<PAGE>

                                                                   EXHIBIT 10.39
                                                                   -------------

                          NUMERICAL TECHNOLOGIES, INC.
                          ----------------------------

                              PRODUCTION LICENSE*


     This PRODUCTION LICENSE (this "Agreement") is entered into as of the 31st
day of December, 2000 ("Effective Date") by and between United Microelectronics
Corporation, ("UMC"), and Numerical Technologies, Inc. ("Numerical
Technologies"), and describes the terms and conditions pursuant to which
Numerical Technologies shall license to UMC and support certain patents and
software.  In consideration of the mutual promises and upon the terms and
conditions set forth below, the parties agree as follows:

1.  Definitions.
    ------------

1.1  "Average Sale Price" means the average price actually charged by UMC for
Royalty Bearing Wafers during a particular calendar quarter, calculated using
gross revenues of Royalty Bearing Wafers, as determined in accordance with UMC
normal and customary business records and under Taiwan GAAP, less Standard
Deductions.  Average Sale Price shall exclude any Backend Processing and shall
be based on the value at Wafer Out at the fab.

1.2  "Backend Processing" means the processing of a wafer after wafer out, and
includes for example and without limitation, packaging.


1.3  "Confidential Information" means any information disclosed by either party
to the other party, either directly, in writing, orally or by inspection of
tangible objects (including without limitation, documents, prototypes and
samples) which is marked "confidential," "proprietary" or some similar
designation.  Information communicated verbally or in non-tangible form shall be
considered "Confidential Information" if such information is designated as
confidential at the time of disclosure and is confirmed in writing as being
confidential within thirty (30) days after disclosure. Confidential Information
shall include without limitation, PSM Software.

1.4  "Customer PSM Technology" means that PSM Technology or PSM Documentation
relating to technology parameters, yield information, etc. typically disclosed
by UMC to customers or potential customers for such customer's evaluation
purposes and implementation purposes and pursuant to an appropriate non-
disclosure agreement.

1.5  "Derivative Works" shall have the meaning set forth in the U.S. copyright
code as interpreted by applicable case law.

1.6  "Designated Seat" means a single UMC workstation licensed hereunder for Use
of the PSM Software.

1.7  "Design Service" means a business relationship in which UMC designs some or
all of the integrated circuits for a third party which distributes or markets
such integrated circuits under a trademark different than UMC's.

1.8   "Flows" means a collection of UMC Scripts.
__________________

    * Certain information in this document has been omitted and filed separately
with the Commission. Confidential treatment has been requested with respect to
the omitted portions.
<PAGE>

1.9  "IDF" means the following companies: (1)*, (2)*, (3)*, (4)* and (5)*.

1.10 "List of Customers" means that written list of UMC's customers or potential
customers which: (1) UMC shall provide to Numerical Technologies within 30 days
of expiration or termination of this Agreement; and (2) includes only the
identification of (a) customers with products in test or production as of the
date of such termination or expiration, and (b) customers or potential customers
who had initiated discussions with UMC for a specific product using a specific
UMC Process (meaning a semi-conductor process generation used by UMC to
manufacture wafers (e.g. 0.25 um, 0.18 um) on or before the date of termination
or expiration; and (3) includes the process generation to be used by such
customer or potential customer.

1.11 "Maintenance and Support" means the services described in Section 7.

1.12 "NTI Enhancement" means a modification of the PSM Technology or PSM
Software made by and/or for Numerical Technologies where such enhancement is
based on information or input of UMC based on which UMC could claim any rights
in such modification absent this Agreement.

1.13 "Production Royalties" means those royalties UMC shall pay Numerical
Technologies for the fabrication of Royalty Bearing Wafers, based on the royalty
rates set forth herein.

1.14 "Production Wafer" means a wafer, manufactured at any UMC Wafer Fabrication
Site which is provided to a third party. Production Wafers shall include all
wafers split into integrated circuits for further sale by UMC. Production Wafers
shall not include wafers that: (1) are scrapped or returned (and not resold);
(2) wafers that are provided to third parties solely for product design or
testing, or (3) wafers which are not provided to third parties.

1.15 "PSM Documentation" shall mean any documents provided by Numerical
Technologies pursuant to this Agreement describing the PSM Technology, PSM
Software or PSM Patents.

1.16 "PSM Software" means the following software: iN-Phase v. X.x (iN-Phase
Design, iN-Phase OPC, iN-Phase Verification), Model Generator v. X.x and Rule
Generator v. X.x, and all Updates provided by Numerical Technologies under this
Agreement.

1.17 "PSM Technology" means a use of two masks, or reticles, for defining a
layer of material in an integrated circuit. The first mask or reticle has phase
shifting areas in an opaque field for defining at least a  transistor gate. The
second mask or reticle has opaque areas and clear areas. The opaque areas define
an interconnect structure in the layer to interconnect the transistor gate with
other structures in the layer. The opaque areas also prevent erasure of the
transistor gate. The clear areas further define the interconnect structure.

1.18 "PSM Patents" means U.S. Patent No. 5,858,580 (and any continuations or
divisional applications thereof, and any foreign counterparts thereto), and any
other semiconductor process patent owned or controlled by Numerical Technologies
that is useful or necessary to use or implement PSM Technology.

1.19 "Royalty Bearing Wafer" means Production Wafers that: (i) infringe U.S.
patent 5,858,580 (and any continuations or divisional applications thereof, and
any foreign counterparts thereof) or are made using a process that infringes
U.S. patent 5,858,580 (and any continuations or divisional applications thereof,
and any foreign counterparts thereof), or (ii) infringe any other PSM Patent or
are made using a process that infringes such PSM Patents and UMC chooses to have
such Production Wafers covered by the licenses granted herein.  Any wafers
manufactured by UMC that are not considered Royalty Bearing Wafers under this
Agreement shall be unlicensed wafers.

1.20 "Standard Deductions" (a) normal and customary rebates, and cash and trade
discounts actually given, (b) amounts allowed or credited due to returns (not to
exceed the original billing or invoice amount), and (c) sales, use and/or other
excise taxes or duties actually paid, (d) the cost of any packages and packing,
(e) insurance costs and outbound transportation charges prepaid or allowed, and
(f) import and/or export duties actually paid..

1.21 "Taiwan GAAP" means Generally Accepted Accounting Procedures used in
Taiwan. In the event that any amounts owing under this Agreement to Numerical
Technologies are materially less than what would have been paid had the relevant
books and records been kept in accordance with GAAP based in

__________________

    * Certain information in this document has been omitted and filed separately
with the Commission. Confidential treatment has been requested with respect to
the omitted portions.

                                      -2-
<PAGE>

the U.S., UMC agrees to pay the full extent of such difference; provided that
Numerical Technologies shall be solely responsible for all costs associated with
calculating amounts using U.S. GAAP whether incurred by Numerical Technologies
auditors or incurred by UMC to verify such results.

1.22 "UMC" shall mean United Microelectronic Corporation, its majority owned
non-fabrication subsidiaries, and all UMC Wafer Fabrication Sites.

1.23 "UMC Enhancement" means a modification of any UMC manufacturing process,
recipes, and/or manufacturing, fabrication, assembly and/or test techniques or
any other UMC technology made by and/or for UMC where such enhancement is based
upon information or input of Numerical Technologies based on which Numerical
Technologies could claim any rights in such modification absent this Agreement.

1.24 "UMC Wafer Fabrication Site" means (i) a facility used for the manufacture
of wafers in which is wholly owned by UMC; (ii) a facility used for the
manufacture of wafers in which UMC owns or controls thirty percent (30%) or more
of the stock or other equity interest entitled to vote for the election of
directors or equivalent governing body of the entity that owns or controls the
facility and which UMC notifies Numerical Technologies in writing of UMC's
intention to include such facility within the definition of UMC Wafer
Fabrication Site under this Agreement; and (ii) any other facility for the
production of Production Wafers approved by Numerical Technologies in writing.

1.25 "Update" means a release or version of the Software containing functional
enhancements, extensions, error corrections or fixes that is generally made
available free of charge (other than media and handling charges) to Numerical
Technologies' customers who have contracted for Maintenance and Support.

1.26 "UMC Scripts" means that software which is created by or for UMC
(including, without limitation, by NTI) following the Effective Date of this
Agreement which allows for the communication of data between the PSM Software
and software other than Numerical Technologies' software.

1.27 "Use" means utilization of the PSM Software by UMC by no more than the
number of Designated Seats as set forth on Exhibit B, by copying or transferring
                                           ---------
the same into UMC's computer equipment.

2.  Grant of License.
    -----------------

2.1  Patent License.  Subject to the terms and conditions of this Agreement,
     --------------
Numerical Technologies grants to UMC a time-limited, non-transferable, non-
exclusive, worldwide right and license under the PSM Patents to (1) make Royalty
Bearing Wafers at UMC Wafer Fabrication Sites, and (2) to use, sell, offer to
sell, import or export Royalty Bearing Wafers made at UMC Wafer Fabrication
Sites.  UMC has no right to use the rights granted herein to provide Design
Services to third parties unless UMC also makes the subject Production Wafers
under this Agreement.  UMC has no right to sublicense the rights granted herein
in Section 2.1(1), but may sublicense the rights granted in Section 2.1(2).

2.2  Copyright Licenses.
     ------------------

     Subject to the terms and conditions of this Agreement, Numerical
Technologies hereby grants to UMC a time-limited, non-exclusive and non-
transferable license under Numerical Technologies' copyrights: (a) to reproduce
and Use the PSM Software for the purpose of the production of Production Wafers
at UMC Wafer Fabrication Sites, (b) to use, reproduce and modify the PSM
Documentation in connection with the manufacture of Production Wafers, anc (c)
to create UMC Scripts and Flows.  UMC has no right to sublicense the rights
granted herein.

     Subject to the terms and conditions of this Agreement, UMC hereby grants to
Numerical Technologies a time-limited, non-exclusive and non-transferable
license under UMC's copyrights in the UMC Scripts and Flows to use, reproduce
and make Derivative Works thereof solely as necessary to fulfill its obligations
under this Agreement.  Numerical Technologies has no right to sublicense the
rights granted herein, and shall under no circumstances disclose UMC Scripts and
Flows or Derivative Works thereof to any third party, except as such disclosure
is required in connection with the enforcement of this Agreement or rights under
this Agreement, or to the extent that Numerical Technologies is required to make
such disclosure pursuant to any applicable law (provided that Numerical
Technologies shall provide reasonable prior notice to UMC of such disclosure).

     (c) Numerical Technologies grants UMC a worldwide, non-exclusive, time-
limited right to reproduce and distribute Customer PSM Technology to UMC
customers or potential customers subject to the terms of an appropriate non-
disclosure agreement.

                                      -3-
<PAGE>

2.3  Delivery.  Numerical Technologies shall issue to UMC, as soon as
     --------
practicable, machine-readable copies of the PSM Software as set forth in Exhibit
                                                                         -------
A, along with one (1) copy of the appropriate Documentation.
-

2.4  Copies.  UMC will be entitled to make a reasonable number of machine-
     ------
readable copies of the PSM Software for backup or archival purposes.  UMC may
not copy the PSM Software, except as permitted by this Agreement.  UMC shall
maintain accurate and up-to-date records of the number and location of all
copies of the PSM Software and provide such information to Numerical
Technologies upon a written request from Numerical Technologies..  All copies of
the PSM Software will be subject to all terms and conditions of this Agreement.
Whenever UMC is permitted to copy or reproduce all or any part of the PSM
Software, all titles, trademark symbols, copyright symbols and legends, and
other proprietary markings must be reproduced.

3.  License Restrictions
    --------------------

3.1  Designated Seat. Except as permitted under  Section 4.2, UMC shall not
     ---------------
allow access to any licensed copy of the PSM Software unless and until UMC has
paid Numerical Technologies the license fees for such Designated Seat..

3.2  Reservation.  Except for the limited and express licenses granted to UMC
     -----------
under 2, Numerical Technologies does not grant proprietary or intellectual
property rights to the PSM Software, PSM Documentation, or any other copyrights,
patents, of Numerical Technologies.

3.3  Other Restrictions.  UMC agrees that it will not itself, or through any
     ------------------
parent, subsidiary, affiliate, agent or other third party:

sell, lease, license or sublicense (except as expressly provided in Section 2 of
this Agreement) the PSM Software or the PSM Documentation;

decompile, disassemble, or reverse engineer the PSM Software, in whole or in
part;

except as expressly provided in Section 2,  write or develop any Derivative
Works of the PSM  Software or PSM Documentation;

use the PSM Technology or the PSM Software to provide processing services to
third parties without the concomitant production of the subject Production
Wafers, or otherwise use the PSM Software on a time-share, application service
provider, or 'service bureau' basis; or

provide, disclose, divulge or make available to, or permit use of the PSM
Technology or the PSM Software by any third party without Numerical
Technologies' prior written consent except as otherwise permitted under other
provisions of this Agreement.

3.4  No Implied Licenses.  No licenses are to be implied from any term of this
     -------------------
Agreement other than the licenses expressly granted herein.

3.5  Ownership.
     ---------

     (a) By Numerical Technologies.  Numerical Technologies shall own all right,
         -------------------------
title and interest in intellectual property owned by Numerical Technologies
prior to this Agreement, PSM Software and PSM Documentation provided by
Numerical Technologies, and NTI Enhancements, including all intellectual
property rights therein (collectively, the "NTI-IP").

     Numerical Technologies shall have the exclusive rights to apply for and
register any patents, mask work rights, copyrights and such other proprietary
protections with respect to the NTI-IP.

     (b)  By UMC.
          ------

     UMC shall own all right, title and interest (i) the UMC's intellectual
property owned by UMC prior to this Agreement and all UMC Enhancements, (ii) UMC
Scripts and Flows, and (iii) all Derivative Works of the PSM Documentation
created by UMC subject to NTI's ownership rights in the underlying PSM
Documentation,  and all intellectual property rights therein (collectively, the
"UMC-IP").

     UMC shall have the exclusive rights to apply for and register any patents,
mask work rights, copyrights and such other proprietary protections with respect
to the UMC-IP.

  (c) Joint Ownership.  In the event any modification is or could be considered
      ---------------
both a NTI Enhancement and UMC Enhancement, it shall be jointly owned by the
parties and each party may exploit such modification within the scope of the
definitions of UMC Enhancement and NTI Enhancement.

                                      -4-
<PAGE>

4.  Royalties, License Fees and Taxes.
    ----------------------------------

4.1  Production Royalties.  In consideration of the license granted pursuant to
     --------------------
Section 2.1 and 2.2 and the right to undertake production granted therewith, UMC
agrees to pay Numerical Technologies the Production Royalties according to the
following formula:

Number of Royalty Bearing Wafers x Average Sale Price x Royalty Rate =
Production Royalties

The Royalty Rate shall be listed on Exhibit A hereto.
                                    ---------

4.2  Software Price Limit.  Until the completion of the third milestone as set
     --------------------
forth in Exhibit C, Numerical Technologies shall license the PSM Software to UMC
         ---------
in accordance herewith at no cost.  Upon completion of the third milestone, if
UMC should desire to continue Use of the PSM Software, UMC shall so notify
Numerical Technologies, and Numerical Technologies shall offer volume
discounting for licenses to Designated Seats (which shall include the
Maintenance Fees set forth in Section 4.8 below); provided that such pricing
shall not exceed $* per year per Designated Seat (inclusive of taxes and
support) ("Software Fees").  Any further Use of the PSM Software by UMC shall
only be pursuant to the purchase of a license or licenses to Designated Seats.

4.3  UMC Preferred Pricing.
     ---------------------

(a)  In the event that Numerical Technologies grants or has granted, any IDF a
license to PSM Patents that sets forth a more favorable per wafer royalty rate
than that set forth in Exhibit A, then Numerical Technologies shall offer,
within 30 days of the effective date of such agreement, the same royalty rates
to UMC; provided that UMC must also accept the same or substantially similar
terms as those contained within a binding agreement with such IDF in the
following areas: (1) term (duration) of the agreement, (2) the same
indemnification and limitation of liability terms (3) the same minimum wafer
production commitments, and (4) the same maximum wafer production commitments.
Notwithstanding this Section 4.3(a), Numerical Technologies shall not be
obligated to offer such terms to UMC where the agreement with such IDF: (1)
grants back to NTI, material license rights or ownership rights to material
technology, or (2) provides for the payment of material fees to Numerical
Technologies for Numerical Technologies' future technology.

(b)  In the event that Numerical Technologies grants, in agreements executed
after the execution of this Agreement, any IDF a license to PSM Software that
sets a more favorable license fee than that charged to UMC pursuant to Section
4.2 above, then Numerical Technologies shall, within 30 days of the effective
date of such agreement, offer the same license fees to UMC; provided that UMC
must also accept the same or substantially similar terms as those contained
within a binding agreement with such IDF in the following areas: (1) number of
seats licensed; (2) term (duration) of the agreement, and (3) the same
indemnification and limitation of liability terms.

(c)  Except as expressly provided in this Section 4.3, Numerical Technologies
shall have no obligation to provide more favorable pricing than that set forth
in this Agreement. In the event that the parties adjust the Royalty Rate or
   --------------
Software Fees pursuant to this Section 4.3, the parties shall amend this
Agreement in writing and Numerical Technologies shall not be obligated to refund
or return to UMC any royalties owed to Numerical Technologies before such change
in Royalty Rates went into effect unless Numerical Technologies fails to offer
such amended terms to UMC in a timely manner as set forth herein.

4.4  Taxes.  Numerical Technologies shall pay any taxes, duties, or similar
     -----
charges imposed by any government on the licenses of the PSM Patents and PSM
Software, or any other Numerical Technologies' product or service which is
levied based on this Agreement, except taxes based on the net income, capital or
net worth of UMC, or sales by UMC.  Numerical Technologies shall be responsible
for any withholding or similar taxes due on any fees or royalties paid by UMC
hereunder.  The parties shall cooperate to mutually reduce the tax burden to
each, and shall make all filings and take such other actions as are required by
applicable law to obtain the lowest tax rate, and shall promptly provide the
other party official tax receipts evidencing any such payment.  If either party
assigns this Agreement to a subsidiary or affiliate and, as a result of such
assignment an increased tax burden is incurred by the non-assigning party, such
assigning party shall pay the non-assigning party any excess amount incurred by
virtue of the assignment.

__________________

    * Certain information in this document has been omitted and filed separately
with the Commission. Confidential treatment has been requested with respect to
the omitted portions.

                                      -5-
<PAGE>

4.5  Late Payments.  All amounts payable by either party to the other party
     -------------
under this Agreement shall be due and payable within 30 days of the date of
invoice in U.S. Dollars. Any currency conversions required in calculating
Production Royalties shall be made using the published, independent third party
currency conversion rates that are used by UMC for its own recordkeeping and
financial reporting purposes.  UMC current procedures for currency conversion
are set forth in Exhibit E.  In the event UMC changes its procedures for
currency conversion and Numerical Technologies reasonably objects to such
change, the parties will mutually agree upon an acceptable procedure or revert
back to the procedure used prior to the change by UMC.  UMC shall send Numerical
Technologies a copy of its accounting pursuant to Section 4.6 each month, and
Numerical Technologies shall issue an invoice promptly thereafter for each
calendar quarter.  If any payment is not received within 30 days of the date of
invoice, interest will be imposed on such amount from the date due until paid in
full at a rate of interest per annum equal to the rate announced from time to
time by the Chase Manhattan Bank as its prime or reference rate, plus four
percent (4%).

4.6  Accounting.  Each month, no later than 30 days after the last day of the
     ----------
previous month, UMC shall send Numerical Technologies a written record detailing
the total number of Royalty Bearing Wafers produced and the amount of Production
Royalties due, including all such reasonable information as is required to
ensure compliance with the license terms herein.

4.7  Audit.  No more than once per year, upon reasonable written notice,
     -----
Numerical Technologies may at its expense have an independent auditor from a
nationally recognized accounting firm conduct an audit during UMC's normal
business hours for the purpose of verifying UMC compliance with the license
terms and payment obligations hereunder.  Such independent auditor(s) shall sign
an appropriate non-disclosure agreement with UMC which will permit the
independent auditor to disclose only the extent of any non-compliance by UMC or
any overpayment by UMC.  If any such audit should disclose improper use of
licensed rights hereunder (including underpayment), UMC shall bring itself into
compliance with the Agreement within fifteen (15) days of notice of such non-
compliance and issuance of an applicable invoice, and if applicable, pay
Numerical Technologies for any shortfall determined.  In the case of an audit
showing underpayment of more than 7.5%, UMC shall also pay for the reasonable
expenses of such audit.  In the event an audit discloses material non-compliance
by UMC, Numerical Technologies may increases the frequency of such audits to two
times per year until no such material non-compliance has been reported for two
audits.

4.8  Maintenance Fees. Until the completion of the third milestone as set forth
     ----------------
in Exhibit C, Numerical Technologies shall provide the software Maintenance and
   ---------
Support in Section 7 at no cost.

5.  Consulting Services. At the request of UMC, Numerical Technologies shall
    -------------------
make available to UMC PSM design flow implementation and testing services, in
accordance with those criteria as set forth on   Exhibit C hereto, and at *
                                                 ---------
until the first production milestone in Exhibit C.
                                        ---------

6.  Training.
    ---------

Numerical Technologies shall provide initial training for PSM Software to UMC at
no cost until the first production milestone in Exhibit C.
                                                ---------
7.  Maintenance and Support.
    ------------------------

Subject to the terms of this conditions of this Agreement (including payment in
accordance with Section 4), UMC will be entitled to Maintenance and Support as
specified in this Section 7.

7.1  Maintenance and Support Services.  Subject to UMC paying the applicable
     --------------------------------
license fees, Numerical Technologies shall provide to UMC the highest level of
support it generally makes available to its other customers.  NTI's current
highest level of Maintenance and Support is set forth in Exhibit D, and shall
include, without limitation:  (a) Updates, if any, and appropriate
Documentation, and (b) telephone, fax-back and email assistance with respect to
the PSM Software, including, as appropriate (i) clarification of functions and
features of the PSM Software; (ii) clarification of Documentation pertaining to
the PSM Software;       (iii) guidance in the operation of the PSM Software; and
(iv) error verification, analysis and correction to the extent possible by
telephone.  Maintenance and Support will be provided only with respect to
versions of the PSM Software that, in accordance with Numerical

__________________

    * Certain information in this document has been omitted and filed separately
with the Commission. Confidential treatment has been requested with respect to
the omitted portions.

                                      -6-
<PAGE>

Technologies' policy, are then being supported by Numerical Technologies.

7.2  Eligibility.  Maintenance and Support will not include services requested
     -----------
as a result of, or with respect to, the following, and any services requested as
a result thereof will be billed to UMC at Numerical Technologies' then-current
rates:

accident; unusual physical, electrical or electromagnetic stress; neglect;
misuse; failure of electric power; operation of the PSM Software with other
media not meeting or not maintained in accordance with the manufacturer's
specifications; or causes other than ordinary use;

improper installation or operation by UMC or use of the PSM Software that
deviates from any hardware, configuration, environmental or operating procedures
established by Numerical Technologies in the applicable Documentation;

modification, alteration or addition or attempted modification, alteration or
addition of the PSM Software undertaken by persons other than Numerical
Technologies or Numerical Technologies' authorized representatives; or

software created or supplied by UMC and UMC Scripts and Flows.

7.3  Responsibilities of UMC.  Numerical Technologies' provision of Maintenance
     -----------------------
and Support to UMC is subject to the following:

(a)  UMC shall provide Numerical Technologies with access to UMC's personnel and
     computer equipment during normal business hours in Taiwan, as necessary or
     appropriate for Numerical Technologies to perform Maintenance and Support
     Services.

(b)  In the event UMC requests support, UMC shall document and promptly report
     any errors or malfunctions of the PSM Software to Numerical Technologies
     that it wishes to have corrected.  UMC shall take all steps reasonably
     necessary to carry out procedures for the rectification of such errors or
     malfunctions within a reasonable time after such procedures have been
     received from Numerical Technologies.

8.  Limited Warranty and Limitation of Liability.
    ---------------------------------------------

8.1  Numerical Technologies warrants that the PSM Software will perform in
substantial accordance with the Documentation for ninety (90) days from the
Effective Date ("Warranty Period").  If during this time period the PSM Software
does not perform as warranted, Numerical Technologies shall respond to such
problems in accordance with Section 7.  In addition, Numerical Technologies
warrants that the media on which the PSM Software is distributed will be free
from defects in materials and workmanship under normal use for a period of
ninety (90) days from the Effective Date.  Numerical Technologies will replace
any defective media returned to Numerical Technologies within the 90-day period.

8.2  The foregoing are UMC's sole and exclusive remedies for breach of warranty.
The warranty set forth above is made to and for the benefit of UMC only.  The
warranty will apply only if:

the PSM Software has been properly installed and used at all times and in
accordance with the instructions for Use; and

no modification, alteration or addition has been made to the PSM Software by
persons other than Numerical Technologies.

EXCEPT AS SET FORTH ABOVE, NEITHER PARTY MAKES ANY WARRANTIES, WHETHER EXPRESS,
IMPLIED, STATUTORY OR OTHERWISE REGARDING OR RELATING TO THE PSM SOFTWARE OR THE
DOCUMENTATION, OR ANY MATERIALS OR SERVICES FURNISHED OR PROVIDED TO THE OTHER
PARTY UNDER THIS AGREEMENT, INCLUDING MAINTENANCE AND SUPPORT. NUMERICAL
TECHNOLOGIES SPECIFICALLY DISCLAIMS ALL IMPLIED WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT WITH RESPECT TO THE NTI-
IP.

8.3  LIMITATION OF LIABILITY. IN NO EVENT WILL EITHER PARTY BE LIABLE FOR ANY
     -----------------------
LOSS OF PROFITS, LOSS OF USE, BUSINESS INTERRUPTION, LOSS OF DATA, COST OF COVER
OR INDIRECT, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES OF ANY KIND IN
CONNECTION WITH OR ARISING OUT OF THE FURNISHING, PERFORMANCE OR USE OF THE PSM
SOFTWARE OR SERVICES PERFORMED HEREUNDER, WHETHER ALLEGED AS A BREACH OF
CONTRACT OR

                                      -7-
<PAGE>

TORTUOUS CONDUCT, INCLUDING NEGLIGENCE, EVEN IF THE PARTY HAS BEEN ADVISED OF
THE POSSIBILITY OF SUCH DAMAGES. EXCEPT FOR NUMERICAL TECHNOLOGIES' LIABILITY
ARISING OUT OF SECTION 9 BELOW AND AMOUNTS OWING BY UMC PURSUANT TO SECTION 4,
NEITHER PARTY'S LIABILITY UNDER THIS AGREEMENT FOR DAMAGES SHALL, IN ANY EVENT,
EXCEED THE LICENSE FEES AND/OR ROYALTIES PAID BY UMC TO NUMERICAL TECHNOLOGIES
UNDER THIS AGREEMENT IN THE 24 MONTHS PRECEDING THE EVENT UPON WHICH LIABILITY
IS ALLEGED. NOTWITHSTANDING THE FOREGOING, NUMERICAL TECHNOLOGIES' LIABILITY
UNDER THIS AGREEMENT FOR DAMAGES FOR PATENT INFRINGEMENT (INCLUDING
INDEMNIFICATION AMOUNTS UNDER SECTION 9) WILL NOT, IN ANY EVENT, EXCEED * TIMES
(* X) THE AMOUNT OF THE LICENSE FEES AND ROYALTIES PAID BY UMC TO NUMERICAL
TECHNOLOGIES UNDER THIS AGREEMENT.

9.  Indemnification for Infringement.  Numerical Technologies shall, at its
    --------------------------------
expense, defend or settle any suit or proceeding brought against UMC to the
extent that it is based on a claim that the PSM Technology or PSM Software used
within the scope hereunder constitutes the misappropriation of a trade secret or
infringement of a copyright or patent right of any third party and shall pay any
final judgments awarded or settlements entered into except in the case of patent
infringement, with respect to which Numerical Technologies will not pay any
amount in excess of the limitation of liability set forth in Section 8.3.  The
foregoing defense and indemnification is contingent upon UMC giving prompt
written notice to Numerical Technologies of any such claim, action or proceeding
of infringement and giving Numerical Technologies the authority to proceed as
contemplated herein.  Numerical Technologies will have the exclusive right to
defend any such claim, action or allegation and make settlements thereof at its
own discretion, and UMC may not settle or compromise such claim, action or
allegation, except with prior written consent of Numerical Technologies, except
for claims of patent infringement, in which UMC shall have the right to jointly
participate in such defense and/or settlement.  UMC shall give such assistance
and information as Numerical Technologies may reasonably require to settle or
oppose such claims.  In the event any such infringement, claim, action or
allegation is brought or threatened, Numerical Technologies may, at its sole
option and expense:

(a) procure for UMC the right to continue Use of the PSM Technology or PSM
Software, or infringing part thereof; or

(b )modify or amend the PSM Technology or PSM Software or infringing part
thereof, or replace the PSM Technology or PSM Software or infringing part
thereof with other software having substantially the same or better
capabilities; or, if neither of the foregoing is commercially practicable,

(c) terminate UMC's license for the PSM Software and refund to UMC all license
fees paid by UMC for the PSM Software, upon which time  Numerical Technologies
and UMC will be released from any further obligation to the other under this
Agreement, except for the obligations of indemnification provided for above and
such other obligations that survive termination.

Notwithstanding the above, in the event Numerical Technologies decides to
terminate UMC's license pursuant to this subsection for patent infringement (c),
UMC may choose to continue being licensed under this Agreement but any
indemnification obligations of Numerical Technologies shall terminate for patent
infringement arising out of UMC's use after the date of notice of termination
and refund by NTI.

The foregoing obligations shall not apply to the extent the infringement arises
as a result of modifications to the PSM Technology or PSM Software not provided
by Numerical Technologies.

THE FOREGOING STATES THE SOLE REMEDY AND THE ENTIRE LIABILITY OF EITHER PARTY
WITH RESPECT TO INFRINGEMENT OF ANY PATENT, COPYRIGHT, TRADE SECRET OR OTHER
PROPRIETARY RIGHT OF A THIRD PARTY.

__________________

    * Certain information in this document has been omitted and filed separately
with the Commission. Confidential treatment has been requested with respect to
the omitted portions.

                                      -8-
<PAGE>

10.  Confidential Information.
     -------------------------

10.1  Treatment and Use of Confidential Information.  For a period of two (2)
      ---------------------------------------------
years following the return of confidential information to the disclosing party,
the receiving party agrees to protect Confidential Information disclosed to it
by the disclosing party with at least the same degree of care as it normally
exercises to protect the receiving party's own information of like importance,
but at least use reasonable care, in safeguarding the disclosing party's
Confidential Information against disclosure.  The receiving party shall use the
Confidential Information solely in accordance with the provisions of this
Agreement, including without limitation, for the creation of UMC Enhancements by
UMC and NTI Enhancement by Numerical Technologies.

10.2  Exclusions to Confidential Information. A party's Confidential
      --------------------------------------
Information shall not include information that:  (a) is now or becomes available
to the public without breach of this Agreement, (b) is lawfully obtained by a
third party, (c) is known to the receiving party prior to disclosure by the
disclosing party and had not been obtained by the receiving party either
directly or indirectly from the disclosing party with a duty of confidentiality,
(d) is developed by the receiving party independently of any disclosure by the
disclosing party, or (e) is released in writing by the disclosing party.

10.3  Permitted Disclosure.  A receiving party may disclose the Confidential
      --------------------
Information of the other party (i) in accordance with the prior written approval
of disclosing party, or (ii) after providing prior written notice to disclosing
party and after taking "Reasonable Measures" to obtain confidential treatment of
such Confidential Information where receiving party is required to disclose such
information pursuant to the order or requirement of a court, administrative
agency, or other governmental body. For the purposes of this Section 10.3
"Reasonable Measures" shall mean designating Confidential Information for
protection under a previously existing protective order, or providing the
disclosing party reasonable assistance in such disclosing party's efforts to
obtain a protective order.

10.4  Terms of Agreement.  Each party agrees that the terms and conditions of
      ------------------
this Agreement shall be treated as Confidential Information and that no
reference to this Agreement or to activities pertaining thereto can be made in
any form of public or commercial advertising without the prior written consent
of the other party;  provided however, that each party may disclose the terms
                     -------- -------
and conditions of this Agreement to: (1) legal counsel of the parties, (2) in
confidence, to accountants, banks, and financing sources and their advisors; (3)
in confidence, in connection with a merger or acquisition or proposed merger or
acquisition, or the like; (4) in accordance with applicable law and/or
securities regulations; or (5) to customers, vendor and partners the terms
contained in Articles 2, 5, 7, 10, 11, 12 or 14, or Sections 3.3.or 3.5.

10.5  Return of Confidential Information.  Upon termination of this Agreement
      ----------------------------------
as specified in Section 11, each party agrees to return Confidential Information
of the other party to said other party, along with copies made, or to certify
that all such Confidential Information has been destroyed, except that each
party may retain archival copies to be used only in a dispute concerning this
Agreement, and provided further that UMC may retain any NTI Confidential
Information that is necessary to support customers for whom UMC continues to
manufacture products in accordance with Section 11 below, provided that UMC will
return or destroy (as provided above) any NTI Confidential Information used to
support such customers upon the cessation of manufacturing the subject products.

10.6  Confidential Information from or for third parties.  Neither party will
      --------------------------------------------------
disclose to the other party any confidential information belonging to third
parties unless it has obtained written authorization to do so.

11.  Term and Termination.
     ---------------------
11.1  Term.  This Agreement will take effect on the Effective Date and will

remain in force for a term of * (*) years unless otherwise terminated in
accordance with this Agreement.

11.2  Termination for Cause.  Either party may, by written notice to the
      ---------------------
other party, terminate this Agreement if any of the following events
("Termination Events") occur:

the other(a) a party fails to pay any amount due the other within thirty (30)
days after the unpaid party gives

_____________________

*  Certain information on this page has been omitted and filed separately with
the Commission. Confidential treatment has been requested with respect to the
omitted portions.

                                      -9-
<PAGE>

the obligated party written notice of such nonpayment; or

the other(b) a party is in material breach of any non-monetary term, condition
or provision of this Agreement, which breach, if capable of being cured, is not
cured within thirty (30) days after the non-breaching party gives the breaching
party written notice of such breach; or

(c) upon written notice by the other party if either party (i) terminates or
suspends its business, (ii) becomes insolvent, admits in writing its inability
to pay its debts as they mature, makes an assignment for the benefit of
creditors, or becomes subject to direct control of a trustee, receiver or
similar authority, or (iii) becomes subject to any Chapter 7 bankruptcy or
insolvency proceeding under applicable law which is not terminated within six
months.

11.3  Renewal Terms; Early Termination. The parties shall discuss in good faith
      --------------------------------
the * year renewal of this Agreement six months prior to expiration of the
current term, unless both parties agree to allow the current Agreement to
expire.  If either party desires to terminate the Agreement before the
expiration of the then-current term (other than termination pursuant to Section
11.2 for cause), such party shall send a written notice so notifying the other
party.   Within 15 days of receipt of such notice, the notified party shall
engage the requesting party in good faith discussion of possible termination of
this Agreement.  If such discussion does not result in a renewal, then this
Agreement shall expire at the end of the current term.

11.4  Effect of Termination.
      ---------------------

If any Termination Event occurs, termination will become effective immediately
or on the date set forth in the written notice of termination.

     Any termination or expiration of this Agreement will not affect Sections 1,
3, 4, 7 (provided that UMC was under support coverage at the time of
termination), 8, 9, 10, 11, 12, 13 and 14, which shall survive the termination
or expiration of this Agreement.   Upon expiration or termination (for any
reason other than UMC's breach of Section 3.3 or pursuant to Section 14.7): (i)
all licenses granted under this Agreement to UMC shall terminate provided that
UMC may continue to manufacture Royalty Bearing Wafers, and continue to Use the
PSM Software for which UMC has paid license fees to manufacture Royalty Bearing
Wafers, under any specific UMC Process that UMC has already been licensed to use
or that have been the subject of specific discussions concerning possible use
with entities that are identified on the List of Customers, and  (ii) UMC shall
continue to pay Production Royalties for Royalty Bearing Wafers after such
termination or expiration.

     The provisions of Article 4 (except for Section 4.4) shall terminate six
(6) months after UMC ceases to manufacture Royalty Bearing Wafers.

     In the event of termination of this Agreement by reason of UMC's breach of
Section 3.3 or pursuant to Section 14.7, all licenses granted under this
Agreement shall terminate immediately and automatically.

11.5  Return of Materials.  Within thirty (30) days after the date of
      -------------------
termination or expiration of this Agreement for any reason whatsoever, UMC shall
return or certify the destruction of the PSM Software and all copies, in whole
or in part, all Documentation relating thereto, and any other NTI Confidential
Information in its possession that is in tangible form, except to the extent
that the PSM Software, Documentation or NTI Confidential Information is required
for use by UMC pursuant to Section 11.4. Within thirty (30) days after the date
of termination or expiration of this Agreement for any reason whatsoever,
Numerical Technologies shall return or certify the destruction of all UMC
Confidential Information in its possession that is in tangible form.

12.  Assignment.
     -----------

Neither this Agreement nor any rights under this Agreement may be assigned or
otherwise transferred by either party, in whole or in part, whether voluntary or
by operation of law, including by way of sale of assets, merger or
consolidation, without the prior written consent of the other party, such
consent which shall not be unreasonably withheld or delayed.  The foregoing
notwithstanding, either party may assign this Agreement in full to a wholly
owned subsidiary as part of a corporate restructuring; provided that such
assigning party gives prior written notice to the other party.  Subject to the
foregoing, this Agreement will be

_____________________

*  Certain information on this page has been omitted and filed separately with
the Commission. Confidential treatment has been requested with respect to the
omitted portions.

                                      -10-
<PAGE>

binding upon and will inure to the benefit of the parties and their respective
successors and assigns..

13.  Notices.
     --------

Any notice required or permitted under the terms of this Agreement or required
by law must be in writing and must be (a) delivered in person, (b) sent by first
class registered mail, or air mail, as appropriate, or (c) sent by overnight air
courier, in each case properly posted and fully prepaid to the appropriate
address set forth below.  Notices will be considered to have been given at the
time of actual delivery in person, three (3) business days after deposit in the
mail as set forth above, or one (1) day after delivery to an overnight air
courier service. Notices shall be sent to the following persons:


For Numerical Technologies:

Y.C. Buno Pati
President and CEO
Numerical Technologies, Inc.
70 W. Plumeria Dr.
San Jose, CA 95134

Kent Richardson
Corporate Counsel
Numerical Technologies, Inc.
70 W. Plumeria Dr.
San Jose, CA 95134

For UMC:


United Microelectronics Corporation
No. 3, Li-Hsin Road II
Science Based Industrial Park
Hsin-Chu City, Taiwan 30077
Attn: Fu-Tai Liou

Copy to:
Law+
993 Highlands Circle
Los Altos, CA 94024
Attn: Peter Courture, Esq.
Fax: (650) 968-8885

14.  Miscellaneous.
     --------------

14.1  Force Majeure.  Neither party will incur any liability to the other
      -------------
party on account of any loss or damage resulting from any delay or failure to
perform all or any part of this Agreement if such delay or failure is caused, in
whole or in part, by events, beyond the control of the parties, including
without limitation acts of God, strikes, lockouts, riots, acts of war,
earthquake, fire and explosions, but the inability to meet financial obligations
is expressly excluded.

14.2  Waiver.  Any waiver of a party's rights or remedies under this
      ------
Agreement must be in writing to be effective.  Failure, neglect, or delay by a
party to enforce the provisions of this Agreement or its rights or remedies at
any time, will not be construed and will not be deemed to be a waiver of such
party's rights under this Agreement.

14.3  Severability.  If any term, condition, or provision in this Agreement is
      ------------
found to be invalid, unlawful or unenforceable to any extent, such invalid term,
condition or provision will be severed from the remaining terms, conditions and
provisions, which will continue to be valid and enforceable to the fullest
extent permitted by law.

14.4  Integration.  This Agreement (including the Exhibits) contains the
      -----------
entire agreement of the parties with respect to the subject matter of this
Agreement and supersedes all previous agreements, either oral or written,
between the parties with respect to said subject matter. This Agreement may not
be amended, except by a writing signed by both parties.

14.5  Export.  UMC may not export or re-export the PSM Software without the
      ------
prior written consent of Numerical Technologies or without the appropriate
United States and foreign government licenses.  Numerical Technologies will
notify UMC of any applicable export laws which it knows to be applicable to the
PSM Technology or PSM Software.

14.6  Publicity.  Both parties acknowledge that one party may desire to use the
      ---------
other party's name in press releases, product brochures and financial reports
indicating that UMC is a customer of Numerical Technologies or UMC is licensed
under the PSM Technology, PSM Software and/or PSM Patents, and each party hereby
consents to the other party's use of their respective names in such a manner.
UMC and Numerical Technologies agree to prepare and release a press release
regarding this Agreement within fourteen (14) days of execution of this
Agreement. UMC and Numerical Technologies also agree to work together to jointly
promote PSM Technology to UMC customers through joint papers, workshops, and
such other means as the parties may agree from time to time, provided

                                      -11-
<PAGE>

that the extent of any participation by a party shall be in its sole discretion.

14.7  Intellectual Property Contests.  In the event UMC provides Support (as
      -------------------------------
defined below) to any third party contest or challenge to the PSM Patents, all
licenses granted to UMC under Section 2 shall terminate immediately and
automatically upon written notice to UMC by Numerical Technologies. For the
purposes of this Section 14.7, "Support" means that UMC will not (1) allow its
employees to act as an expert witness in any challenge to the PSM Patents; (ii)
provide consulting services to a challenge of the PSM Patents; or (iii) provide
financial or legal support to a challenge of the PSM Patents.

14.8  Counterparts.  This Agreement may be executed in counterparts, each of
      ------------
which so executed will be deemed to be an original and such counterparts
together will constitute one and the same agreement.

14.9  Language.  This Agreement is in the English language only, which
      --------
language will be controlling in all respects, and all versions hereof in any
other language shall be for accommodations only and shall not be binding upon
the parties.  All communications and notices to be made or given pursuant to
this Agreement shall be in the English language.

14.10 Governing Law.  This Agreement will be interpreted and construed in
      -------------
accordance with the laws of the State of California, without regard to conflict
of law principles, and as applied to agreements entered into by California
residents and performed entirely within the state of California.

14.11 Arbitration. The parties will endeavor to settle amicably by mutual
      -----------
discussions any disputes, differences, or claims whatsoever related to this
Agreement.  Failing such amicable settlement, any controversy, claim, or dispute
between the parties arising under or relating to this Agreement, including the
existence, validity, interpretation, performance, termination or breach thereof,
shall finally be settled by arbitration in accordance with the Arbitration Rules
of the American Arbitration Association ("AAA").  There will be three (3)
arbitrators (the "Arbitration Tribunal"), the first of which will be appointed
by the claimant in its notice of arbitration, the second of which will be
appointed by the respondent within thirty (30) days of the appointment of the
first arbitrator and the third of which will be jointly appointed by the party-
appointed arbitrators within thirty (30) days thereafter.  The language of the
arbitration shall be English.  The Arbitration Tribunal will not have the
authority to award punitive damages to either party.  Each party shall bear its
own expenses, but the parties will share equally the expenses of the Arbitration
Tribunal and the AAA.  This Agreement will be enforceable, and any arbitration
award will be final, and judgment thereon may be entered in any court of
competent jurisdiction.  The arbitration will be held in Honolulu, Hawaii, USA.
Notwithstanding the foregoing, claims for preliminary injunctive relief and
other pre-judgment remedies may be brought in any court with jurisdiction over
the subject matter and parties.  All aspects of the arbitration shall be treated
as strictly confidential.

                                      -12-
<PAGE>

IN WITNESS WHEREOF, the parties have executed this Agreement.

United Microelectronics, Inc. (UMC)   NUMERICAL TECHNOLOGIES, INC.

By:   /s/ Fu-Tai Liou                 By:   /s/ Y.C. (Buno) Pati
      -------------------------             ---------------------------------

     Fu-Tai Liou, CTO                      Y.C. (Buno) Pati, CEO
-------------------------------       ---------------------------------------
(Print Name and Title)                (Print Name and Title)

Date: 12/31/00                        Date: December 31, 2000
      -------------------------       ---------------------------------------

Address:                              Address:

No. 3, Li-Hsin Rd. 2, Science-Based
Industrial Park,                      70 W. Plumeria Dr.
------------------------------------  ---------------------------------------

Hsinchu, Taiwan                       San Jose, CA  95134 U.S.A.
------------------------------------  ---------------------------------------

                                      -13-
<PAGE>

                                   EXHIBIT A
                                   ---------


                              PRODUCTION ROYALTIES


<TABLE>
<CAPTION>
-----------------------------------------------------------------------------------------------
 Wafer Number (annually, resetting to 0 on                         Royalty Rate
 January 1 of each year)
-----------------------------------------------------------------------------------------------
<S>                                             <C>
*                                               *  %
-----------------------------------------------------------------------------------------------
*                                               *  %
-----------------------------------------------------------------------------------------------
*                                               *  %
-----------------------------------------------------------------------------------------------
*                                               *  %
-----------------------------------------------------------------------------------------------
*                                               *  %
-----------------------------------------------------------------------------------------------
*                                               *  %
-----------------------------------------------------------------------------------------------
</TABLE>

---------------
 *  Certain information on this page has been omitted and filed separately with
the Commission. Confidential treatment has been requested with respect to the
omitted portions.

<PAGE>

                                   EXHIBIT B
                                   ---------



                        Designated Seats Licensed by UMC
                        ---------- ----- ---------------


<TABLE>
<CAPTION>
---------------------------------------------------------------------------------------------------------
Location                                       Equipment                       Other Information
<S>                                            <C>                             <C>
---------------------------------------------------------------------------------------------------------
</TABLE>

<PAGE>

                                   EXHIBIT C
                                   ---------

                                   MILESTONES



PSM Design Flow Implementation and Testing Services
---------------------------------------------------


PSM design flow implantation and testing services means services to design,
implement, and test, a production worthy flow that begins with GDSII layout data
as input and produces phase shifted, OPC corrected, and verified output ready
for mask data preparation. These services further include the creation and
testing of scripts necessary to implement this flow.


MILESTONES
----------


<TABLE>
<CAPTION>
----------------------------------------------------------------------------------------------
MILESTONE                                                                          DATE
<S>                                                                                <C>
----------------------------------------------------------------------------------------------
*                                                                                    *
----------------------------------------------------------------------------------------------
*                                                                                    *
----------------------------------------------------------------------------------------------
*                                                                                    *
----------------------------------------------------------------------------------------------
</TABLE>
---------------
 * Certain information on this page has been omitted and filed separately with
the Commission. Confidential treatment has been requested with respect to the
omitted portions.
<PAGE>

SPECIFICATION
-------------

*
-------------
 * Certain information on this page has been omitted and filed separately with
the Commission. Confidential treatment has been requested with respect to the
omitted portions.
<PAGE>

                                   EXHIBIT D
                                   ---------

                                    SUPPORT


1.  Telephone Support:  Telephone support provided 9 a.m. to 5:30 p.m. (local
    Taiwan time) Monday-Friday.

2.  Fax-Back Service:  Written responses provided to specific questions,
    problems and recommendations from licensees.

3.  Email:  Emailed responses provided to specific questions, problems and
    recommendations from licensees.

<PAGE>

                                   EXHIBIT E
                                   ---------

                         CURRENCY CONVERSION PROCEDURES