ESE 570: Digital Integrated Circuits and VLSI Fundamentals Lec 4: January 24, 2017 MOS Transistor Theory, MOS Model Penn ESE 570 Spring 2017 Khanna
Lecture Outline! Semiconductor Physics " Band gaps " Field Effects! MOS Physics " Cut-off " Depletion " Inversion " Threshold Voltage 2
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
Semiconductor Physics 4
Silicon Lattice! Cartoon two-dimensional view 5
Energy State View Energy Valance Band all states filled 6
Energy State View Conduction Band all states empty Energy Valance Band all states filled 7
Energy State View Conduction Band all states empty Energy Band Gap Valance Band all states filled 8
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
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
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
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
Capacitor Charge! Remember capacitor charge + + + + + + + + gate drain source - - - - - - - - - semiconductor 13
MOS Field?! What does capacitor field do to the Donor-doped semiconductor channel? V gs =0 No field - - - - - - 14
MOS Field?! What does capacitor field do to the Donor-doped semiconductor channel? V gs =0 No field - - - - - - + + + + - - - V cap >0 15
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
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 + + + + + - - - - - - - - - - - - 17
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
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
Field Effect?! Effect of positive field on Acceptor-doped Silicon? V gs =0 No field + + + + 20
Field Effect?! Effect of positive field on Acceptor-doped Silicon? V gs =0 No field + + + + + + + + - - - V cap >0 21
Field Effect?! Effect of positive field on Acceptor-doped Silicon? V gs =0 No field + + + + + + + + - - - V cap >0 = + + + + + V gs >0 No conduction 22
Field Effect?! Effect of negative field on Acceptor-doped Silicon? V gs =0 No field + + + + + - - - + + + V cap <0 23
Field Effect?! Effect of negative field on Acceptor-doped Silicon? V gs =0 No field + + + + + - - - + + + V cap <0 = - - - + + + + + V gs >0 Conduction 24
MOSFETs! Donor doping " Excess electrons " Negative or N-type material " NFET! Acceptor doping " Excess holes " Positive or P-type material " PFET 25
MOSFET! Semiconductor can act like metal or insulator! Use field to modulate conduction state of semiconductor - - - - - - + + + + + 26
MOS Physics - nmos
Two-Terminal MOS Structure 2 GATE Si Oxide interface n+ n+ (Mass Action Law) 28
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 10-19 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
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
MOS Capacitor Energy Bands 31
MOS System Band Diagram! Three components put in physical contact " Fermi levels must line up 32
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
Accumulation Region 34
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
Depletion Region t ox - - - - - mobile holes 36
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
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
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
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
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
Inversion Region V G V T (threshold voltage) t ox - -- - - - - (Density of mobile electrons = density of holes in bulk) 42
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
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
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
Band Diagram 46
2-terminal MOS Cap # 3-terminal nmos VS V G V D - - - - - - - - - depletion region - - - - 47
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
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
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
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
Threshold Voltage V SB 52
Big Idea! 3 operation regions " Cut-off " Depletion " Inversion! Doping and V SB change V T 53
Admin! HW 2 due Thursday, 1/26 " Submit in canvas before class! Office hours updated on Course website " Grader updated 54