`Yuh et al.
`
`USOO6577368B1
`US 6,577,368 B1
`Jun. 10, 2003
`
`(10) Patent No.:
`(45) Date of Patent:
`
`(54) IPS-LCD HAVING ATHIRD ELECTRODE
`HAVING APERTURE AND FORMED ON
`COUNTER SUBSTRATE
`
`(75) Inventors: Jin-Tae Yuh, Kyungki-do (KR);
`Kye-Hun Lee, Kyungki-do (KR);
`Byoung-Sun Na, Kyungki-do (KR);
`Dong-Gyu Kim, Kyungki-do (KR);
`Jong-Woong Chang, Kyungki-do (KR);
`Jung-Uk Shim, Kyungki-do (KR);
`Jang-Kun Song, Seoul (KR);
`Hyun-Sik Lee, Seoul (KR)
`(73) Assignee: Samsung Electronics Co., Ltd., Suwon
`(KR)
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 0 days.
`
`(*) Notice:
`
`(21) Appl. No.: 09/184,953
`(22) Filed:
`Nov. 3, 1998
`(30)
`Foreign Application Priority Data
`Nov. 3, 1997 (KR) ............................................ 97-57823
`Jan. 21, 1998 (KR) ............................................. 98-1702
`Feb. 20, 1998 (KR) .....
`... 98-5288
`Feb. 26, 1998 (KR) .....
`... 98-6087
`Mar. 12, 1998 (KR) .....
`... 98-8231
`Mar. 12, 1998 (KR) .....
`... 98-8233
`Mar. 12, 1998 (KR) .....
`98-8235
`(51) Int. Cl." ................
`... GO2F1/1393
`(52) U.S. Cl. ....................................................... 349/141
`(58) Field of Search ............................ 349/141, 38, 39,
`34.9/139, 143
`
`(56)
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`1/1997 Kondo et al. ................. 349/39
`5,598.285 A
`5,982,460 A * 11/1999 Zhang et al. ................. 349/39
`6,005,650 A * 12/1999 Kim et al. .................. 349/141
`6,097.465 A * 8/2000 Hiroki et al. ............... 349/141
`6,130,737 A * 10/2000 Aratani et al. .............. 349/141
`6,246,453 B1 * 6/2001 Zhang et al. ................. 349/39
`6.256,081 B1
`7/2001 Lee et al. ................... 349/141
`6,285,428 B1
`9/2001 Kim et al. .................. 349/141
`
`* cited by examiner
`
`LLP;
`
`Primary Examiner Toan Ton
`(74) Attorney, Agent, or Firm McGuireWoods
`Hae-Chan Park
`(57)
`ABSTRACT
`A liquid crystal display having electrodes on a single Sub
`Strate. A transparent planar electrode elongated in the trans
`verse direction is formed on the inner Surface of a Substrate,
`and an insulating film is deposited thereon. A plurality of
`linear electrodes, which are elongated in the longitudinal
`direction and either transparent or opaque, are formed on the
`insulating film. Potential difference between the planar and
`the linear electrodes generated by applying Voltages to the
`electrodes yields an electric field. The electric field is
`Symmetrical with respect to the longitudinal central line of
`the linear electrodes and the longitudinal central line of a
`region between the linear electrodes, and has parabolic or
`Semi-elliptical lines of force having a center on a boundary
`line between the planar and the linear electrodes. The line of
`force on the planar and the linear electrodes and on the
`boundary line between the planar and the linear electrodes
`has the Vertical and the horizontal components, and the
`liquid crystal molecules are re-arranged to have a twist angle
`and an tilt angle. The polarization of the incident light varies
`due to the rearrangement of the liquid crystal molecules.
`
`5,576,861 A 11/1996 Abileah et al. ............... 359/73
`
`13 Claims, 73 Drawing Sheets
`
`251
`
`
`
`
`
`5
`
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`.
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`SSSASYASA Ayaasaya YaYa waYaYSSYSSYSSaaSayyyyyyyyyyyySYSSYSSNNASSN
`ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ2
`
`1 OO
`
`Page 1 of 90
`
`Tianma Exhibit 1005
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`
`
`U.S. Patent
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`Jun. 10, 2003
`
`Sheet 1 of 73
`
`US 6,577,368 B1
`
`FG.1
`
`
`
`FG.2
`
`
`
`
`
`natural light
`
`
`
`5OO
`
`1
`
`
`
`W.A.N.
`
`
`
`
`
`EAAA, IN A INA
`
`
`
`back light
`
`Page 2 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 2 of 73
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`US 6,577,368 B1
`
`FG.3
`
`
`
`FG4
`
`sh R- hLC
`
`E C A(O)
`
`B
`
`D position
`
`Page 3 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 3 of 73
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`US 6,577,368 B1
`
`FIG.5
`
`qs R
`
`qLC()
`
`O.O
`
`height (11 m)
`
`d
`
`FG.6
`
`2OO
`
`F
`
`Rz.
`NS . X
`
`F
`
`1 OO
`
`Page 4 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 4 of 73
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`US 6,577,368 B1
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`FIG.7
`
`FG.8
`
`O.O NU-1
`
`height (pl. m)
`
`d
`
`E C A(O) B D
`
`position
`
`Page 5 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 5 of 73
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`US 6,577,368 B1
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`FG.9
`
`2O.O
`position(a m)
`
`4O.O
`
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`
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`
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`
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`
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`
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`
`OOO
`O.O 1.0 2.0 3.0 4-O 5.O 6.O
`applied voltage(V)
`
`Page 6 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 6 of 73
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`US 6,577,368 B1
`
`FIG 11
`
`
`
`
`
`
`
`//2. Gá. &AX
`XXIX
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`Xyx
`NY S! Q X//
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`Exx
`
`
`
`
`
`Page 7 of 90
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`Jun. 10, 2003
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`Sheet 7 of 73
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`US 6,577,368 B1
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`F.G. 12
`
`
`
`FIG. 13
`
`as R-d LC
`
`E C A(O)
`
`B
`
`D position
`
`Page 8 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 8 of 73
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`US 6,577,368 B1
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`F.G. 14
`
`$ LC( )
`
`ps R
`
`O.O
`
`height(pl. m)
`
`d
`
`FC 15
`
`2OO
`
`F
`
`Page 9 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 9 of 73
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`US 6,577,368 B1
`
`FG 16
`
`FG.17
`
`E C A(O) B D
`
`position
`
`Page 10 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 10 of 73
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`US 6,577,368 B1
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`F.G. 18
`
`
`
`F.G. 19
`
`ld R-#LC
`
`E C A(O)
`
`B
`
`D position
`
`Page 11 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 11 of 73
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`US 6,577,368 B1
`
`FIG.2O
`
`p K
`
`q) LC()
`
`O.O
`
`height(film)
`
`d
`
`FG.21
`
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`
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`
`6E
`
`.
`
`Rzx
`
`.
`
`1 OO
`
`Page 12 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 12 0f 73
`
`US 6,577,368 B1
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`FG.22
`
`FIG.23
`
`
`
`cks height (44 m)
`
`d
`
`E C A(O) B D
`
`position
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`Page 13 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 13 of 73
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`US 6,577,368 B1
`
`FIG.24
`
`
`
`C
`EA
`
`B
`
`2
`
`1
`
`D
`
`1
`
`EA
`
`B
`
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`
`FIG.25
`
`|h R- ? LC
`
`E C A(O)
`
`B
`
`D position
`
`Page 14 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 14 Of 73
`
`US 6,577,368 B1
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`FG.26
`
`g5 R
`
`O.O
`
`height (1 m)
`
`d
`
`FG.27
`
`200
`
`F
`
`ae
`K-Rzx
`
`6E
`
`Ezx
`
`Page 15 of 90
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`
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`Jun. 10, 2003
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`Sheet 15 0f 73
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`US 6,577,368 B1
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`FIG.28
`
`FG.29
`
`height(1 m)
`
`E CAO)
`
`D
`
`position
`
`Page 16 of 90
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`
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 16 of 73
`Sheet 16 of 73
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`US 6,577,368 B1
`US 6,577,368 B1
`
`U.S. Patent
`U.S. Patent
`
`
`
`FIG 31
`FIG. 31
`
`
`-CS=
`
`---- ? //
`
`----M
`
`Page 17 of 90
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`Page 17 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 17 of 73
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`US 6,577,368 B1
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`FG.32
`
`
`
`
`
`
`
`23
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`Page 18 of 90
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`US 6,577,368 B1
`US 6,577,368 B1
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`100
`00 ||
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`Jun. 10, 2003
`Jun. 10, 2003
`
`Sheet 18 of 73
`Sheet 18 of 73
`
`
`
`FIG.34
`
`U.S. Patent
`U.S. Patent
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`Page 19 of 90
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`Page 19 of 90
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`
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 19 of 73
`Sheet 19 of 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`FG.35A
`FIG.35A
`
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`24
`
`54
`
`
`
`
`
`Page 20 of 90
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`Page 20 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 20 of 73
`Sheet 20 0f 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`243435
`
`2040
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`12i 100
`001
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`
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`75
`
`1627/265136
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`32113140
`
`100
`
`FIG.35B
`
`Page 21 of 90
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`FIG.35C
`
`Page 21 of 90
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`
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 21 of 73
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`US 6,577,368 B1
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`F.G. 56A
`
`
`
`24
`
`-
`s
`V2C
`
`Page 22 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 22 of 73
`Sheet 22 of 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`N
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`FIG.46C
`
`FIG.36B
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`Page 23 of 90
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`Page 23 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 23 of 73
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`US 6,577,368 B1
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`FIG.37A
`
`
`
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`
`34
`
`Page 24 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 24 of 73
`Sheet 24 of 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`Page 25 of 90
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`FIG.37C
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`Page 25 of 90
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`Jun. 10, 2003
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`Sheet 25 0f 73
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`US 6,577,368 B1
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`FIG.38A
`
`
`
`Page 26 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 26 of 73
`Sheet 26 0f 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`
`Page 27 of 90
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`FIG.38C
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`Page 27 of 90
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`U.S. Patent
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`Sheet 27 of 73
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`US 6,577,368 B1
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`FIG.39A
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`
`
`Page 28 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 28 of 73
`Sheet 28 0f 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`
`
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`FIG.39C
`
`FIG.39B
`
`Page 29 of 90
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`Page 29 of 90
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`Sheet 29 of 73
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`US 6,577,368 B1
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`FG4O
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`Page 30 of 90
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`Sheet 30 of 73
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`US 6,577,368 B1
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`FG.41
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`
`
`72 62 61 71
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`FG42
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`
`Page 31 of 90
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`U.S. Patent
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`Sheet 31 of 73
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`US 6,577,368 B1
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`FIG.43
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`
`
`
`
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`
`Page 32 of 90
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`Sheet 32 of 73
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`US 6,577,368 B1
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`2OO
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`Page 33 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
`Jun. 10, 2003
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`Sheet 33 of 73
`Sheet 33 of 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`FIG.47
`FIG.47
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`Page 34 of 90
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`Page 34 of 90
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`U.S. Patent
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`Sheet 34 of 73
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`US 6,577,368 B1
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`FIG.49
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`applied voltage(V)
`
`Page 35 of 90
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`Sheet 35 0f 73
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`US 6,577,368 B1
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`FIG.50
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`Page 36 of 90
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`U.S. Patent
`U.S. Patent
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`Jun. 10, 2003
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`Sheet 36 of 73
`Sheet 36 of 73
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`US 6,577,368 B1
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`
`
`FIG.51
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`Page 37 of 90
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`Page 37 of 90
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`Sheet 37 0f 73
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`US 6,577,368 B1
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`Page 38 of 90
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`U.S. Patent
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`Jun. 10, 2003
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`Sheet 38 of 73
`Sheet 38 of 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`Page 39 of 90
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`Page 39 of 90
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`Sheet 39 of 73
`Sheet 39 0f 73
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`US 6,577,368 B1
`US 6,577,368 B1
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`3
`S
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`Page 40 of 90
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`Page 40 of 90
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`Sheet 40 of 73
`Sheet 40 0f 73
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`US 6,577,368 B1
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`3
`100
`
`8
`100
`
`3
`100
`
`FIG.54B
`
`9
`
`S
`12
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`Page 41 of 90
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`1
`IPS-LCD HAVING ATHIRD ELECTRODE
`HAVING APERTURE AND FORMED ON
`COUNTER SUBSTRATE
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`BACKGROUND OF THE INVENTION
`1. Field of the Invention
`The present invention relates to a liquid crystal display
`(LCD). More particularly, the present invention relates to an
`LCD having a modified electrode array.
`2. Description of the Related Art
`Generally, an LCD is a display having two Substrates and
`a liquid crystal layer therebetween. A plurality of electrodes
`are formed on the inner Surfaces of either or both the
`Substrates, a pair of polarizers are attached to the outer
`Surfaces of the Substrates, and the liquid crystal layer Serves
`as an optical Switching medium. When a potential difference
`is applied to the electrodes, liquid crystal molecules are
`re-arranged due to the potential difference, and the
`re-arranged liquid crystal molecules Scatter the incident
`light, which have passed through one of the polarizers, or
`change the transmission characteristics of the light, thereby
`controlling the transmittance of the light out of the other
`polarizer (which is usually called an analyzer) and display
`ing images.
`As an example of a conventional LCD, U.S. Pat. No.
`5,576,861 discloses a twisted nematic LCD (TN-LCD)
`where an upper electrode and a lower electrode formed
`respectively on the inner Surfaces of upper and lower
`Substrates and a nematic liquid crystal material is injected
`therebetween, and where the liquid crystal molecules are
`twisted with being parallel to the substrates. In the above
`LCD, the potential difference between the two electrodes
`generated by applying Voltages to the upper and the lower
`electrodes yields an electric field perpendicular to the Sub
`Strates. The liquid crystal molecules are re-arranged Such
`that the torque due to the dielectric anisotropy and the torque
`due to the aligning treatment is balanced with each other.
`The torque due to the dielectric anisotropy forces the long
`axes of the liquid crystal molecules to be parallel to the field
`direction, and the magnitude of this torque depends on the
`intensity of the electric field. The elastic torque generated by
`the aligning treatment Such as rubbing forces the long axes
`of the liquid crystal molecules to be parallel to a predeter
`mined direction. When the director of the liquid crystal
`twists by 90 degrees on going from the lower electrode to the
`upper electrode, and the polarization directions of the polar
`izers are perpendicular to each other, the polarization of the
`incident light, in absence of the electric field, rotates by 90
`degrees, and thus the light passes through the analyzer,
`thereby causing white State. However, when Sufficient elec
`tric field is applied to the liquid crystal layer, Since the
`incident light passes through the liquid crystal layer without
`changing its polarization, the light cannot pass through the
`analyzer, thereby causing black State.
`As another example of a conventional LCD, U.S. Pat. No.
`5,598,285 discloses an LCD, where two linear electrodes
`parallel to each other are formed on either of the two
`Substrates, and a liquid crystal layer lies over the region
`between the two electrodes, and where the liquid crystal
`molecules are aligned parallel to the Substrates. In this LCD,
`the potential difference between the two electrodes yields an
`electric field Substantially parallel to the Substrates and
`perpendicular to the two electrodes. The liquid crystal
`molecules are rearranged Such that the torque due to the
`dielectric anisotropy and the elastical torque due to rubbing
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`are balanced with each other. When the polarization direc
`tions of the polarizers are perpendicular to each other, in
`absence of electric field, the crossed polarizer blocks the
`incident light and makes the liquid crystal display to be in
`black state. However, when sufficient electric field is applied
`to the liquid crystal layer, the polarization of the incident
`light varies and the light passes through the analyzer, thereby
`causing white State.
`The above-mentioned LCDs have disadvantages
`described hereinafter respectively.
`The principal disadvantage of the TN-LCD is its narrow
`Viewing angle. In the TN-LCD, the larger an angle made by
`the direction of the user's eye and the direction normal to a
`Surface of a display, the larger the value 4 n d where
`birefringence An is the difference of the refractive indices
`between in the direction of the long axes and the short axes
`of the liquid crystal molecules and d is the thickness of the
`liquid crystal layer. Accordingly, the contrast, which is
`defined as the luminance of the brightest state divided by
`that of the darkest State, abruptly decreases. In addition, gray
`inversion phenomenon also occurs. Accordingly, the View
`ing angle at which the contrast is equal to 10 is very narrow,
`and thus image quality is abruptly deteriorated when viewed
`at an angle larger then the viewing angle.
`To compensate the viewing angle, methods using phase
`difference compensating films are Suggested in U.S. Pat. No.
`5,576,861, but they have disadvantages in manufacturing
`cost and the number of the process Steps Since the phase
`difference compensating films are additionally attached.
`Furthermore, the Satisfactory viewing angle may not be still
`obtained even though the phase retardation compensation
`films are used.
`The U.S. Pat. No. 5,598.285 has disadvantages in power
`consumption and aperture ratio. The LCD disclosed in the
`above U.S. Pat. No. 5,598.285 has an electric field of which
`Strength is dependent on the positions, that is, the field
`Strength is weaker as far from the electrodes. Therefore, in
`order to obtain sufficient field strength at the far point from
`the electrodes, high driving Voltage is required. In addition,
`Since all the electrodes are formed on one Substrate and
`Storage capacitors are formed to obtain Sufficient
`capacitance, the aperture ratio is Small.
`In the meantime, Since the liquid crystal display is a
`passive display, it requires an external light Source. A white
`light is usually used for the light Source of the liquid crystal
`display, and red, green and blue color filters are used for
`color display. The color filters are formed on one of the
`Substrates, and a black matrix for preventing light leakage at
`the boundaries of the color filters is formed therebetween.
`The light from the light Source changes its properties,
`Such as polarization, in the liquid crystal layer, and the
`transmittance of the light depends on the wavelength of the
`light. The transmittance also depends on the driving mode of
`the liquid crystal display.
`In the case of TN LCDs, the transmittance of the blue light
`differs from those of the red and green lights by 10%.
`Moreover, the IPS LCD has the difference of the transmit
`tances of the blue, red and green lights more than 40%.
`In order to reduce the difference of the transmittance, two
`methods are conventionally used, one using a backlight unit
`and a driving circuit having additional characteristics and
`the other making a cell gap to be different for the pixels of
`different colors by adjusting the height of the color filters.
`However, the former method may increase the yield cost and
`the number of process Steps, and the latter may cause uneven
`rubbing.
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`3
`SUMMARY OF THE INVENTION
`An object of the present invention is to obtain a wide
`Viewing angle.
`Another object of the present invention is to reduce power
`consumption of the liquid crystal display.
`Still another object of the present invention is to enlarge
`the aperture ratio.
`In order to accomplish the above-mentioned objects, the
`array of the electrodes of the LCD is modified.
`First electrodes and Second electrode insulated from each
`other are overlapped with each other at least in part. The
`Second electrode forms a continuous plane between the first
`electrodes, and one pixel includes at least one first electrode
`and one Second electrode.
`The potential difference between the two electrodes gen
`erated by applying Voltages to the electrodes yields an
`electric field. The shape of an electric line of force is
`Semi-ellipse or parabola having a center on a boundary line
`or a boundary region between the first electrode and the
`second electrode, whereby the electric field on the electrodes
`has the Vertical and the horizontal components.
`The liquid crystal molecules on the first or the Second
`electrode and on the boundary region between the two
`electrodes are re-arranged to have a twist angle and a tilt
`angle due to the vertical and the horizontal components of
`the electric field. Therefore, the polarization of the incident
`light varies by the rearrangement of liquid crystal molecules.
`AS described above, a wide Viewing angle may be
`obtained since the liquid crystal molecules are re-arranged to
`have both the twist angle and the tilt angle.
`In addition, the liquid crystal molecules on the first
`electrode and the Second electrode contribute to displaying
`images Since the electric field has the vertical and the
`horizontal components on the first electrode and the Second
`electrode as well as on the boundary region between the two
`electrodes.
`In addition, power consumption is low Since the Strength
`of the electric field is large on the boundary region between
`the first electrode and the Second electrode.
`In addition, aperture ratio may be enlarged Since a Storage
`capacitor for obtaining Sufficient Storage capacitance is not
`additionally required Since the two electrodes are overlapped
`via an insulating film when using a thin film transistor (TFT)
`as a Switching element.
`Additional objects and advantages of the present inven
`tion are set forth in part in the description which follows, and
`in part will be obvious from the description, or may be
`learned by practice of the invention. The objects and advan
`tages of the invention will be realized and attained by means
`of the elements and combinations particularly pointed out in
`the appended claims.
`BRIEF DESCRIPTION OF THE DRAWINGS
`The accompanying drawings, illustrate embodiments of
`the present invention and, together with the description,
`Serve to explain the principles of the invention.
`FIG. 1 is a layout view of electrodes of a liquid crystal
`display (LCD) according to a first embodiment of the
`present invention;
`FIG. 2 is a cross-sectional view taken along line II-II' in
`FIG. 1, which shows both upper and lower substrates as well
`as equipotential lines and lines of electrical force between
`the two Substrates;
`FIG. 3 illustrates the twist angle of liquid crystal mol
`ecules in the first embodiment of the present invention;
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`US 6,577,368 B1
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`4
`FIG. 4 is a graph illustrating the variation of the twist
`angle of the liquid crystal molecules as a function of the
`horizontal position according to the first embodiment of the
`present invention;
`FIG. 5 is a graph illustrating the variation of the twist
`angle of the liquid crystal molecules as a function of height
`according to the first embodiment of the present invention;
`FIG. 6 shows the tilt angle of the liquid crystal molecules
`according to the first embodiment of the present invention;
`FIG. 7 is a graph illustrating the variation of the tilt angle
`of the liquid crystal molecules as a function of height
`according to the first embodiment of the present invention;
`FIG. 8 is a graph illustrating the variation of the tilt angle
`of the liquid crystal molecules as a function of horizontal
`position according to the first embodiment of the present
`invention;
`FIG. 9 is a graph illustrating the transmittance as a
`function of horizontal position in the LCD according to the
`first embodiment of the present invention;
`FIG. 10 is a graph illustrating the transmittance as a
`function of applied Voltage in the LCD according to the first
`embodiment of the present invention;
`FIG. 11 is a graph illustrating a viewing angle in the LCD
`according to the first embodiment of the present invention;
`FIG. 12 illustrates the twist angle of liquid crystal mol
`ecules in the Second embodiment of the present invention;
`FIG. 13 is a graph illustrating the variation of the twist
`angle of the liquid crystal molecules as a function of the
`horizontal position according to the Second embodiment of
`the present invention;
`FIG. 14 is a graph illustrating the variation of the twist
`angle of the liquid crystal molecules as a function of height
`according to the Second embodiment of the present inven
`tion;
`FIG. 15 shows the tilt angle of the liquid crystal molecules
`according to the Second embodiment of the present inven
`tion;
`FIG. 16 is a graph illustrating the variation of the tilt angle
`of the liquid crystal molecules as a function of height
`according to the Second embodiment of the present inven
`tion;
`FIG. 17 is a graph illustrating the variation of the tilt angle
`of the liquid crystal molecules as a function of horizontal
`position according to the Second embodiment of the present
`invention;
`FIG. 18 illustrates the twist angle of liquid crystal mol
`ecules in the third embodiment of the present invention;
`FIG. 19 is a graph illustrating the variation of the twist
`angle of the liquid crystal molecules as a function of the
`horizontal position according to the third embodiment of the
`present invention;
`FIG. 20 is a graph illustrating the variation of the twist
`angle of the liquid crystal molecules as a function of height
`according to the third embodiment of the present invention;
`FIG.21 shows the tilt angle of the liquid crystal molecules
`according to the third embodiment of the present invention;
`FIG.22 is a graph illustrating the variation of the tilt angle
`o