Journal of Electronic Materials, Vol. 19, No. 2, 1990

Epitaxial Layer Thickness Measurements Using Fourier Transform Infrared Spectroscopy (FTIR) R. A. MOELLERING, L. B. BAUER and C. L. BALESTRA McDonnell Douglas Electronic Systems Company Y 4 3 8 / l l l / 3 / M C 111-1151 P. O. Box 516 St. Louis, MO 61366 Non-destructive characterization of III-V compounds has recently received much attention. The demands of efficient use of resources require full wafer processing. Usingthe fact that semiconductors are semi-transparent at energies below their bandgaps, the theory of thin film interference can be used to measure the thickness of epitaxial layers across the wafer. Ellipsometry and reflection spectroscopy have previously been used for this type of characterization. We have non-destructively measured epitaxial layer thicknesses of the Graded Index Separate Confinement Heterostructure (GRINSCH-SQW) using simple transmission spectroscopy. Key words:

Nondestructive testing, III-V compounds, GRINSCH-SQW

1. INTRODUCTION The growth, processing, and packaging of devices made from III-V compounds are rapidly maturing technologies. Extensive work is in progress to advance the state of the art in this field. A production environment requires rapid, non-destructive characterization of material at various stages of development. A critical point in the fabrication of devices is at the post-growth, pre-processing stage. The quality of the final device depends on accurate knowledge of the thickness of the epitaxial layers. Scanning electron microscopy (SEM) or transmission electron microscopy (TEM) are very accurate methods of measuring thickness of epitaxial layers, but require considerable sample preparation time as well as destruction of the wafer. It is also difficult with SEM and TEM to produce detailed acrossthe wafer maps. If an incident photon has an energy below that of the semiconductor bandgap, the material will be somewhat transparent. This study concentrates on AI~Ga~_~As layers grown on GaAs substrates for x less than or equal to 0.6, which have bandgaps in the 0.7 to 0.9 ~ range; near infrared light can be used without considerable absorption. At far infrared wavelengths (>10 tz), free carrier absorption effects become important. Between 1 and 10 microns, however, the refractive index differences from layer to layer modulate the transmission or reflection properties of the GaAs substrate, producing an interference pattern. The theory of thin film interference is well established I and will be used here for epitaxial layers. Ellipsometry2-4 and reflection spectroscopy ~ have recently been used to find layer thicknesses in IIIV compound semiconductor heteroepitaxial structures. In this paper we describe a similar technique based on Fourier Transform Infrared Spectroscopy (Received J u l y 27, 1989; revised October 30, 1989) 0361-5235/1999/1401-18155.009

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(FTIR) which measures AlxGal-xAs epitaxial layer thickness across a 2-inch wafer. The structure studied here is a Graded Index Separate Confinement Heterostructure with a Single Quantum Well (GRINSCH-SQW), grown by Metal Organic Chemical Vapor Deposition (MOCVD) and shown schematically in Fig. 1. Epitaxial layer thicknesses are found by fitting a computer model to experimental FTIR data. The model uses the characteristic matrix method of a stratified medium 1 to simulate the transmission spectrum of multiple dielectric layers on an absorbing substrate. Analysis of multiple FTIR spectra produces a wafer mapping, providing a good measure of the across-the-wafer uniformity of the epitaxial layers. Results are compared with SEM for confirmation.

Theory We have applied the principles of thin film interference to the semiconductor epitaxial layers of the GRINSCH-SQW structure. Interference arises due to the refractive index discontinuities between the epitaxial layers and the substrate. A transmission spectrum consists of the background transmission of the substrate modified by interference fringes. For a single layer, the thickness T is given by T=

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The GRINSCH-SQW structure can be modeled as several dielectric layers stacked upon one another. In this case, one 2 • 2 matrix describing the interference properties of the entire structure is given by the product of all matrices in the stack. Although GRINSCH-SQW has eight layers, the graded layers have been split into 8 smaller layers each with linearly stepped indices of refraction. Increasing this number beyond eight gives a very small change in resulting total epitaxial layer thickness (less t h a n 10 Angstroms out of 4.5/~m). This gives a product of 22 matrices t h a t describes the entire dielectric stack. From the product matrix one can derive the reflection and transmission coefficients of the film.

Epitaxial Layer Thickness Measurements Using Fourier Transform Infrared Spectroscopy (FTIR) Although the absorption of the thin layers is assumed negligible, the as-grown GaAs substrate is approximately 400 ~ thick, giving a significant amount of absorption in the far infrared (wavelengths longer than 5 /zm) due to free carrier absorption. Using Jordan's method, 7 the GaAs absorption coefficient in the infrared is calculated from the addition of five contributions: bandgap, interconduction band, free-carrier absorption by LO phonons, scattering by acoustic phonons, and impurity scattering. Jordan has used this method to match previously obtained experimental data 8 on the infrared absorption coefficient in GaAs. A computer model was developed to handle the necessary calculations. After reading in the data file, the model assumes a nominal structure for the layer thicknesses. A characteristic matrix generated FTIR spectrum is compared to the data. The model proceeds by changing the layer thicknesses and recalculating spectra until the best fit with experimental data can be found. An example of this curve fitting is shown in Fig. 2. There are some differences between the experimental and model curves. Due to the complexity of the GRINSCH-SQW structure and slight differences in material characteristics across a wafer (e.g. doping levels), it is difficult to produce a model which will exactly match the experimental curve for all points on the wafer. We have therefore placed a greater emphasis on matching the peaks of the interference pattern. This ensures that the optical length through the material will be the same in the experimental and model epitaxial structure. The output of the model gives the resulting thickness of each of the epitaxial layers.

Experimental The GRINSCH-SQW structure was grown by MOCVD on 2-inch GaAs substrates. Wafers were

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183

placed as grown inside the nitrogen purged FTIR sample chamber so that the Globar infrared source entered the wafer at normal incidence. Spectral resolution was set at 4 cm -1. Beam position at the sample was obtained using a manual translation stage and aligning to a 1 mW Helium-Neon (633 nm) laser. The average infrared beam width was 1 mm. The KBr beam splitter and Deuterated Triglycine Sulfate (DTGS) detector were rated for quality spectra in the range 5000-400 cm -1, although in practice the upper wavenumber limit could sometimes be extended to 5500 cm -1. The average of 200 interferograms was Fourier processed and ratioed against a previously obtained background spectrum, giving the resulting transmission spectrum through the Al~Gal_~As epitaxial layers and GaAs substrate. FTIR data files were transferred via modem to a minicomputer where a FORTRAN program implemented the above mentioned characteristic matrix method. The model consumed approximately 15 rain of CPU time per data file. The data from an entire wafer could be run in a batch mode overnight. The output of the computer model gave epitaxial layer thicknesses, as well as information about the goodness of fit and output data files (e.g. Fig. 2). We used a Scanning Electron Microscope (SEM) to confirm the results of the computer model. After taking FTIR data, the wafers were cleaved at the measurement point across a major axis. In this way, the same position versus layer thickness data for both FTIR and SEM could be compared.

Results and Discussion Using the characteristic matrix method for a stratified medium, we were able to non-destructively determine Al=Ga~_~As epitaxial layer thicknesses across 2-inch GaAs wafers. A computer model was used to curve fit simulated FTIR spectra to experimental data. Examples of confirmation of the

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184

Moellering, Bauer, and Balestra

technique by SEM are shown. Numerical constants that were used can be found in the literature. 9-]2 In principle, this technique can be easily used on II-VI as well as other III-V epitaxial structures, although we have not done so. We have assumed that if the technique works on a complicated structure such as GRINSCH-SQW, then it will work on simpler At~Ga1_~As structures. W e are interested mainly in the material studied here. For other material systems, a knowledge of absorption characteristics and index of refraction over a wide wavelength range must be k n o w n as a function of alloy composition before proceeding with the technique.

a) Total Epitaxial Layer Thickness Our initial goal was to determine total layer thickness across the wafer to calculate as-grown uniformity. Wafers not meeting uniformity specifications will have low optoelectronic device yields. A significant cost savings can be realized by processing only those wafers that have proper uniformity. Figure 3 shows an example of FTIR total layer thickness as a function of position across the wafer, as confirmed by SEM. The error in both the SEM and FTIR experimental data is about + / - 1%. In many cases the FTIR model measurement would be within SEM measurement error bars. It is also important to keep in mind the differences between the two measurement techniques. The FTIR measurement was performed with a relatively wide, incoherent IR source at normal incidence to the epitaxial layers. The wafer was then cleaved and the SEM measurement was taken edge on, so that the actual layers could be seen. With SEM we could easily measure two quantities: the total epitaxial thickness, and the p-layer depth to the quantum well. It was difficult to resolve differences in other layers enough to obtain an accurate measurement of other thicknesses. Due to the fact that errors in the two

measurement techniques are on the order of a couple hundred Angstroms, we have not extracted the thickness of the quantum well from either technique. Photoluminescence is much better suited for this purpose, and is also non-destructive. In order to calculate uniformity we viewed the data as a statistical sample. One sample standard deviation, given as a percentage of the mean thickness, gives a good measure of uniformity. Lower numbers indicate better uniformity. The wafer shown in Fig. 3 has a calculated uniformity of plus or minus 6%. This wafer would not be suitable for processing, but the high amount of variation makes it useful in developing the technique. Uniformity may also be measured by tracking the wavenumber of any of the interference peaks in the FTIR spectra, without the time consumption of the computer model. We could not, however, correlate layer thickness values with the movement of interference peaks, due to the complexity of the GRINSCH-SQW structure.

b) Quantum Well Depth Determination of total layer thickness is useful for qualitative analysis of the wafer. However, other more important features of the GRINSCH-SQW structure must be measured to increase processing yield. An extremely important parameter is the asgrown depth to the quantum well, or total p-type layer thickness. This epitaxial structure is used for making rib laser diodes. The laser mode quality is quite sensitive to the depth of the rib etch. As determined by a beam propagation model using the effective index method, overetching gives multimode lasing, while underetching will result in an unconfined lateral mode. Extracting the quantum well depth has proven to be more difficult than total layer thickness. Figure 4 shows typical FTIR model results versus SEM giving quantum well depth as a function of position across a wafer. The FTIR measurement shows the

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Epitaxial Layer Thickness Measurements Using Fourier Transform Infrared Spectroscopy (FTIR) same thickness trend as does SEM, but offset by approximately 0.10 ft. Other GRINSCH-SQW wafers have shown better matching to SEM, as observed in Fig. 5. We are exploring the reasons for this discrepancy. There seems to be a variation corresponding to wafer growths by different vendors, as seen in Figs. 4 and 5, grown at different locations. Slight differences may exist in substrates used or doping profiles. It is preferable to use the same version of the model for every wafer that comes through the processing line. We are currently conducting more experiments to help rectify this problem. We have also performed an analysis to determine the sensitivity of the FTIR technique to thickness variations and changes in A1 concentration. We can include index of refraction in this discussion because our calculation of the index was based only on the wavelength of the light and the A1 concentration. Our technique can measure differences in epitaxial layer thickness as small as 5-10 Angstroms, because the computer model can find small differences in experimental FTIR spectra. In addition, the sensitivity of the model to variations in A1 concentration is much smaller than that of variations in layer thickness (a factor of 5 or more), justifying our assumption of constant A1 concentration in the layers. This can be explained by the fact that

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the index of refraction does not change rapidly with small differences in A1 concentration. We plan to automate this technique. The current manual translation stage requires opening of the sample chamber between each data point, and subsequent waiting for the N2 purge to recover. Implementation of a two stage, computer controlled translation system will greatly reduce the time spent on each wafer, and enable full wafer mapping of the epitaxial layer thickness. We believe that this will provide more accurate information about the mass transfer characteristics of the growth by showing contours of the thickness across the entire surface of the wafer. Conclusion

We have demonstrated a technique that can nondestructively screen and test as-grown epitaxial layers in GRINSCH-SQW material before processing. Our technique uses a computer model with the characteristic matrix method for a stratified medium to match experimental FTIR data and give epitaxial layer thicknesses. Success has been achieved in measuring total epitaxial layer thickness across the wafer, giving uniformity data. We have also measured the epitaxial layer depth to the quantum well. Measuring the depth to the quantum well consistently from wafer to wafer has proven to be slightly more difficult; current experiments are underway to address this and obtain more consistent results. REFERENCES

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