<PAGE>

                                                                   EXHIBIT 10.84

                   AMENDMENT NO. 6 TO PARTICIPATION AGREEMENT

         THIS AMENDMENT NO. 6 TO PARTICIPATION AGREEMENT, dated as of December
27, 2002 (this "AMENDMENT"), is entered into by and among LAM RESEARCH
CORPORATION, a Delaware corporation (the "LESSEE"), the CUSHING 2000 TRUST, a
Delaware statutory trust (the "LESSOR"), SCOTIABANC INC., a Delaware corporation
(subject to the definition of "Holder" in Annex A to the Participation Agreement
(as defined below) the "HOLDER"), THE BANK OF NOVA SCOTIA and FLEET NATIONAL
BANK (subject to the definition of "Lenders" in Annex A to the Participation
Agreement, collectively, the "LENDERS"), and THE BANK OF NOVA SCOTIA, as the
administrative agent for the Lenders and with respect to the Security Documents,
as agent for the Lenders and the Holder, to the extent of their respective
interests (in such capacity, the "AGENT").

                                    RECITALS

         A.       The Lessee, the Lessor, the Holder, the Lenders and the Agent
are parties to that certain Participation Agreement, dated as of December 6,
2000 (as amended by that certain Amendment No. 1 to Participation Agreement
dated as of February 28, 2001, that certain Amendment No. 2 to Participation
Agreement and Amendment No. 1 to certain Operative Agreements dated as of June
22, 2001, that certain Amendment No. 3 to Participation Agreement dated as of
September 22, 2001, that certain Amendment No. 4 to Participation Agreement and
Limited Waiver, dated as of February 11, 2002, that certain Amendment No. 5 to
Participation Agreement dated as of July 19, 2002, and as the same may be
amended, restated or otherwise modified further, the "PARTICIPATION AGREEMENT").

         B.       The Lessee has requested an amendment to the EBITDAR covenant
in the Participation Agreement. The Participants are willing to amend the
Participation Agreement in the manner in which the Lessee desires, but only to
the extent, subject to the terms and conditions, and in reliance upon the
representations and warranties set forth herein.

                                    AGREEMENT

         NOW, THEREFORE, in consideration of the foregoing recitals, and for
other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, and intending to be legally bound, the parties hereto agree
as follows:

SECTION 1.        DEFINITIONS. Capitalized terms used herein without definitions
shall have the meanings given to such terms in Annex A to the Participation
Agreement.

SECTION 2.        AMENDMENTS TO PARTICIPATION AGREEMENT AND ANNEX A TO
PARTICIPATION AGREEMENT. The Participation Agreement is hereby amended as
follows:

         2.1      A new definition is added to Annex A of the Participation
Agreement as follows:

                  "CONTROL AGREEMENTS" shall mean the Securities Account Control
                  Agreement by and among Lessee, Agent and The Bank of Nova
                  Scotia Trust Company

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                  (Cayman) Limited, and the Control Agreement by and among
                  Lessee, Fleet National Bank and the Treasury Division of Fleet
                  National Bank.

         2.2      The definition of "COLLATERAL AGENT" in Annex A to the
Participation Agreement is hereby amended to read as follows:

                  "COLLATERAL AGENT" shall mean The Bank of Nova Scotia, or, for
                  purposes of the Pledge Agreement, as set forth in the Recitals
                  thereto.

         2.3      The definition of "OPERATIVE AGREEMENTS" in Annex A to the
Participation Agreement is hereby amended by adding a new item (m): "The Control
Agreements".

         2.4      The definition of "VALUE" in Annex A to the Participation
Agreement is hereby amended to read as follows:

                  "VALUE" shall have the meaning given it in Section 1 of the
                  Pledge Agreement for purposes thereof, and, with respect to
                  the Collateral Accounts, shall mean the aggregate Dollar value
                  of the principal balances thereof on the date of
                  determination.

         2.5      SECTION 5.4 of the Participation Agreement is hereby deleted
in its entirety and replaced with the following:

                  "Lessee shall deliver Pledged Collateral (as defined below) to
         the Collateral Agent, or to each Participant as specified herein.
         Lessee shall deliver Pledged Collateral to the Collateral Agent, for
         The Bank of Nova Scotia and Scotiabanc, Inc. in an amount equal to 100%
         of the product of the aggregate Commitment Percentage of such entities
         multiplied by the aggregate outstanding Advances (the "Scotia Pledged
         Collateral Amount"). Lessee shall deliver Pledged Collateral to Fleet
         National Bank in an amount equal to 111.11% of the product of the
         Commitment Percentage for such entity multiplied by the aggregate
         outstanding Advances (the "Fleet Pledged Collateral Amount").
         Thereafter, the Lessee covenants to maintain the Value of the Pledged
         Collateral at a level equal to 100% of the sum of the Scotia Pledged
         Collateral Amount and the Fleet Pledged Collateral Amount (the "Total
         Required Pledged Collateral Amount"), and within two (2) Business Days
         after receipt of notice from the Collateral Agent that the Value of the
         Pledged Collateral is less than 100% of the Total Required Pledged
         Collateral Amount, the Lessee shall be obligated to deliver Pledged
         Collateral in an amount required to maintain the Value of the Pledged
         Collateral at a level equal to 100% of the Total Required Pledged
         Collateral Amount. Lessee hereby assigns, pledges, hypothecates,
         charges, mortgages, delivers and transfers to each Participant, and to
         Collateral Agent, for its benefit and the ratable benefit of each of
         the Participants, and hereby grants to each Participant and to
         Collateral Agent, for its benefit and the ratable benefit of each of
         the Participants, a continuing first priority security interest in and
         against all right, title and interest, whether beneficial or otherwise,
         of Lessee in and to the following, whether now or hereafter existing or
         acquired by Lessee (collectively, the "Pledged Collateral"): Account
         No. 4929 maintained by Lessee with The Bank of Nova Scotia Trust
         Company (Cayman) Limited, and Account No. 942634797-LC maintained by
         Lessee with Fleet National Bank (collectively, the "Collateral
         Accounts"), and the

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         securities, securities entitlements or other investment property,
         instruments and financial assets contained or at any time held or
         maintained in the Collateral Account, together with all investment
         property, instruments and financial assets substituted therefore or for
         any part thereof, all interest, dividends, increases, profits, new
         financial assets or other increments, distributions or rights of any
         kind received on account of any of the foregoing, and all other income
         received in connection therewith and all products or proceeds thereof
         (whether cash or non-cash). For so long as Lessee maintains the Pledged
         Collateral in accordance with this Section 5.4 the Applicable Margin
         shall be thirty-five basis points (0.35%)."

         2.6      SECTION 9.3(j)(v)(A) of the Participation Agreement is hereby
modified by replacing the amount "$450,000,000" in line two thereof with the
amount "$350,000,000".

         2.7      SECTION 9.3(j)(vi) of the Participation Agreement is hereby
deleted in its entirety and replaced with the following:

                           (iv)     MINIMUM QUARTERLY EBITDAR.

                                    (A)      Beginning with the Fiscal Quarter
                                    ending in June 2002 through and including
                                    the Fiscal Quarter ending in June 2003,
                                    maintain EDITDAR of not less than the
                                    following for the applicable period:

<TABLE>
<CAPTION>
----------------------------------------------------------
         PERIOD                            MINIMUM EBITDAR
----------------------------------------------------------
<S>                                        <C>
For the Fiscal Quarter                       $ 5,000,000
ending in June 2002

----------------------------------------------------------
For the Fiscal Quarter                       $10,000,000
ending in September 2002

----------------------------------------------------------
For the Fiscal Quarter                       $10,000,000
ending in December 2002

----------------------------------------------------------
For the Fiscal Quarter                       $10,000,000
ending in March 2003

----------------------------------------------------------
For the Fiscal Quarter                       $15,000,000
ending in June 2003

----------------------------------------------------------
</TABLE>

SECTION 3.        REFERENCE TO AND EFFECT ON THE PARTICIPATION AGREEMENT. Upon
the effectiveness of this Amendment, each reference in the Participation
Agreement to "this Agreement," "hereunder," "hereof," "herein" or words of like
import shall mean and be a reference to the Participation Agreement as amended
by this Amendment, and each reference in any other document in which the
Participation Agreement is referenced shall also mean and be a reference to the
Participation Agreement as amended by this Amendment.

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SECTION 4.        REFERENCES TO "PLEDGED COLLATERAL". Upon the effectiveness of
this Amendment, each reference in the Operative Agreements to "Pledged
Collateral" shall, after the date hereof, be understood to refer to collateral
pledged pursuant to either or both of the Pledge Agreement and Section 5.4 of
the Participation Agreement.

SECTION 5.        LIMITATION OF AMENDMENTS. The amendments set forth in SECTION
2, above, shall be limited precisely as written and shall not be deemed to (i)
be an amendment to any other term or condition of the Participation Agreement,
(ii) prejudice any right or remedy which any party may now have or may have in
the future under or in connection with the Participation Agreement or any other
Operative Agreement, or (iii) be a consent to any future amendment.

SECTION 6.        REPRESENTATIONS AND WARRANTIES. In order to induce the
Participants to enter into this Amendment, the Lessee hereby represents and
warrants to each Participant as follows:

         6.1      Immediately after giving effect to this Amendment (a) the
representations and warranties contained in the Participation Agreement and in
the other Operative Agreements (other than those which expressly speak as of a
particular date, which shall be true as of such date) are true, accurate and
complete in all material respects as of the date hereof and (b) no Default or
Event of Default attributable to the Lessee has occurred and is continuing;

         6.2      The Lessee has the corporate power and authority to execute
and deliver this Amendment and to perform its obligations under the
Participation Agreement, as amended by this Amendment, and each of the other
Operative Agreements to which it is a party;

         6.3      The certificate of incorporation, bylaws and other
organizational documents of the Lessee delivered to the Participants as a
condition precedent to the effectiveness of the Participation Agreement and the
other Operative Agreements are true, accurate and complete and have not been
amended, supplemented or restated, except to the extent that copies thereof have
been previously provided to Agent, and are and continue to be in full force and
effect;

         6.4      The execution and delivery by the Lessee of this Amendment and
the performance by the Lessee of its obligations under the Participation
Agreement, as amended by this Amendment, have been duly authorized by all
necessary corporate action on the part of the Lessee;

         6.5      The execution and delivery by the Lessee of this Amendment and
the performance by the Lessee of its obligations under the Participation
Agreement, as amended by this Amendment, do not and will not contravene (a) any
law or regulation binding on or affecting the Lessee, (b) the certificate of
incorporation, bylaws or other organizational documents of the Lessee, (c) any
order, judgment or decree of any court or other governmental or public body or
authority, or subdivision thereof, binding on the Lessee, or (d) any contractual
restriction binding on or affecting the Lessee; and

         6.6      The execution and delivery by the Lessee of this Amendment and
the performance by the Lessee of its obligations under the Participation
Agreement, as amended by this Amendment, do not require any order, consent,
approval, license, authorization or validation of, or filing, recording or
registration with, or exemption by any governmental or public body or authority,
or subdivision thereof, except as already has been obtained or made.

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SECTION 7.        FEES AND EXPENSES. The Lessee agrees to pay to the Agent, upon
demand, the amount of any and all out-of-pocket expenses, including the
reasonable fees and expenses of its counsel, which the Agent may incur in
connection with the preparation, documentation, and negotiation of this
Amendment.

SECTION 8.        CONDITIONS PRECEDENT TO EFFECTIVENESS. This Amendment shall be
deemed effective as of the date set forth in the preamble to this Amendment once
each of the following conditions shall have been satisfied:

         (a)      The Agent shall have received a copy of this Amendment
originally executed by the Lessee and Lenders comprising Majority Secured
Parties;

         (b)      The Agent shall have received a copy of the Control Agreements
originally executed by Lessee and the securities intermediary with respect to
each Collateral Account;

         (c)      The Agent shall have received confirmation of the filing of a
UCC financing statement with respect to the Pledged Collateral; and

         (d)      In consideration of the Lenders agreeing to enter into this
Amendment, the Agent shall have received, for the ratable benefit of the Lenders
and the Holder, in immediately available funds, an amendment fee equal to 0.25%
of the Aggregate Commitment Amount.

SECTION 9.        FULL FORCE AND EFFECT; REAFFIRMATION. It is hereby agreed that
all terms and conditions of the Participation Agreement and the other Operative
Agreements, as previously amended to date, shall remain in full force and effect
as amended pursuant to the terms of this Amendment. The Lessee hereby reaffirms
its obligations under each of the Operative Agreements to which it is a party.

SECTION 10.       GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY AND SHALL
BE CONSTRUED AND ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

SECTION 11.       COUNTERPARTS. This Amendment may be executed in any number of
counterparts, each of which when so delivered shall be deemed an original, but
all such counterparts taken together shall constitute but one and the same
instrument.

SECTION 12.       INSTRUCTION TO EXECUTE. Scotiabanc Inc., as the sole Holder on
the date hereof, represents to the Property Trustee (as defined in the Trust
Agreement) that it is the Required Holder (as defined in the Trust Agreement)
with the right to instruct the Property Trustee, pursuant to the Trust
Agreement, to execute and deliver this Amendment on behalf of the Lessor and, as
such, hereby directs the Property Trustee to so execute and deliver this
Amendment on behalf of the Lessor.

                            [SIGNATURE PAGES FOLLOW]

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         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed as of the date first written above.

LESSEE                            LAM RESEARCH CORPORATION

                                  By: /s/  Craig Garber
                                         _______________________________________

                                  Name:    Craig Garber
                                       _________________________________________

                                  Title:   Vice President Finance and Treasurer
                                        ________________________________________

LESSOR                            CUSHING 2000 TRUST

                                  By: WILMINGTON TRUST FSB, not in its
                                      individual capacity but solely as
                                      Property Trustee

                                      By:  /s/ Daniel M. Reser
                                         _______________________________________

                                      Name:    Daniel M. Reser
                                           _____________________________________

                                      Title:   Assistant Secretary and
                                               Vice President
                                            ____________________________________

AGENT AND THE LENDERS             THE BANK OF NOVA SCOTIA, as the Agent and as a
                                  Lender

                                  By:   /s/ L.A. Beard
                                     ___________________________________________

                                  Name: L.A. Beard
                                  Title: Director, Technology Group

                                  FLEET NATIONAL BANK, as a Lender

                                  By:   /s/ Lee Merkle-Raymond
                                     ___________________________________________

                                  Name:     Lee Merkle-Raymond
                                       _________________________________________

                                  Title:    Director
                                        ________________________________________

HOLDER                            SCOTIABANC INC.

                                  By:   /s/ William E. Zarrett
                                     ___________________________________________

                                  Name:     William E. Zarrett
                                       _________________________________________

                                  Title:    Managing Director
                                        ________________________________________

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