02 Zjawiska kontaktowe

background image

=-$:,6.$.217$.72:(

3RáF]HQLD PHWDO±SyáSU]HZRGQLN OXE SyáSU]HZRGQLN±SyáSU]H

ZRGQLN Z\WZDU]DM REV]DU\ SU]HMFLRZH ]áF]D JG]LH NRQFHQWUDFMD

QRQLNyZ RGELHJD RG NRQFHQWUDFML Z REMWRFL PDWHULDáX :áDFLZRFL

W\FK REV]DUyZ ]PLHQLDM VL SRQDGWR SR SU]\áR*HQLX QDSLFLD

]HZQWU]QHJR &KDUDNWHU\VW\NL SUGRZRQDSLFLRZH ]áF]\ V QD RJyá

QLHOLQLRZH 1LHOLQLRZRFL WH SRZRGXM *H ]áF]D V SRGVWDZRZ\P

HOHPHQWHPVNáDGRZ\PZLNV]RFLSU]\U]GyZSyáSU]HZRGQLNRZ\FK

3RMFLHP LVWRWQ\P GOD ]UR]XPLHQLD ]MDZLVN NRQWDNWRZ\FK MHVW

SUDFD Z\MFLD HOHNWURQyZ : SU]\SDGNX PHWDOX HOHNWURQ\ VZRERGQH

]QDMGXMFHVLZVLHFLNU\VWDOLF]QHMGRGDWQLFKMRQyZSRVLDGDMXMHPQ

HQHUJL SRWHQFMDOQ áDGXQHN HOHNWURQX MHVW XMHPQ\ -H*HOL HQHUJL

HOHNWURQX Z SUy*QL SU]\MPLHP\ ]D ]HURZ WR PHWDO VWDQRZL GOD

HOHNWURQyZVWXGQLSRWHQFMDOQU\V

m

q

-

0

0

T

>

0

=

T

W

n(W)

(b)

(a)

W

F

5\V(OHNWURQ\VZRERGQHZPHWDOXREVDG]DMFHSR]LRP\HQHUJHW\F]QHZVWXGQL

SRWHQFMDOQHMDRUD]NU]\ZHUR]NáDGXHOHNWURQyZZIXQNFMLHQHUJLLQ:GODGZyFK

Uy*Q\FKWHPSHUDWXUE:

)

MHVWHQHUJL)HUPLHJRPDNV\PDOQDHQHUJLDHOHNWURQyZ

ZPHWDOXZWHPSHUDWXU]H7 .T

Φ

P

R]QDF]DWHUPRG\QDPLF]QSUDFZ\MFLD

$E\SU]HQLHüHOHNWURQ]PHWDOXGRSUy*QLWU]HEDZ\NRQDüSUDF

-HVW RQD PLQLPDOQD ZWHG\ JG\ SU]HQRV]RQ\ HOHNWURQ SRFKRG]L

]SR]LRPX )HUPLHJR L QRVL ZyZF]DV QD]Z WHUPRG\QDPLF]QHM SUDF\

Z\MFLDT

Φ

P

:WHPSHUDWXU]H7!LVWQLHMHOHNWURQ\NWyU\FKHQHUJLH

SU]HNUDF]DM SR]LRP ]HURZ\ U\VE ZWHG\ SHZQD LFK F]ü MHVW

]GROQDRSXFLüPHWDO5LFKDUGVRQSRGDá]DOH*QRüRNUHODMFZLHONRü

SUGXWHUPRHOHNWURQRZHJRMNWyU\]ZL]DQ\MHVW]WHPSHUDWXUPHWDOX7

RUD]SUDFZ\MFLDHOHNWURQyZ

background image

M $7

T

N7

P

=







H[S

Φ

JG]LH$MHVWW]ZVWDá5LFKDUGVRQD

3RGQLHVLHQLHWHPSHUDWXU\OXE ]PLDQD SUDF\ Z\MFLD QS SRSU]H]

QDáR*HQLHWOHQNXQDSRZLHU]FKQLPHWDOXSRZRGXMHJZDáWRZQ\Z]URVW

SUGX WHUPRHOHNWURQRZHJR JG\* RELH WH ZLHONRFL Z\VWSXM Z

Z\NáDGQLNX

(OHNWURQ\RSXV]F]DMFHSyáSU]HZRGQLNPRJSRFKRG]Lü]DUyZQR

]SDVPDSU]HZRGQLFWZDMDNUyZQLH*]SDVPDZDOHQF\MQHJRF]\WH*]H

VWDQyZGRPLHV]NRZ\FKU\V

7HUPRG\QDPLF]QSUDFZ\MFLDGODSyáSU]HZRGQLNDRNUHODVL

DQDORJLF]QLH MDN GOD PHWDOX MDNR Uy*QLF HQHUJLL PLG]\ SR]LRPHP

]HURZ\P L SR]LRPHP )HUPLHJR ERZLHP W\ONR WDNLH SU]HMFLH QLH

SRZRGXMH]PLDQ\WHPSHUDWXU\SyáSU]HZRGQLND

0

C

W

F

W

d

W

V

W

p

q

-

n(W)

5\V(PLVMDHOHNWURQyZ]SyáSU]HZRGQLND

: ]MDZLVNDFK NRQWDNWRZ\FK V]F]HJyOQLH GOD SyáSU]HZRGQLNyZ

LVWRWQUROPR*HRGJU\ZDüREHFQRüVWDQyZSRZLHU]FKQLRZ\FK6WDQ\

WDNLH ]ZL]DQH ] QLHFLJáRFL VWUXNWXU\ NU\VWDOLF]QHM GHIHNWDPL VLHFL

MDNUyZQLH*FKHPLF]QLH]ZL]DQ\PLREF\PLDWRPDPLF]\F]VWHF]NDPL

VWDQRZLGRGDWNRZHFHQWUDZ\FKZ\WXMFHOXEXZDOQLDMFHHOHNWURQ\7H

GRGDWNRZH FHQWUD áDGXQNRZH Z\ZLHUDM ZSá\Z QD ZDUVWZ

SU]\SRZLHU]FKQLRZ SU]\FLJDMF áDGXQNL SU]HFLZQHJR ]QDNX

LSRZRGXMFMHMZ]ERJDFHQLHOXE]XER*HQLHZQRQLNL:]DOH*QRFLRG

URG]DMX FHQWUyZ áDGXQNRZ\FK L W\SX SyáSU]HZRGQLND PRJ SRZVWDü

Uy*QHURG]DMHREV]DUyZSU]\SRZLHU]FKQLRZ\FK3U]\NáDGRZRMH*HOLQD

SRZLHU]FKQL LVWQLHM VWDQ\ DNFHSWRURSRGREQH áDGXQHN XMHPQ\

DSyáSU]HZRGQLN MHVW W\SX Q WR SRZVWDMH SU]\ SRZLHU]FKQL REV]DU

]XER*RQ\ GRGDWQL áDGXQHN SU]HVWU]HQQ\ ] QLHGRERUHP HOHNWURQyZ

background image

VZRERGQ\FK3U]\GX*HMJVWRFLVWDQyZSRZLHU]FKQLRZ\FK1

66

NWRUH

SRREVDG]HQLXZ\ND]XMáDGXQHNSRZLHU]FKQLRZ\

4

T1

66

66

= −

ZDUVWZD

SU]\SRZLHU]FKQLRZD PR*H ]PLHQLü W\S SU]HZRGQLFWZD FR QD]\ZDP\

LQZHUVM SyáSU]HZRGQLND U\V =DNU]\ZLHQLH SDVP HQHUJHW\F]Q\FK

NX JyU]H ]ZL]DQH MHVW ]H Z]URVWHP HQHUJLL HOHNWURQyZ

SU]HPLHV]F]DMF\FKVL]SyáSU]HZRGQLNDNXSRZLHU]FKQL

2%6=$5

,1:(56<-1<

C

W

V

W

F

W

4

66

1

66

G]LXU\

5\V,QZHUVMDW\SXSU]HZRGQLFWZD

ZREV]DU]HSU]\SRZLHU]FKQLRZ\PSRG

ZSá\ZHP áDGXQNXSRZLHU]FKQLRZHJR

4

66

-H*HOL 1

66

Z SyáSU]HZRGQLNX SU]HNUDF]D

FP

WR

RZáDFLZRFLDFK ]áF]D QLH GHF\GXM SUDFH Z\MFLD DOH áDGXQHN

SRZLHU]FKQLRZ\ :VSyáF]HVQH WHFKQRORJLH Z\WZDU]DQLD VWUXNWXU

SyáSU]HZRGQLNRZ\FK QS WHFKQRORJLD SODQDUQD VNXWHF]QLH UR]ZL]Dá\

SUREOHPVWDQyZSRZLHU]FKQLRZ\FKJáyZQLHSRSU]H]VWRVRZDQLHZDUVWZ

SDV\ZXMF\FK W\SRZD ZDUVWZD SDV\ZXMFD 6L2

SRZVWDMH áDWZR

ZZ\QLNXWHUPLF]QHJRXWOHQLDQLDSRZLHU]FKQL6L

.217$.70(7$/3Ïà35=(:2'1,.25

'RSURZDG]HQLH GR EH]SRUHGQLHJR NRQWDNWX PHWDOX ]

SyáSU]HZRGQLNLHP SRZRGXMH Z\PLDQ HOHNWURQyZ PLG]\ REX

PDWHULDáDPL D* GR XVWDOHQLD VL UyZQRZDJL WHUPRG\QDPLF]QHM

=DNáDGDMF *H SUDFD Z\MFLD T

Φ

P

HOHNWURQX ] PHWDOX MHVW ZLNV]D QL*

T

Φ

S

GOD SyáSU]HZRGQLND W\SX Q X]\VNXMH VL VWDQ UyZQRZDJL ] W]Z

REV]DUHP]XER*RQ\PSRVWURQLHSyáSU]HZRGQLNDU\V

p

q

-

m

q

-

d

T

'

Φ

5\V6WDQUyZQRZDJLSU]\

EH]SRUHGQLPNRQWDNFLHPHWDOXL

SyáSU]HZRGQLNDW\SXQGMHVWJUXERFL

ZDUVWZ\]XER*RQHMT

Φ

'

R]QDF]D

Z\VRNRüEDULHU\SRWHQFMDáX

background image

3RQLHZD*

Φ

S

Φ

P

ZLF VWUXPLH HOHNWURQyZ ] SyáSU]HZRGQLND GR

PHWDOXSU]HZD*DSRF]WNRZRQDGVWUXPLHQLHPHOHNWURQyZ]PHWDOXGR

SyáSU]HZRGQLND : Z\QLNX WHJR PHWDO ]DF]QLH VL áDGRZDü XMHPQLH

SR]LRP)HUPLHJR:

)P

SRGQRVLVLDSyáSU]HZRGQLNGRGDWQLRSR]LRP

)HUPLHJR:

)S

REQL*DVL3RMDZLDVLEDULHUDGODHOHNWURQyZSá\QF\FK

] SyáSU]HZRGQLND GR PHWDOX L LFK VWUXPLH PDOHMH *G\ SR]LRP\ :

)

Z\UyZQDMVLQDVWSXMHVWDQUyZQRZDJLDEDULHUDSRWHQFMDáXRVLJQLH

ZDUWRü

U

D

m

n

=

Φ

Φ

= WHJR Z]JOGX *H NRQFHQWUDFMD QRQLNyZ VZRERGQ\FK Z

SyáSU]HZRGQLNXMHVW]QDF]QLHPQLHMV]DQL*ZPHWDOXDáDGXQNLSRREX

VWURQDFK ]áF]D PXV] E\ü UyZQH JUXERü áDGXQNX SU]HVWU]HQQHJR Z

SyáSU]HZRGQLNXMHVW]QDF]QLHZLNV]DQL*ZPHWDOXSU]\F]\PJUXERü

ZDUVWZ\ HOHNWURQyZ MHVW U]GX NLONX VWDá\FK VLHFLRZ\FK 'OD V\WXDFML

SRND]DQHM QD U\V SR VWURQLH SyáSU]HZRGQLND SRMDZLD VL ZDUVWZD

QLHUXFKRPHJRáDGXQNX]MRQL]RZDQ\FKGRQRUyZSR]EDZLRQDHOHNWURQyZ

SU]HZRGQLFWZD]XER*RQD*UXERüWHMZDUVWZ\Z\QRVL

G

1 T

'

G

=

ε ε Φ

JG]LH

Φ

'

MHVWRNUHORQHZ]RUHP1

'

MHVWNRQFHQWUDFMGRQRUyZ

ε

ε

R]QDF]DSU]HQLNDOQRüHOHNWU\F]QSyáSU]HZRGQLND

3U]\NáDG 'OD NU]HPX R NRQFHQWUDFML GRQRUyZ 1

G

FP

L

Z\VRNRFL EDULHU\

Φ

'

9

ε

RWU]\PXMH VL ] JUXERü

REV]DUX]XER*RQHJRG

µ

P

2PDZLDQDEDULHUDWZRU]FDVLQDVW\NXPHWDOSyáSU]HZRGQLNQD]\ZDQD

MHVWEDULHU6FKRWWN\CHJR

Φ

'

3U]\áR*HQLH QDSLFLD ]HZQWU]QHJR GR ]áF]D PS SRZRGXMH

Z]URVW OXE REQL*HQLH EDULHU\ Z ]DOH*QRFL RG NLHUXQNX QDSLFLD 3R

SU]\áR*HQLX QDSLFLD Z NLHUXQNX SU]HZRG]HQLD SRWHQFMDá XMHPQ\ SR

VWURQLH SyáSU]HZRGQLND W\SX Q ZV]\VWNLH SR]LRP\ SyáSU]HZRGQLND

SRGQRV]VLRT8LRWDNVDPZDURüPDOHMHEDULHUDSRWHQFMDáX3R

SU]\áR*HQLXQDSLFLDZNLHUXQNX]DSRURZ\PEDULHUDSRWHQFMDáXURQLHR

T8LURQLHWH*JUXERüZDUVWZ\]DSRURZHM

(

)

G

8

T1

'

G

=

+

ε ε Φ

=PLDQ\ Z\VRNRFL EDULHU\ VSRZRGRZDQH SU]\áR*HQLHP QDSLFLD

]HZQWU]QHJR PDM ZSá\Z QD ZLHONRü Sá\QFHJR SU]H] ]áF]H SUGX

3U]\EUDNXQDSLFLDSUGM

P

Sá\QF\]PHWDOXGRSyáSU]HZRGQLNDLSUG

background image

j

p

Sá\QF\]SyáSU]HZRGQLNDGRPHWDOXNRPSHQVXMVL(

)

j

j

j

m

p

s

=

=

3U]\áR*HQLH QDSLFLD Z NLHUXQNX SU]HZRG]HQLD L ]PQLHMV]HQLH EDULHU\

RT8 VSRZRGXMH *H ]JRGQLH ]H VWDW\VW\N %ROW]PDQQD M

S

Z]URQLH

H[ST8N7 UD]\ 3UG M

P

QLH ]PLHQL VL L Z ]ZL]NX ] W\P SUG

Z\SDGNRZ\EG]LHZ\QRVLá

M M

M

M

T8 N7

M

M

T8 N7

S

P

V

V

V

=

=

− =

H[S>

@

H[S>

@

3R SU]\áR*HQLX QDSLFLD Z NLHUXQNX ]DSRURZ\P WU]HED ]PLHQLü ]QDN

SU]\ 8 Z Z\UD*HQLX L ZWHG\ RWU]\PXMH VL MX* GOD VWRVXQNRZR

QLHGX*\FK QDSLü QDV\FDMF VL ZDUWRü SUGX M M

V

]ZDQ SUGHP

ZVWHF]Q\P3RQLHZD*SUGZNLHUXQNXSU]HZRG]HQLDMHVWGX*RZLNV]\

RG SUGX Z NLHUXQNX ]DSRURZ\P RWU]\PXMH VL NRQWDNW PS

RZáDFLZRFLDFKSURVWXMF\FKU\V

j

U

S

j

5\V3URVWRZDQLHQD]áF]XPHWDO

SyáSU]HZRGQLNGOD]áF]DP6LQDSLFLH

ZNLHUXQNXSU]HZRG]HQLDQLHSU]HNUDF]D

QDRJyáZDUWRFL9

'RNáDGQD WHRULD SU]HSá\ZX SUGX SU]H] EDULHU PS XZ]JOGQLD ZLHOH

F]\QQLNyZ WDNLFK MDN JVWRü VWDQyZ SRZLHU]FKQLRZ\FK UR]PLDU

EDULHU\ URG]DM UXFKX QRQLNyZ Z REV]DU]H EDULHU\ =QDQH WHRULH

GLRGRZD %HWKHJR G\IX]\MQD 6FKRWWN\CHJR GDM Z\UD*HQLD ]EOL*RQH

NV]WDáWHPGRDUy*QLFHSRMDZLDMVLZZ\UD*HQLDFKQDM

V

=à&=(53

=áF]HP SQ QD]\ZDP\ REV]DU SyáSU]HZRGQLND Z NWyU\P

QDVWSXMH]PLDQDSU]HZRGQLFWZD]W\SXSQDW\SQ6DPDSRZLHU]FKQLD

JUDQLF]QD UR]G]LHODMFD SyáSU]HZRGQLNL R RGPLHQQ\FK W\SDFK

SU]HZRGQLFWZDQD]\ZDVL]áF]HPWHFKQRORJLF]Q\P3RREXVWURQDFK

]áF]D WHFKQRORJLF]QHJR ]QDMGXMH VL ZDUVWZD SU]HMFLRZD EGFD

GLSRORZZDUVWZQLHUXFKRPHJRáDGXQNX

:áDFLZRFL ]áF]D ]DOH* RG URG]DMX X*\WHJR SyáSU]HZRGQLND

KRPR]áF]H OXE URG]DMX REX Uy*Q\FK SyáSU]HZRGQLNyZ WZRU]F\FK

W]ZKHWHUR]áF]HW\SXGRPLHV]HNLVSRVREXLFKUR]NáDGX

background image

5R]NáDG GRPLHV]NL XZDUXQNRZDQ\ MHVW Z ]QDF]QHM PLHU]H

URG]DMHP WHFKQRORJLL X*\WHM GR Z\WZRU]HQLD ]áF]D =áF]D

ZVSyáF]HQLHZ\WZDU]DQHPR*QDSRG]LHOLüQDVWSXMFR
=áF]HG\IX]\MQH

=áF]D WHJR W\SX Z\WZDU]DQH V PHWRG G\IX]ML SLHUZLDVWND

VSHáQLDMFHJRUROGRPLHV]NLGRQRURZHMGRSyáSU]HZRGQLNDW\SXSOXE

DNFHSWRURZHMGRSyáSU]HZRGQLNDW\SXQ'\IX]MSU]HSURZDG]DVLZ

SRGZ\*V]RQHM WHPSHUDWXU]H U]GX

R

& GOD 6L D GRPLHV]ND PR*H

E\üZSRVWDFLSDU\OXEFLHF]\QDQLHVLRQHMQDSRZLHU]FKQL'\IX]MERUX

GR NU]HPX SU]H] RNQR Z\WUDZLRQH Z ZDUVWZLH 6L2

VSHáQLDMFHM URO

PDVNLSU]HGVWDZLDU\VD

p-Si

n-Si

2

SiO

B

(a)

p

n

(b)

j

x

d

N

(x)

N

a

)

0

(

N

a

x

5\VD'\IX]MDERUXGRNU]HPXZZ\EUDQ\PREV]DU]HSyáSU]HZRGQLNDRUD]E

SURILOUR]NáDGXWHMGRPLHV]NL

5R]NáDG ZSURZDG]RQHM GRPLHV]NL Z\QLND ] SUDZ G\IX]ML L ]DOH*\

UyZQLH*RGWHJRF]\Z\GDMQRü(UyGáDZWUDNFLHSURFHVXE\áDVWDáDF]\

PDOHMFDZF]DVLH3URILOUR]NáDGXGRPLHV]NLDNFHSWRURZHMGOD(UyGáDR

QLHRJUDQLF]RQHM Z\GDMQRFL ZG\IXQGRZDQHM GR SyáSU]HZRGQLND

]DZLHUDMFHJR GRPLHV]N GRQRURZ SU]HGVWDZLD U\VE .V]WDáW

NU]\ZHM 1

D

[ RNUHORQ\ MHVW W]Z IXQNFM EáGX :VSyáU]GQD ]áF]D

WHFKQRORJLF]QHJR[

M

Z\]QDF]RQDMHVWSU]H]UyZQDQLH

1 [

1

D

M

G

=

:SREOL*X[

M

SURILOUR]NáDGXPR*QDDSURNV\PRZDü]DOH*QRFLOLQLRZ

1 [

1

1

D[

D

G

=

≈ −

L]áF]HWDNLHQRVLQD]ZOLQLRZHJR]áF]DSQ
=áF]HLPSODQWRZDQH

=áF]D WHJR W\SX Z\WZDU]D VL Z Z\QLNX ERPEDUGRZDQLD

NU\V]WDáX MRQDPL GRPLHV]HN UR]SG]RQ\FK GR HQHUJLL U]GX VHWHN NH9

>@ =PLHQLDMF HQHUJL ERPEDUGXMF\FK MRQyZ PR*QD NV]WDáWRZDü

background image

SURILOGRPLHV]NRZDQLDU\V

a

N

N

d

N

p

n

x

j

x

5\V5R]NáDGNRQFHQWUDFML

GRPLHV]NLGRQRURZHMZSURZDG]RQHM

GRSyáSU]HZRGQLNDPHWRG

ZLHORNURWQHMLPSODQWDFMLMRQyZR

Uy*Q\FKHQHUJLDFK

,QQ\PL ]DOHWDPL PHWRG\ LPSODQWDFML V PR*OLZRü Z\ERUX GRZROQHM

GRPLHV]NL PR*OLZRü SURZDG]HQLD SURFHVX Z QLVNLFK WHPSHUDWXUDFK

RUD] áDWZRü MHJR DXWRPDW\]DFML =áF]H SU]HGVWDZLRQH QD U\V MHVW

SU]\NáDGHPW]Z]áF]DVNRNRZHJRDQJDEUXSW
=áF]HHSLWDNVMDOQH

: WUDNFLH QDQRV]HQLD ZDUVWZ\ HSLWDNVMDOQHM SyáSU]HZRGQLND QD

]RULHQWRZDQH SRGáR*H PR*QD ZSURZDG]Lü GRGDWNRZR GR DWPRVIHU\

JD]RZHM SDU\ ]ZL]NX NWyU\ Z\WZRU]\ GRPLHV]NL Z SLHUZLDVWNX

PDFLHU]\VW\PZZ\QLNXUHDNFMLFKHPLF]Q\FK:WHQVSRVyEáDWZRMHVW

Z\WZRU]\ü]áF]HW\SXVNRNRZHJRU\V

a

N

d

N

d

a

-N

N

j

x

x

5\V3U]\NáDG]áF]DVNRNRZHJR

RWU]\PDQHJRPHWRGHSLWDNVML

6WDQUyZQRZDJRZ\]áF]D

%H]SRUHGQLNRQWDNW REV]DUyZ Q RUD] S SURZDG]L GR Z]DMHPQHM

G\IX]MLQRQLNyZHOHNWURQyZGRREV]DUXW\SXSLG]LXUGRREV]DUXW\SX

QQDVNXWHNLVWQLHMF\FKJUDGLHQWyZNRQFHQWUDFML:WHQVSRVyESRREX

VWURQDFK ]áF]D WHFKQRORJLF]QHJR SRZVWDQ ZDUVWZ\ QLHUXFKRPHJR

áDGXQNXSU]HVWU]HQQHJRWZRU]FHZDUVWZGLSRORZ:SyáSU]HZRGQLNX

W\SX S SRZVWDQLH ZDUVWZD áDGXQNX XMHPQHJR ]MRQL]RZDQ\FK

DNFHSWRUyZ D Z SyáSU]HZRGQLNX W\SX Q ZDUVWZD áDGXQNX GRGDWQLHJR

]MRQL]RZDQ\FKGRQRUyZU\V

background image

a

-qN

d

qN

n

d

q(x)

x

p

d

5\V:DUVWZDGLSRORZDáDGXQNX

SU]HVWU]HQQHJRGOD]áF]DVNRNRZHJRS

QZREV]DU]HG

S

G

Q

EUDNMHVWáDGXQNyZ

VZRERGQ\FKREV]DU]XER*RQ\

&DáNRZLW\áDGXQHNZDUVWZ\GLSRORZHMPXVLE\üMHGQDNUyZQ\]HURFR

GOD]áF]DSU]HGVWDZLRQHJRQDU\VGDMH

qd N

qd N

n

d

p

a

=

0

5yZQDQLH RNUHOD JáERNRü ZQLNDQLD ZDUVWZ\ áDGXQNX

SU]HVWU]HQQHJRZREV]DUSyáSU]HZRGQLND:QLNDQLHWRMHVWW\PZLNV]H

LPPQLHMV]DMHVWNRQFHQWUDFMDGRPLHV]NLZGDQ\PREV]DU]H

àDGXQHN SU]HVWU]HQQ\ ]JRGQLH ] SUDZDPL HOHNWURVWDW\NL MHVW

SU]\F]\Q SRZVWDQLD SROD HOHNWU\F]QHJR ] RGSRZLHGQLP UR]NáDGHP

SRWHQFMDáX FR PR*QD Z\]QDF]\ü ] SUDZD 3RLVVRQD 'OD SU]\SDGNX

MHGQRZ\PLDURZHJRSUDZRWRPDSRVWDü

G 9

G[

= − ρ

ε ε

(

9

= −

JUDG

D

JG]LH

ρ

R]QDF]DJVWRüáDGXQNXSU]HVWU]HQQHJR

E

MHVWQDW*HQLHPSROD

HOHNWU\F]QHJR D 9SRWHQFMDáHP 'OD ]áF]D VNRNRZHJR UR]NáDG

áDGXQNXMDNQDU\VUR]ZL]DQLHUyZQDLDGDMHSU]HELHJL

SU]HGVWDZLRQHQDU\V

:EXGRZDQH SROH HOHNWU\F]QH Z\WZDU]D SUG\ XQRV]HQLD

HOHNWURQyZ L G]LXU NWyUH V VNLHURZDQH SU]HFLZQLH GR SUGyZ

G\IX]\MQ\FK : VWDQLH UyZQRZDJL SUG\ G\IX]\MQH L XQRV]HQLD

UyZQRZD*VL

= DQDOL]\ SUGyZ REX URG]DMyZ PR*QD Z\OLF]\ü Z\VRNRü EDULHU\

SRWHQFMDáX

ψ

=



 =



N7

T

Q

Q

N7

T

S

S

Q

S

Q

S

OQ

OQ

JG]LH ZVND(QLN GROQ\ R]QDF]D NRQFHQWUDFM QRQLNyZ Z PDWHULDOH

RGSRZLHGQLHJR W\SX Z VWDQLH UyZQRZDJL WHUPRG\QDPLF]QHM

=UyZQDQLDZ\QLND*HEDULHUDMHVWW\PZ\*V]DLPZLNV]DMHVW

background image

Uy*QLFD PLG]\ NRQFHQWUDFMDPL QRQLNyZ GDQHJR ]QDNX Z REX

REV]DUDFK

max

E

E(x)

0

p

d

n

d

x

V(x)

(a)

(b)

k

V

p

V

x

x

j

ψ

=

9 9

N

S

5\V3ROHHOHNWU\F]QH

ÄZEXGRZDQH´DLSRWHQFMDáE

Z\WZRU]RQHZVNRNRZ\P]áF]X

SQZZ\QLNXLVWQLHQLDáDGXQNX
GLSRORZHJR

ψ

R

MHVWEDULHU

SRWHQFMDáX

3U]\NáDGREOLF]HQLDZ\VRNRFLEDULHU\

0DWHULDáZ\MFLRZ\6L'ODNRQFHQWUDFMLGRQRUyZ1

G

FP

RWU]\PXMHVLNRQFHQWUDFMHOHNWURQyZQ

Q

RSRGREQHMZDUWRFL

'OD NRQFHQWUDFML DNFHSWRUyZ 1

D

FP

RWU]\PXMH VL

NRQFHQWUDFMG]LXUS

S

RSRGREQHMZDUWRFL

:WHPSHUDWXU]H.NRQFHQWUDFMDQRQLNyZVDPRLVWQ\FKZ\QRVL

Q

L

FP

=SUDZDG]LDáDQLDPDVGOD6LW\SXQRWU]\PXMHVL]DOH*QRüQ

Q

S

Q

Q

L

] F]HJR PR*QD Z\OLF]\ü NRQFHQWUDFM G]LXU QRQLNL

PQLHMV]RFLRZHZW\PREV]DU]H

S

Q

Q

Q

L

Q

=

=

=

FP

$QDORJLF]QLHGOD6LW\SXSNRQFHQWUDFMDQRQLNyZPQLHMV]RFLRZ\FK

Z\QRVL

Q

Q

S

S

L

S

=

=

FP

3RXWZRU]HQLX]áF]DZREV]DU]H]XER*RQ\PPDP\SUDNW\F]QLHGR

F]\QLHQLD]VDPRLVWQNRQFHQWUDFMQRQLNyZa

FP

ZREHF

NRQFHQWUDFML

FP

ZREV]DUDFKSR]DEDULHURZ\FKQRUD]S

:\VRNRü EDULHU\ GOD GDQHJR ]áF]D Z\OLF]RQD ] UyZQDQLD

Z\QRVL>@

ψ

=



 =







=

N7

T

Q

Q

Q

S

OQ

OQ

9

5R]PLDU SU]HVWU]HQQ\ EDULHU\ PR*QD Z\OLF]\ü ]H ]PLDQ

background image

SRWHQFMDáX Z ]áF]X U\VE L ZDUXQNX QHXWUDOQRFL HOHNWU\F]QHM

:Z\QLNXRWU]\PXMHVL

G G

G

1

1

T1 1

8

S

Q

D

G

D

G

=

+

=

+

ε ε

ψ

JG]LH8MHVWSU]\áR*RQ\PQDSLFLHP]HZQWU]Q\P=DWHPGODQDSLFLD

]DSRURZHJR XMHPQHJR V]HURNRü EDULHU\ SRWHQFMDáX URQLH 5RQLH

UyZQLH*Z\VRNRüEDULHU\GRZDUWRFL

ψ

+

8

'ODQDSLFLDSRODU\]DFML

Z NLHUXQNX SU]HZRG]HQLD 8! PDOHMH ]DUyZQR Z\VRNRü MDN L

V]HURNRüEDULHU\

3U]HSá\ZSUGXSU]H]]áF]HSQ

-DN MX* ZVSRPQLDQR Z UR]G] Z VWDQLH UyZQRZDJL EUDN

QDSLFLD]HZQWU]QHJRSUGZ\SDGNRZ\SU]H]]áF]HMHVWUyZQ\]HUR

U\V

C

W

F

W

V

W

D

qU

p

n

p

D

j

n

D

-j

p

U

j

n

U

-j

5\V=áF]HSQZVWDQLHUyZQRZDJL8

3UGG\IX]\MQ\HOHNWURQyZM

'Q

MHVWUyZQRZD*RQ\SU]H]SUGXQRV]HQLD

HOHNWURQyZM

8Q

SUGQRQLNyZPQLHMV]RFLRZ\FKRUD]SUGG\IX]\MQ\

G]LXU M

'S

MHVW UyZQRZD*RQ\ SU]H] SUG XQRV]HQLD G]LXU M

8S

SUG

QRQLNyZPQLHMV]RFLRZ\FK

3U]\áR*HQLH QDSLFLD ]DSRURZHJR GR ]áF]D SQ ELHJXQ XMHPQ\

(UyGáDSRODU\]XMDFHJRGRSDGRGDWQLGRQU\VSRZRGXMHZ]URVW

EDULHU\SRWHQFMDáXGODQRQLNyZZLNV]RFLRZ\FKLVLOQ\VSDGHNSUGX

G\IX]\MQHJR

QRQLNyZ

ZLNV]RFLRZ\FK

3UG

QRQLNyZ

PQLHMV]RFLRZ\FK SUDNW\F]QLH QLH ]PLHQLD VL L Z HIHNFLH GHF\GXMH R

W]ZSUG]LH]DSRURZ\P

3U]\ SRODU\]DFML ]áF]D Z NLHUXQNX SU]HZRG]HQLD Z\VRNRü

EDULHU\ GOD QRQLNyZ ZLNV]RFLRZ\FK PDOHMH L SUG W\FK QRQLNyZ

V]\ENRURQLHZUD]]QDSLFLHP0Dá\SUGQRQLNyZPQLHMV]RFLRZ\FK

background image

QLH]PLHQLDVLLQLHRGJU\ZDZW\PSU]\SDGNXZLNV]HMUROL

C

W

p

F

W

V

W

p

U

j

n

U

-j

n

F

W

p

d

n

d

qU

T

8

ψ

+

5\V=áF]HVSRODU\]RZDQHZNLHUXQNX]DSRURZ\P8

-H*HOL]DQLHGEDVL]MDZLVNDJHQHUDFMLLUHNRPELQDFMLQRQLNyZZ

]áF]X SQ FR MHVW GREU\P SU]\EOL*HQLHP GOD ]áF] FLHQNLFK WR

Z\UD*HQLHQDSUGSá\QF\SU]H]]áF]HSU]\ELHUDNV]WDáW

, ,

8

Q

6

7

=



 −



H[S

ϕ

JG]LH8MHVWQDSLFLHPSRODU\]DFML]áF]DDQMHVWW]ZZVSyáF]\QQLNLHP

QLHLGHDOQRFL ]áF]D R ZDUWRFLDFK QLHFR ZLNV]\FK RG MHGQRFL

:VSyáF]\QQLN Q ]RVWDá ZSURZDG]RQ\ DE\ XSRGREQLü FKDUDNWHU\VW\N

LGHDOQHJR ]áF]D SQ GR ]áF] U]HF]\ZLVW\FK 0D WR ]QDF]HQLH SU]\

SURMHNWRZDQLXXNáDGyZJG\Z\PDJDQD MHVW GX*D GRNáDGQRü QS SU]\

SURMHNWRZDQLXXNáDGyZVFDORQ\FK


Wyszukiwarka

Podobne podstrony:
02 Zjawiska Kontaktowe (2)
Rozdział 03 Zjawiska kontaktowe i powierzchniowe w półprzewodnikach
02.1.notatki całe do emocje-pamiec, Zniekształcenia, iluzje i niezwykłe zjawiska pamięciowe
TSI 02 Durkheim - Próba określenia zjawisk religijnych, teorie socjologiczne
ZJAWISKA TRANSPORTU, Szkoła, Fizyka 02
Biblia o kontaktach z duchami, PARANORMALNE ZJAWISKA
02 Nawiązywanie i utrzymywanie kontaktów międzyludzkich
02.1.notatki całe do emocje-pamiec, Zniekształcenia, iluzje i niezwykłe zjawiska pamięciowe
02 Nawiązywanie i utrzymywanie kontaktów społecznych
02 Nawiązywanie i utrzymywanie kontaktów międzyludzkich 2
02 Nawiązywanie i utrzymywanie kontaktów międzyludzkich 4
02 Nawiązywanie i utrzymywanie kontaktów międzyludzkich 5
02 Nawiązywanie i utrzymywanie kontaktów społecznych
02 Nawiązywanie i utrzymywanie kontaktów społecznych 2
02 Nawiązywanie i utrzymywanie kontaktów społecznych

więcej podobnych podstron