电容,氧化物电荷对金属氧化物电容器的影响

电容,氧化物电荷对金属氧化物电容器的影响,通过测试金属氧化物的电荷和电容来对比其对金属氧化物电容器比电容大小的影响。
展开查看详情

1. Lecture #22 OUTLINE The MOS Capacitor • Capacitance • Effect of Oxide Charges Reading: Course Reader (Part III, Chap. 2) Spring 2003 EE130 Lecture 22, Slide 1 Review: Threshold Voltage • For p-type Si (“NMOS”): 2qN Aε Si (2ψ B ) VT = VFB + 2ψ B + Cox • For n-type Si (“PMOS”): 2qN Dε Si 2ψ B VT = VFB + 2ψ B − Cox Spring 2003 EE130 Lecture 22, Slide 2 1

2. ψs and Wd vs. VG (p-type Si) 2φ F ψs: qN Aε si  2C (V − VFB )  2 2 ψs =  1 + ox G − 1 (for VFB < VG < VT ) Aε si 2 2Cox  qN  0 VG accumulation V depletion V inversion FB T 2ε Si (2ψ F ) Wdm = qN A Wd: 2ε Siψ S ε Si  2C (V − VFB )  2 Wd = =  1 + ox G − 1 (for VFB < VG < VT ) qN A Cox  qN Aε si   0 VG accumulation V depletion V inversion FB T Spring 2003 EE130 Lecture 22, Slide 3 Total Charge Density in Si, Qs Qacc = −Cox (VG − VFB ) depletion inversion 0 accumulation VG Qs = Qacc + Qdep + Qinv VFB VT accumulation depletion inversion accumulation depletion inversion 0 VG VFB VT VG Qdep = − qN AW 0 VFB VT accumulation depletion inversion 0 VG Qinv VFB VT slope = -Cox Qinv = −Cox (VG − VT ) Spring 2003 EE130 Lecture 22, Slide 4 2

3. MOS Capacitance Measurement • VG is scanned slowly • Capacitive current due to vac is measured iac dvac GATE iac = C dt vac dQGATE dQs Si C= = dVG dVG C-V Meter MOS Capacitor Spring 2003 EE130 Lecture 22, Slide 5 MOS C-V Characteristics (p-type Si) accumulation depletion inversion VG dQs VFB VT C= dVG Qinv C slope = -Cox Cox Ideal C-V curve: VG VFB VT accumulation depletion inversion Spring 2003 EE130 Lecture 22, Slide 6 3

4.Capacitance in Accumulation (p-type Si) • As the gate voltage is varied, incremental charge is added/subtracted to/from the gate and substrate. • The incremental charges are separated by the gate oxide. M O S ∆Q Q dQacc C= = Cox -Q dVG −∆Q Cox Spring 2003 EE130 Lecture 22, Slide 7 Flat-Band Capacitance • At the flat-band condition, variations in VG give rise to the addition/subtraction of incremental charge in the substrate, at a depth LD • LD is the “extrinsic Debye Length” – characteristic shielding distance, or the distance where the electric field emanating from a perturbing charge falls off by a factor of 1/e ε Si kT LD = q2 N A 1 1 L = + D CFB Cox ε Si Spring 2003 EE130 Lecture 22, Slide 8 4

5. Capacitance in Depletion (p-type Si) • As the gate voltage is varied, the width of the depletion region varies. → Incremental charge is effectively added/subtracted at a depth Wd in the substrate. M O S ∆Q dQdep 1 2(VG − VFB ) C= = + Q Wd dVG Cox 2 qN Aε Si −∆Q -Q 1 1 1 1 Wd = + = + C Cox Cdep Cox ε Si Cox Cdep Spring 2003 EE130 Lecture 22, Slide 9 Capacitance in Inversion (p-type Si) CASE 1: Inversion-layer charge can be supplied/removed quickly enough to respond to changes in the gate voltage. → Incremental charge is effectively added/subtracted at the surface of the substrate. ∆Q Time required to build inversion-layer M O S charge = 2NAτo/ni , where WT τo = minority-carrier lifetime at surface −∆Q dQinv C= = Cox dVG Cox Spring 2003 EE130 Lecture 22, Slide 10 5

6. Capacitance in Inversion (p-type Si) CASE 2: Inversion-layer charge cannot be supplied/removed quickly enough to respond to changes in the gate voltage. → Incremental charge is effectively added/subtracted at a depth Wd in the substrate. ∆Q 1 1 1 = + M O S C Cox Cdep Wdm 1 Wdm −∆Q = + Cox ε Si 1 2(2ψ B ) 1 = + ≡ Cox Cdep Cox qN Aε Si C min Spring 2003 EE130 Lecture 22, Slide 11 Supply of Substrate Charge (p-type Si) gate gate Accumulation: Cox Depletion: Cox + + + + + + C dep Wd p-type Si p-type Si Case 1 Case 2 Inversion: gate gate Cox Cox N+ - - - - - - DC - - - - - - Cdep,min - AC DC and AC Wdm WT p-type Si p-type Si Spring 2003 EE130 Lecture 22, Slide 12 6

7. Capacitor vs. Transistor C-V (or LF vs. HF C-V) p-type Si: C MOS transistor at any f, MOS capacitor at low f, or quasi-static C-V Cmax=Cox CFB MOS capacitor at high f Cmin VG accumulation depletion inversion VFB VT Spring 2003 EE130 Lecture 22, Slide 13 Quasi-Static C-V Measurement p-type Si: C Cmax=Cox CFB Cmin VG accumulation depletion inversion VFB VT The quasi-static C-V characteristic is obtained by slowly ramping the gate voltage (< 0.1V/s), while measuring the gate current IG with a very sensitive DC ammeter. C is calculated from IG = C·dVG/dt. Spring 2003 EE130 Lecture 22, Slide 14 7

8. Examples: C-V Characteristics C QS Cox HF-Capacitor VG VFB VT Does the QS or the HF-capacitor C-V characteristic apply? (1) MOS capacitor, f=10kHz. (2) MOS transistor, f=1MHz. (3) MOS capacitor, slow VG ramp. (4) MOS transistor, slow VG ramp. Spring 2003 EE130 Lecture 22, Slide 15 Deep Depletion • If VG is scanned quickly, Qinv cannot respond to the change in VG. The increase in substrate charge density Qs must then come from an increase in depletion charge density Qdep ⇒ depletion depth Wd increases as VG increases ⇒ C decreases as VG increases C Cox Cmin VG VFB VT Spring 2003 EE130 Lecture 22, Slide 16 8

9. Parameter Extraction from C-V From a single C-V measurement, we can extract much information about the MOS device. • Suppose we know that the gate-electrode material is heavily doped n-type poly-Si (ΦM=4.05eV), and that the gate dielectric is SiO2 (εr=3.9): – From Cmax = Cox we determine the oxide thickness tox – From Cmin and Cox we determine substrate doping (by iteration) – From substrate doping and Cox we calculate the flat-band capacitance CFB – From the C-V curve, we can find VFB = VG C =C FB – From ΦM, ΦS, Cox, and VFB we can determine Qf Spring 2003 EE130 Lecture 22, Slide 17 Example: Effect of Doping C/Cox 1 VG VFB VT • How would C-V characteristic change if substrate doping NA were increased? – VFB – VT – Cmin Spring 2003 EE130 Lecture 22, Slide 18 9

10. Example: Effect of Oxide Thickness C/Cox 1 VG VFB VT • How would C-V characteristic change if oxide thickness tox were decreased? – VFB – VT – Cmin Spring 2003 EE130 Lecture 22, Slide 19 Oxide Charges In real MOS devices, there is • In the oxide: always some charge in the oxide – Trapped charge Qot and at the Si/oxide interface. • High-energy electrons and/or holes injected into oxide – Mobile charge QM • Alkali-metal ions, which have sufficient mobility to drift in oxide under an applied electric field • At the interface: – Fixed charge QF • Excess Si (?) – Trapped charge Qit • Dangling bonds Spring 2003 EE130 Lecture 22, Slide 20 10

11. Effect of Oxide Charges • In general, charges in the oxide cause a shift in the gate voltage required to reach the threshold condition: t ox 1 ∆VT = − ε SiO ∫ xρ 0 ox ( x)dx 2 (x defined to be 0 at metal-oxide interface) • In addition, they may alter the field-effect mobility of mobile carriers (in a MOSFET) due to Coulombic scattering Spring 2003 EE130 Lecture 22, Slide 21 Fixed Oxide Charge QF M O S qQF / Cox 3.1 eV Ec= EFM Ev |qVFB | Ec QF EFS VFB = φ MS − Ev Cox 4.8 eV Spring 2003 EE130 Lecture 22, Slide 22 11

12. Determination of QF Measure C-V characteristics of capacitors with different oxide thicknesses. Plot VFB as a function of tox. VFB 10nm 20nm 30nm x ox 0 tox –0.15V VFB = φ MS − QF × ε SiO 2 × –0.3V × Spring 2003 EE130 Lecture 22, Slide 23 Mobile Ions • Odd shifts in C-V characteristics were once a mystery: QM ∆VFB = − Cox • Source of problem: Mobile charge moving to/away from interface, changing charge centroid Spring 2003 EE130 Lecture 22, Slide 24 12

13. Interface Traps Traps cause “sloppy” C-V and also greatly degrade mobility in channel Q (ψ ) ∆VG = − IT S Cox Spring 2003 EE130 Lecture 22, Slide 25 13