EEE 531: Semiconductor Device Theory I Instructor: Dragica Vasileska Department of Electrical Engineering Arizona State University Topics covered: 1. Introduction to MOSFET operation EEE 531: Semiconductor Device Theory I 1. Introduction • Firs proposal for a MOSFET 5 Critical Dimension ] Cell Edge device was given by s r e t Lilienfeld and Heil in 1930. e m 1 o r • First operational device was c i m [ made in 1947 at Bell Labs. n o i • Since then, the MOSFET s n e m 0.1 dimensions have been con- i D tinuously scaled to achieve 0.05 1990 1995 2000 2005 2010 more functions on a chip. yYeear r FFrroomm S SIAIA r rooaaddmmaapp f foorr sseemmicicoonndduuccttoorrss ( (11999977)) EEE 531: Semiconductor Device Theory I • MOSFET is a four-terminal device. Basic device configura- tion is illustrated on the figures below. Side-view of the device Top-view of the device Basic device parameters: channel length L channel width W oxide thickness d junction depth r ox substrate dopingj N A EEE 531: Semiconductor Device Theory I • There are basically four types of MOSFETs: (a) n-cnannel, enhancement mode device G I S D D symbol n+ n+ p-type SC V V G T (b) n-cnannel, depletion mode device G S D I symbol D n+ n+ p-type SC V V G T EEE 531: Semiconductor Device Theory I (c) p-cnannel, enhancement mode device I G D V S D T V symbol G p+ p+ n-type SC (d) p-cnannel, depletion mode device I G D S D V symbol T V G p+ p+ n-type SC EEE 531: Semiconductor Device Theory I • The role of the Gate electrode for n-channel MOSFET: VV == 00 source drain GG VV >> VV source drain GG TT Positive gate voltage does two things: (1) Reduces the potential energy barrier seen by the electrons from the source and the drain regions. (2) Inverts the surface, and increases the conductivity of the channel. EEE 531: Semiconductor Device Theory I • The role of the Drain electrode for n-channel MOSFET: dn/dE VV == 00,, VV >> 00 GG DD dn/dE source E Large potential barrier allows only few C electrons to go from the source to the drain drain (subthreshold conduction) dn/dE VV >> VV ,, VV >> 00 GG TT DD dn/dE source E Smaller potential barrier allows a large drain C number of electrons to go from the source to the drain EEE 531: Semiconductor Device Theory I • Qualitative description of MOSFET operation: G ((aa)) VV >> VV, , VV >> 00 ((ssmmaalll)) S D GG TT DD Variation of electron density n+ n+ along the channel is small: p-type SC I D VD G ((bb))VV >> VV,, V V >> 00 ((llaarrggeerr)) S D GG TT DD + + Increase in the drain current n n reduces due to the reduced conductivity of the channel at p-type SC the drain end. EEE 531: Semiconductor Device Theory I G ((cc))VV >> VV,, V V == VV --VV S D GG TT DD GG TT n+ n+ Pinch-off point. Electron density at the drain-end of the p-type SC channel is identically zero. G ((dd))VV >> VV,, V V >> VV --VV S D GG TT DD GG TT n+ n+ Post pinch-off characteristic. L The excess drain voltage is dropped across the highly re- p-type SC sistive pinch-off region deno- ted by L. EEE 531: Semiconductor Device Theory I • IV-characteristics (long-channel devices): I D (c) (d) Linear (b) region Saturation (a) region V D EEE 531: Semiconductor Device Theory I 17 3 N A 810 cm , dox 3 nm VG 0.8 V, VD 20 mV, VT 0.33 V ] V e [ c E d n a b n o i t c u d n o drain C source D i st an ce [ m ] [m] Distance EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 20 mV Accumulation of carriers Surface inversion ] 3 - m [ y t i s n drain e d n o r source t c e l E m] [ ce Dista tan nce is [m] D EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 0.2V, VT 0.33 V Negating effect of the drain ] 3 - m [ y t i s n drain e d n o r t c source e l E m] Dis [ tance ce [m tan ] Dis EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 0.56V, VT 0.33 V ] V e [ c E d n a b source n o i t c u d n drain ] o m C [ ce n ta is Distance [m] D EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 0.56V, VT 0.33 V ] 3 - m [ y t i s n e d drain n o r t source c e l E m] [ ce an Dista ist nce [m] D EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 0.9V, VT 0.33 V Pinched-off ] channel 3 - m [ y t i s n e drain d n o r t source c e l E m] [ e D nc istance sta [m] Di EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 1.56V, VT 0.33 V 3D View Contour plot 0.1 ] V e [ c 0.08 E d n 0.06 a b n source o i 0.04 t ] c u m d [ n 0.02 o e C c n drain a t 0 Distanc is 0 0.05 0.1 0.15 e [m] D Distance [m] EEE 531: Semiconductor Device Theory I VG 0.8 V, VD 1.56V, VT 0.33 V Pinched-off channel ] 3 - m [ y t i s n e d n drain o r t c e l source E ] [m D ce istance [ tan m] Dis EEE 531: Semiconductor Device Theory I EEE 531: Semiconductor Device Theory I Instructor: Dragica Vasileska Department of Electrical Engineering Arizona State University Topics covered: 2. Gradual channel approximation for current calculation (A) square-law theory (B) bulk-charge theory (C) transconductance, output conductance and series resistance (D) limitations of the two models EEE 531: Semiconductor Device Theory I 2. Gradual channel approximation • This model is due to Shockley. • Assumption: The electric field variation in the direction parallel to the SC/oxide interface is much smaller than the electric field variation in the direction perpendicular to the interface: z G W x S D oxide y n+ n+ L dF dF x y p-type SC dx dy EEE 531: Semiconductor Device Theory I • Recall the expressions for the threshold voltage for real MOS capacitor: 1 Gate voltage: VT 2F 2qN Aks0 2F VFB Cox Q 1 Qit f Qot Qm Flat band voltage: VFB MS ot m q Cox Cox Cox Cox • Beyond the point that determines the onset of strong inversi- on ( =2 ), any excess charge on the gate balanced with s F excess charge in the semiconductor, is given by: QG QB QN Ctot VG VT QN Cox VG VT QB QB QB s QB 2F • Based on how we consider Q , we have: B (A) Square-law theory: Q = 0 B (B) Bulk-charge theory: Q 0 B EEE 531: Semiconductor Device Theory I (A) Square-law theory • The charge on the gate is completely balanced by Q (x), i.e: N QN (x) Ctot VG VT V (x) V = 0 S E V(x) FS V x D E x=0 C E = E - V • Total current density in the channel: FD FS D dn dV J qn F(x) qD qn n n n dx n dx negligible Note: Total current density approximately equal to the electron current density (unipolar device). EEE 531: Semiconductor Device Theory I • Integrating the current density, we obtain drain current I : D W yc (x) dV I dz dy qn(x, y) (x, y) D n 0 0 dx dV yc (x) W qn(x, y)n (x, y)dy dx 0 Q(x) N eff High-resolution transmission electron micrograph of the interface dV between Si and SiO Q (x) W 2 N eff dx (Goodnick et al., Phys. Rev. B 32, p. 8171, 1985) dV 2.71 Å 3.84 Å C W V V V (x) ox eff G T dx EEffffeeccttiivvee eelleeccttrroonn mmoobbiilliittyy,, iinn wwhhiicchh i inntteerrffaaccee--rroouugghhnneessss iiss ttaakkeenn i innttoo aaccccoouunntt.. EEE 531: Semiconductor Device Theory I • The role of interface-roughness on the low-field electron mobility: Phonon Coulomb 1500 (aN + bN )-1 400 s depl ] ] s s - - -1/3 V N V 300 / s 1000 17 3 / 2 N 7 10 cm A 2 m m c c [ [ 200 y experimental data y t i t l i 500 uniform i l i b b step-like (low-high) o o retrograde (Gaussian) M M 0 100 1015 1016 1017 1018 1012 1013 Doping [cm-3] Inversion charge density N [cm-2] s Interface-roughness BBuullkk ssaammpplleess SSiiiinnvveerrssiioonn l laayyeerrss EEE 531: Semiconductor Device Theory I • The experimentally observed universal mobility behavior is due to the dominant surface-roughness influence on the low- field electron mobility under strong inversion conditions. • Various models proposed for the variation of the effective transverse electric field upon the inversion (N ) and deple- s tion (N ) charge density: depl Stern and Howard: F 11 N N eff 32 s depl Matsumoto and Uemura: Feff 0.5Ns Ndepl Krutsick and White: <z> Feff 0 .5Ns 1 Ndepl (a=0.5 and b<1) W EEE 531: Semiconductor Device Theory I • There are several empirical expressions for the effective field dependence of the low-field electron mobility: Effective-field dependence: 1105 342 , n,eff 0.657 p,eff 0.617 1 Feff / 30.5 1 Feff /15.4 Gate-voltage dependence: 0 n,eff , 0.02 0.08 1/V 1 (VGS VT ) • Universal mobility eff N N N behavior: A3 A2 A1 N A1 N A2 N A3 Feff EEE 531: Semiconductor Device Theory I • We now use the conservation of current argument, to get: V L D IDdx Weff Cox VG VT V (x) dV 0 0 W C I eff ox V V V 1V 2 , for V V V D L G T D 2 D D G T • This last result represents the expression for the current, valid up to the pinch-off point.