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Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-1
LECTURE 100 – MOS CAPACITOR MODEL AND LARGESIGNAL MODEL DEPENDENCE
LECTURE ORGANIZATIONOutline• MOSFET capacitor model• Dependence of the large signal model on process• Dependence of the large signal model on voltage• Dependence of the large signal model on temperature• SummaryCMOS Analog Circuit Design, 2nd Edition ReferencePages 79-86
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-2
whereAS = area of the sourcePS = perimeter of the sourceCJSW = zero bias, bulk source sidewall capacitanceMJSW = bulk-source sidewall grading coefficient
For the bulk-drain depletion capacitance replace "S" by "D" in the above.
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-5
As the gate-source voltage varies from 0 to VT, the channel-bulk capacitor varies from avery large capacitor (because of a very small depletion region) to a capacitor muchsmaller than C2.Capacitors in Cutoff:
Process Variation “Corners”For strong inversion operation, the primary influence is the oxide thickness, tox. We seethat K’ will tend to increase with decreasing oxide thickness whereas VT tends todecrease.If the “speed” of a transistor is increasedby increasing K’ and decreasing VT, thenthe variation of technology can beexpressed on a two-dimensional graphresulting in a rectangular area of“acceptable” process limitation.
Three corner versus five corner models060118-10
PMOSSpeed
NMOS Speed
Fast PMOS
SlowPMOS
SlowNMOS
FastNMOS
AcceptableTechnologyParameters
Large KʼSmall VT
Small KʼLarge VT
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-15
DEPENDENCE OF THE LARGE SIGNAL MODEL ON VOLTAGEWhat is Voltage Variation?Voltage variation is the influence of power supply voltage on the component.(There is also power supply influence on the circuit called power supply rejection ratio,PSRR. We will deal with this much later.)Power supply variation comes from:1.) Influence of depletion region widths on components.2.) Nonlinearity3.) Breakdown voltage
Note: Because the large-signal model for the MOSFET includes all the influences ofvoltage on the transistor, we will focus on passive components except for breakdown.
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-16
Models for Voltage Dependence of a Component1.) ith-order Voltage Coefficients
In general a variable y = f(v) which is a function of voltage, v, can be expressed as aTaylor series,
y(v = V0) y(V0) + a1(v- V0) + a2(v- V0)2+ a3(v- V0)3 + ···where the coefficients, ai, are defined as,
a1 = df(v)dv
|v=V0 , a2 =
12
d2f(v)dv2
|v=V0 , ….
The coefficients, ai, are called the first-order, second-order, …. voltage coefficients.
2.) Fractional Voltage Coefficient or Voltage CoefficientGenerally, only the first-order coefficients are of interest.In the characterization of temperature dependence, it is common practice to use a termcalled fractional voltage coefficient, VCF, which is defined as,
VCF(v=V0) = 1
f(v=V0) df(v)dv
|v=V0 parts per million/V (ppm/V)
or more simply,
VCF = 1
f(v) df(v)dv parts per million/V (ppm/V)
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-17
Influence of Voltage on a Diffused Resistor – Depletion Region
Influence of the depletion region on the p+ resistor:
060305-01
p- substrate
p+
Older LOCOS Technology
p+
n-well
STI STI
p+
Depletion region
Thickness ofp+ Resistor
n- well
FOX FOX
Thickness ofp+ Resistor
As the voltage at the terminals of the resistor become smaller than the n-well potential,the depletion region will widen causing the thickness of the resistor to decrease.
R = L
t W VR
where VR is the reverse bias voltage from the resistor to the well.
This effect is worse for well resistors because the doping concentration of the resistor issmaller.Voltage coefficient for diffused resistors 200-800 ppm/VVoltage coefficient for well resistors 8000 ppm/V
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-18
Voltage Coefficient of Polysilicon ResistorsWhy should polysilicon resistors be sensitive to voltage?There is a small depletion region between the polysilicon and its surrounding materialthat has a very small dependence on the voltage between the polysilicon and thesurrounding material.
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-19
Voltage Nonlinearity and Breakdown VoltageConductivity modulation:As the current in a resistor increases, the conductivity becomes modulated and theresistance increases.Example of a n-well resistor:
As the reverse bias voltage across a pn junctionbecomes large, at some point, called the breakdownvoltage, the current will rapidly increase. Bothtransistors, diodes and depletion capacitors experiencethis breakdown.Model for current multiplication factor:
M = 1
1 +vRBV
n
060311-01
i
v
i = vR
Conductivitymodulation
0.1A
060311-02
iR
vR
Breakdownvoltage
BV
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-20
Zero Temperature Coefficient (ZTC) Point for MOSFETsFor a given value of gate-source voltage, the drain current of the MOSFET will beindependent of temperature. Consider the following circuit:
Assume that the transistor is saturated and that:
μ = μo
TTo
-1.5 and VT(T) = VT(To) + (T-To)
where = -0.0023V/°C and To = 27°C
ID(T) = μoCoxW
2L TTo
-1.5[VGS – VT0 - (T-To)]2
dIDdT =
-1.5μoCox
2To
TTo
-2.5[VGS-VT0- (T-To)]2+ μoCox
TTo
-1.5[VGS-VT0- (T-To)] = 0
VGS – VT0 - (T-To) = -4T
3 VGS(ZTC) = VT0 - To - 3
Let K’ = 10μA/V2, W/L = 5 and VT0 = 0.71V.At T=27°C(300°K), VGS(ZTC)=0.71-(-0.0023)(300°K)-(0.333)(-0.0023)(300°K)=1.63V
At T = 27°C (300°K), ID = (10μA/V2)(5/2)(1.63-0.71)2 = 21.2μAAt T=200°C(473°K),VGS(ZTC)=0.71-(-0.0023)(300°K)-(0.333)(-0.0023)(473°K)=1.76V
ID
VGS
Fig. 4.5-12
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-22
Experimental Verification of the ZTC PointThe data below is for a 5μm n-channel MOSFET with W/L=50μm/10μm,NA=1016 cm-3, tox = 650Å, uoCox = 10μA/V2, and VT0 = 0.71V.
0600613-01
0
20
40
60
80
100
0 0.6 1.2 1.8 2.4 3
25°C100°C
150°C200°C250°C275°C
300°C
VDS = 6V
Zero TC Point
25°C100°C
150°C200°C
250°C
275°C
VGS (V)
I D (
A)
A similar result holds for the p-channel MOSFET.
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-23
Temperature Modeling of the PN JunctionPN Junctions (Reverse-biased only):
iD Is = qA Dppno
Lp+
DnnpoLn
qAD
L n
2i
N = KT 3exp VGo
Vt
Differentiating with respect to temperature gives,dIs
dT = 3KT 3
T exp VGo
Vt +
qKT 3VGo
KT 2 exp VGo
Vt =
3Is
T + Is
T VGo
Vt
TCF = dIs
IsdT = 3T +
1T
VGoVt
ExampleAssume that the temperature is 300° (room temperature) and calculate the reversediode current change and the TCF for a 5° increase.SolutionThe TCF can be calculated from the above expression as TCF = 0.01 + 0.155 = 0.165.Since the TCF is change per degree, the reverse current will increase by a factor of 1.165for every degree (or °C) change in temperature. Multiplying by 1.165 five times givesan increase of approximately 2. Thus, the reverse saturation current approximatelydoubles for every 5°C temperature increase.Experimentally, the reverse current doubles for every 8°C increase in temperaturebecause the reverse current is in part leakage current.
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-26
Temperature Modeling of the PN Junction – ContinuedPN Junctions (Forward biased – vD constant):
iD Is exp vDVt
Differentiating this expression with respect to temperature and assuming that the diodevoltage is a constant (vD = VD) gives
diDdT =
iDIs
dIsdT -
1T
VDVt
iD
The fractional temperature coefficient for iD is1iD
diDdT =
1Is
dIsdT -
VDTVt
= 3T +
VGo - VDTVt
If VD is assumed to be 0.6 volts, then the fractional temperature coefficient is equal to0.01+(0.155-0.077) = 0.0879. The forward diode current will approx. double for a 10°C.PN Junctions (Forward biased – iD constant):
VD = Vt ln(ID/Is)Differentiating with respect to temperature gives
dvDdT =
vDT - Vt
1Is
dIsdT =
vDT -
3VtT -
VGoT = -
VGo - vDT -
3VtT
Assuming that vD = VD = 0.6 V the temperature dependence of the forward diode voltageat room temperature is approximately -2.3 mV/°C.
Lecture 100 – MOS Capacitor Model and Large Signal Model Dependence (3/24/10) Page 100-28
Resistor Dependence on TemperatureDiffused Resistors:The temperature dependence of resistors depends mostly on the doping level of diffusedand implanted resistors. As the doping level or sheet resistance increases from 100 /to 400 / , the temperature coefficient varies from about +1000 ppm/°C to +4000ppm/°C. Diffused and implanted resistors have good thermal conduction to the substrateor well.Polysilicon Resistors:
Typically has a sheet resistance of 20 / to 80 / and has poor thermal conductionbecause it is electrically isolated by oxide layers.Metal:Metal is often used for resistors and has a positive temperature coefficient.Temperature Coefficients of Resistors:
SUMMARY• The large signal capacitance model includes depletion and parallel plate capacitors• The depletion capacitors CBD and CBS vary with their reverse bias voltage
• The capacitors CGD, CGS, and CGB have different values for the regions of cutoff, activeand saturated
• The large signal model varies with process primarily through μo and tox
• Voltage dependence of resistors and capacitors is primarily due to the influence ofdepletion regions
• The temperature dependent large signal model of the MOSFET yields a gate-sourcevoltage where the derivative of drain current with respect to temperature is zero
• Other MOSFET temperature dependence comes from the leakage currents acrossreverse biased pn junctions