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**FETs-1 (Field Effect Transistors)**

Engineering 43 FETs-1 (Field Effect Transistors) Bruce Mayer, PE Registered Electrical & Mechanical Engineer

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**Learning Goals Understand the Basic Physics of MOSFET Operation**

Describe the Regions of Operation for a MOSFET Device Use the Graphical LOAD-LINE method to analyze the operation of basic MOSFET Amplifiers Determine the LARGE-SIGNAL Bias-Point (Q-Point) for MOSFET circuits

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Learning Goals Use SMALL-SIGNAL models to analyze various FET Amplifiers Calculate Performance Metrics for various FET Amplifiers Apply FETs to the Design and Construction of CMOS Logic Gates

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Transistor What is it? Transistor is a contraction for “Transfer Resistor” These devices have THREE connections: Input Output Control The transistor’s Fluidic-Analog is a Metering (Needle) Valve (a Faucet)

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**The concept of voltage-controlled resistance**

An independent Voltage Applied to the Control connection (the “Gate) regulates the flow of Current Thru the device Drain (or Source) Gate Source (or Drain)

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**Flavors of FETS Junction Field Effect Transistor → JFET**

A Normally ON transistor Reverse Biasing two PN Junctions will “Pinch Off” a Conducting Channel

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**Flavors of FETS Depletion Mode MOSFET**

Another Normally ON transistor Applying a Gate Voltage Drives Carriers OUT of the conducting Channel to turn off the transistor No direct Gate↔Channel Connection An Isulated Gate Field Effect Transistor (IGFET)

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**Flavors of FETS Enhancement Mode MOSFET**

Normally OFF transistor Another IGFET Applying a Gate Voltage Attracts & Creates carriers to FORM a conducting Channel to turn ON the transistor These Make Great Switches

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**MOSFET What does that mean?**

M → Metal O → Oxide S → Silicon F → Field E → Effect T → Transistor Short for “Transfer Resistor” Often times for Pfets the Substrate is tied to the drain. This was the case in Mr. Phillips Lab

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**Enhancement Mode - IGFET**

Insulated Gate Field Effect Transistors are Normally-Off devices Applying a Positive Voltage to the Gate will attract e− to the Channel This will eventually “invert” a thin region below the gate to N-type, creating a conducting channel between S & D IGFETs are Great Switches Used in almost all digital IC’s Back-to-Back PN Jcns Between “source” & “drain”

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**MOSFET Nomenclature & Dims**

We will consider only Enhancement FETs n+ ≡ Heavily Doped n-Type An n-Channel (nFET) enhancement mode FET

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**MOSFET: Current & Speed**

In General the performance of an Enhancement Mode MOSFET Current Carrying Capacity Increases with Increasing Width, W On/Off Switching Speed Increases with Decreasing Gate Length, L As of 2011 the minimum (best) value for L was about 22 nm

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**MOSFET On/Off Operation**

Step 1: Apply Gate Voltage SiO2 Insulator (Glass) Gate Source Drain 5 volts holes N N electrons P electrons to be transmitted Step 3: Channel becomes saturated with electrons. Electrons in source are able to flow across channel to Drain. Step 2: Excess electrons surface in channel, holes are repelled.

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**nMOSFET Circuit Symbol**

n-Channel MOSFET electrons move from Source→Drain to produce the Drain Current PN Junction forms between Substrate and Channel when FET is “ON”

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**MOSFET Operation: CutOff**

As seen in previous diagrams, unpowered MOSFETS have two OPOSING PN junctions Channel→Source Channel→Drain With NO Potential applied to the gate No current can flow From the Previous slide the Minimum Gate Voltage required for current-flow is called the “Threshold” Voltage, Vto or Vth A MOSFET with VGS < Vth is “CutOff” i.e.; The MOSFET is Off, and the Drain Current, iD = 0

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**MOSFET Circuit in CutOff**

The Diagram at Right shows an nMOSFET in CutOff For vGS<Vto the PN Jcn between the Drain & Body is Reversed Biased by vDS and NO Current flows Vto is typically Volts Mathematically this is simple; in CutOff, the Drain Current

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**Power MOSFET Data Sheet**

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CutOff Summarized VGS < Vto → No Drain Current Flows

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**MOSFET IN Triode (Ohmic) Region**

In this case the nMOSFET Voltage conditions: Electrons are ATTRACTED to the Positive-Gate and a thin Conducting Channel Forms In this Region the Drain Current depends on BOTH vDS and vGS Fluid Analogy → needle valve The region is “TRIode” as the condition of all three connections determines iD

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**nMOSFET in Triode Operation**

When vGS > Vto a conducting channel forms below the gate

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Triode Operation When vGS > Vto a conducting channel forms below the gate. That is the “type” of the silicon is INVERTED from p-Type to n-Type Thus this conducting Channel is often called an “Inversion Layer” The greater vGS The more the conducting the channel becomes The Channel resistance is a fcn of vGS

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**Triode Operation In the Triode Region, iD increases for**

Increasing vGS Increasing vDS Thus current thru the device depends on the voltage at ALL three connections as long as vDS < (vGS − Vto) The Three-Connection dependency is why this region is called TRIODE

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Triode Operation In Triode Operation, the iD curve is a concave-down Parabola given by Where The Device Transconductance Parameter, KP, Depends on the Construction of the FET KP for nFETs is typically µA/V2

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PinchOff In order to form a complete channel, every point, x, along the channel must have a voltage difference greater than Vto That is, need The greater this qty, the thicker the conducting Layer Now as vDS is increased eventually at x = L where vchan = vDS The Channel Thickness goes to ZERO. This is called PINCH-OFF

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PinchOff Illustrated The layer is THICKEST at the Source and ZERO at the Drain when Thus Have PinchOff when At this Point the channel is Very Thick at the Source-End, and Zero-Thick at the Drain End → Pinched Off at Drain

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**TriOde Region Summarized**

vDS ≤ (vGS − Vto) → iD = f(vDS , VGS) Start of TriOde → Channel Formation Finish of TriOde → Drain PinchOff

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**PinchOff iD Saturation**

As vDS increases the “PinchOff Point”, xpop, Moves BACKWARDS towards the Source Once the channel Pinches Off, the drain current, iD, NO Longer increases with increasing vDS In other words, for a given vGS, the Current “Saturates” (stays constant) After PinchOff as shown below

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**nMOSFET complete vi Curve**

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**MOSFET Operation Summary**

Cut-Off Region – In this region the gate voltage is less than the Threshold voltage Vto and therefore very little current flows. Triode Region – In this mode the device is operating below pinch-off and is effectively a variable resistor. Saturation Region – This is the main operating region for the device. The drain voltage has to be greater than the gate voltage minus the Threshold voltage.

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**Operation in Saturation**

Notice that in SAT iD varies with vGS Note that vDS does NOT appear in this Equation vDS (on vi curve) does NOT affect iD after Channel-PinchOff In SAT a MOSFET is true 3-terminal device; current depends ONLY on the CONTROL Signal, vGS

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**Saturation Summarized**

vDS ≥ (vGS − Vto) → iD ≠ f(vDS) PinchOff Moved BACK from Drain

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**Triode↔Saturation Boundary**

At the boundary Line the nMOSFET just Barely Pinches Off at the Drain end thus: By KVL Substituting Find Or at the Boundary Boundary Line Sub for vGS into iD,sat Eqn

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nFET KVL 𝒗 𝑮𝑫 = 𝒗 𝑮𝑺 − 𝒗 𝑫𝑺

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**Triode↔Saturation Boundary**

Then then iD along the Boundary The Boundary is described by a Concave-UP Parabola that passes thru the origin Boundary Line

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Example 12.1 make vi Plot Use Parameters from Example 12.1 to plot in MATLAB the vi Curve for an nMOSET The Parameters W = 160 µm L = 2 µm (pretty large) KP = 50 µA/V2 Vto = 2V Plot has multiple operating regions → must concatenate

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The completed Plot

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**MATLAB Code-1 % Bruce Mayer, PE % ENGR43 * 14Jan12**

% file = nMOSFET_Plot_ex12_1_1201.m W = 160; % µm L = 2; % µm KP = 50; % µA/sq-V Vto = 2' % V % % calc Parameter K K = (W/L)*KP/2; % µA/sqV) % set vGS values that exceed CutOff at 2V vGS = [3, 4, 5, 6]; % calc boundary Triode/Sat boundary by finding iD at the START of sat % region iDsat_uA = K*(vGS-Vto).^2; % in µA iDsat_mA = iDsat_uA/1000 % show cutoff line vDSco = linspace(0,10, 200); iDco = zeros(200); % DeBug Command => plot(vDSco, iDco, 'LineWidth', 3) % Calc iD in Triode Region for vGS>Vto (Pinched off at Drain) %* use eqn (12.6) in text vDSsat = sqrt(iDsat_uA/K) % must take care with units plot(vDSsat,iDsat_mA, '--*', 'LineWidth', 3), grid, xlabel('vDSsat'), ylabel('iDsat') disp('showing Triode-Sat Boundary - Hit any key to continue') pause MATLAB Code-1

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**MATLAB Code-2 % then iD in triode region**

vDSt1 = linspace(0, vDSsat(1)); % V vDSt2 = linspace(0, vDSsat(2)) vDSt3 = linspace(0, vDSsat(3)) vDSt4 = linspace(0, vDSsat(4)) iDt1_mA = K*(2*(vGS(1)-Vto)*vDSt1-vDSt1.^2)/1000; % mA iDt2_mA = K*(2*(vGS(2)-Vto)*vDSt2-vDSt2.^2)/1000; % mA iDt3_mA = K*(2*(vGS(3)-Vto)*vDSt3-vDSt3.^2)/1000; % mA iDt4_mA = K*(2*(vGS(4)-Vto)*vDSt4-vDSt4.^2)/1000; % mA % % DeBug Command =>plot(vDSt1,iDt1_mA, vDSt4,iDt4_mA) % use TwoPoint Plots in Sat iDsat1 =[iDsat_mA(1),iDsat_mA(1)] iDsat2 =[iDsat_mA(2),iDsat_mA(2)] iDsat3 =[iDsat_mA(3),iDsat_mA(3)] iDsat4 =[iDsat_mA(4),iDsat_mA(4)] vDSsat1 = [vDSsat(1), 10] vDSsat2 = [vDSsat(2), 10] vDSsat3 = [vDSsat(3), 10] vDSsat4 = [vDSsat(4), 10]

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**MATLAB Code-3 % % Now Concatenate to ocver Triode & Saturation Regions**

iD1 = [iDt1_mA,iDsat1] vDS1 = [vDSt1, vDSsat1] iD2 = [iDt2_mA,iDsat2] vDS2 = [vDSt2, vDSsat2] iD3 = [iDt3_mA,iDsat3] vDS3 = [vDSt3, vDSsat3] iD4 = [iDt4_mA,iDsat4] vDS4 = [vDSt4, vDSsat4] % Finally Make Plot plot(vDSco, iDco,'b', vDS1, iD1,'c', vDS2, iD2,'g', vDS3, iD3,'m', vDS4, iD4,'r', 'LineWidth', 3),... grid, xlabel('vDS (Volts)'), ylabel('iD (mA)'), title('nMOSFET vi Curve - Ex 12.1'),... gtext('VGS<Vto'), gtext('vGS=3V'), gtext('vGS=4V'), gtext('vGS=5V'), gtext('vGS=6V')

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**pMOSFET A “pMOS” FET is the “Complement” to the nMOS version.**

The channel is normally n-Type and a hole-populated conducting Channel is formed by applying a NEGATIVE vGS Basically the pMOS version looks like the nMOS FET with voltage-polarities inverted pMOSFET Circuit Symbol In this case HOLES flow from Source-to-Drain so Current flow S→D Channel

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p & n MOSFET Comparison nFET are generally FASTER than pFETS

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**3 & 4 Connection nFET All Done for Today**

The BODY is often hard-connected to the SOURCE for nFETS

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**Appendix Diode vi Curves**

Engineering 43 Appendix Diode vi Curves Bruce Mayer, PE Registered Electrical & Mechanical Engineer

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