hapter 5 MOS apacitor MOS: Metal-Oxide-Semiconductor metal ate ate SiO 2 N + SiO 2 N + Si body P-body MOS capacitor MOS tranitor Semiconductor Device for Interated ircuit (. Hu) Slide 5-1
hapter 5 MOS apacitor E c N + polyilicon 3.1 e E c 3.1 e SiO 2 P-Silicon body E c ate 9e body (a) (b) How doe one arrive at thi enery-band diaram for 0? Semiconductor Device for Interated ircuit (. Hu) Slide 5-2
5.1 Flat-band ondition and Flat-band oltae χ SiO2 0.95 e E c E 0 qψ 3.1 e 3.1 e χ Si q ψ χ Si + (E c ) 4.05e E c, N + -poly-si E 0 : acuum level E 0 : Work function E 0 E c : Electron affinity Si/SiO 2 enery barrier 9e SiO 2 4.8 e P-body E c The band i flat at a particular ate voltae. ψ ψ Semiconductor Device for Interated ircuit (. Hu) Slide 5-3
5.2 Surface Accumulation 3.1e E c, E 0 q qφ M O S E c Make <. + φ + φ : urface potential, band bendin : voltae acro the ide φ i neliible when the urface i in accumulation becaue a little band-bendin lead to a lare accumulation chare. Semiconductor Device for Interated ircuit (. Hu) Slide 5-4
< 5.2 Surface Accumulation - - - - - - - + + + + + + + accumulation chare, Q acc P-Si body Gau Law SiO 2 ate Q acc Q / Q / ( ) acc Semiconductor Device for Interated ircuit (. Hu) Slide 5-5
5.3 Surface Depletion ate + + + + + + SiO 2 ------- depletion layer chare, Q dep P-Si body > E c, q q qφ - - - - W dep depletion reion E c Ev M O S (a) (b) Q Q dep qn a W dep qn a 2ε φ Semiconductor Device for Interated ircuit (. Hu) Slide 5-6
5.3 Surface Depletion + φ + + φ + qn a 2ε φ an thi equation be olved to yield φ? Semiconductor Device for Interated ircuit (. Hu) Slide 5-7
5.4 Threhold ondition and Threhold oltae threhold (of inverion) E c threhold : n N a, or (E c ) urface ( ) bulk, or q q t D A qφ Β B E i AB, and D E c, φ t 2φ B kt 2 ln q N n i a M O S qφ B E 2 ( E f E v ) bulk kt q ln N n i v kt q ln N N v a kt q ln N n i a Semiconductor Device for Interated ircuit (. Hu) Slide 5-8
Threhold oltae + + t + 2 φ + B qn a 2ε 2φ B Alternative definition of the threhold condition : φ t t φ B kt N a + 0.45 ln + 0.45 q n + φ + 0.45 + B i 2qN a 2ε ( φ B + 0.45 ) Semiconductor Device for Interated ircuit (. Hu) Slide 5-9
Threhold oltae t (), N + ate/p-body T 20nm t (), P + ate/n-body + for P-body, for N-body: t Body Dopin Denity (cm -3 ) ± 2 φ ± B qn ub 2ε 2φ B Semiconductor Device for Interated ircuit (. Hu) Slide 5-10
5.5 Stron Inverion Beyond Threhold > t W dep W dmax 2ε φt qn a > t - E c ate ++++++++++ SiO 2 - - - - - - - - - - - - - - - E c, q - - - - Ev Q dep P-Si ubtrate Q inv M O S Semiconductor Device for Interated ircuit (. Hu) Slide 5-11
Inverion Layer hare, Q inv (/cm 2 ) t + φ Q t inv Q dep Q inv Q inv + φ t + qn a 2ε φ t ( t Q ) inv > t > t ate ate SiO 2 SiO 2 N + - - - - - - - N + N-Si P-body P-body Semiconductor Device for Interated ircuit (. Hu) Slide 5-12
Review : Baic MOS apacitor Theory φ 2φ t accumulation depletion inverion W dep W dmax W dmax (2ε 2φ Β /qν a ) 1/2 (φ ) 1/2 accumulation depletion t inverion Semiconductor Device for Interated ircuit (. Hu) Slide 5-13
Review : Baic MOS apacitor Theory Q dep qn a W dep (a) accumulation depletion inverion 0 qn a W dep t qna Wdmax total ubtrate chare, Q Q Q + Q + Q acc dep inv Q inv Q (b) accumulation depletion inverion t accumulation reime depletion reime inverion reime lope 0 t Q acc lope Q inv (c) t lope accumulation depletion inverion Semiconductor Device for Interated ircuit (. Hu) Slide 5-14
5.6 MOS haracteritic i cap dq d dq d v ac ~ Meter MOS apacitor Semiconductor Device for Interated ircuit (. Hu) Slide 5-15
5.6 MOS haracteritic dq d dq d Semiconductor Device for Interated ircuit (. Hu) Slide 5-16
haracteritic In the depletion reime: accumulation depletion inverion t 1 1 1 + dep 1 1 2 + 2( qn a ε ) Semiconductor Device for Interated ircuit (. Hu) Slide 5-17
Supply of Inverion hare May be Limited ate + + + + + + + + + Accumulation P-ubtrate ate ------ dep Depletion P-ubtrate W dep ate ate N + Inverion - - - - - - - - D and A P-ubtrate W dmax D A - - - - - - - - - - - - dmax -- Inverion P-ubtrate W dmax In each cae,? Semiconductor Device for Interated ircuit (. Hu) Slide 5-18
apacitor and Tranitor (or HF and LF ) MOS tranitor at any f, LF capacitor, or quai-tatic HF capacitor accumulation depletion inverion t Semiconductor Device for Interated ircuit (. Hu) Slide 5-19
Quai-Static of MOS apacitor t accumulation depletion inverion The quai-tatic i obtained by the application of a low linearramp voltae (< 0.1/) to the ate, while meaurin I with a very enitive D ammeter. i calculated from I d /dt. Thi allow ufficient time for Q inv to repond to the low-chanin. Semiconductor Device for Interated ircuit (. Hu) Slide 5-20
EXAMPLE : of MOS apacitor and Tranitor MOS tranitor, QS HF capacitor Doe the QS or the HF capacitor apply? (1) MOS tranitor, 10kHz. (Anwer: QS ). (2) MOS tranitor, 100MHz. (Anwer: QS ). (3) MOS capacitor, 100MHz. (Anwer: HF capacitor ). (4) MOS capacitor, 10kHz. (Anwer: HF capacitor ). (5) MOS capacitor, low ramp. (Anwer: QS ). (6) MOS tranitor, low ramp. (Anwer: QS ). Semiconductor Device for Interated ircuit (. Hu) Slide 5-21
5.7 Oxide hare A Modification to and t Q /, E c E c, E c 0 + + E c ate ide body ate ide body (a) (b) ψ 0 Q / ψ Q / Semiconductor Device for Interated ircuit (. Hu) Slide 5-22
5.7 Oxide hare A Modification to and t Three type of ide chare: Fixed ide chare, Si + Mobile ide chare, Na + (due to odium contamination) Stre-induced chare-a reliability iue Semiconductor Device for Interated ircuit (. Hu) Slide 5-23
EXAMPLE: Interpret thi meaured dependence on ide thickne. The ate electrode i N + poly-ilicon. 10 nm 20 nm 30 nm 0 T 0.15 0.3 What doe it tell u? Body work function? Dopin type? Other? Solution: ψ ψ Q T / ε Semiconductor Device for Interated ircuit (. Hu) Slide 5-24
from intercept ψ ψ 0.15 E 0, vacuum level ψ ψ ψ + 0.15, E c E c N + -Siate Sibody N-type ubtrate, N d n N c e 0.15 e kt 10 17 cm -3 from lope Q 1.7 10 8 / cm 2 Semiconductor Device for Interated ircuit (. Hu) Slide 5-25
5.8 Poly-Silicon Gate Depletion Effective Increae in T Gau Law W ε / qn P + dpoly P + poly-si poly + + + + + + + + poly 1 + ε T + W 1 dpoly poly / 3 1 T ε W + ε dpoly 1 N-body If W dpoly 15 Å, what i the effective increae in T? Why i a reduction in undeirable? Semiconductor Device for Interated ircuit (. Hu) Slide 5-26
Effect of Poly-Gate Depletion on Q inv Q inv φ ( poly t ) W dpoly E c, How can poly-depletion by minimized? qφ poly E c P + -ate N-ubtrate Semiconductor Device for Interated ircuit (. Hu) Slide 5-27
EXAMPLE : Poly-Silicon Gate Depletion, the voltae acro a 2 nm thin ide, i 1. The P + polyate dopin i N poly 8 10 19 cm -3 and ubtrate N d i 10 17 cm -3. Find (a) W dpoly, (b) φ poly, and (c). Solution: (a) W dpoly ε / qn poly ε 3.9 8.85 10 7 2 10 cm 1.6 10 1.3 nm 14 19 / T qn poly (F/cm) 1 19 8 10 cm 3 Semiconductor Device for Interated ircuit (. Hu) Slide 5-28
EXAMPLE : Poly-Silicon Gate Depletion (b) W dpoly 2ε φ qn poly poly φ dpoly 2 qn polywdpoly / 2ε 0.11 (c) + φ t + + φ poly E kt Nc ln q q Nd 0.95 0.85 1 1.1 0.15 0.11 1.01 0.95 I the lo of 0.11 from the 1.01 inificant? Semiconductor Device for Interated ircuit (. Hu) Slide 5-29
5.9 Inverion and Accumulation hare-layer Thickne Quantum Mechanical Effect Averae inverion-layer location below the Si/SiO 2 interface i called the inverion-layer thickne, T inv. Electron Denity ate poly-si depletion reion SiO 2 Quantum mechanical theory Å -50-40 -30-20 -10 0 10 20 30 40 50 A Phyical T effective T What equation need to be olved to find n(x)? Doe T inv chane with varyin? Semiconductor Device for Interated ircuit (. Hu) Slide 5-30
Electrical Oxide Thickne, T e T e T + Wdpoly / 3 + Tinv / 3 at dd ( + t )/T can be hown to be the averae electric field in the inverion layer. T inv of hole i larer than that of electron becaue of difference in effective ma. Semiconductor Device for Interated ircuit (. Hu) Slide 5-31
Q inv Effective Oxide Thickne and Effective Oxide apacitance e( t T e T + Wdpoly / 3 + Tinv ) / 3 Baic with poly-depletion data with poly-depletion and chare-layer thickne Which i wore in reduction : P + -poly over N-body or N + -poly over P-body? Semiconductor Device for Interated ircuit (. Hu) Slide 5-32
5.10 D Imaer E c - E c - - + E c, E c, (a) Deep depletion, Q inv 0 (b) Expoed to liht Semiconductor Device for Interated ircuit (. Hu) Slide 5-33
3 2 1 D hare Tranfer 1 > 2 3 (a) ide - - - - - - - - - - - - - depletion reion P-Si 1 3 1 2 3 1 2 2 > 1 > 3 (b) - - - - - depletion reion ide - - - P-Si 2 > 1 3 1 2 3 1 2 3 1 (c) - - - - - depletion reion ide - - - P-Si Semiconductor Device for Interated ircuit (. Hu) Slide 5-34
5.11 hapter Summary N-type device: N + -polyilicon ate over P-body P-type device: P + -polyilicon ate over N-body ψ ψ ( Q / T ) + φ + ( + φ poly ) + φ Q / ( + φ poly ) Semiconductor Device for Interated ircuit (. Hu) Slide 5-35
5.11 hapter Summary φ ± 2 or ( φ + 0.45 ) t φ B ± B φ B kt ln q N n ub i t +φ ± t qn ub 2ε φ t + : N-type device, : P-type device Semiconductor Device for Interated ircuit (. Hu) Slide 5-36
5.11 hapter Summary N-type Device (N + -ate over P-ubtrate) P-type Device (P + -ate over N-ubtrate) <0 Flat-band >0 t >0 Threhold t <0 What the diaram like at > t? at 0? Semiconductor Device for Interated ircuit (. Hu) Slide 5-37
5.11 hapter Summary N-type Device (N + -ate over P-ubtrate) QS Tranitor P-type Device (P + -ate over N-ubtrate) apacitor (HF) What i the root caue of the low in the HF branch? Semiconductor Device for Interated ircuit (. Hu) Slide 5-38