m,)]. (19)

This formula results from the logarithm of the ratio I,“(m,)/ ZR”(m,). In our experiments we have found’ that k,(286”C),,,, = 0.23, which is in agreement with the data shown in the literature13.

Both of the basic optical constants of the film depend on temperature. Their temperature coefficients Bn = (An/AT)/n,, and /Ik = (Ak/AT)/k,, may, however, also be determined with VLI. Having grown a film of a definite thickness of the growth temperature T, and knowing from former evaluations the refractive index T,, one may cool down the film to the temperature To, simultaneously counting the number Am of the maxima which have occurred in the ‘interferogram’ curve during the cooling

process. While the thickness of the film may be considered to be constant (in the first approximation) the refractive index at temperature T,, may be evaluated by calculating the new number of the final maximum and using the formula m( 7’,) = m( T,) -Am. With this procedure, we have determined the temperature coefficients of the refractive indices of the GaP wafer and the grown ZnTe epitaxial film as being equal to

Pn(ZnTe) = 7.2. 10p5K-’ and P,(GaP) = 9.5. 10p5Kp’,

for temperatures near to 250°C. In order to evaluate the temperature coefficient of flk, the

extinction coefficient, one has to grow twice the films of the

investigated material ; one at temperature T, and then a new film on the same substrate at temperature r,. Using equation (19) in both cases the temperature coefficient fik may be evaluated.

In conclusion, it should be emphasised that the VLI technique delivers important information of great value, not only in thin film technology, but also in production activities concerning the heated parts of vacuum technological equipment.

Acknowledgements

The authors would like to thank 0 Fuchs and L Vaskovich for technical assistance and E Hanz for typing the manuscript. The scientific project was supported by the ‘Fonds zur Forderung der wissenschaftlichen Forschung in osterreich’, Project No. : P 9695.

75


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exact determination of the real substrate temperature and film thickness in vacuum epitaxial growth...

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