Electrical Characteristics of MOS Devices


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1 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 Thresholdvoltage adjustment by implantation Capacitance vs. voltage characteristics MOS FieldEffect Transistor IV characteristics Parameter etraction 1
2 1) Revisit EE143 Week#2 Reading Assignment  Introduction to IC Devices,  Streetman, Chap 3 Energy Band and Charge carriers in Semiconductors. 2) Visit the Device Visualization Website and run the visualization eperiments of 1) Charge carriers and Fermi level, 2) pn junctions 3) MOS capacitors 4) MOSFETs 2
3 Metal OideSemiconductor Transistor [ nchannel] V G < V threshold V G > V threshold Negligible electron concentration underneath Gate region; SourceDrain is electrically open High electron concentration underneath Gate region; SourceDrain is electrically connected 3
4 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
5 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+ polysi p+ polysi 5
6 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 ntype Si E V ptype Si E V Φ s (volts) = Φ F Φ s (volts) = Φ F 6
7 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
8 Flat Band Voltage V FB is the builtin voltage of the MOS: Φ Φ VFB Gate work function Φ M : Al: 4.1 V; n+ polysi: 4.15 V; p+ polysi: 5.27 V Semiconductor work function Φ S : M S Φ s (volts) = Φ F for nsi Φ s (volts) = Φ F for psi V o = voltage drop across oide (depends on V G ) V Si = voltage drop in the silicon (depends on V G ) 8
9 MOS Operation Modes A) Accumulation: V G < V FB for ptype substrate M O Si (psi) 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
10 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 (psi) 10
11 MOS Operation Modes (cont.) C) Depletion: V G > V FB d = 2εSiV qn B Si M O S (psi) 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
12 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
13 MOS Operation Modes (cont.) D) Threshold of Inversion: V G = V T n surface = N B => V Si = 2 Φ F (for ptype substrate) This is a definition for onset of strong inversion M O S (psi) dma qn B Q n V G 2 ε s ( 2 Φ F ) qn B = V T = V FB C o Φ F 13
14 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 (psi) 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
15 15
16 16
17 psi 17
18 Suggested Eercise Most derivations for MOS shown in lecture notes are done with ptype substrate (NMOS) as eample. Repeat the derivations yourself for ntype substrate (PMOS) to test your understanding of MOS. 18
19 psi substrate (NMOS) Accumulation (holes) V FB depletion V T strong inversion (electrons) V G (more positive) nsi substrate (PMOS) V G (more negative) Strong inversion (holes) V T depletion V FB Accumulation (electrons) 19
20 Voltage drop = area under Efield 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 Efield sketches 20
21 Appendi Electron Energy Band  Fermi Level Electrostatics of device charges 21
22 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
23 The Simplified Electron Energy Band Diagram 23
24 Energy Band Diagram with Efield Electron Electron Energy  Efield + Energy Efield 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
25 The FermiDirac 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= ev/k T=0K f(e) 0.5 E E f 25
26 Properties of the FermiDirac 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
27 Fermi Energy (E i ) of Intrinsic Semiconductor Ec E g /2 E i E g /2 Ev 27
28 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
29 How to find E f when n(or p) is known E c q Φ F E i E f (ntype) E v E f (ptype) n = n i ep [(E f E i )/kt] Let qφ F E f E i n = n i ep [qφ F /kt] 29
30 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
31 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
32 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 E F  + E E 32
33 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 V a > 0 V a < 0 Potential difference across depletion region = V bi V a 33
34 PN junctions Thermal Equilibrium N A and p ρ() is 0 Efield Depletion region N + D and n ρ() is Quasineutral region Quasineutral region psi N A only ρ() is  nsi N D+ only ρ() is + Complete Depletion Approimation used for charges inside depletion region r() N D+ () N A () 34
35 Electrostatics of Device Charges 1) Summation of all charges = 0 ρ 2 d2 = ρ 1 d1 2) Efield =0 outside depletion regions ptype ρ() Semiconductor ntype Semiconductor ρ2   d1 ρ1 d2 E = 0 =0 E 0 E = 0 35
36 3) Relationship between Efield and charge density ρ() d [ε E()] /d = ρ() Gauss Law 4) Relationship between Efield and potential φ E() =  dφ()/d 36
37 Eample Analysis : n+/ psi junction ρ() n+ Si Depletion region is very thin and is approimated as +Q' =0 Depletion region psi 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 Efield curve = voltage across depletion region = qn a d2 /2ε s 37
38 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
39 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
40 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
41 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
42 nsurface = nbulk e qvsi/kt nsurface qv Si psi N a =10 16 /cm3 nbulk = /cm3 E i 0.35eV E f Onset of strong inversion (at V T ) VSi nsurface E E E E E E E E E E+19 42
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