LIMITED POWER OF ATTORNEY

        Know all by these presents, that each of the undersigned hereby makes,
constitutes and appoints Jerry Allison, Gil C. Tily, Christie B. Tillapaugh and
Richard D. Rosen (any of whom may act individually) as the true and lawful
attorney-in-fact of each of the undersigned, with full power and authority as
hereinafter described on behalf of and in the name, place and stead of each of
the undersigned to:

(1)     prepare, execute, acknowledge, deliver and file Forms 3, 4, and 5
(including any amendments thereto) and any Schedule 13D (including any
amendments thereto) with respect to the securities of Amkor Technology, Inc., a
Delaware corporation (the "Company"), with the United States Securities and
Exchange Commission, any national securities exchanges and the Company, as
considered necessary or advisable under Section 16(a) of the Securities Exchange
Act of 1934 and the rules and regulations promulgated thereunder, as amended
from time to time (the "Exchange Act"), including obtaining any filing codes or
reissuance of existing filing codes, if necessary, in connection therewith;

(2)     seek or obtain, as the representative of each of the undersigned and on
behalf of each of the undersigned, information on transactions in the Company's
securities from any third party, including brokers, employee benefit plan
administrators and trustees, and the undersigned hereby authorizes any such
person to release any such information to such attorney-in-fact and approves and
ratifies any such release of information; and

(3)     perform any and all other acts which in the discretion of such attorney-
in- fact are necessary or desirable for and on behalf of the undersigned in
connection with the foregoing.

        Each of the undersigned acknowledges that:

(1)     this Power of Attorney authorizes, but does not require, such attorney-
in- fact to act in his or her discretion on information provided to such
attorney-in-fact without independent verification of such information;

(2)     any documents prepared and/or executed by such attorney-in-fact on
behalf of any of the undersigned pursuant to this Power of Attorney will be in
such form and will contain such information and disclosure as such attorney-in-
fact, in his or her discretion, deems necessary or desirable;

(3)     neither the Company nor such attorney-in-fact assumes (i) any liability
for any of the undersigneds' responsibility to comply with the requirements of
the Exchange Act, (ii) any liability of any of the undersigned for any failure
to comply with such requirements, or (iii) any obligation or liability of any of
the undersigned for profit disgorgement under Section 16(b) of the Exchange Act;

(4)     this Power of Attorney does not relieve any of the undersigned from
responsibility for compliance with any of the undersigneds' obligations under
the Exchange Act, including without limitation the reporting requirements under
Section 16 of the Exchange Act; and

(5)     this Power of Attorney supersedes and replaces any prior power of
attorney executed by any of the undersigned for any of the purposes set forth
herein.

        Although this Power of Attorney supersedes and replaces any prior power
of attorney executed by any of the undersigned for any of the purposes set forth
herein, each of the undersigned hereby ratifies and approves of any actions
taken pursuant to any prior power of attorney for any of the purposes set forth
herein, including without limitation the granting thereof by any of the
undersigned on his, her or its behalf.  Each of the undersigned hereby gives and
grants the foregoing attorney-in-fact full power and authority to do and perform
all and every act and thing whatsoever requisite, necessary or appropriate to be
done in and about the foregoing matters as fully to all intents and purposes as
the undersigned might or could do if present, hereby ratifying all that such
attorney-in-fact shall lawfully do or cause to be done of, for and on behalf of
any of  the undersigned by virtue of this Power of Attorney.

        This Power of Attorney may be executed in several counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

        This Power of Attorney shall remain in full force and effect until
revoked by any of the undersigned in a signed writing delivered to the attorney-
in-fact.

        IN WITNESS WHEREOF, the undersigned have each caused this Power of
Attorney to be executed as of the 22 day of May, 2018.

Entity covered by this Power of Attorney:
Family Trust Under John T. Kim 2012 Irrevocable Trust Agreement dtd 12/11/12


                                            FAMILY TRUST UNDER JOHN T. KIM 2012
                                            IRREVOCABLE TRUST AGREEMENT dtd
                                            12/11/12


                                            By: /s/ John T. Kim
                                                --------------------------------
                                                John T. Kim, Trustee

                                            By: /s/ James J. Kim
                                                --------------------------------
                                                James J. Kim, Trustee