- Email: [email protected]
Infra-red transmission spectroscopy of GaAs during molecular beam epitaxy
38
Journal of Crystal Growth 81(1987) 38—42 North-Holland, Amsterdam
INFRA-RED TRANSMISSION SPECTROSCOPY OF GaAs DURING MOLECULAR BEAM EPITAXY E.S. HELLMAN and J.S. HARRIS, Jr. Stanford Electronics Laboratory, Stanford University, Stanford, California 94305, USA
Direct radiative heating of GaAs substrates for molecular beam epitaxy (MBE) has a very useful side-benefit: the infra-red light which heats the substrate can also serve as a light source for transmission spectroscopy. We demonstrate the use of in-situ transmission spectroscopy in two important applications, temperature measurement and growth rate measurement. The substrate temperature can be accurately determined by measuring the position of the band-gap absorption edge. The band gap of GaAs shifts about 50 mV per 100°Cin the usual temperature range of MBE growth, and has been well characterized previously. We can measure the position of the absorption edge to better than 5 mV, so a temperature can be determined with an accuracy of better than 10°C. The precision of the measurement is ±2°C.We have measured GaAs substrate temperatures as low as 450°C, and the technique is easily extendable to much lower temperatures. We have used this technique to calibrate the thermocouple used to control our substrate heater during normal MBE growth. The growth rates of Al,Ga 1_~As and GaAs can be determined by measuring the Fabry—Pérot interference fringes resulting from thin layers. For a single Al ,Ga1 As layer, the amplitude of the fringes observed as a function of time is a good measure of the index difference between the layer and the substrate. From published data about the GaAs index at high temperature, we can get the Al~Ga1._~As index, and thus an estimate of the Al mole fraction of the layer. By counting the fringes as the layer is grown, we can determine the thickness of the layer. For a single layer of Al0 ~Ga07As on GaAs. we observe fringes of magnitude 3.85% ±0.62% at 1.468 ~m. The optical thickness can be determined to within ±24 nm. For multi-layer structures, the variations of the transmittance with wavelength become large, so that the optical thickness of both GaAs and AlAs can be extracted from a single wavelength scan. An accurate determination of the refractive indices of these materials at high temperatures could make this technique very important for the reproducible growth of Al~Ga1 As—GaAs heterostructures. because a high precision calibration could be done during each growth.
1. Introduction The realization of molecular beam epitaxy (MBE) as a commercially viable production technology has required the abandonment of substrate mounting using indium. Direct radiative heating [1,2] has become the favored method for heating substrates mounted without indium, because it can achieve good temperature uniformity over full 75 mm wafers without introducing mechanical stress in the wafer, and because it has allowed the growth of very high purity material [3]. However, the measurement of the absolute substrate temperature can be rather difficult. Usually this is done using infra-red pyrometers, which measure the intensity of black body radiation emitted by the wafer. For materials like GaAs, which are transparent in the infrared, the radiation of the heater interferes with this measurement. GaAs is opaque to photons with energy greater than its band gap,
so that pyrometry can still be done if only these short wavelength photons are measured. A blackbody at the typical growth temperatures emits rather few of these photons, so the accuracy of the temperature measurement is reduced. Additional uncertainties, such as the spectral emittance of GaAs, especially in multilayer structures, and the transmittance of the chamber window, which changes as a function of time, also reduce the accuracy. The solution to the temperature measurement problem can be found in the same heater radiation which complicates pyrometric measurements. The infra-red light used to heat the wafer can also be used as a light source for transmission spectroscopy of the substrate. The wavelength at which the wafer becomes opaque is an excellent measure of the band gap of the material. Since the dependence of band gap on temperature is well known for GaAs [4], the temperature of a GaAs substrate
0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ES. Heilman, J.S. Harris, Jr.
/
JR transmission spectroscopy of GaAs during MBE
39
can be deduced from a measurement of its band gap. Transmission spectroscopy can also be used for the measurement of film thicknesses. When a film of Al~Ga~~As on a GaAs substrate is one half of a wavelength thick, the reflections from the two surfaces add up coherently and the transmission is reduced. Destructive interference occurs for quarter wavelength films, which show increased transmission. Analysis of the time dependence of the transmission during layer growth can give an accurate measure of both the composition and growth rate of the layer. In this paper, we will demonstrate the use of infrared transmission spectroscopy for temperature measurement of GaAs substrates and for determination of Al~Gai_~As
diameter GaAs wafers with mirror finishes on both sides. They are mounted in 3 in. molybdenum rings for use with the 3 in. substrate heater in our Varian GEN-Il MBE system. The apparatus for measuring the transmittance of the substrate is depicted in fig. 1. It consists of the heater/light source, the imaging system, and the spectrometer. The substrate heater and wafer mounting technique have been described previously [1]. For normal growth, the power to the heater coils is regulated to maintain a constant temperature at a thermocouple situated behind the wafer. In this mode, the heater power can change markedly if the emissivities of the substrate and molybdenum ring change, as they do when Al~Ga5~Asis
film thickness and composition during MBE growth.
grown on GaAs. When the heater is used as a light source for spectroscopy, however, such power changes are undesirable, so we use a constant power supply instead. The substrate can be seen at normal incidence during growth through a quartz window in the growth chamber. This window is typically coated with a thin layer of arsenic. The substrate heater is imaged at a magnification of about one by a single lens onto the end of a 1/8 in. diameter fiber optic light guide. The light guide is on ancan x—y so thatThe a specific area of mounted the substrate bestage measured. small sampling area (— 0.02 inch2) eliminates errors due to
2. Experimental procedure The transmission measurements described in this paper were made on 0.5 mm thick 50 mm Th)I I I (~rat~eate~
oc -in ampi ier I k
PbS detector
fl I
GaAs substrate
lateral temperature non-uniformities. The light from the other end of the guide is chopped and focussed onto the spectrometer slit. The output of
-.
-~
monochromator
/
/
focussing lenses
—.-
window chopper
image
fiber light guide
a PbS detector is fed to a lock-in amplifier, where it is mixed with the chopping signal. The intensity of light inctdent on the substrate is determined by measuring the light emitted by the heater with an empty holder as a function of the voltage applied to then taken to be the the heater. ratio ofThe the transmissivity light intensityis measured with and without a wafer for the same heater voltage.
Fig. 1. Experimental set-up for in-Situ infra-red transmission spectroscopy. The substrate can be seen at normal incidence during growth through a quartz window in the growth chamber. The substrate heater is imaged at a magnification of about one by a single lens onto the end of a 1/8 in. diameter fiber optic light guide. The light guide is mounted on an x — y stage so that a specific area of the substrate can be measured. The light from the other end of the guide is chopped and focussed onto the spectrometer slit. The output of a PbS detector is fed to a lock-in amplifier, where it is mixed with the chopping signal.
3. Temperature measurements Measurements of the band gap energy of GaAs at temperatures higher than 300°C have been made by Panish and Casey [4J.They measured the photon energy for which the optical absorption coefficient a in a thin GaAs crystal was 40 cm —
40
E.S. Hellman, J.S. Harris, Jr.
/
JR transmission spectroscopy of GaAs during MBE
for several temperatures. The shift of the band gap energy was then assumed to be equal to the shift of this constant absorptivity energy. Thurmond [5] used their data along with low temperature data of others to fit a single equation which describes the temperature dependence of the band gap for the entire temperature range 0—1000 K:
102 +
E +
+ 5)
D D
~
+
I’) 0
+
0
E5(T)=1.519—5.405X104T2/(T+204)eV. (1)
Do
+ +
.2 +
D
X
Ix 575~CI 623~CI 1+° 665~CI I
.0 +
where T is the temperature. The standard deviation of the high temperature data from this expression is less than 3 mY, after corrections are made for the room temperature band gap. To measure the substrate temperature in our MBE system, we repeat the measurement of Panish and Casey to find the band gap, comparing the absorption edge measured at high temperature to that measured at room temperature using a spectrophotometer. We then use eq. (1) to determine the temperature. The absorption coefficient a as a function of wavelength for an undoped GaAs substrate at three different temperatures is shown in fig. 2. The transmissivity is measured for a point 14 mm from the center of the wafer. Following Panish and Casey, we extract the absorption coefficient from the transmission measurements using the usual formula for transmissivity through a slab of thickness d and refractive index n: =
R
=
—
1 (n
— —
R )2 exp( ad) R2 exp(—2ad) 1)/(n + 1). —
(2) (3)
We use a refractive of 3.6 [6] for GaAs and make no attempt to correct for the near-edge dispersion. The blackbody radiation from the wafer measured above the edge is subtracted from all the transmitted intensities. Since the intensity of the heater radiation may change somewhat when a substrate is put in front of it, the near edge transmission is normalized using an intensity measured well below the absorption edge, where the transmission can be calculated from the known indices. By choosing a single absorption coefficient at which to measure the absorption edge shift, we
100
1.02
1.04
1.06 1.08 1.10 Photon Energy (eV)
1.12
1.14
Fig. 2. The absorption coefficient a as a function of wavelength for an undoped GaAs substrate at three different heater powers. The temperatures given are those deduced from the positions of the absorption edge.
assume that the shape of the absorption edge is unchanged by temperature or from sample to sample. In the data of Panish and Casey, the absorption edge slope was independent of temperature to within experimental error. The 3 mY standard deviation in the fit of eq. (1) to the data of Panish and Casey is a result of this error, and contributes an uncertainty of ±6° C to our determination of the substrate temperature. Since the GaAs crystals are relatively thick, both in our work and that of Panish and Casey, the range of absorption coefficients we can measure is very far down on the exponential tail of the absorption edge. In this range, the slope may well depend somewhat on the temperature. Thus the shift of the absorption edge may depend on our choice of absorption coefficient at which we measure the shift. To cancel out the systematic errors caused by possible slope differences, we have used the same 40 cm~ point to calculate the absorption edge shifts. Despite these limits to the accuracy of the temperature measurement, the precision of the measurement is ±2°C.We have also measured the absorption edge for silicon doped substrates at growth temperatures. It is much more difficult to get an accurate temperature measurement for doped substrates because the absorption edge depends on the fermi level, and thus the relative positions of the absorption edge and the band gap are temperature dependent.
ES. He//man, J.S. Harris, Jr.
/
JR transmission spectroscops’ of GaAs during MBE
Since the absorption edge measurement is relatively slow, it does not appear to be immediately suitable for active control of the substrate temperature. However, radiatively coupled thermocouples have worked exceedingly well for this purpose [1], although the accuracy of their temperature measurement has been uncertain. We find that the thermocouples are reasonably close to the actual wafer temperature. For example, on an undoped wafer at thermocouple temperatures of 466, 569 and 671°C we measure actual temperatures of 495, 589 and 670°C, respectively. Using this “calibrated” wafer, we measured some “well defined” temperatures. The change of the reflection high-energy electron diffraction (RHEED) pattern which we associate with oxide desorption occurs between 655 and 665°C. This is 50 to 120°C higher than previously reported [7], and indicates that oxide desorption is not a reliable measure of the temperature. Oxide desorption may depend on the substrate cleaning and mounting procedure, particularly if indium solder is used. The time required for the surface to go from As to Ga stable after closing the As shutter, as determined by the RHEED pattern, was 1 s at a temperature of 659°C and 5 s at 653°C, with a background As flux of 1.5 x 10-8 Torr.
4. Thickness measurements Fabry—Perot interference fringes occur when reflections from the surfaces of a thin dielectnc film add in or out of phase. An Al Ga~ As film on GaAs has a refractive index between that of GaAs and that of vacuum, so that maxima in the transmission occur when the film has thickness -
d
=
(2m + 1)X/4n,
where m is an integer, n is the refractive index of the Al ~Ga As and X is the free space wavelength of the light. The transmission through this film is (1 Rf)(1 Rr) T 1 + R fR (4) -
—
=
—
‘
where R and R r are the reflectivities of the front and rear surfaces. At the transmission maxima,
41
the front surface reflectivity is given by R=[(n—nL)/(n+nL)j
2
(5)
where n L is the refractive index of the epitaxial layer, while at the minima, the transmission is given by eq. (3). From these equations, we can calculate the expected amplitude of the oscillations in the transmitted intensity which occur during growth of the thin film. We measured these oscillations during the growth of a 2.42 jim Al~Gai5As film at 660°C. We observed a penodic increase of the transmission at 1.468 jim of 3.85% ±0.672%. Assuming a refractive index for GaAs of 3.56 [8] at this wavelength and temperature, we can determine from this that that the Al~Ga1~As must have a refractive index between 3.37 and 3.42, which corresponds to an Al mole fraction of about 0.3 [9].By counting the transmission oscillations (or fringes), the thickness of the film can be determined quite easily. The optical growth rate (real growth rate times the index) can be measured to an accuracy of a fraction of 1% on a 2 jim layer in this way. Fringe counting has been widely used for determination of film thicknesses in a wide variety of deposition and etching processes, and is equally applicable to MBE. Another approach to measurement of film thicknesses is to grow a multi-layer structure. In a stack of quarter wave films of alternating high and low indices, all the reflections add in phase, so that the reflectivity at one wavelength will be strongly enhanced. Fig. 3 shows the transmissivity measured in-situ versus wavelength for a multilayer structure consisting of eight 143 nm AlAs layers and seven 155 nm GaAs layers on a GaAs substrate. The temperature was measured to be 589°C. The refractive indices of AlAs are not .
.
.
accurately known at these temperatures and wavelengths, so it has been used as a fitting parameter for a theoretical calculation of the transmissivity shown as the solid curve in fig. 3. The calculation uses the formulae given by Born and Wolf for periodically stratified media [10]. The fit uses n(AIAs) 3.3 and n(GaAs) 3.46. The quality of the fit is quite sensitive to the index differences and to the total optical thickness of the GaAs and AlAs layers. It is relatively insensitive to the ratio of the two layer thicknesses. The poor fit at shorter wavelength is due to lower signal to noise ratio =
=
42
E.S. He//man, J. S. Harris, Jr.
0.6
/
JR transmission spectroscopv of GaAs during MBE
useful for substrate temperature measurement, and for measurement of film thicknesses. An accurate determination of the refractive indices of these materials at high temperatures could make this technique very important for the reproducible growth of Al~Gai As—GaAs heterostructures, because a high precision calibration could be done during each growth.
+
0.5~+
—
C
0.4
+
+
experiment calculated fit
__________________________________ 0.3
‘
1.2
Acknowledgments
I
1.4
1.6
1.8
2.0
2.2
Wavelength (jim) Fig. 3. Transmissivity measured in-situ versus wavelength for a multilayer structure consisting of eight 143 nm AlAs layers and seven 155 nm GaAs layers on a GaAs substrate. The substrate temperature was 589°C. The solid curve is a theoretical fit to the data using n(A1A5) = 3.3 and n(GaAs) = 3.46.
and our omission of wavelength dispersion in the calculation. The index we obtain for AlAs is significantly higher than what we would extrapolate from room temperature, and implies a much smaller index difference between AlAs and GaAs at high temperatures. Both approaches to thickness measurement might be combined to measure the Al~Ga1._~As and GaAs growth rates in a single calibration procedure. The fringe counting could be used to measure the growth rate on an initial Al~Gai_~As layer. A quarter wave layer of GaAs, and perhaps additional AlAs layers could then be grown, so that a wavelength scan would determine the GaAs thickness. Since the required layers would be less than 1 jim thick, such a calibration might be done before each growth as part of a buffer layer underneath the active layers. Such a calibration would be complementary to growth rate measurements using RHEED oscillations [11] because it measures thicknesses of relatively thick layers and is insensitive to initial flux transients.
5. Conclusions We have demonstrated infra-red transmission spectroscopy during MBE growth using the substrate heater as the light source. This technique is
We would like to thank E.C. Larkins for arguing about the “real” temperature. This work is supported by DARPA and ONR under Contract No. N00014-84-K-0077. This work has benefited from facilities made available to us by the NSFMRL Program through the center for Materials Research at Stanford University. E.S.H. Would like to acknowledge financial support from IBM. References [1] ES. Hellman, P.M. Pitner, A. Harwit, D. Liu, G.W. Yoffe, iS. Harris, Jr., B. Caffee and T. Hierl, J. Vacuum Sci. Technol. B4 (1986) 574. [2] K. Oe and Y. Imamura, Japan. J. AppI. Phys. 24 (1985) 779.
[3] E.C. Larkins, ES. Hellman, D G. Schlom, J.S. Harris, Jr, M.H. Kim and G.E. Stillman, AppI. Phys. Letters 49 (1986) 391. [4] MB. Pamsh and H.C. Casey, J. Appl. Phys. 40(1969)163. [5] CD. Thurmond, J. Electrochem. Soc. 122 (1975) 1133. [6] We assume that the index close to the band edge is independent of temperature, apart from the band edge shift. This can be seen in the data of D.T.F. Marple, J. Appl. Phys. 35 (1964) 1241, for low temperatures. [7] A.Y. Cho and JR. Arthur, Progr. Solid State Chem. 10
(1975) 157; A.Y. Cho, Thin Solid Films 100 (1983) 291. [8] The infra-red GaAs refractive index at high temperatures can be estimated from the known temperature dependence of the high frequency refractive index n,,0 given by iS. Blakemore, J. Appi. Phys. 53 (1982) R123, and from the energy dispersion measured by Marple [6] taking into account the shift of the absorption edge. [9] The index difference between Al~,Gai— ,As and AlAs is estimated to be temperature independent and equal to that given by S. Adachi, J. Appi. Phys. 58 (1985) Ri. [10] M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Pergamon, Oxford, 1980) section 1.6.5. [11] Jfl Neave, BA. Joyce, P.J. Dobson and N. Norton, AppI. Phys. A31 (1983) 1.
Journal of Crystal Growth 81(1987) 38—42 North-Holland, Amsterdam
INFRA-RED TRANSMISSION SPECTROSCOPY OF GaAs DURING MOLECULAR BEAM EPITAXY E.S. HELLMAN and J.S. HARRIS, Jr. Stanford Electronics Laboratory, Stanford University, Stanford, California 94305, USA
Direct radiative heating of GaAs substrates for molecular beam epitaxy (MBE) has a very useful side-benefit: the infra-red light which heats the substrate can also serve as a light source for transmission spectroscopy. We demonstrate the use of in-situ transmission spectroscopy in two important applications, temperature measurement and growth rate measurement. The substrate temperature can be accurately determined by measuring the position of the band-gap absorption edge. The band gap of GaAs shifts about 50 mV per 100°Cin the usual temperature range of MBE growth, and has been well characterized previously. We can measure the position of the absorption edge to better than 5 mV, so a temperature can be determined with an accuracy of better than 10°C. The precision of the measurement is ±2°C.We have measured GaAs substrate temperatures as low as 450°C, and the technique is easily extendable to much lower temperatures. We have used this technique to calibrate the thermocouple used to control our substrate heater during normal MBE growth. The growth rates of Al,Ga 1_~As and GaAs can be determined by measuring the Fabry—Pérot interference fringes resulting from thin layers. For a single Al ,Ga1 As layer, the amplitude of the fringes observed as a function of time is a good measure of the index difference between the layer and the substrate. From published data about the GaAs index at high temperature, we can get the Al~Ga1._~As index, and thus an estimate of the Al mole fraction of the layer. By counting the fringes as the layer is grown, we can determine the thickness of the layer. For a single layer of Al0 ~Ga07As on GaAs. we observe fringes of magnitude 3.85% ±0.62% at 1.468 ~m. The optical thickness can be determined to within ±24 nm. For multi-layer structures, the variations of the transmittance with wavelength become large, so that the optical thickness of both GaAs and AlAs can be extracted from a single wavelength scan. An accurate determination of the refractive indices of these materials at high temperatures could make this technique very important for the reproducible growth of Al~Ga1 As—GaAs heterostructures. because a high precision calibration could be done during each growth.
1. Introduction The realization of molecular beam epitaxy (MBE) as a commercially viable production technology has required the abandonment of substrate mounting using indium. Direct radiative heating [1,2] has become the favored method for heating substrates mounted without indium, because it can achieve good temperature uniformity over full 75 mm wafers without introducing mechanical stress in the wafer, and because it has allowed the growth of very high purity material [3]. However, the measurement of the absolute substrate temperature can be rather difficult. Usually this is done using infra-red pyrometers, which measure the intensity of black body radiation emitted by the wafer. For materials like GaAs, which are transparent in the infrared, the radiation of the heater interferes with this measurement. GaAs is opaque to photons with energy greater than its band gap,
so that pyrometry can still be done if only these short wavelength photons are measured. A blackbody at the typical growth temperatures emits rather few of these photons, so the accuracy of the temperature measurement is reduced. Additional uncertainties, such as the spectral emittance of GaAs, especially in multilayer structures, and the transmittance of the chamber window, which changes as a function of time, also reduce the accuracy. The solution to the temperature measurement problem can be found in the same heater radiation which complicates pyrometric measurements. The infra-red light used to heat the wafer can also be used as a light source for transmission spectroscopy of the substrate. The wavelength at which the wafer becomes opaque is an excellent measure of the band gap of the material. Since the dependence of band gap on temperature is well known for GaAs [4], the temperature of a GaAs substrate
0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ES. Heilman, J.S. Harris, Jr.
/
JR transmission spectroscopy of GaAs during MBE
39
can be deduced from a measurement of its band gap. Transmission spectroscopy can also be used for the measurement of film thicknesses. When a film of Al~Ga~~As on a GaAs substrate is one half of a wavelength thick, the reflections from the two surfaces add up coherently and the transmission is reduced. Destructive interference occurs for quarter wavelength films, which show increased transmission. Analysis of the time dependence of the transmission during layer growth can give an accurate measure of both the composition and growth rate of the layer. In this paper, we will demonstrate the use of infrared transmission spectroscopy for temperature measurement of GaAs substrates and for determination of Al~Gai_~As
diameter GaAs wafers with mirror finishes on both sides. They are mounted in 3 in. molybdenum rings for use with the 3 in. substrate heater in our Varian GEN-Il MBE system. The apparatus for measuring the transmittance of the substrate is depicted in fig. 1. It consists of the heater/light source, the imaging system, and the spectrometer. The substrate heater and wafer mounting technique have been described previously [1]. For normal growth, the power to the heater coils is regulated to maintain a constant temperature at a thermocouple situated behind the wafer. In this mode, the heater power can change markedly if the emissivities of the substrate and molybdenum ring change, as they do when Al~Ga5~Asis
film thickness and composition during MBE growth.
grown on GaAs. When the heater is used as a light source for spectroscopy, however, such power changes are undesirable, so we use a constant power supply instead. The substrate can be seen at normal incidence during growth through a quartz window in the growth chamber. This window is typically coated with a thin layer of arsenic. The substrate heater is imaged at a magnification of about one by a single lens onto the end of a 1/8 in. diameter fiber optic light guide. The light guide is on ancan x—y so thatThe a specific area of mounted the substrate bestage measured. small sampling area (— 0.02 inch2) eliminates errors due to
2. Experimental procedure The transmission measurements described in this paper were made on 0.5 mm thick 50 mm Th)I I I (~rat~eate~
oc -in ampi ier I k
PbS detector
fl I
GaAs substrate
lateral temperature non-uniformities. The light from the other end of the guide is chopped and focussed onto the spectrometer slit. The output of
-.
-~
monochromator
/
/
focussing lenses
—.-
window chopper
image
fiber light guide
a PbS detector is fed to a lock-in amplifier, where it is mixed with the chopping signal. The intensity of light inctdent on the substrate is determined by measuring the light emitted by the heater with an empty holder as a function of the voltage applied to then taken to be the the heater. ratio ofThe the transmissivity light intensityis measured with and without a wafer for the same heater voltage.
Fig. 1. Experimental set-up for in-Situ infra-red transmission spectroscopy. The substrate can be seen at normal incidence during growth through a quartz window in the growth chamber. The substrate heater is imaged at a magnification of about one by a single lens onto the end of a 1/8 in. diameter fiber optic light guide. The light guide is mounted on an x — y stage so that a specific area of the substrate can be measured. The light from the other end of the guide is chopped and focussed onto the spectrometer slit. The output of a PbS detector is fed to a lock-in amplifier, where it is mixed with the chopping signal.
3. Temperature measurements Measurements of the band gap energy of GaAs at temperatures higher than 300°C have been made by Panish and Casey [4J.They measured the photon energy for which the optical absorption coefficient a in a thin GaAs crystal was 40 cm —
40
E.S. Hellman, J.S. Harris, Jr.
/
JR transmission spectroscopy of GaAs during MBE
for several temperatures. The shift of the band gap energy was then assumed to be equal to the shift of this constant absorptivity energy. Thurmond [5] used their data along with low temperature data of others to fit a single equation which describes the temperature dependence of the band gap for the entire temperature range 0—1000 K:
102 +
E +
+ 5)
D D
~
+
I’) 0
+
0
E5(T)=1.519—5.405X104T2/(T+204)eV. (1)
Do
+ +
.2 +
D
X
Ix 575~CI 623~CI 1+° 665~CI I
.0 +
where T is the temperature. The standard deviation of the high temperature data from this expression is less than 3 mY, after corrections are made for the room temperature band gap. To measure the substrate temperature in our MBE system, we repeat the measurement of Panish and Casey to find the band gap, comparing the absorption edge measured at high temperature to that measured at room temperature using a spectrophotometer. We then use eq. (1) to determine the temperature. The absorption coefficient a as a function of wavelength for an undoped GaAs substrate at three different temperatures is shown in fig. 2. The transmissivity is measured for a point 14 mm from the center of the wafer. Following Panish and Casey, we extract the absorption coefficient from the transmission measurements using the usual formula for transmissivity through a slab of thickness d and refractive index n: =
R
=
—
1 (n
— —
R )2 exp( ad) R2 exp(—2ad) 1)/(n + 1). —
(2) (3)
We use a refractive of 3.6 [6] for GaAs and make no attempt to correct for the near-edge dispersion. The blackbody radiation from the wafer measured above the edge is subtracted from all the transmitted intensities. Since the intensity of the heater radiation may change somewhat when a substrate is put in front of it, the near edge transmission is normalized using an intensity measured well below the absorption edge, where the transmission can be calculated from the known indices. By choosing a single absorption coefficient at which to measure the absorption edge shift, we
100
1.02
1.04
1.06 1.08 1.10 Photon Energy (eV)
1.12
1.14
Fig. 2. The absorption coefficient a as a function of wavelength for an undoped GaAs substrate at three different heater powers. The temperatures given are those deduced from the positions of the absorption edge.
assume that the shape of the absorption edge is unchanged by temperature or from sample to sample. In the data of Panish and Casey, the absorption edge slope was independent of temperature to within experimental error. The 3 mY standard deviation in the fit of eq. (1) to the data of Panish and Casey is a result of this error, and contributes an uncertainty of ±6° C to our determination of the substrate temperature. Since the GaAs crystals are relatively thick, both in our work and that of Panish and Casey, the range of absorption coefficients we can measure is very far down on the exponential tail of the absorption edge. In this range, the slope may well depend somewhat on the temperature. Thus the shift of the absorption edge may depend on our choice of absorption coefficient at which we measure the shift. To cancel out the systematic errors caused by possible slope differences, we have used the same 40 cm~ point to calculate the absorption edge shifts. Despite these limits to the accuracy of the temperature measurement, the precision of the measurement is ±2°C.We have also measured the absorption edge for silicon doped substrates at growth temperatures. It is much more difficult to get an accurate temperature measurement for doped substrates because the absorption edge depends on the fermi level, and thus the relative positions of the absorption edge and the band gap are temperature dependent.
ES. He//man, J.S. Harris, Jr.
/
JR transmission spectroscops’ of GaAs during MBE
Since the absorption edge measurement is relatively slow, it does not appear to be immediately suitable for active control of the substrate temperature. However, radiatively coupled thermocouples have worked exceedingly well for this purpose [1], although the accuracy of their temperature measurement has been uncertain. We find that the thermocouples are reasonably close to the actual wafer temperature. For example, on an undoped wafer at thermocouple temperatures of 466, 569 and 671°C we measure actual temperatures of 495, 589 and 670°C, respectively. Using this “calibrated” wafer, we measured some “well defined” temperatures. The change of the reflection high-energy electron diffraction (RHEED) pattern which we associate with oxide desorption occurs between 655 and 665°C. This is 50 to 120°C higher than previously reported [7], and indicates that oxide desorption is not a reliable measure of the temperature. Oxide desorption may depend on the substrate cleaning and mounting procedure, particularly if indium solder is used. The time required for the surface to go from As to Ga stable after closing the As shutter, as determined by the RHEED pattern, was 1 s at a temperature of 659°C and 5 s at 653°C, with a background As flux of 1.5 x 10-8 Torr.
4. Thickness measurements Fabry—Perot interference fringes occur when reflections from the surfaces of a thin dielectnc film add in or out of phase. An Al Ga~ As film on GaAs has a refractive index between that of GaAs and that of vacuum, so that maxima in the transmission occur when the film has thickness -
d
=
(2m + 1)X/4n,
where m is an integer, n is the refractive index of the Al ~Ga As and X is the free space wavelength of the light. The transmission through this film is (1 Rf)(1 Rr) T 1 + R fR (4) -
—
=
—
‘
where R and R r are the reflectivities of the front and rear surfaces. At the transmission maxima,
41
the front surface reflectivity is given by R=[(n—nL)/(n+nL)j
2
(5)
where n L is the refractive index of the epitaxial layer, while at the minima, the transmission is given by eq. (3). From these equations, we can calculate the expected amplitude of the oscillations in the transmitted intensity which occur during growth of the thin film. We measured these oscillations during the growth of a 2.42 jim Al~Gai5As film at 660°C. We observed a penodic increase of the transmission at 1.468 jim of 3.85% ±0.672%. Assuming a refractive index for GaAs of 3.56 [8] at this wavelength and temperature, we can determine from this that that the Al~Ga1~As must have a refractive index between 3.37 and 3.42, which corresponds to an Al mole fraction of about 0.3 [9].By counting the transmission oscillations (or fringes), the thickness of the film can be determined quite easily. The optical growth rate (real growth rate times the index) can be measured to an accuracy of a fraction of 1% on a 2 jim layer in this way. Fringe counting has been widely used for determination of film thicknesses in a wide variety of deposition and etching processes, and is equally applicable to MBE. Another approach to measurement of film thicknesses is to grow a multi-layer structure. In a stack of quarter wave films of alternating high and low indices, all the reflections add in phase, so that the reflectivity at one wavelength will be strongly enhanced. Fig. 3 shows the transmissivity measured in-situ versus wavelength for a multilayer structure consisting of eight 143 nm AlAs layers and seven 155 nm GaAs layers on a GaAs substrate. The temperature was measured to be 589°C. The refractive indices of AlAs are not .
.
.
accurately known at these temperatures and wavelengths, so it has been used as a fitting parameter for a theoretical calculation of the transmissivity shown as the solid curve in fig. 3. The calculation uses the formulae given by Born and Wolf for periodically stratified media [10]. The fit uses n(AIAs) 3.3 and n(GaAs) 3.46. The quality of the fit is quite sensitive to the index differences and to the total optical thickness of the GaAs and AlAs layers. It is relatively insensitive to the ratio of the two layer thicknesses. The poor fit at shorter wavelength is due to lower signal to noise ratio =
=
42
E.S. He//man, J. S. Harris, Jr.
0.6
/
JR transmission spectroscopv of GaAs during MBE
useful for substrate temperature measurement, and for measurement of film thicknesses. An accurate determination of the refractive indices of these materials at high temperatures could make this technique very important for the reproducible growth of Al~Gai As—GaAs heterostructures, because a high precision calibration could be done during each growth.
+
0.5~+
—
C
0.4
+
+
experiment calculated fit
__________________________________ 0.3
‘
1.2
Acknowledgments
I
1.4
1.6
1.8
2.0
2.2
Wavelength (jim) Fig. 3. Transmissivity measured in-situ versus wavelength for a multilayer structure consisting of eight 143 nm AlAs layers and seven 155 nm GaAs layers on a GaAs substrate. The substrate temperature was 589°C. The solid curve is a theoretical fit to the data using n(A1A5) = 3.3 and n(GaAs) = 3.46.
and our omission of wavelength dispersion in the calculation. The index we obtain for AlAs is significantly higher than what we would extrapolate from room temperature, and implies a much smaller index difference between AlAs and GaAs at high temperatures. Both approaches to thickness measurement might be combined to measure the Al~Ga1._~As and GaAs growth rates in a single calibration procedure. The fringe counting could be used to measure the growth rate on an initial Al~Gai_~As layer. A quarter wave layer of GaAs, and perhaps additional AlAs layers could then be grown, so that a wavelength scan would determine the GaAs thickness. Since the required layers would be less than 1 jim thick, such a calibration might be done before each growth as part of a buffer layer underneath the active layers. Such a calibration would be complementary to growth rate measurements using RHEED oscillations [11] because it measures thicknesses of relatively thick layers and is insensitive to initial flux transients.
5. Conclusions We have demonstrated infra-red transmission spectroscopy during MBE growth using the substrate heater as the light source. This technique is
We would like to thank E.C. Larkins for arguing about the “real” temperature. This work is supported by DARPA and ONR under Contract No. N00014-84-K-0077. This work has benefited from facilities made available to us by the NSFMRL Program through the center for Materials Research at Stanford University. E.S.H. Would like to acknowledge financial support from IBM. References [1] ES. Hellman, P.M. Pitner, A. Harwit, D. Liu, G.W. Yoffe, iS. Harris, Jr., B. Caffee and T. Hierl, J. Vacuum Sci. Technol. B4 (1986) 574. [2] K. Oe and Y. Imamura, Japan. J. AppI. Phys. 24 (1985) 779.
[3] E.C. Larkins, ES. Hellman, D G. Schlom, J.S. Harris, Jr, M.H. Kim and G.E. Stillman, AppI. Phys. Letters 49 (1986) 391. [4] MB. Pamsh and H.C. Casey, J. Appl. Phys. 40(1969)163. [5] CD. Thurmond, J. Electrochem. Soc. 122 (1975) 1133. [6] We assume that the index close to the band edge is independent of temperature, apart from the band edge shift. This can be seen in the data of D.T.F. Marple, J. Appl. Phys. 35 (1964) 1241, for low temperatures. [7] A.Y. Cho and JR. Arthur, Progr. Solid State Chem. 10
(1975) 157; A.Y. Cho, Thin Solid Films 100 (1983) 291. [8] The infra-red GaAs refractive index at high temperatures can be estimated from the known temperature dependence of the high frequency refractive index n,,0 given by iS. Blakemore, J. Appi. Phys. 53 (1982) R123, and from the energy dispersion measured by Marple [6] taking into account the shift of the absorption edge. [9] The index difference between Al~,Gai— ,As and AlAs is estimated to be temperature independent and equal to that given by S. Adachi, J. Appi. Phys. 58 (1985) Ri. [10] M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Pergamon, Oxford, 1980) section 1.6.5. [11] Jfl Neave, BA. Joyce, P.J. Dobson and N. Norton, AppI. Phys. A31 (1983) 1.