minimum suhu kerja maksimum Toleransi Kapasitansi Simbol
Co Simbol Co Simbol Persen
Z +10 2 +45 A +/- 1.0% Y -30 4 +65 B +/- 1.5% X -55 5 +85 C +/- 2.2% 6 +105 D +/- 3.3% 7 +125 E +/- 4.7% 8 +150 F +/- 7.5% 9 +200 P +/- 10.0% R 15.0% +/- S +/- 22.0% T +22% / - 33% U +22% / - 56% V +22% / - 82%
Tole ra n si
Sepert i kom ponen lainnya, besar kapasit ansi nom inal ada t oleransinya. Tabel diat as m enyaj ikan nilai t oleransi dengan kode- kode angka at au huruf t ert ent u. Dengan t able di at as pem akai dapat dengan m udah m enget ahui t oleransi kapasit or yang biasanya t ert era m enyert ai nilai nom inal kapasit or. Misalnya j ika t ert ulis 104 X7R, m aka kapasit asinya adalah 100nF dengan t oleransi + / -15% . Sekaligus diket haui j uga bahwa suhu kerj a yang direkom endasikan adalah ant ara -55Co sam pai + 125Co ( lihat t abel kode
karakt erist ik)
I n su la t ion Re sist a nce ( I R)
Walaupun bahan dielekt rik m erupakan bahan yang non- kondukt or, nam un t et ap saj a ada arus y ang dapat m elewat inya. Art inya, bahan dielekt rik j uga m em iliki resist ansi. walaupun nilainya sangat besar sekali. Phenom ena ini dinam akan arus bocor DCL ( DC Leakage Current ) dan resist ansi dielekt rik ini dinam akan I nsulat ion Resist ance ( I R) . Unt uk m enj elaskan ini, berikut adalah m odel rangkaian kapasit or.
m odel kapasit or
C = Capacitance
ESR = Equivalent Series Resistance
L = Inductance
IR = Insulation Resistance
Jika t idak diberi beban, sem est inya k apasit or dapat m enyim pan m uat an selam a-lam anya. Nam un dari
m odel di at as, diket ahui ada resit ansi dielekt rik I R( I nsulat ion Resist ance) yang paralel t erhadap kapasit or. I nsulat ion resist ance ( I R) ini sangat besar (MOhm) . Konsekuensinya t ent u saj a arus bocor ( DCL) sangat kecil (uA) . Unt uk m endapat kan kapasit ansi yang besar diperlukan perm ukaan elekt roda yang luas, t et api ini akan m enyebabkan resist ansi dielekt rik m akin kecil. Karena besar I R selalu berbanding t erbalik dengan kapasit ansi ( C) , karakt erist ik resist ansi dielekt rik ini biasa j uga disaj ikan dengan besaran RC ( I R x C) yang sat uannya ohm - farads at au
m egaohm - m icro farads.
D issipa t ion Fa ctor ( D F) da n I m pe dan si ( Z)
Dissipat ion Fact or adalah besar persent asi rugi- rugi (losses) kapasit ansi j ika kapasit or bekerj a pada aplikasi frekuensi. Besaran ini m enj adi fakt or yang diperhit ungkan m isalnya pada aplikasi m ot or phasa, rangkaian ballast, t uner dan lain- lain. Dari m odel rangkaian kapasit or digam barkan adanya resist ansi seri ( ESR) dan indukt ansi ( L) . Pabrik pem buat biasanya m eyert akan dat a DF dalam persen. Rugi- rugi (losses) it u didefenisikan sebagai ESR yang besarnya adalah persent asi dari im pedansi kapasit or Xc. Secara
m at em at is di t ulis sebagai berikut :
Dari penj elasan di at as dapat dihit ung besar t ot al im pedansi (Z t ot al) k apasit or adalah :
Karakt erist ik respons frekuensi sangat perlu diperhit ungkan t erut am a j ika kapasit or bekerja pada frekuensi t inggi. Unt uk perhit ungan- perhit ungan respons frekuensi dikenal j uga sat uan fakt or qualit as Q (qualit y fact or) yang t ak lain sam a dengan 1/ DF.
M e t a l Ox ide Silicon Ca pa cit a nce
1 . I n t r odu ct ion
Capacit ance volt age m easurem ent s of MOS capacit or st ruct ure provide a wealt h of inform at ion about t he st ruct ure which is of direct int erest when one evaluat es an MOS process. Since t he MOS st ruct ure is sim ple t o fabricat e t he t echnique is widely used.
To underst and capacit ance- volt age m easurem ent s one m ust first be fam iliar wit h t he frequency dependence of t he m easurem ent . This frequency dependence occurs prim arily in inversion since a cert ain t im e is needed t o generat e t he m inorit y carriers in t he inversion layer. Therm al equilibrium is t herefore not obt ained im m ediat ely.
The low fr e que ncy or quasi- st at ic m easurem ent m aint ains t herm al equilibrium at all t im es. This capacit ance is t he difference in charge divided by t he difference in gat e volt age while t he capacit or is in equilibrium at each volt age. A t ypical m easurem ent is perform ed wit h an elect rom et er which m easured t he charge added per unit t im e as one slowly varies t he applied gat e v olt age.
The h igh fre qu e ncy capacit ance is obt ained from a sm all signal capacit ance m easurem ent at high frequency. The gat e volt age is varied slowly t o obt ain t he capacit ance versus volt age. Under such condit ions one finds t hat t he charge in t he inversion layer does not change from t he equilibrium value corresponding t o t he applied DC volt age. The high frequency capacit ance t herefore reflect s t he charge variat ion in t he deplet ion layer and t he ( rat her sm all) m ovem ent of t he inversion layer charge.
I n t his sect ion we first derive t he sim ple capacit ance m odel which is based on t he full deplet ion approxim at ions and our basic assum pt ion. The com parison wit h t he exact low frequency capacit ance
reveals t hat t he largest error occurs at t he flat band volt age. We t herefore derive t he exact flat band capacit ance using t he linearized Poisson's equat ion. Then we discuss t he full exact analysis followed by a discussion of deep deplet ion as well as t he non- ideal effect s in MOS capacit ors.
2 . Sim ple ca pa cit a nce m ode l
The capacit ance of an MOS capacit or is obt ained using t he sam e assum pt ions as in t he analysis in sect ion 6.5. The MOS st ruct ure is t reat ed as consist ing of a series connect ion of t wo capacit ors: t he capacit ance of t he oxide and t he capacit ance of t he deplet ion layer.
I n accum ulat ion t here is no deplet ion layer. The rem aining capacit or is t he oxide capacit ance, so t hat t he capcit ance equals:
(mc11)
I n deplet ion t he MOS capacit ance is obt ained from t he series connect ion of t he oxide capacit ance and t he capacit ance of t he deplet ion layer, or:
(mc12)
where xd is t he variable deplet ion layer widt h which is calculat ed from :
(mc2)
I n order t o find t he capacit ance corresponding t o a specific value of t he gat e volt age we also need t o use t he relat ion bet ween t he pot ent ial across t he deplet ion region and t he gat e v olt age, given by:
I n inversion t he capacit ance becom es independent of t he gat e volt age. The low frequency capacit ance equals t he oxide capacit ance since charge is added t o and from t he inversion layer in a low frequency m easurem ent . The high frequency capacit ance is obt ained from t he series connect ion of t he oxide capacit ance and t he capacit ance of t he deplet ion layer having it s m axim um widt h, xd,m ax. The capacit ances are given by:
(mc13)
The capacit ance of an MOS capacit or as calculat ed using t he sim ple m odel is shown in t he figure below. The dot t ed lines represent t he sim ple m odel while t he solid line corresponds t o t he low frequency capacit ance as obt ained from t he exact analysis.
mosexact.xls - moslfcap.gif
Fig. 6 .6 .1 Low frequency capacit ance of an MOS capacit or. Shown are t he exact solut ion for t he low frequency capacit ance ( solid line) and t he low and high frequency capacit ance obt ained wit h t he sim ple m odel ( dot t ed lines) . The red square indicat es t he flat band v olt age and capacit ance, while t he green square indicat es t he t hreshold v olt age and
3 . Fla t ba n d ca pa cit a nce
The sim ple m odel predict s t hat t he flat band capacit ance equals t he oxide capacit ance. However, t he com parison wit h t he exact solut ion of t he low frequency capacit ance as shown in t he above figure reveals t hat t he error can be subst ancial. The reason for t his is t hat we have ignored any charge v ariat ion in t he sem iconduct or. We will t herefore now derive t he exact flat band capacit ance.
To derive t he flat band capacit ance including t he charge variat ion in t he sem iconduct or we first linearize Poisson's equat ion. Since t he pot ent ial across t he sem iconduct or at flat band is zero, we expect t he pot ent ial t o be sm all as we vary t he gat e volt age around t he flat band volt age. Poisson's equat ion can t hen be sim plified t o:
(mc16)
The solut ion t o t his equat ion is:
(mc17)
where LD is called t he Debye lengt h. The solut ion of t he pot ent ial enables t he derivat ion of t he capacit ance of t he sem iconduct or under flat band condit ions, or:
(mc18)
The flat band capacit ance of t he MOS st ruct ure at flat band is obt ained by calculat ing t he series connect ion of t he oxide capacit ance and t he capacit ance of t he sem iconduct or, yielding:
4 . Ex a ct an a lysis
For a descript ion of t he derivat ion of t he MOS capacit ance using t he exact analysis we refer t he reader t o t hat sect ion.
5 . D e e p de ple t ion ca pa cit an ce
Deep deplet ion occurs in an MOS capacit or when m easuring t he high- frequency capacit ance while sweeping t he gat e volt age " quickly" . Quickly here m eans t hat t he gat e volt age m ust be changed fast enough so t hat t he st ruct ure is not in t herm al equilibrium . One t hen observes t hat when ram ping t he volt age from flat band t o t hreshold and beyond t he inversion layer is not or only part ially form ed as t he generat ion of m inorit y carriers can not keep up wit h t he am ount needed t o form t he inversion layer. The deplet ion layer t herefore keeps increasing beyond it s m axim um t herm al equilibrium value, xd,T result ing in a capacit ance which furt her decreases wit h v olt age.
The t im e required t o reach t herm al equilibrium when abrupt ly biasing t he MOS capacit or at a volt age larger t hen t he t hreshold volt age can be est im at ed by t aking t he rat io of t he t ot al charge in t he inversion layer t o t he t herm al generat ion rat e of m inorit y carriers. A com plet e analysis should include bot h a surface generat ion rat e as well as generat ion in t he deplet ion layer and t he quasi-neut ral region. A good approxim at ion is obt ained by considering only t he generat ion rat e in t he deplet ion region xd,dd. This yields t he following equat ion:
(mc14)
where t he generat ion in t he deplet ion layer was assum ed t o be const ant . The rat e of change required t o observe deep deplet ion is t hen obt ained from :
(mc15)
This equat ion enables t o predict t hat deep deplet ion is less likely at higher am bient t em perat ure since t he int rinsic concent rat ion ni increases
exponent ially wit h t em perat ure, while it is m ore likely t o occur in MOS st ruct ures m ade wit h wide bandgap m at erials ( for inst ance SiC for which Eg = 3 eV) as t he int rinsic concent rat ion decreases exponent ially wit h t he v alue of t he energy bandgap.
I n silicon MOS st ruct ures one finds t hat t he occurance of deep deplet ion can be linked t o t he m inorit y carrier lifet im e: while st ruct ures wit h a long ( 0.1 m s) lifet im e require a few seconds t o reach t herm al equilibrium which result s in a pronounced deep deplet ion effect at room t em perat ure , st ruct ures wit h a short (1 m s) lifet im e do not show t his effect .
Carrier generat ion due t o light will increase t he generat ion rat e beyond t he t herm al generat ion rat e which we assum ed above and reduce t he t im e needed t o reach equilibrium . Deep deplet ion m easurem ent s are t herefore done in t he dark.
6 . Ex pe r im en t a l r e su lt s a n d com par ison w ith t h e or y
As an exam ple we show below t he m easured low frequency ( quasi- st at ic) and high frequency capacit ance- volt age curves of an MOS capacit or. The capacit ance was m easured in t he presence of am bient light as well as in t he dark as explained in t he figure capt ion.
cv1.gif
Fig. 6 .6 .2 Low frequency ( quasi-st at ic) and high frequency capacit ance of an MOS
capacit or. Shown are, from t op t o bot t om , t he low frequency capacit ance m easured in t he presence of am bient light ( t op curve) , t he low frequency capacit ance m easured in t he dark, t he high frequency capacit ance m easured in t he presence of am bient light and t he high frequency capacit ance m easured in t he dark ( bot t om curve) . All curves were m easured from left t o right . The MOS param et ers are Na = 4 x
1015 cm- 3 and tox = 80 nm . The device area is
0.0007 cm2
The figure illust rat es som e of t he issues when m easuring t he capacit ance of an MOS capacit ance. First of all one should m easure t he devices in t he dark; t he presence of light causes carrier generat ion in t he capacit or which affect s t he m easured capacit ance. I n addit ion one m ust avoid t he deep deplet ion effect s such as t he init ial linearly varying capacit ance of t he high frequency capacit ance m easured in t he dark on t he above figure ( bot t om curve) . The larger t he carrier lifet im e, t he slower t he volt age is t o be changed t o avoid deep deplet ion.
The low frequency m easured is com pared t o t he t heorical value in t he figure below. The high frequency capacit ance m easured in t he presence of light is also
shown on t he figure. The figure illust rat es t he agreem ent bet ween experim ent and t heory. A com parison of t he experim ent al low ( rat her t han high) frequency capacit ance wit h t heory is som ewhat easier t o carry out since t he t heoret ical expression is easier t o calculat e while t he low frequency m easurem ent t ends t o be less sensit ive t o deep deplet ion effect s.
cv2.gif
Fig. 6 .6 .3 Com parison of t he t heoret ical low frequency capacit ance ( solid line) and t he experim ent al dat a ( open squares) obt ained in t he dark. Also shown is t he high frequency m easurem ent in t he presence of light of t he MOS capacit or ( filled squares) and t he low and high frequency capacit ance obt ained wit h t he sim ple m odel ( dot t ed lines) . Fit t ing param et ers are Na = 3.95 x 1015 cm- 3 and tox = 80 nm
.
7 . N on - I de a l e ffect s in MOS ca pa cit or s
Non- ideal effect s in MOS capacit ors include fixed charge, m obile charge and charge in surface st at es. All t hree t ypes of charge can be ident ified by perform ing a capacit ance-volt age m easurem ent .
Fix e d ch a r ge in t he oxide sim ply shift s t he m easured curve. A posit ive fixed charge at t he oxide-
sem iconduct or int erface shift s t he flat band volt age by an am ount which equals t he charge divided by t he oxide capacit ance. The shift reduces linearly as one reduces t he posit ion of t he charge relat ive t o t he gat e elect rode and becom es zero if t he charge is locat ed at t he m et al- oxide int erface. A fixed charge is caused by ions which are incorporat ed in t he oxide during growt h or deposit ion.
The flat band v olt age shift due t o m obile ch ar ge is described by t he sam e equat ion as t hat due t o fixed charge. However t he m easured curves differ since a posit ive gat e volt age causes m obile charge t o m ove away from t he gat e elect rode, while a negat ive volt age at t ract s t he charge t owards t he gat e. This causes t he curve t o shift t owards t he applied volt age. One can recognize m obile charge by t he hyst eresis in t he high frequency capacit ance curve when sweeping t he gat e volt age back and fort h. Sodium ions incorporat ed in t he oxide of silicon MOS capacit ors are known t o yield m obile charge. I t is because of t he high sensit ivit y of MOS st ruct ures t o a variet y of im purit ies t hat t he indust ry carefully cont rols t he purit y of t he wat er and t he chem icals used.
Charge due t o elect rons occupying su rfa ce st at e s
also yields a shift in flat band volt age. However as t he applied volt age is varied, t he ferm i energy at t he oxide- sem iconduct or int erface changes also and affect s t he occupancy of t he surface st at es. The int erface st at es cause t he t ransit ion in t he capacit ance m easurem ent t o be less abrupt . The com binat ion of t he low frequency and high frequency capacit ance allows t o calculat e t he surface st at e densit y. This m et hod provides t he surface st at e densit y over a lim it ed ( but highly relevant ) range of energies wit hin t he bandgap. Measurem ent s on n-t ype and p- t ype capacit ors at different t em perat ures provide t he surface st at e densit y t hroughout t he bandgap.
Re sist or
Pada dasarnya sem ua bahan m em iliki sifat resist if nam un beberapa bahan sepert i t em baga, perak, em as dan bahan m et al um um nya m em iliki resist ansi yang sangat kecil.
Bahan- bahan t ersebut m enghant ar arus list rik dengan baik, sehingga dinam akan kondukt or. Kebalikan dari bahan yang kondukt if, bahan m at erial sepert i karet , gelas, karbon m em iliki resist ansi yang lebih besar m enahan aliran elekt ron dan disebut sebagai insulat or.
Bagaim ana prinsip konduksi, dij elaskan pada art ikel t ent ang sem ikondukt or.
Resist or adalah kom ponen dasar elekt ronika yang digunakan unt uk m em bat asi j um lah arus yang m engalir dalam sat u rangkaian. Sesuai dengan nam anya resist or bersifat resist if dan um um nya t erbuat dari bahan karbon .
Dari hukum Ohm s diket ahui, resist ansi berbanding t erbalik dengan j um lah arus yang m engalir m elaluinya. Sat uan resist ansi dari suat u resist or disebut Ohm at au dilam bangkan dengan sim bol ( Om ega) .
Tipe resist or yang um um adalah berbent uk t abung dengan dua kaki t em baga di kiri dan kanan. Pada badannya t erdapat lingkaran m em bent uk gelang kode warna unt uk m em udahkan pem akai m engenali besar resist ansi t anpa m engukur besarnya dengan Ohm m et er.
Kode warna t ersebut adalah st andar m anufakt ur yang dikeluarkan oleh EI A ( Elect ronic I ndust ries Associat ion) sepert i yang dit unj ukkan pada t abel berikut . Wakt u penulis m asuk pendaft aran kuliah elekt ro, ada sat u t est yang harus dipenuhi yait u diharuskan t idak but a warna. Belakangan baru diket ahui bahwa m ahasiswa elekt ro waj ib unt uk bisa m em baca warna gelang resist or ( barangkali) .
W a rn a N ila i fa k t or pe n ga li Tole ra n si Hit am 0 1 Cok lat 1 10 1% Merah 2 100 2% Jingga 3 1.000 Kuning 4 10.000 Hij au 5 100.000 Biru 6 106 Violet 7 107 Abu- abu 8 108 Put ih 9 109 Em as - 0.1 5% Perak - 0.01 10% Tanpa warna - - 20%
Tabel - 1 : nilai warna gelang
Resist ansi dibaca dari warna gelang yang paling