ECE 333 Linear Electronics Chapter 5 MOS Field-Effect Transistors (MOSFETs) Why MOSFETs  Device Structure  Physical Operation  I-V Characteristics  MOSFET Circuits at DC  The Body Effect and Other Topics

Introduction The invention of MOSFETs (page 248) MOSFET vs. BJT MOSFET in Integrated Circuits VLSI Digital Circuit and Analog Circuit Memory

5.1 Device Structure and Physical Operation

5.1.1 Device Structure (b) cross section. Typically L = 0.03 μm to 1 μm, W = 0.05 μm to 100 μm, and the thickness of the oxide layer (tox) is in the range of 1 to 10 nm.

5.1.2 Operation with Zero Gate Voltage Two pn junctions back-to-back Prevent current conduction from drain to source when vD is applied Very high resistance (of the order of 1012 Ω)

5.1.3 Creating a Channel for Current Flow Figure 5.2 The enhancement-type NMOS transistor with a positive voltage applied to the gate. An n channel is induced at the top of the substrate beneath the gate.

5.1.3 Creating a Channel for Current Flow Overdrive voltage vOV Electron Charge in the channel Oxide Capacitance 𝑣 𝑂𝑉 = 𝑣 𝐺𝑆 − 𝑉 𝑇 |𝑄|= 𝐶 𝑜𝑥 (𝑊𝐿) 𝑣 𝑂𝑉 𝐶 𝑜𝑥 = 𝜖 𝑜𝑥 𝑡 𝑥𝑜

5.1.4 Applying a Small vDS

5.1.4 Applying a Small vDS

5.1.4 Applying a Small vDS |𝑄| 𝑢𝑛𝑖𝑡 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ = 𝐶 𝑜𝑥 𝑊 𝑣 𝑂𝑉 Electron drift velocity = 𝜇 𝑛 𝐸 = 𝜇 𝑛 𝑣 𝐷𝑆 𝐿 𝑖 𝐷 =[( 𝜇 𝑛 𝐶 𝑜𝑥 )( 𝑊 𝐿 ) 𝑣 𝑂𝑉 ] 𝑣 𝐷𝑆

5.1.4 Applying a Small vDS |𝑄| 𝑢𝑛𝑖𝑡 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ = 𝐶 𝑜𝑥 𝑊 𝑣 𝑂𝑉 Electron drift velocity = 𝜇 𝑛 𝐸 = 𝜇 𝑛 𝑣 𝐷𝑆 𝐿 𝑖 𝐷 =[( 𝜇 𝑛 𝐶 𝑜𝑥 )( 𝑊 𝐿 ) 𝑣 𝑂𝑉 ] 𝑣 𝐷𝑆 𝑟 𝐷𝑆 = 1 𝜇 𝑛 𝐶 𝑜𝑥 𝑊 𝐿 𝑣 𝑂𝑉 𝑟 𝐷𝑆 = 1 𝜇 𝑛 𝐶 𝑜𝑥 𝑊 𝐿 (𝑣 𝐺𝑆 − 𝑉 𝑡 ) 𝑘 𝑛 = 𝜇 𝑛 𝐶 𝑜𝑥 𝑊 𝐿

5.1.5 Operation as vDS is Increased

5.1.5 Operation as vDS is Increased 1 2 [ 𝑉 𝑂𝑉 + 𝑉 𝑂𝑉 − 𝑣 𝐷𝑆 ]∙ 𝑣 𝐷𝑆 𝑖 𝐷 = 𝑘′ 𝑛 ( 𝑊 𝐿 )( 𝑉 𝑂𝑉 − 1 2 𝑣 𝐷𝑆 ) 𝑣 𝐷𝑆

5.1.5 Operation as vDS is Increased 𝑖 𝐷 = 𝑘′ 𝑛 ( 𝑊 𝐿 )( 𝑉 𝑂𝑉 − 1 2 𝑣 𝐷𝑆 ) 𝑣 𝐷𝑆 𝑖 𝐷 = 𝑘 ′ 𝑛 𝑊 𝐿 [ (𝑣 𝐺𝑆 − 𝑉 𝑡 ) 𝑣 𝐷𝑆 − 1 2 𝑣 𝐷𝑆 2 ]

5.1.6 Operation for vDS>VOV: Channel Pinch-off and Current Saturation 𝑣 𝐷𝑆 = 𝑉 𝑂𝑉 𝑎𝑟𝑒𝑎= 1 2 𝑉 𝑂𝑉 ∙ 𝑣 𝐷𝑆 | at this point Triode region 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 𝑣 𝑂𝑉 2

5.1.6 Operation for vDS>VOV: Channel Pinch-off and Current Saturation 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 𝑣 𝑂𝑉 2 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 ( 𝑣 𝐺𝑆 − 𝑉 𝑡 ) 2 Example 5.1 Consider a process technology for which Lmin=0.4um, tox=8nm, un=450 cm2/Vs, and Vt=0.7V. Find Cox and k’n. For a MOSFET with W/L=8 um / 0.8 um, calculate VOV, VGS and VDSmin needed to operate the transistor in the saturation region with a dc current ID=100uA. For the device in (b), find the values of VOV and VGS required to cause the device to operate as a 1000-Ω resistor for very small vDS.

5.1.7 The p-Channel MOSFET To form a channel, it must have 𝑣 𝐺𝑆 ≤ 𝑉 𝑡𝑝 |𝑣 𝐺𝑆 |≥| 𝑉 𝑡𝑝 |

5.1.8 Complementary MOS or CMOS

5.2 Current-Voltage Characteristics 5.2.1 Circuit Symbol Figure 5.11 (a) Circuit symbol for the n-channel enhancement-type MOSFET. (b) Modified circuit symbol with an arrowhead on the source terminal to distinguish it from the drain and to indicate device polarity (i.e., n channel). (c) Simplified circuit symbol to be used when the source is connected to the body or when the effect of the body on device operation is unimportant.

5.2.2 i-v

5.2.2 i-v Figure 5.12 The relative levels of the terminal voltages of the enhancement NMOS transistor for operation in the triode region and in the saturation region.

5.2.2 i-v

5.2.3 The iD – vGS Characteristics When the MOSFET is used to design an amplifier, it is operated in the saturation region. 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 ( 𝑣 𝐺𝑆 − 𝑉 𝑡𝑛 ) 2 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 𝑣 𝑂𝑉 2 Nonlinear  linear amplifier? (chapter 7)

5.2.3 The iD – vGS Characteristics

5.2.3 The iD – vGS Characteristics Figure 5.15: Large-signal, equivalent-circuit model of an n-channel MOSFET operating in the saturation region.

Example 5. 2 Consider an NMOS transistor fabricated in a 0 Example 5.2 Consider an NMOS transistor fabricated in a 0.18-um process with L=0.18 um and W=2um. The process technology is specified to have Cox=8.6 fF/um, un=450cm2/Vs and Vtn=0.5V. (a)Find VGS and VDS that result in the MOSFET operating at the edge of saturation with iD=100uA. (b) If VGS is kept constant, find VDS that results in iD=50uA. (c) To investigate the use of the MOSFET as a linear amplifier, let it be operating in saturation with VDS=0.3V. Find the change in iD resulting from vGS changing from 0.7 V by 0.01V and by -0.01V. Solution: Kn=unCox(W/L)=4.3 mA/V2 With nMOSFET in saturation: So, vOV=0.22V VGS=vOV + Vtn = 0.72 V At the edge: VDS = VGS – Vtn = 0.22 V 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 𝑣 𝑂𝑉 2

(b) With VGS kept constant at 0 (b) With VGS kept constant at 0.72V, iD reduced  the nMOSFET will now be operating in triode region Because VOV is 0.22 V with VGS = 0.72V, We have: VDS = 0.06 V or 0.39 V (two solutions from the above eq. Because 0.39 V is above VOV, not in triode region, so only VDS=0.06V is correct solution. (c) For vGS=0.7V, VOV=0.2V and VDS=0.3V, the transistor is operating in saturation region: Now with VGS=0.71V, VOV=0.21V, iD=94.8 uA With VGS=0.69V, VOV=0.19V, iD=77.6 uA. The change of + or – 0.01V, the change of iD is similar 8.8 ~ 8.4 uA 𝑖 𝐷 = 𝑘′ 𝑛 ( 𝑊 𝐿 )( 𝑉 𝑂𝑉 − 1 2 𝑣 𝐷𝑆 ) 𝑣 𝐷𝑆 𝑖 𝐷 = 1 2 𝑘 𝑛 𝑣 𝑂𝑉 2 =86 𝜇𝐴

5.2.4 Finite output resistance in Saturation Channel-length modulation (real MOSFET) 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 𝑣 𝐺𝑆 − 𝑉 𝑡𝑛 2 (1+𝜆 𝑣 𝐷𝑆 )

5.2.4 Finite output resistance in Saturation 𝑖 𝐷 = 1 2 𝑘 ′ 𝑛 𝑊 𝐿 𝑣 𝐺𝑆 − 𝑉 𝑡𝑛 2 (1+𝜆 𝑣 𝐷𝑆 ) ro: output resistance 𝑟 𝑜 = 𝑑 𝑖 𝐷 𝑑 𝑣 𝐷𝑆 −1 𝑤𝑖𝑡ℎ 𝑣 𝐺𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 VA: A device parameter in V

5.2.4 Finite output resistance in Saturation 𝑟 𝑜 = 𝑑 𝑖 𝐷 𝑑 𝑣 𝐷𝑆 −1 𝑤𝑖𝑡ℎ 𝑣 𝐺𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑟 𝑜 = 𝑉 𝐴 𝐼 ′ 𝐷

5.2.5 Characteristics of the p-Channel MOSFET Figure 5.19 (a) Circuit symbol for the p-channel enhancement-type MOSFET. (b) Modified symbol with an arrowhead on the source lead. (c) Simplified circuit symbol for the case where the source is connected to the body.

5.3 MOSFET Circuits at DC Simple model: 𝜆=0

5.4 The Body Effect and Other Topics

Temperature Effects: Vt decreases by about 2 mV for every 1oC rise in temperature K’ decreases with temperature increase – dominant effect So current decreases with increasing temperature

Breakdown and input protection Velocity Saturation (107 cm/s limit) Depletion-type MOSFET