ESE 57: Digital Integrated Circuits and VLSI Fundamentals Lec 4: January 24, 217 MOS Transistor Theory, MOS Model Lecture Outline! Semiconductor Physics " Band gaps " Field Effects! MOS Physics " Cutoff " Depletion " Inversion " Threshold Voltage Penn ESE 57 Spring 217 Khanna 2 Review: MOSFET NType, PType! N negative carriers " electrons! P positive carriers " holes Semiconductor Physics! Switch turned on positive V GS! Switch turned on negative V GS V th,n > V GS > V th,n to conduct V th,p < V GS < V th,p to conduct 3 4 Silicon Lattice Energy State View! Cartoon twodimensional view Energy Valance Band all states filled 5 6 1
Energy State View Energy State View Conduction Band all states empty Conduction Band all states empty Energy Energy Band Gap Valance Band all states filled Valance Band all states filled 7 8 Band Gap and Conduction Doping Insulator 8ev Metal OR! Add impurities to Silicon Lattice " Replace a Si atom at a lattice site with another! E.g. add a Group 15 element " E.g. P (Phosphorus) Semiconductor 1.1ev 9 1 Doping with P Doped Band Gaps! End up with extra electrons " Donor electrons! Not tightly bound to atom " Low energy to displace " Easy for these electrons to move! Addition of donor electrons makes more metallic " Easier to conduct Semiconductor.45ev 1.1ev E D 11 12 2
Capacitor Charge! Remember capacitor charge MOS Field?! What does capacitor field do to the Donordoped semiconductor channel? gate drain source semiconductor 13 14 MOS Field? MOS Field?! What does capacitor field do to the Donordoped semiconductor channel?! What does capacitor field do to the Donordoped semiconductor channel? + V cap > + V cap > V gs > Conducts 15 16 MOS Field Effect Doping with B! Charge on capacitor " Attract or repel charges to form channel " Modulates conduction " Positive " Attracts carriers " Enables conduction " Negative? " Repel carriers " Disable conduction! End up with electron vacancies Holes " Acceptor electron sites! Easy for electrons to shift into these sites " Low energy to displace " Easy for the electrons to move " Movement of an electron best viewed as movement of hole 17 18 3
Doped Band Gaps! Addition of acceptor sites makes more metallic " Easier to conduct! Effect of positive field on Acceptordoped Silicon? Semiconductor.45ev 1.1ev E A 19 2! Effect of positive field on Acceptordoped Silicon?! Effect of positive field on Acceptordoped Silicon? + + V cap > + V cap > V gs > No conduction 21 22! Effect of negative field on Acceptordoped Silicon?! Effect of negative field on Acceptordoped Silicon? + + V cap < + V cap < V gs > Conduction 23 24 4
MOSFETs MOSFET! Donor doping " Excess electrons " Negative or Ntype material " NFET! Acceptor doping " Excess holes " Positive or Ptype material " PFET! Semiconductor can act like metal or insulator! Use field to modulate conduction state of semiconductor 25 26 TwoTerminal MOS Structure MOS Physics nmos GATE 2 Si Oxide interface n+ n+ (Mass Action Law) 28 Ptype Doped Semiconductor Band Gap Ptype Doped Semiconductor Band Gap Free space Electron affinity of silicon Free space Electron affinity of silicon Conduction band Intrinsic Fermi level Fermi level Valence band! qφ and E are in units of energy electronvolts (ev); where 1 ev 1.6 x 1 19 J. E i E C E V 2 Fermi potential: Conduction band Intrinsic Fermi level Fermi level Valence band Φ F E F E i kt q q ln n i! 1 ev corresponds to energy acquired by a free electron that is accelerated by an electric potential of one volt. Work function (Fermitospace): qχ + (E C E F )! Φ and V corresponds to potential difference in volts. 29 3 5
MOS Capacitor Energy Bands MOS System Band Diagram! Three components put in physical contact " Fermi levels must line up 31 32 MOS Capacitor with External Bias! Three Regions of Operation: " Accumulation Region V G < " V G >, small " Inversion Region V G, large Accumulation Region 33 34 Accumulation Region Energy Bands Accumulation V G < Si surface Band bending due to V G < E Fm mobile holes qv G E Fp E Fm qφ(x) q E Fp x 35 36 6
Energy Bands Depletion V G > (small) Si surface Band bending due to V G > Φ F kt q ln n i < 26 mv at room T qφ(x) Φ Φ S Surface potential Bulk potential qv G E Fp E Fm q E Fp E Fm x 37 38 Φ F kt q ln n i < 26 mv at room T Φ F kt q ln n i < 26 mv at room T Φ Φ S Surface potential Bulk potential Φ Φ S Surface potential Bulk potential dφ x dx dq q dx dφ Q Mobile hole charge density (per unit area) in thin layer below surface Potential required to displace dq by distance x dφ x dx 39 dφ Φ S x 2 dx q N x A d 2 2 4 Inversion Region Φ F kt q ln n i < 26 mv at room T V G (threshold voltage) Φ Φ S Surface potential Bulk potential 2 Q q 2 (Density of mobile electrons density of holes in bulk) Q q 2q 41 42 7
Inversion Region Energy Bands Energy Bands Inversion V G > Si surface Depletion V G > (small) Si surface Band bending due to V G > q qφ(x) qv G E Fp E Fm E Fp qv G E Fp E Fm q E Fp E Fm E Fm m x x 43 44 Inversion Region Band Diagram V G (threshold voltage) (Density of mobile electrons density of holes in bulk) Q 2q 2q 2 45 46 2terminal MOS Cap # 3terminal nmos nmos MOS cap + source/drain V SB V S V G V D VS V G V D depletion region 2 2 V SB 47 48 8
Threshold Voltage Φ GC Q ox Q B V FB GC Q ox C GC ox Q B 2q 2Φ F Φ GC V FB with V SB. n,p [ > VT in SPICE] + for nmos and pmos work function between gate and channel ) l 49 Threshold Voltage for V SB for V SB! γ Φ GC Q ox Q B Φ GC Q ox Q B Φ GC Q ox Q B Q B Q B Q B Q B ( ) Q Q B B 2q 2Φ F V SB +γ ( 2Φ F V SB ) 5 Threshold Voltage Threshold Voltage V SB is in nmos, in pmos $ is positive in nmos (n ), negative in pmos (p ) V SB 51 52 Big Idea! 3 operation regions " Cutoff " Depletion " Inversion Admin! HW 2 due Thursday, 1/26 " Submit in canvas before class! Office hours updated on Course website " Grader updated! Doping and V SB change 53 54 9