ESE 570: Digital Integrated Circuits and VLSI Fundamentals

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1 ESE 570: Digital Integrated Circuits and VLSI Fundamentals Lec 4: January 24, 2017 MOS Transistor Theory, MOS Model Penn ESE 570 Spring 2017 Khanna

2 Lecture Outline! Semiconductor Physics " Band gaps " Field Effects! MOS Physics " Cut-off " Depletion " Inversion " Threshold Voltage 2

3 Review: MOSFET N-Type, P-Type! N negative carriers " electrons! Switch turned on positive V GS! P positive carriers " holes! Switch turned on negative V GS V th,n > 0 V GS > V th,n to conduct V th,p < 0 V GS < V th,p to conduct 3

4 Semiconductor Physics 4

5 Silicon Lattice! Cartoon two-dimensional view 5

6 Energy State View Energy Valance Band all states filled 6

7 Energy State View Conduction Band all states empty Energy Valance Band all states filled 7

8 Energy State View Conduction Band all states empty Energy Band Gap Valance Band all states filled 8

9 Band Gap and Conduction Insulator E c Metal E c E v 8ev OR E v E v E c Semiconductor 1.1ev E c E v 9

10 Doping! 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) 10

11 Doping with P! End up with extra electrons " Donor electrons! Not tightly bound to atom " Low energy to displace " Easy for these electrons to move 11

12 Doped Band Gaps! Addition of donor electrons makes more metallic " Easier to conduct 0.045ev 1.1ev Semiconductor E c E D E v 12

13 Capacitor Charge! Remember capacitor charge gate drain source semiconductor 13

14 MOS Field?! What does capacitor field do to the Donor-doped semiconductor channel? V gs =0 No field

15 MOS Field?! What does capacitor field do to the Donor-doped semiconductor channel? V gs =0 No field V cap >0 15

16 MOS Field?! What does capacitor field do to the Donor-doped semiconductor channel? V gs =0 No field V cap >0 = V gs >0 Conducts 16

17 MOS Field Effect! Charge on capacitor " Attract or repel charges to form channel " Modulates conduction " Positive " Attracts carriers " Negative? " Enables conduction " Repel carriers " Disable conduction

18 Doping with B! 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 18

19 Doped Band Gaps! Addition of acceptor sites makes more metallic " Easier to conduct Semiconductor E c 0.045ev 1.1ev E A E v 19

20 Field Effect?! Effect of positive field on Acceptor-doped Silicon? V gs =0 No field

21 Field Effect?! Effect of positive field on Acceptor-doped Silicon? V gs =0 No field V cap >0 21

22 Field Effect?! Effect of positive field on Acceptor-doped Silicon? V gs =0 No field V cap >0 = V gs >0 No conduction 22

23 Field Effect?! Effect of negative field on Acceptor-doped Silicon? V gs =0 No field V cap <0 23

24 Field Effect?! Effect of negative field on Acceptor-doped Silicon? V gs =0 No field V cap <0 = V gs >0 Conduction 24

25 MOSFETs! Donor doping " Excess electrons " Negative or N-type material " NFET! Acceptor doping " Excess holes " Positive or P-type material " PFET 25

26 MOSFET! Semiconductor can act like metal or insulator! Use field to modulate conduction state of semiconductor

27 MOS Physics - nmos

28 Two-Terminal MOS Structure 2 GATE Si Oxide interface n+ n+ (Mass Action Law) 28

29 P-type Doped Semiconductor Band Gap Free space Electron affinity of silicon Conduction band Intrinsic Fermi level qφ S Fermi level Valence band! qφ and E are in units of energy = electron-volts (ev); where 1 ev = 1.6 x J.! 1 ev corresponds to energy acquired by a free electron that is accelerated by an electric potential of one volt.! Φ and V corresponds to potential difference in volts. 29

30 P-type Doped Semiconductor Band Gap Free space Electron affinity of silicon E i = E C E V 2 Conduction band Intrinsic Fermi level qφ S Fermi level Fermi potential: Work function (Fermi-to-space): Φ F = E F E i q Valence band Φ Fp = kt q ln n i N A qφ S = qχ + (E C E F ) 30

31 MOS Capacitor Energy Bands 31

32 MOS System Band Diagram! Three components put in physical contact " Fermi levels must line up 32

33 MOS Capacitor with External Bias! Three Regions of Operation: " Accumulation Region V G < 0 " Depletion Region V G > 0, small " Inversion Region V G V T, large 33

34 Accumulation Region 34

35 Accumulation Region Energy Bands Accumulation V G < 0 Si surface Band bending due to V G < 0 E Fm qv G = E Fp E Fm qφ S qφ(x) qφ Fp E Fp 0 x 35

36 Depletion Region t ox mobile holes 36

37 Depletion Region Energy Bands Depletion V G > 0 (small) Si surface Band bending due to V G > 0 qφ(x) qv G = E Fp E Fm qφ S qφ Fp E Fp E Fm x d 0 x 37

38 Depletion Region Φ Fp = Φ F = kt q ln n i N A < 0 t ox 26 mv at room T Φ Φ S Φ Fp Surface potential Bulk potential 38

39 Depletion Region Φ Fp = Φ F = kt q ln n i N A < 0 t ox 26 mv at room T Φ Φ S Φ Fp Surface potential Bulk potential dq = qn A dx dφ = x dq ε Si Mobile hole charge density (per unit area) in thin layer below surface Potential required to displace dq by distance x dφ = q N A x ε Si dx 39

40 Depletion Region t ox Φ Fp = Φ F = kt q ln n i N A < 0 26 mv at room T Φ Φ S Φ Fp Surface potential Bulk potential dφ = q N A x ε Si dx Φ Fp dφ = Φ S x d 0 q N A x ε Si dx = q N 2 A x d 2ε Si = Φ Fp Φ S x d = 2ε Si Φ Fp Φ S q N A 40

41 Depletion Region Φ Fp = Φ F = kt q ln n i N A < 0 t ox 26 mv at room T Φ Φ S Φ Fp Surface potential Bulk potential x d = 2ε Si Φ Fp Φ S q N A Q = qn A x d 2ε Si Φ Fp Φ S Q = qn A = 2qN A ε Si Φ Fp Φ S q N A 41

42 Inversion Region V G V T (threshold voltage) t ox (Density of mobile electrons = density of holes in bulk) 42

43 Inversion Region Energy Bands Inversion V G V T0 > 0 Si surface qφ Fp qv G = E Fp E Fm qφ S E Fp E Fm 0 x dm x 43

44 Depletion Region Energy Bands Depletion V G > 0 (small) Si surface Band bending due to V G > 0 qφ(x) qv G = E Fp E Fm qφ S qφ Fp E Fp E Fm x d 0 x 44

45 Inversion Region V G V T (threshold voltage) t ox (Density of mobile electrons = density of holes in bulk) Q = 2qN A ε Si Φ Fp Φ S = 2qN A ε Si 2Φ Fp 45

46 Band Diagram 46

47 2-terminal MOS Cap # 3-terminal nmos VS V G V D depletion region

48 nmos = MOS cap + source/drain V SB = 0 V G V D V S x d = 2ε Si 2Φ Fp V SB q N A 48

49 Threshold Voltage V T 0 = Φ GC Q ox C ox 2Φ F Q B0 C ox V T0n,p [V T0 -> VT0 in SPICE] for nmos and pmos V FB = GC Q ox C GC ox Q B0 = 2qN A ε Si 2Φ F with V SB = 0. ) Φ GC V FB work function between gate and channel l 49

50 Threshold Voltage for V SB = 0 for V SB!= 0 V T =V T 0 = Φ GC Q ox C ox 2Φ F Q B0 C ox V T = Φ GC Q ox C ox 2Φ F Q B C ox V T = Φ GC Q ox C ox 2Φ F Q B0 C ox Q B Q B0 C ox γ V T =V T 0 Q B Q B0 C ox Q Q B B0 = 2qN Aε Si ( 2Φ F V SB 2Φ ) F C ox C ox V T = V T 0 +γ ( 2Φ F V SB 2Φ ) F 50

51 Threshold Voltage V SB is 0 in nmos, 0 in pmos $ V T0 is positive in nmos (V T0n ), negative in pmos (V T0p ) 51

52 Threshold Voltage V SB 52

53 Big Idea! 3 operation regions " Cut-off " Depletion " Inversion! Doping and V SB change V T 53

54 Admin! HW 2 due Thursday, 1/26 " Submit in canvas before class! Office hours updated on Course website " Grader updated 54

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