Electrical Characteristics of MOS Devices The MOS Capacitor Voltage components Accumulation, Depletion, Inversion Modes Effect of channel bias and substrate bias Effect of gate oide charges Threshold-voltage adjustment by implantation Capacitance vs. voltage characteristics MOS Field-Effect Transistor I-V characteristics Parameter etraction 1
1) Revisit EE143 Week#2 Reading Assignment - Introduction to IC Devices, www.icknowledge.com - Streetman, Chap 3 Energy Band and Charge carriers in Semiconductors. 2) Visit the Device Visualization Website http://jas.eng.buffalo.edu/ and run the visualization eperiments of 1) Charge carriers and Fermi level, 2) pn junctions 3) MOS capacitors 4) MOSFETs 2
Metal -Oide-Semiconductor Transistor [ n-channel] V G < V threshold V G > V threshold Negligible electron concentration underneath Gate region; Source-Drain is electrically open High electron concentration underneath Gate region; Source-Drain is electrically connected 3
Work Function of Materials METAL SEMICONDUCTOR Work function = qφ E o E f Vacuum energy level q Φ E o E C E f E V qφ M is determined by the metal material qφ S is determined by the semiconductor material, the dopant type, and doping concentration 4
Work Function (qφ M ) of MOS Gate Materials E o = vacuum energy level E f = Fermi level E C = bottom of conduction band E V = top of conduction band qχ = 4.15eV (electron affinity) E o E o E o qφ M qχ = 4.15eV qχ = 4.15eV qφ M E f 0.56eV E C 0.56eV E C E f qφ M Al = 4.1 ev TiSi 2 = 4.6 ev E i 0.56eV E V E f 0.56eV E i E V n+ poly-si p+ poly-si 5
Work Function of doped Si substrate * Depends on substrate concentration N B Φ F = kt ln q N n B i E o E o qφ s qχ = 4.15eV qχ = 4.15eV E f Ei E C 0.56eV qφ F 0.56eV qφ s E f Ei 0.56eV E C qφ F 0.56eV n-type Si E V p-type Si E V Φ s (volts) = 4.15 +0.56 - Φ F Φ s (volts) = 4.15 +0.56 + Φ F 6
The MOS Capacitor V G+ o metal oide + _ + _ + _ V FB V o V Si semiconductor V = V + V + G FB o V Si C o ε o = [F/cm 2 ] o Oide capacitance/unit area 7
Flat Band Voltage V FB is the built-in voltage of the MOS: Φ Φ VFB Gate work function Φ M : Al: 4.1 V; n+ poly-si: 4.15 V; p+ poly-si: 5.27 V Semiconductor work function Φ S : M S Φ s (volts) = 4.15 +0.56 - Φ F for n-si Φ s (volts) = 4.15 +0.56 + Φ F for p-si V o = voltage drop across oide (depends on V G ) V Si = voltage drop in the silicon (depends on V G ) 8
MOS Operation Modes A) Accumulation: V G < V FB for p-type substrate M O Si (p-si) holes Thickness of accumulation layer ~0 V Si 0, so V o = V G - V FB Q Si = charge/unit area in Si =C o (V G - V FB ) 9
MOS Operation Modes B) Flatband: V G = V FB No charge in Si (and hence no charge in metal gate) V Si = V o = 0 M O S (p-si) 10
MOS Operation Modes (cont.) C) Depletion: V G > V FB d = 2εSiV qn B Si M O S (p-si) d qn B V G = V FB + qn C B o d + qn B 2ε s 2 d (can solve for d ) Depletion layer V o V Si 11
Depletion Mode :Charge and Electric Field Distributions by Superposition Principle of Electrostatics Metal ρ() Q' Oide Semiconductor = o + d Metal ρ() Q' Oide Semiconductor Metal ρ() Oide Q' Semiconductor = o + d =0 = o ρ =0 - Q' = o =0 = o ρ Metal E() Oide Semiconductor = o + d = Metal E() Oide Semiconductor = o + d + Metal E() Oide Semiconductor = o + d =0 = o =0 = o =0 = o 12
MOS Operation Modes (cont.) D) Threshold of Inversion: V G = V T n surface = N B => V Si = 2 Φ F (for p-type substrate) This is a definition for onset of strong inversion M O S (p-si) dma qn B Q n V G 2 ε s ( 2 Φ F ) qn B = V T = V FB + + 2 C o Φ F 13
MOS Operation Modes (cont.) E) Strong Inversion: V G > V T dma is approimately unchanged d ma = 4ε Si qn Φ B F when V G > V T M O S (p-si) dma V Q o n = qn C B o ( V d ma C G o + Q V T ) n Q n qn a electrons 14
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p-si 17
Suggested Eercise Most derivations for MOS shown in lecture notes are done with p-type substrate (NMOS) as eample. Repeat the derivations yourself for n-type substrate (PMOS) to test your understanding of MOS. 18
p-si substrate (NMOS) Accumulation (holes) V FB depletion V T strong inversion (electrons) V G (more positive) n-si substrate (PMOS) V G (more negative) Strong inversion (holes) V T depletion V FB Accumulation (electrons) 19
Voltage drop = area under E-field curve Accumulation V o = Q a /C o V Si ~ 0 V o =qn a d /C o Depletion V Si = qn a d2 /(2ε s ) V o = [qn a dma +Q n ]/C o Inversion V Si = qn a dma2 /(2ε s ) = 2 Φ F * For simplicity, dielectric constants assumed to be same for oide and Si in E-field sketches 20
Appendi -Electron Energy Band - Fermi Level -Electrostatics of device charges 21
Electron Potential Energy Conduction Band and Valence Band Available states at discreet energy levels Available states as continuous energy levels inside energy bands Isolated atoms Atoms in a solid 22
The Simplified Electron Energy Band Diagram 23
Energy Band Diagram with E-field Electron Electron Energy - E-field + Energy E-field + - 2 1 E C 2 1 E C E V Electric potential φ(2) < φ(1) E V Electric potential φ(2) > φ(1) Electron concentration n n(2) n(1) = e e qφ(2) / kt qφ(1) / kt = e q[ φ(2) φ(1)]/ kt 24
The Fermi-Dirac Distribution (Fermi Function) Probability of available states at energy E being occupied f(e) = 1/ [ 1+ ep (E- E f ) / kt] where E f is the Fermi energy and k = Boltzmann constant=8.617 10-5 ev/k T=0K f(e) 0.5 E -E f 25
Properties of the Fermi-Dirac Distribution Probability of electron state at energy E will be occupied (1) f(e) ep [- (E- E f ) / kt] for (E- E f ) > 3kT Note: At 300K, kt= 0.026eV This approimation is called Boltzmann approimation (2) Probability of available states at energy E NOT being occupied 1- f(e) = 1/ [ 1+ ep (E f -E) / kt] 26
Fermi Energy (E i ) of Intrinsic Semiconductor Ec E g /2 E i E g /2 Ev 27
How to find n, p when Na and Nd are known n- p = Nd - Na (1) pn = ni 2 (2) (i) If Nd -Na > 10 ni : n Nd -Na (ii) If Na - Nd > 10 ni : p Na- Nd 28
How to find E f when n(or p) is known E c q Φ F E i E f (n-type) E v E f (p-type) n = n i ep [(E f -E i )/kt] Let qφ F E f -E i n = n i ep [qφ F /kt] 29
Dependence of Fermi Level with Doping Concentration E i (E C +E V )/2 Middle of energy gap When Si is undoped, E f = E i ; also n =p = n i 30
The Fermi Energy at thermal equilibrium At thermal equilibrium ( i.e., no eternal perturbation), The Fermi Energy must be constant for all positions Electron energy Material A Material B Material C Material D E F Position 31
Electron Transfer during contact formation System 1 System 2 System 1 System 2 Before contact formation E F1 e E F2 E F1 e E F2 After contact formation System 1 System 2 Net + - Net positive + - negative charge + - charge E F System 1 System 2 - - + + E F - + E E 32
Applied Bias and Fermi Level Fermi level of the side which has a relatively higher electric potential will have a relatively lower electron energy ( Potential Energy = -q electric potential.) Only difference of the E 's at both sides are important, not the absolute position of the Fermi levels. E f1 qv a E f2 E f1 q V a E f 2 Side 1 Side 2 Side 1 Side 2 + - + - V a > 0 V a < 0 Potential difference across depletion region = V bi -V a 33
PN junctions Thermal Equilibrium N A- and p ρ() is 0 E-field Depletion region N + D and n ρ() is 0 -- ++ Quasi-neutral region -- ++ Quasi-neutral region p-si N A- only ρ() is - n-si N D+ only ρ() is + Complete Depletion Approimation used for charges inside depletion region r() N D+ () N A- () http://jas.eng.buffalo.edu/education/pn/pnformation2/pnformation2.html 34
Electrostatics of Device Charges 1) Summation of all charges = 0 ρ 2 d2 = ρ 1 d1 2) E-field =0 outside depletion regions p-type ρ() Semiconductor n-type Semiconductor ρ2 - - d1 ρ1 d2 E = 0 =0 E 0 E = 0 35
3) Relationship between E-field and charge density ρ() d [ε E()] /d = ρ() Gauss Law 4) Relationship between E-field and potential φ E() = - dφ()/d 36
Eample Analysis : n+/ p-si junction ρ() n+ Si Depletion region is very thin and is approimated as +Q' =0 Depletion region p-si d -qna E () E ma =qn a d /ε s 3) Slope = qn a /ε s d 2) E = 0 a thin sheet charge 1) Q = qn a d 4) Area under E-field curve = voltage across depletion region = qn a d2 /2ε s 37
Superposition Principle ρ() If ρ 1 () E 1 () and V 1 () ρ 2 () E 2 () and V 2 () then ρ 1 () + ρ 2 () E 1 () + E 2 () and V 1 () + V 2 () - -qn A - p + n +qn D =0 ρ 1 () ρ 2 () Q=+qN A p +qn D - p + -qn A + n Q=-qN A p =0 =0 38
ρ 1 () ρ 2 () - p Q=+qN A p +qn D -qn A + n =0 E 1 () Q=-qN A p =0 E 2 () - p + n - Slope = -qn A /ε s =0 + - =0 Slope = +qn D /ε s 39
Sketch of E() E() = E 1 ()+ E 2 () - p + n =0 Slope = - qn A /ε s Slope = + qn D /ε s - Ema = - qn A p /ε s = - qn D n /ε s 40
δ Why dma ~ constant beyond onset of strong inversion? G Higher than V T δ V = V + V + V n ln FB E i E f ( n ) e δ kt OX Picks up all the changes in V G Si Approimation assumes V Si does not change much Justification: If surface electron density changes by n V OX n C OX but the change of V Si changes only by kt/q [ ln ( n)] small! 41
n-surface = n-bulk e qvsi/kt n-surface qv Si p-si N a =10 16 /cm3 n-bulk = 2.1 10 4 /cm3 E i 0.35eV E f Onset of strong inversion (at V T ) VSi n-surface 0 2.10E+04 0.1 9.84E+05 0.2 4.61E+07 0.3 2.16E+09 0.4 1.01E+11 0.5 4.73E+12 0.6 2.21E+14 0.7 1.04E+16 0.8 4.85E+17 0.9 2.27E+19 42