Lecture 25 MOSFET Basics (Understanding with Math) …

1 ECE 3040 - Dr. Alan DoolittleGeorgia TechLecture 25 MOSFET Basics (Understanding with Math) Reading: Pierret and Jaeger and NotesECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V DerivationWith our expression relating the Gate voltage to the surface potential and the fact that S=2 F we can determine the value of the threshold voltage areaunit per ecapacitanc oxide theiswhere,devices) channel-p(for 222devices) channel-n(for 222oxoxoxFSDoxSFTFSAoxSFTxCqNCVqNCV Where we have made use of the use of the expression,oSSK ECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V DerivationCoordinate Definitions for our NMOS Transistorx=depth into the semiconductor from the oxide along the channel from the source contactz=width of the channelxc(y) = channel depth (varies along the length of the channel).n(x,y)= electron concentration at point (x,y) n(x,y)=the mobility of the carriers at point (x,y)Device width is ZChannel Length is LAssume a Long Channel device (for now do not worry about the channel length modulation effect)ECE 3040 - Dr.

2 Alan DoolittleGeorgia TechMOS Transistor I-V DerivationConcept of Effective mobilityThe mobility of carriers near the interface is significantly lower than carriers in the semiconductor bulk due to interface the electron concentration also varies with position, the average mobility of electrons in the channel, known as the effective mobility, can be calculated by a weighted average, )(02)(0)(0)(0),(),()(/arg),()(,),(),(),( yxxxnNnyxxxNyxxxyxxxnnccccdxyxnyxyQqcmec hdxyxnqyQdefiningordxyxndxyxnyx Empirically constants are ,1 andwhereVVoTGSon ECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V DerivationDrain Current-Voltage RelationshipIn the Linear Region, VGS>VTand 0<VDS<VdsatdydnqnEqJJnqDnEqJnynNyNNnN Neglecting the diffusion current, and recognizing the current is only in the y-direction,ECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V DerivationDrain Current-Voltage RelationshipIn the Linear Region, VGS>VTand 0<VDS<Vdsat DSDSDSccVNnDVNnDVNnLyyDNnyxxxnyxxxNyNyDd QLZIdQZLIdQZdyIdydQZdxyxnyxqdydZdxJZdxdz JI 0000)(0)(0),(),(To find ID, we need an expression relating the electrostatic potential, and QNECE 3040 - Dr.

3 Alan DoolittleGeorgia TechMOS Transistor I-V Derivation Capacitor-Like Model for QNAssumptions: Neglect all but the mobile inversion charge (valid for deep inversion) For the MOSFET , the charge in the semiconductor is a linear function of position along the semiconductor side of the plate. Thus, varies from 0 to VDSMOS CapacitorMOS Transistor TGSVVfor TGSoxNVVCQ TGSVVfor TGSoxNVVCQS ourceDrain,dVdQCSinceox Neglect the depletion region chargeNote: Assuming a linear variation of potential along the channel leads to an underestimation of current but is a good estimate for hand voltages above threshold create inversion chargeECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V DerivationUsing Capacitor-Like Model for QNwe can estimate IDas: TGSDsatDSDSDSTGSoxnDVTGoxnDVNnDVVandVVVV VVLCZIdVVCLZIdQLZIDSDS 02200 This is known as the square law describing the Current-Voltage characteristics in the Linear or Triode the linear behavior for small VDS(can neglect VDS2term).

4 Note the negative parabolic dependence for larger VDSbut still VDS<VDsat(can NOT neglect VDS2term). ECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V Derivation Capacitor-Like Model for QNFor VDS>Vdsatthe voltage drop across our channel is VDsatwith the remaining voltage (VDS-VDsat) dropped across the pinch-off region DSDsatDsatDsatTGSoxnDsatDVVVVVVLCZII 22 But the charge at the end of the channel is zero due to the pinched off channel, DsatTGSDsatTGSoxNVVVorVVVCLyQ 0)(Thus, DSDsatTGSoxnDsatDVVVVLCZII 22 But what about the saturation region?ECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor I-V DerivationTGSDsatVVV DSDsatTGSoxnDsatDVVVVLCZII 22 TGSDsatDSDSDSTGSoxnDVVandVVVVVVLCZI 022 Summary of MOSFET IV RelationshipECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor ApplicationsVoltage variable ResistorAn n-channel MOSFET has a gate width to length ratio of Z/L=100, un=200 cm2/Vsec, Cox= uF/cm2and VT=1V.

5 We want to develop a resistor that has a resistance that is controlled by an external voltage. Such a device would be used in variable gain amplifiers , automatic gain control devices , compressors and many other electronic devices. Define what range of VDSmust be maintained to achieve proper voltage variable resistance operation. Find the On-resistance (VDS/ID) of the transistor from <VGS<4 Vfor small , to achieve voltage variable resistance operation, we must operate in the linear region. Otherwise, the current is either a constant regardless of drain voltage (saturation region) or is approximately zero (cutoff due to the capacitor being in either accumulation and depletion). Thus, VGS -VT>VDS. Given the values above, 0<VDS< 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor ApplicationsVoltage variable ResistorUsing the linear region IDequation: 600100,1 smallfor 22DS2 DSGSDSTGSoxnDSTGSoxnDSDDSDSDSTGSoxnDSDST GSoxnDRThusVcmFeRVVCZLVVVLCZVIVRVVVLCZVV VVLCZI ECE 3040 - Dr.

6 Alan DoolittleGeorgia TechMOS Transistor ApplicationsCurrent SourceThe same transistor is to be used for a Current Source . Define the range of drain-source voltage that can be used to achieve a fixed current of 50 a constant current regardless of Drain-Source voltage, we must use the saturation region: This source will operate over a VDS>VGS-VTor VDS> VECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: Deviations From IdealChannel Length Modulation EffectAbove pinch-off (when VDS>VDsat=VGS-VT) the channel length reduces by a value , the expression for drain current,Becomes, DSDsatTGSoxnDsatDVVVVLCZII 22 DSDsatTGSoxnDsatDDSDsatTGSoxnDsatDVVLLVV LCZIILLLLLVVVVLLCZII 12111 L,L *sinceor 222 *In many modern devices, this assumption does not hold. Thus, the channel length modulation parameter we are deriving does not describe the IV expressions 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: Deviations From IdealChannel Length Modulation EffectDSVLL But the fraction of the channel that is pinched off depends linearly on VDSbecause the voltage across the pinch-off region is (VDS-VDsat) so, DSDsatDSTGSoxnDsatDVVVVVLCZII 122where is known as the Channel-Length Modulation parameterand is typically: V-1< V Channel Length Modulation causes the dependence of drain current on the drain voltage in 3040 - Dr.

7 Alan DoolittleGeorgia TechMOS Transistor: Deviations From IdealBody Effect (Substrate Biasing)Until now, we have only considered the case where the substrate (Body) has been the substrate (Body) is often intentionally biased such that the Source-Body and Drain-Body junctions are reversed body bias, VBS, is known as the backgate biasand can be used to modify the threshold that now our channel potential has an offset equal to VBS, ..ECE 3040 - Dr. Alan DoolittleGeorgia Tech devices) channel-p(for 222devices) channel-n (for222 FSDoxSFTFSAoxSFTqNCVqNCV MOS Transistor: Deviations From IdealBody Effect (Substrate Biasing)Thus, our threshold potential with the body grounded,The Gate- Body Threshold becomes, devices) channel-n(for 222devices) channel-p(for 222 BSFSAoxSBSFGBBSFSDoxSBSFGBVqNCVVVqNCVVT hresholdThreshold But we would like to have this in terms of VGSinstead of , VGS=VGB+VBS devices) channel-p(for 222devices) channel-n(for 222 BSFSDoxSFGSBSFSAoxSFGSVqNCVVqNCVT hresholdThreshold Surface Potential SVT=ECE 3040 - Dr.

8 Alan DoolittleGeorgia TechMOS Transistor: Deviations From IdealBody Effect (Substrate Biasing) oxFBSFTOTPTFBSFTOTNTCVVJ aegerVPierretVVVJ aegerVPierretVSA2qNwhere,devices) channel-p(for 22devices) channel-n(for 22 This can be rewritten in the following form (more convenient to reference the threshold voltage to the VBS=0 case).is known as the body effect parameterECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: Enhancement Mode verses Depletion Mode MOSFETWe have been studying the enhancement mode MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor). It is called enhancement because conduction occurs only after the channel conductance is improved or enhanced . In this case, VTN>0 and VTP<0 Transistors can be fabricated such that:These transistors have conduction for VGS=0 due to a channel already existing without the need to invert the near surface region . To modulate currents, a field must applied to the gate that depletes the channel.

9 Thus, transistors of this nature are called Depletion mode MOSFETs .0V and 0 VTPTN ECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: Enhancement Mode verses Depletion Mode MOSFETECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: SummaryJaeger uses the notation: Pierret)in (Z Width Gate theisW wherePMOS Pierret)in (Z Width Gate theisW where''LWCLWKKLWCLWKKNMOS oxpppoxnnn 4-Terminal3-TerminalNMOS(n-channel)PMOS( p-channel)EnhancementEnhancementDepletio nDepletionECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: SummaryNMOSPMOSR egardless of ModeCutoffLinearSaturationThreshold VoltageVTfor Enhancement ModeVTfor Depletion ModePierret)in Z W:(Note ' LWCLWKK oxnnn Pierret)in ZW :(Note ' LWCLWKK oxppp TNGSDSVVforI 0 TPGSDSVVforI 0 0122 TNGSDSTNGSDSTNGSoxnDSVVVandVVVVVLCZI 0122 TPGSDSTPGSDSTPGSoxnDSVVVandVVVVVLCZI 022 DSTNGSTNGSDSDSTNGSoxnDSVVVandVVVVVVLCZI 022 DSTPGSTPGSDSDSTPGSoxnDVVVandVVVVVVLCZI 0 TNV0 TNV0 TPV0 TPV FBSFTOTPVVV 22 FSBFTOTNVVV 22 ECE 3040 - Dr.

10 Alan DoolittleGeorgia TechMOS Transistor: Bias Circuitry-Enhancement Mode NMOSDue to zero DC current flow in the gate, the bias analysis of a MOSFET is significantly easier than a Form Thevenin circuits looking out the gate, drain, and sourceECE 3040 - Dr. Alan DoolittleGeorgia TechDSDSGSthGVRIVVRIV 3103 But IG=0 so VGS=3V Assume Saturation operation (selected for easy math because IDSdoes not depend on VDSsince no was given =0): DSDSTNGSDSTNGSnDSVC heckAxiVvvforVvKi 50132102502262 VVVVVVkuAVTNGSDSDS25)100(5010 Assumption of Saturation operation was correct! If it were not correct simply make another assumption ( linear region) and Transistor: Bias Circuitry-Enhancement Mode NMOSIDSIGECE 3040 - Dr. Alan DoolittleGeorgia TechMOS Transistor: Bias Circuitry-Depletion Mode NMOS Bias circuit of a depletion mode device is much simpler due to the fact that the device conducts drain current for VGS=0V What value of R1 results in 100 uA drain current?