Extraneous atoms and material in or on the silicon wafer become

							Model-Based Parameter Distributions

Extraneous atoms and material in or on the silicon wafer become "defects" only when they degrade the
yield of devices fabricated on the wafer. Therefore, to determine the specifications for potential
defects, it is necessary to know the following:

      (1)    the total surface or volume density of the potential defects,

      (2)    the fraction of the potential defects that actually are defects (that is that cause yield
             degradation), and

      (3)    the relationship between the defect density (as contrasted with the total extraneous material
             density) and the device yield.

Many such relationships have been published in the literature. The one used in constructing Table 20
is the "Maly" equation (Ref 1 to Table 20) published in 1994. This contains an area factor as well as
the so-called "kill ratio" that describes the effectiveness of the defect in reducing yield. The kill ratio is
generally not known with any precision; different values, given in the footnotes to the table, have been
utilized for different potential defects in constructing Table 20. For surface metals, the fraction of
potential defects that cause yield degradation is computed using an extension of the work of Henley et
al (Ref 2 to Table 20). This relationship was derived for iron contamination; its applicability to other
metals has been assumed.

An additional complication arises from the fact that the characteristics of the starting materials are
dramatically modified during device processing. This makes it extremely difficult to obtain accurate
relationships between starting material characteristics (including densities of potential defects) and
device yield. Nevertheless, such relationships are the necessary foundation for model-based parameter
specifications.

(1)   Description of Technology: Accurate models must be developed, either empirically or from
      first principles, to relate the defect (or total) density to the device yield distributions. This is an
      extremely challenging task for the reasons enumerated above. However, once this is done, the
      ideal methodology to control overall material contributed yield loss would be to partition loss
      allocations by defect types so that an overall yield of 99% is achieved. The yield loss for a
      particular type is

                                    Yi     Pr(Failure|u ) f (u )du ,
                                            A
                                                            i     i   i


      where:
       Yi                    is the yield:
       A                     is the range of values over which the defect distribution is to be considered;
       Pr(Failure|ui)        is the probability that a failure will occur given a specific value, ui, for the
                             defect (as established by a typical yield curve): and
        f (ui)               is the distribution of the defect (as established by an appropriate
                             distribution function, often the log-normal distribution).
      With this approach, one can determine acceptable product distributions, which can then be
      utilized as materials acceptance criteria. Rather than a table of allowable parameter limits, this
      methodology would tailor fit specifications to individual supplier product distributions.

(2)   Key Characteristics: With accurate yield models, partitioning of the allowable defect densities
      can occur and suitable tradeoffs made. This approach would provide a much more accurate
      indication of the relative effect of different defects on the device yield and, in conjunction with
      the use of statistical specifications for material acceptance, would allow optimum selection of
      cost-effective materials.

(3)   State of Development: Yield modeling remains in a rather primitive state, despite the extensive
      work done in this field over the past several decades. This situation is especially acute in
      attempting to assess the impact of starting material characteristics on device yield because of the
      previously noted extensive modification of starting materials (including contamination levels)
      during device processing. The effects of particulate contamination on pattern-related defects are
      reasonably well understood. However, the relationship between other characteristics, such as
      flatness and structural defects in conjunction with the degree of metallic decoration, is not at all
      well defined, let alone understood.

      Wafer manufacturers have good information on the overall distribution of various parameters of
      the wafers produced. However, run times are usually short enough that extrapolation of
      distributions to cover long production periods is not reliable.

(4)   Timing: At present, efforts directed at relating starting material defects to device yield are being
      performed sporadically at universities and IC manufacturing houses. Unless this situation is
      significantly altered, the timing for achieving the results desired is “always in the future.” The
      priority of this approach has not been considered to be high in the past because the material
      characteristics provided by the silicon wafer industry for IC applications have generally been
      more than adequate for advanced production requirements. This will change, however, in the
      near future and will be further exacerbated by the advent of the low-cost generic wafer for Fab
      economies.

(5)   Important references in public domain: Two references are cited in Table 20. Also see
      selected publications in the Semiconductor Silicon Series published by the ECS and the various MRS
      Silicon Related Proceedings Volumes.

(6)   Barriers to success: The primary technical barrier is the lack of well defined relationships
      between starting material characteristics and the changes in material characteristics during device
      processing and their impact on device/circuit performance and yield.

      Non technical barriers include the following factors:
       (a) the lack of priority given to this issue by IC companies together with the need for a
           significant paradigm shift in receiving incoming materials on the part of these companies;
       (b) the probablility that there will be no sharing of parameter distribution data outside of
           specific individual supplier-user relationships; and
       (c) the untenable situation generated for the supplier arising from the lack of credible IC
           sensitivity data so that the supplier has no recourse but to supply the requested specified
           material even though the customer cannot justify a particular desired specification.
Supplier-purchaser demand dynamics will play a significant role in adoption of this approach,
which must be coupled with the general use of statistical specifications (q.v.) to be fully effective.

(7)   Other: No further comments.