Physics of Nanoscale Transistors

Transcription

1 Physics of Nanoscale ransistors Mark Electrical and Computer Engineering University, West Lafayette, IN 1. Introduction 2. he Ballistic MOSFE 3. Scattering heory of the MOSFE 4. Beyond the Si MOSFE 5. Summary additional information at: Acknowledgements collaborators: Professor Supriyo Datta, Jing Guo, Sayed Hasan, Zhibin Ren, Jung-Hoon Rhew, Anisur Rahman, Ramesh Venugopal, Jing Wang sponsors: NSF, SRC MARCO Focus Center on Materials, Devices Structures ARO DURIN Indiana 21st Century Research and echnology Fund

2 1. Introduction Molecular FEs? Drain MOSFE CNFE Bachtold, et al., Science, Nov Source G A E 1. Introduction Gate Source Drain V D - qv DS 1) self-consistent electrostatics 2) transport

3 1. Introduction Source Gate V D + F F DS Q= Q ( E ) + Q ( E qv ) + D F F DS I = I ( E ) I ( E qv ) - qv DS Drain E(k) Q= CGSVGS + CDSVDS (electrostatics) - qv DS -k Q ( E qv ) F DS I ( E qv ) F DS + +k Q ( E qv ) + F DS I ( E qv ) F DS 1. Introduction Gate Qx Source V D at x = qv DS Drain x Q() 0 C V + C V C C GS DS C GS GS GD GD ox << C GS (constant) Q() 0 C V V ox GS 1) Compute Q(V GS,V DS ) 2) Determine 3) Compute I D

4 1. Introduction Now let s see how these ideas work out for MOSFEs 1. Introduction nanomos simulations V G effective mass Hamiltonian V S V D t ox = 0.6 nm L=10nm t Si = 3 nm energy (ev) position (nm) Z. Ren, R. Venugopal, S. Datta, and M., IEDM, 2001

5 1. Introduction energy band diagrams (a) (b) V GS V GS V DS =0.05 V DS =0.6 (c) V DS. V DS (d) V GS =0.05 V GS = Introduction energy band diagrams ε 2 y z x Energy (ev) ε 1 ε 2 ε 1 E C (z) z

6 1. Introduction transport V GS =V DS =0.6 z x y 2D Electrostatics Strong off-equilibrium transport Scattering 2. he Ballistic MOSFE Natori s theory E(k) Gate -qv DS Source Drain V GS linear current ε 1 (x) I DS E(k) -qv DS V DS on-current ε 1 (x)

7 n (E ) 2. he Ballistic MOSFE... thermionic emission Q i (0) V G x f - + Small V DS y f e ~ e o large V DS small V DS Eε 1 C (x) n (E ) E kb m x kb = / * υ 2 / 2 f υ x Large V DS + υ x 2. he Ballistic MOSFE... charge control in a well-tempered MOSFE Q i (0) C ox (V GS - V ) VG f Small V DS y x small V DS large V DS ε 1 (x) - f + + υ x Large V DS υ x

8 2. he Ballistic MOSFE... numerical solution of the ballistic BE ε 1 vs. x for V GS = 0.5V f (k x, k y ) ε 1 (ev) ---> Increasing V DS J.-H. Rhew, University 2. he Ballistic MOSFE... charge control ε 1 vs. x for V GS = 0.5V ε 1 (ev) ---> Increasing V DS Q inv (0) ---> Q inv (0) X (nm) ---> V DS (V) ---> i) Q i (0) constant

9 2. he Ballistic MOSFE... ε 1 vs. x for V GS = 0.5V i) Q i (0) constant ii) <υ(0)> --> υ ε 1 (ev) ---> Increasing V DS υ ave (10 7 cm/s) ---> Increasing V DS X (nm) ---> X (nm) ---> 2. he Ballistic MOSFE... ε 1 vs. x for V GS = 0.5V velocity saturation in a ballistic FE i) Q i (0) constant ii) <υ(0)> --> υ ε 1 (ev) ---> Increasing V DS υ inj (10 7 cm/s) ---> υ(0) X (nm) ---> υ() 0 υ V DS --->

10 2. he Ballistic MOSFE... I F1/ 2( ηf UDS) 1 F1/ 2( ηf ) = WQ( V ) υ F UI F 0( η DS + ) 1 F0 ( ηf ) DS i GS I ( on) = W C υ V V DS ox GS I DS quantum conductance G = M 2e 2 /h ( V V ) α G V DS 2. he Ballistic MOSFE... comparison with measurements... L eff = 115/125 nm technology NMOS: ~ 50% of limit PMOS: ~ 33% of limit measured ballistic (with measured Rs) F. Assad, et al. (1999 IEDM) G. imp, J. Bude, et al., (1999 IEDM) D. Rumsey (ECHON 2000) A. Lochtefeld, D. Antoniadis (EDL, Feb 2001)

11 3. Scattering heory of the MOSFE... ε 1 (ev) ---> Increasing V DS υ inj (10 7 cm/s) ---> ballistic scattering ballistic scattering X (nm) ---> V DS ---> J Q i constant C ox (V GS - V ) I 3. Scattering heory of the MOSFE... - qv DS J = n υ J = ( 1 ) J + + J ball I Wq J J D = Q( V ) = F1/ 2( ηf UDS) 1 F F = WQ V 1/ 2( η ) υ F F UDS η 1 2 F0 ( ηf ) DS i GS J + i GS ( + ) qj ( + J ) υ +

12 3. Scattering heory of the MOSFE... Landauer/McKelvey model NEGF simulation I = WC V V DS ox GS υ 2 F1/ 2( ηf UDS) 1 F1/ 2( ηf ) F1/ 2( ηf ) η F ηf U DS ln( 1 + e ) ln( 1 e ) ηf 2 ln( 1 + e ) V (, V ) GS DS I DS (µa/µm) 0.1 V DS (V) ballistic 0.6 inelastic scattering a (1-)a 3. Scattering heory of the MOSFE... computing : low V DS x L λ0 = a L + λ υ IDS = WCox V V V k q / I = µ C B W L + GS DS V V V DS eff ox GS DS λ 0 0

13 3. Scattering heory of the MOSFE... computing : high V DS first scattering event E i E b energy? X qv(x) p p y p i p p x ε 1 (x) position, x x 1 longitudinal energy 2 12mυ > qv( x 1 ) x 3. Scattering heory of the MOSFE... computing : high V DS 1 1- ε 1 (x) l mobility is important for nanoscale FEs P(x 1 ): probability of returning to the source after scattering first at x 1 ( E E ) x 1 < l P(x 1 ) large i b x 1 > P(x 1 ) small qv() l E E l i λo l + λ o b

14 3. Scattering heory of the MOSFE... Landauer/McKelvey model I = WC υ ( V V 2 ) 0.6 I = WC V V D ox GS I D 0.1 υ / 2 ID = WCox V V V k q / B V DS GS DS DS ox GS υ 2 F1/ 2( ηf UDS) 1 F 1/ 2( ηf ) η F U DS ln( + e ) 2 ηf ln( 1 + e ) λo = l + λ o transmission theory provides a clear picture of MOSFEs at the scaling limit: -source velocity is limited by thermal injection -velocity saturation occurs at the source -the scattering that matters occurs near the source - mobility is relevant to nanoscale MOSFEs

15 4. Beyond the Si MOSFE... 1) MOSFE V G 3) CNFE V S V D Bachtold, et al., Science, Nov ) SBFE V S V G V D Drain G A E 4) Molecular FEs? Source 4. Beyond the Si MOSFE... the Schottky barrier MOSFE V G V S V D off-state t ox = 0.6 nm t si = 3 nm 12 nm Jing Guo () on-state

16 4. Beyond the Si MOSFE... the Schottky barrier MOSFE equivalent MOSFE = 025. ev = 00. ev = 01. ev 4. Beyond the Si MOSFE... the Schottky barrier MOSFE MOSFE SBFE = 025. ev = 01. ev = 00. ev = 025. ev

17 4. Beyond the Si MOSFE... the Schottky barrier MOSFE E(k) E(k) -qv DS -qv DS MOSFE SBFE < 0 4. Beyond the Si MOSFE... the CNFE graphene (n, m) carbon nanotube k C= 2π q C= na + ma 1 2 E (n-m) = multiple of 3 (n-m) multiple of 3 E E k y k y k y k x k x k x

18 4. Beyond the Si MOSFE... the CNFE coaxial geometry planar geometry CNFE V S V G V D insulator gate 1 nm κ=4 Gate 4. Beyond the Si MOSFE... the CNFE D = 1 nm t ins = 1 nm κ ins = 4 V DD = 0.4

19 5. Summary Essential physics of nanoscale transistors is controlled by: -electrostatics -state filling -transmission ransmission theory provides insights into nanoscale MOSFE physics -velocity saturation at the source -importance of scattering near the source -relevance of mobility he performance of transistors based on charge control is largely material-independent