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3.4.1 Semiconductor Growth Rate

James J. Filliben

Mark G. Vangel

Statistical Engineering Division, ITL

Mike Tietjen

Semiconductor Electronics Division, EEEL

In the semiconductor industry there are 3 common ways of estimating semiconductor growth rate (which in turn allows accurate achievement of pre-specified wafer thickness and accurate estimation of wafer proportional composition):

1) spectroscopic ellipsometry (which makes use of light scattering); 2) x-ray diffration (which makes use of x-rays); 3) RHEED (= Reflective High Energy Electronic Diffraction) (which makes use of electron gun diffraction).

Of the three, the RHEED method is most heavily used; lack of an accuracy estimate for the growth rate from RHEED is an industry impediment to the precise growing of wafers.

Mike Tietjen (and Joe Pelligrino) of the Semiconductor Devices Division of EEEL are addressing the problem of RHEED method accuracy. In particular, they are assessing and determining the accuracy of the RHEED method for measuring growth rate and composition of 3-element (aluminum-gallium-arsenic) III-IV semiconductor wafers.

Project questions include: 1) How accurate is that growth rate estimate? 2) How to set up a designed experiment to arrive at a robust estimate of growth rate? 3) How to convert the growth rate into estimates for the composition percentages (there are 2 complementary formulas)? 4) How good are the composition estimates? 5) How many replicates are needed?

SED contributed to this project in the following fashion: 1) An appropriate designed experiment was constructed; 2) The virtues of a spectral analysis (as opposed to a Fourier analysis) were passed on. 3) Growth rate estimates based on the spectrum and on FFT were carried out. 4) The industry software FFT was failing under certain (low-frequency) circumstances. SED/Dataplot provided such estimates. 5) Mike had some concern about the accuracy of the industry-software FFT algorithm. Numerically accurate estimates of the FFT were provided (in the spirit of StRD). 6) Precision values were computed for the growth rate. 7) Composition percentage estimates were computed. 8) Propagation of error was carried out to arrive at uncertainty estimates for the composition percentage estimates.


Figure 25: The first set of plots (raw data traces) shows the characteristic sinosoidal nature of the deposition process. The second set of plots (spectral plots) shows the consistency of the dominant frequency. The third set of plots (complex demodulation amplitude plots with demodulation frequency .016 cycles per observation) shows the linear damping of the process.

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Date created: 7/20/2001
Last updated: 7/20/2001
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