COMPUTER AIDED ANALYSIS OF THE MOS CAPACITOR IN LOW FREQUENCY CONDITIONS

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1 IN centfc Bulletn of the Electrcal Engneerng aculty Year 4 No.4 (8) OMPUTER IE NYI O THE MO PITOR IN OW REQUENY ONITION G. PREU epartment of Electroncs, Telecommuncatons and Energy Engneerng, Valaha Unversty of Targovste E-mal: gpredusca@gmal.com bstract. Ths paper wants to development a mathematcal model to determnate capactance-voltage (-V) curve of MO capactor. Ths mathematcal model s nserted wth Matlab, n order to obtan capactance-voltage curves under dfferent condtons. nally, the capactance-voltage curves obtaned wll be compared wth expermental results. Ths way t wll be fnalsed a detaled feature of the technology qualty of fabrcaton of semconductors devces wth capactance-voltage curves MO, relatng a lot of advantages and dsadvantages of the entre system. Keywords: MO capactor, low-frequency, capactance-voltage curves, Matlab.. INTROUTION The MO capactor (Metal Oxde emconductor) s a structure made of a thn layer of solator put n a metal electrode and a layer of semconductor. In general, MO s the l O system []. The frst dea of usng MO as a devce of featurng O nterface appeared n 959. Ths belongs to Moll and t was put n practce n 96 by hs Ph student, Terman []. The MO structure became the bass element of modern mcroelectroncs area. In the last decades, numbers of authors searched the MO capactor s power usng the electrons dopng. Ths way t was demonstrated a dependence of the MO capacty system dependng on the voltage V, and then to obtan three capactes: depleton, nverson and accumulaton [3], [4], [5], [6].. GENER ETURE The transstor s an electronc devce composed of a heterogeneous semconductor, and ts functon s based on movng the charge carrers nsde at the semconductor s, under the acton of an electrcal voltage appled to ths one n a convenent way. The MO transstor s an electronc devce based on the conducton of electrc current on the semconductor s surface, the conducton controlled by an electrcal feld, appled to an solated electrode by a semconductor (gate). These constructve features defne the transstors famly wth a feld effect an solated gate or, on the short way, ET-MI (eld Effect Transstors - Metal Insulator emconductor) or MOET (Metal Oxde emconductor - eld Effect Transstors). MOET s the only representatve of ths famly [7]. If the substrate s a P-type, then the source and the dran wll be an N-type. To establsh on electrcal current between a source and a dran, the surface of the semconductor must be of the N-type. It results that on the surface t appears a conductor channel, of N-type, whch tes the source of the dran. Invertng the conductvty type of the surface, and the channel s resstance too, t can be done by the gate. That s why a major nterest for ths study s gven by the cross secton through a transstor. Ths structure s known as MO capactor [8]. It s consdered an deal MO capactor, featured by: - the semconductor s behavour on the surface dentcal to the one from the volume; - the absence of any oxde capactes or on the oxdeslcon nterface; - neglectng the nternal potental dfference between metal and semconductor. If the structure polarzes wth gate voltage lower than zero, ths goes to holes accumulaton on the semconductor s surface (among the electrostatc attracton effect). ue to the good qualty solator of the oxde through ts structure s practcally null, so the erm level from the semconductor s constant (as well as at the thermal equlbrum) [9]. The negatve electrcal charge on the metal electrode fnds ts correspondent n semconductor through the postve capacty of the holes accumulated on the surface. pplyng a postve voltage goes to the rejecton of the holes on the semconductor s surface, so to the accumulaton of an empty area of space charge. Ths regme of work of the MO capactor s called depleton regme. On the metallc electrode we fnd a postve capacty. In semconductor, n the depleton regon, there s a negatve capacty gven by the accepted ons. The energy bands curb on the surface, on the semconductor s establshed a dfference of potental, called the semconductor surface potental n relaton wth the metallc contact potental of the substrate consdered 5

2 centfc Bulletn of the Electrcal Engneerng aculty Year 4 No.4 (8) IN zero. If the voltage rses to a certan value, the energy bands curb so that on the surface, the erm level rses n the upper sde of the band-gap; so n ths case, the semconductor s surface gets the N-type, and that means the semconductor s nverson takes place, and the capacty from the semconductor s gven by the accepted ons, but as well as by the electrons from the surface nverson layer. The voltage where the nverson s nstalled s called the threshold voltage []. The analytcal expresson of MO capacty s gven by the relaton: = + () MO, Where s the oxde capactance per unt area and t s: ox = () X and s the low-frequency slcon capactance as t s wrtten n the followng ecuaton: = sgn ( U ) ch U sh U ( U ) N ( U ) ch( U ) N N n N n U (3) where: N = n the case that p-mo and = n the case n-mo; U are normalzed potental on the slcon surface and t s: U Indetermnaton for U = nvolves: ϕ = (4) kt / q = (5) U = pplyng Hosptal twce the ecuaton (3) goes to the followng result: = = (6) U = B The bound between the appled voltage on the capactor V G and normalzed potental of U surface s: ( U ) kt kt sgn V = U + U (7) ( ) G q q where (U) functon s gven by the: N N ( U ) = ch( U U ) ch( U ) U n 3. OMPUTER MOEING The mathematcal model s ntroduced wth Matlab n the computer to obtan capactance-voltage (-V) curves n dfferent condtons []-[]. o, changng dfferent nput parameters have obtaned the followng results: The accumulaton capactance ac (n/cm ) gure. The ac - curve of the MO capactor for the case = 4 cm -3 rom gure, t can be notced that, the more thckness of the oxde layer decreases, the more the accumulaton capacty ncreases from value 3,4 n/cm to 34 n/cm. The nverson capactance nv (n/cm ) 3 (8) - - The thckness of the oxd layer (μm) (μm) = gure. The ac - curves of the MO capactor for the case =.6 µm,.3 µm,.6 µm.3.6 The dopng concentraton of the slcon (cm -3 ) 6

3 IN centfc Bulletn of the Electrcal Engneerng aculty Year 4 No.4 (8) Tabel. The nverson capacty wth functon of and. =.6 =.3 =.6 (cm -3 ) nv (n/cm ) nv (n/cm ) nv (n/cm ) 4 3,8 3, ,89,5 5,35 rom Table we can observe that the more ncreases and the oxde layer thckness decreases, the nverson capacty ncreases. gure 3. The V G - φ s curves of the MO capactor for the case = 4 cm -3 and =.6 µm,.3 µm,.6 µm In gure 3, V G ncreases, touchng a value of,3733v for =.6 µm, once the surface potental of the slcon surface ncreases. MO capacty normalzed to the oxd capacty MO / o.5.5 (cm -3 ) = 4 (μm) = The surface potental of the slcon φ (cm -3 ) = 4 (μm) =.6 (μm) =.3 (μm) = gure 4. The - V G curves of the MO capactor for the case = 4 cm -3 and =.6 µm,.3 µm,.6 µm rom gure 4, t results that MO /, decreases to a mnmum of.787, to a thckness level of =.6 and = 4 cm -3, the gate voltage V G wth a value of,5v. MO / o MO capacty normalzed to the oxd capacty (μm) =.6 (cm -3 ) = 6 (cm -3 ) = 5 (cm -3 ) = gure 5. The - V G curves of the MO capactor n the case that =.6 µm and = 4 cm -3, 5 cm -3, 6 cm -3 The MO / characterstc, from gure 5, touches a lmt value of.787 for = 4 cm -3, =.6 µm and V G =,5V. MO capacty normalzed to the oxd capacty MO / o (μm) =.6 (μm) =.3 (μm) =.6 N (cm -3 ) = gure 6. The - V G curves of the MO capactor for the case N = 4 cm -3 and =.6 µm,.3 µm,.6 µm rom gure 6, t results that MO / decreases to a mnmum value of.787 for a thckness level of =.6 µm and N = 4 cm -3, the gate voltage V G wth a value of -.5V. 7

4 centfc Bulletn of the Electrcal Engneerng aculty Year 4 No.4 (8) IN MO capacty normalzed to the oxd capacty MO / o gure 7. The - V G curves of the MO capactor n the case that =.6-5 cm and N = 4 cm -3, 5 cm -3, 6 cm -3 The MO / characterstc, from gure 7, touches the lmt value of.787 for N = 4 cm -3, =.6 µm and V G =-,5V. 4. T NYI urng data analyss t was used: - The semconductor charge densty Q s : Q = Q + Q (9) s B n( p) Where Q B s bulk charge densty and Q n(p) s the electron/hole charge densty of nverson layer. o t can be wrtten lke: Qs = Qn qnw, MO-p () Qs = Qp + qnw, MO-n () - normalzed potental to the thermal potental U: Wth (cm -3 ) = 6 kt q p n exp( U U) (cm -3 ) = 5 (cm -3 ) = 4 ϕ U = () kt / q = 5.9 mv, at T=3 K (3) = and n n exp( U U ) = (4) (μm) = kt = q q n Where = = - /cm and q=, The extrnsc ebye length : (5) kt =, p-mo capactor (6) q q N kt =, n-mo capactor (7) q q N - The erm potental normalzed U : U U N = + ln >, p-mo capactor (8) n N = ln <, n-mo capactor (9) n - The hyperbolc trgonometrcal functons: x x x x e e e + e sh( x) =, ch( x) = () - The permttvty of oxde: - the sgn (±) of U =sgn(u ): ox =,34 /cm () sgn(u ) = +, U >, sgn(u ) = -, U < () 5. ONUION The obtaned graphcs results the ncreasng of nverson capacty of low frequency, whch mples the substantal extenson of depleton regon wth the dopng ncreasng (Table and Table ) Table. The normalzed potental of the slcon surface and the semconductor charge densty n the case MO-p U/Q MO p (U > ) accumulaton depleton nverson U < > > Q > < < Q n - - < Q p Wth n = cm -3, at T = 3 K. - The ntrnsc ebye length =, : 8

5 IN centfc Bulletn of the Electrcal Engneerng aculty Year 4 No.4 (8) Table. The normalzed potental of the slcon surface and the semconductor charge densty n the case MO-n U/Q MO n (U < ) accumulaton depleton nverson U > < < Q < > > Q n Q p - - > 6. KNOWEGMENT The author would lke to thank an achelare for helpful dscusson. 7. REERENE []. achelare, Bazele dspoztvelor semconductoare, Edtura MatrxRom, Bucureşt, 3. [] J.. Moll, Physcs of emconductors, McGraw Hll, 964. [3] Ha-Yan Jang, Png-Wen Zhang, Model analyss and parameter extracton for MO capactor ncludng quantum mechancal effects, Journal of omputatonal Mathematcs, Vol.4, No.3, 6, pp.4-4. [4] Je Bnbn, ah hhtang, MO capactance-voltage characterstcs III, Trappng capactance from - charge-state mpurtes, Journal of emconductors, Vol.3, No.,, pp.-6. [5].P. Borges Zlotto, M. Bellod, Evaluaton of hgh temperature nfluence on MO capactor hgh frequency -V curves behavor, E Transactons, Vol.4(6),. [6]. Kar (ed.), Hgh permttvty gate delectrc materals, prnger eres n dvanced Mcroelectroncs 43, hapter : MOET: Bascs, characterstcs and characterzaton, 3, pp [7].G.Mlnes,.. eucht, Heterojunctons and Metal emconductor Junctons, cademc Press, New York, 97. [8]. achelare, emconductoare ş heterostructur, Edtura MatrxRom, Bucureşt,. [9] E.H.Ncollan, J.R. Brews, MO Physcs and Technology, Wley, New York, 98. [] E.Ș. akatoș, N. Olaru,.. Puchanu, spoztve ș crcute electronce. Modelare ș smulare, Edtura GIR, Bucurest. [].K. chroder, emconductor materal and devce characterzaton, Thrd edton, Jon Wley&ons, New Jersey, 6. [] G. Predusca,. achelare, Matlab pentru mcroelectronca, Ed. MatrxRom, Bucureşt,. 9