Part 4: Heterojunctions - MOS Devices. MOSFET Current Voltage Characteristics

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1 MOS Device Uses: Part 4: Heterojunctions - MOS Devices MOSCAP capacitor: storing charge, charge-coupled device (CCD), etc. MOSFET transistor: switch, current amplifier, dynamic random access memory (DRAM-volatile), NVM (non-volatile memory), etc. Present day Challenges - Ultrathin : begin to observe quantum effects M O S poly-crystalline Si V Source W Source Contact Insulator n + source + V gate n ++ Poly Si Gate Contact or Electrode - Gate oxide channel p-si Wafer Drain Contact Insulator n + drain V Drain + Crystalline Si L t ox C ox o ra okoxa t t ox ox 1 MOSFET Current Voltage Characteristics I D (ma) I DS (ma) 10 V DS(sat) V GS =10V 10 V DS =20V Saturation, I D I DS 8V 5 5 6V V th =4V 5V 4V V DS V GS Kasap, Fig. 6.38, p. 538 (a) (b) (a) Typical I D vs V DS characteristics of an enhancement MOSFET (Vth = 4 V) for various fixed gate voltages V GS. (b) Dependence of I D on V GS at a given V DS (>V DS(sat)). 2 W V DS ID Cox VGS VT VDS ; (+ = nmos; - = pmos) L 2 W I 2 Dsat Cox VGS VT ; (+ = nmos; - = pmos) 2L Fig. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005) 2 1

2 m < sc Heterojunctions - MOS M O S ac M O S E c m sc sc E f,m ev FB p-si Ef,s/c E f,m E f,s/c Φ s band bending in Si p-si ev ox band bending in oxide Flat band ev FB ev ox Φ s Equilibrium Depletion Regime 3 m > sc Heterojunctions - MOS M O S M O S sio2 ac ev ox band bending in oxide m sc sc ev FB E f,m M p-si Φ s band bending in Si E f,s/c E E Ef,m g f,s/c p-si Flat band ev FB ev ox Φ s Equilibrium Accumulation Regime 4 2

3 Heterojunctions E m < sc MOSCAP e- M O S M O S M O S Eg Inversion E f,s/c Accumulation Φ s band bending in Si Φ s band bending in Si qv A qv Eg A E E f,s/c qv c E Φ A f,m s band bending in E f,s/c Si p-si p-si ev ox band p-si ev ox band bending in bending in Very strong accumulation 5 Heterojunctions -MOS Neaman, Semiconductor Devices 6 3

4 Heterojunctions m < sc MOSCAP qv A qv A Depletion Accumulation Very strong accumulation 7 Heterojunctions MOSCAP 8 4

5 m < sc q SiO2 q m q Si q Si q F Depletion Depletion 9 q SiO2 q m q Si q Si At Si/ p=n So: E f = E i qv A =q V G q s [ ] s = surface potential depletion q F NOTE: Flat Band: q F E i E f q F At Flat Band, no Surface Potential, q s, exists. But, when E f coincides with E i at the interface, then q F = q s F kt q N ln n D opant i q F s = F onset of inversion 10 5

6 Assume: m < sc or S Oxide S/C F F F E i F F E f & E A F 1 Colinge & Colinge, Physics of Semiconductor Devices (Kluwer Academic Publishers, 2002 ) p , qv G At Si/ E f = E i q F s = F Colinge & Colinge, Physics of Semiconductor Devices (Kluwer Academic Publishers, 2002 ) s = F = ms V ox + V G F kt N ln q n i A onset of inversion V G = s ms + V ox = F ms + V ox 12 6

7 [1] [1] One might think that the definition for the threshold of inversion should be the onset of inversion BUT IT IS NOT. There are varying opinions on this! Onset of strong inversion: S = F Threshold of inversion 2,6, Onset of strong inversion 3 or Onset of strong inversion 1,2,4,5 : S = 2 F When: S = 2 F, V g =V T s = 2 F = ms V ox + V T kt A F ln V G = s ms + V ox = 2 F ms + V q n ox i N 1 Colinge & Colinge, Physics of Semiconductor Devices (Kluwer Academic Publishers, 2002 ) p , Anderson & Anderson, Fundamentals of Semiconductor Devices, (McGraw Hill, 2005) p Muller & Kamins, Device Electronics for Integrated Circuits, 3 rd Ed. (Wiley, 2003) p Streetman & Banerjee, Solid State Electronic Devices, 5 th Ed (Prentice Hall, 2000) p Taur & Ning, Fundamentals of Modern VLSI Devices, (Cambridge, ) p ; 6 Kasap, Prin. Of Electronic Materials & Devices 3 rd Ed (McGraw Hill,, 2006) p O S Assume: m < sc E D E i E A & E f F F 2 F Flatband Depletion At Si/ At Si/ At Si/ E f = E i E f > E D n=p [1] onset of inversion S = F E f = E D n=n A threshold of Inversion Or Onset of Strong Inversion S = 2 F strong inversion 14 7

8 Threshold Voltage: V t V T,start : modeled by MEDICI, a TCAD program V T,2 F : V T at 2 F V T,extrapol : extrapolated V T D. Schroder, Semiconductor Material & Device Characterization 2rd Ed (Wiley Interscience, 1998) p [1] [4] [3] [5] 1 Colinge & Colinge, Physics of Semiconductor Devices (Kluwer Academic Publishers, 2002 ) p , Anderson & Anderson, Fundamentals of Semiconductor Devices, (McGraw Hill, 2005) p Muller & Kamins, Device Electronics for Integrated Circuits, 3 rd Ed. (Wiley, 2003) p Streetman & Banerjee, Solid State Electronic Devices, 5 th Ed (Prentice Hall, 2000) p Taur & Ning, Fundamentals of Modern VLSI Devices, (Cambridge, ) p Something is important when: S = 2 F Inversion takes over depletion & E f =E D 16 8

9 Degenerate E f is in the CB Degenerate E f is in the VB 0Φ F 2Φ F 1Φ F V FB V T 5 Taur & Ning, Fundamentals of Modern VLSI Devices, (Cambridge, ) p Something is important when: S = 2 F Inversion takes over depletion & E f =E D 17 Capacitance Voltage: Q C V or Q [5] [4] E i V T [1] 1 Colinge & Colinge, Physics of Semiconductor Devices (Kluwer Academic Publishers, 2002 ) p , Anderson & Anderson, Fundamentals of Semiconductor Devices, (McGraw Hill, 2005) p Muller & Kamins, Device Electronics for Integrated Circuits, 3 rd Ed. (Wiley, 2003) p Streetman & Banerjee, Solid State Electronic Devices, 5 th Ed (Prentice Hall, 2000) p Taur & Ning, Fundamentals of Modern VLSI Devices, (Cambridge, ) p

10 Capacitance Voltage: Q C V or Q 0Φ F 1Φ F 2Φ F [4] E i V T 4 Streetman & Banerjee, Solid State Electronic Devices, 5 th Ed (Prentice Hall, 2000) p V A = V G V A At Si/ E f = E i At Si/ E f >> E i depletion onset of inversion strong inversion 20 10

11 Heterojunctions MOSCAP 21 Heterojunctions Drain (V+) e - Gate e - e- Source (V-) e - e - MOSFET 22 11

12 MOSFET Current Voltage Characteristics I D (ma) I DS (ma) 10 V DS(sat) V GS =10V 10 V DS =20V Saturation, I D I DS 8V 5 5 6V V th =4V 5V 4V V DS V GS Kasap, Fig. 6.38, p. 538 (a) (b) (a) Typical I D vs V DS characteristics of an enhancement MOSFET (Vth = 4 V) for various fixed gate voltages V GS. (b) Dependence of I D on V GS at a given V DS (>V DS(sat)). 2 W V DS ID Cox VGS VT VDS ; (+ = nmos; - = pmos) L 2 W I 2 Dsat Cox VGS VT ; (+ = nmos; - = pmos) 2L Fig. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005) 23 Heterojunctions MOSCAP depletion Neaman, Semiconductor Devices 24 12