2.3
FOx ®
FOx ®
FOx ® Flowable Oxide is a low density spin-on material that performs well for inter- and intra-level gap fill and planarization for geometries in the deep submicron region, while simplifying manufacturing by providing non-etchback processing. It combines low dielectric constant (low
κ
) for interconnect capacitance reduction, while providing thermal and dielectric stability. This technical brief covers a procedure for calculating the dielectric constant as a function of refractive index. It also explains the Dow Corning test method procedures for determination of dielectric constant based on capacitancevoltage (C-V) measurements.
A dielectric is a substance that is a poor conductor of current because all electrons are bound tightly to atoms and therefore cannot move about freely. The charges within the molecular structure of a dielectric material do, however, respond to the presence of an electric field. Since positive and negative charges tend to be pulled in opposite directions, an electric dipole is created. Usually, there will be an excess of positive charge on one surface of the dielectric and an excess of negative charge on the other, resulting in a “polarization” of the material. Dielectric constant (
κ
) is often used to characterize the material’s degree of polarization in the presence of an electric field.
Most dielectrics are “linear” in that the strength of their dipole moments is directly proportional to the strength of the electric field. In linear dielectrics, the amount by which the dielectric reduces the strength of the electric field can be characterized by their relative ability, compared to a vacuum, to store energy. It is expressed in terms of the dielectric constant (
κ
), with the value for a vacuum taken as unity.
The values of
κ for dielectrics vary from slightly more than 1 for air, up to 100 or more for certain ceramics. Dielectrics, particularly those with high dielectric constants, are used extensively in all branches of electrical engineering, where they are employed to increase the efficiency of capacitors.
There has been a growing need in the semiconductor industry for low
κ material for use as inter-layer dielectric (ILD) films.
Low
κ
ILDs play a very important role in IC performance by reducing the capacitance and cross-talk between metal lines.
This enables higher speeds of operation as feature sizes are scaled into the deep submicron region. Hydrogen silsesquioxane (HSiO
1.5
) n
, which is produced by Dow Corning
Corporation as FOx Flowable Oxide, has been a leading ILD candidate in part due to its low
κ performance.
The primary means for measuring
κ on wafer is the capacitance-voltage (C-V) method. This method is slow and requires expensive electrical equipment to carry out. It is also very sensitive to the dielectric film thickness measurement.
Therefore, a model has been formed by Dow Corning so that a close approximation of dielectric constant can be obtained as a function of the refractive index measurement. This method is very easy to use and yields very good results with respect to standard measurement practices.
The measurement of dielectric constant is achieved indirectly by the measurement of the capacitance of an MIS (Metal
Insulator Semiconductor) structure. The dielectric constant equation requires capacitance, distance between plates
(conductors), and the area of the plates, all of which require measurement for accurate results. Insofar as these measurements are concerned, accurate results are readily obtainable, with verification and repeatability tracked using reference standards and known dielectric constant materials.

Dielectric constant (referred to as
κ
) is defined as “the ratio of the permittivity of a material to the permittivity of free space,” and as such, it is a number without units. It is also plainly seen that
κ cannot be less than 1.
κ is defined as:
=
C
•
T
•
A
Where C is capacitance, T is the distance between the parallel plates, A is the area of the plates, and free space (8.8542x10
-12
ε
Farads/Meter).
° is the permittivity of
The first step in producing MIS structures is to begin with a silicon wafer. Since the wafer itself acts as a substrate and
“plate” of the capacitor structure, it stands to reason that it must act as a conductor. For good conduction, a high conductivity (heavily doped) wafer is required, which has a vast amount of free carriers available. Typically, wafers that are rated at <0.05
Ω
-cm are used.
The second step is the growth of the dielectric film on the silicon wafer (the insulator). This can be done in a variety of ways using spin-on or chemical vapor deposition (CVD) methods.
To complete the MIS structure, a metal “gate” is created on top of the insulator. This is done using Physical Vapor
Deposition (PVD) via a metal sputtering chamber. A mask is placed on top of the wafer (or pieces of wafer if necessary), and the metal is deposited in the sputtering chamber. Typical metal depositions are copper or titanium/aluminum.
The mask has several circular holes, each of which has specific diameters that are tracked over time. These molybdenum masks are manufactured to a high degree of accuracy for use in these types of measurements. The difference in the hole sizes on the mask allow for a range of capacitances that can be read by the equipment. Depending on the thickness and
κ of the material being investigated, some of the gates may not be measurable. This is due to the dynamic range of the capacitance meter being used in the test. An overall MIS structure is depicted below.
Dielectric thickness measurement is accomplished via ellipsometry using a J.A. Woolam Inc. spectroscopic ellipsometer. This thickness is the distance between the plates of the capacitor.
Capacitance measurement is achieved by placing the metallized samples on a vacuum chuck and probing with a capacitance meter. Typically, five differening diameter gates are measured, and then correlated via software. The Keithley 590 C-V analyzer utilizes an AC component at a frequency of 1 MHz. A
DC can also be manipulated on the gate of the MIS capacitor.
Denton sputtering system
Electrical instrumentation rack
Ellipsometer
Vacuum chuck with probe

Uncorrelated errors can be traced to three major sources. The first is the basic accuracy of the capacitance meter. From its internal specifications, this is specified as approximately
0.5%. The second error source is from the nature of measuring the film thickness. This thickness is measured across the center of the sample, and not between each of the MIS sandwiches.
Therefore, an error of 1% can be attributed to variations in film thickness across all the gates. This error can be greatly amplified if the wafer has poor film uniformity due to growth abnormalities or other anomalies. The final error term can be attributed to variations in the hole diameter of the molybdenum mask, which created the metal gate (approximately 1.5%).
The total uncorrelated error is therefore nearly 2% of the measured capacitance on the meter.
The same array of tools that were outlined in this document can be used in essentially the same manner to derive the capacitance and therefore dielectric constant by use of a C-V curve. This method uses the same MIS structure, but with a lower conductivity silicon substrate (typically 1-8 Ω -cm). A lower number of free carriers doped in the silicon substrate is required so that the substrate can be driven into accumulation
(see screen shot below). The C-V curve method is more time consuming than the direct capacitance method. With a large number of samples to measure, throughput can be greatly increased by using the direct method. The C-V method is primarily used in the lab for analysis of copper diffusion in thin films.
Screen shot of software
Screen shot of a C-V curve

Midland, MI (USA Headquarters) .................. 989 496-4000
Europe
Seneffe, Belgium............................................. 32 64 888000
Asia
Tokyo, Japan.................................................... 81 3 32871011
Seoul, Korea.................................................... 82 2 5517600
Singapore......................................................... 65 63593331
Taipei, Taiwan ................................................. 886 2 66003100
Bangkok, Thailand .......................................... 66 2 6347078
Shanghai, China .............................................. 86 21 62882626
We help you invent the future.
™ www.dowcorning.com
LIMITED WARRANTY INFORMATION–PLEASE READ CAREFULLY
The information contained herein is offered in good faith and is believed to be accurate. However, because conditions and methods of use of our products are beyond our control, this information should not be used in substitution for customer’s tests to ensure that Dow Corning’s products are safe, effective, and fully satisfactory for the intended end use. Suggestions of use shall not be taken as inducements to infringe any patent.
Dow Corning’s sole warranty is that the product will meet the Dow Corning sales specifications in effect at the time of shipment.
Your exclusive remedy for breach of such warranty is limited to refund of purchase price or replacement of any product shown to be other than as warranted.
DOW CORNING SPECIFICALLY DISCLAIMS ANY OTHER EXPRESS OR
IMPLIED WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE OR
MERCHANTABILITY.
DOW CORNING DISCLAIMS LIABILITY FOR ANY INCIDENTAL OR
CONSEQUENTIAL DAMAGES.
Dow Corning and FOx are registered trademarks of Dow Corning Corporation.
We help you invent the future is a trademark of Dow Corning Corporation.
©2005 Dow Corning Corporation. All rights reserved.
AMPM170/505
Form No. 10-872A-01