4.1 I-V characteristics of MOSFET Current in MOSFET
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4.1 I-V characteristics of MOSFET
Current in MOSFET
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Physical design
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Physical parameters
The length of MOSFET. Itis typically a feature size of
the technology.
The width of n-chMOSFET
The width of the power source wiring. It depends on
the power consumption.
The width of p-chMOSFET
The performance of the logic circuit depends on the physical parameters of MOSFET and interconnects.
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4.1.1 Summary of I-V characteristics
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Definition of voltage and current in MOSFET
n-ch MOSFET p-ch MOSFET
Gate Gate
Drain Drain
Source Source
Body Body
Current Idsn Current Idsp
Vgsn Vgsp
VdgpVdgn
Vsbn Vsbp
VdspVdsn
Note: A p-ch MOSFET operates with negative voltages and current.
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Measurement circuits of I-V characteristics
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Idsn-Vdsn characteristicIdsn-Vgsn characteristic
Constant
ConstantVariable Variable
VariableVariable
When Vsbn = 0, the variables are Vgsn, Vdsn, and Idsn.
Nore: The values of Vgsn, Vdsn, Idsn are negative for p-ch MOSFET.
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Regions of I-V characteristicsVdsn
Idsn
VgsnVtn0
Idsn
Vdsn
Vgsn
Vdsn = Vgsn –Vtn0 = Vov
Saturation region
Linear region(Triode region)
Sub-threshold
Sub-threshold region
Threshold voltage(閾値電圧)is controlled by the manufacture.
Boundary of the regions
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Approximate expression of I-Vcharacteristics
VdsnIdsn
VgsnVtn0
Idsn
Vdsn
Vgsn
Vdsn = Vgsn –Vtn0 = Vov
Saturation region
Linear region
Sub-threshold region
Quadratic Linear QuadraticConstant
Idsn ≒ 0
Exponential(I ≒ 0)
Saturation region
Linear region
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Threshold voltage
MOS interface
The gate voltage is divided into Vox in SiO2 and s in Si. The channel is generated when the gate voltage exceeds the threshold voltage.
p-type Si
Depletion layer
A depletion layer is generated near MOS interface.
(Animation)
SiO2
Metal (poly-Si)
Si
○ Acceptor ion, h+ Hole, - Free electron
Charge
Free electron (Inversion layer)
Acceptor ion (Depletion layer)
Gate
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4.1.2 Saturation characteristic
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Pinch-off
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p
n
GateDrainSource
Body
nVgsn
＋
n-ch MOSFET
Vdsn = Vgsn – Vtn0 = Pinch-off voltage
Vtn0 is applied between the gate and the drain edge of the channel.
When Vdsn = Vgsn - Vtn0, the channel disappears at the drain edge.
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Saturation of the current
p
n nEl
ectro
n po
tent
ial
Vdsn > Vgsn – Vtn0
SG
D
B
Vgsn > Vtn0
Vdsn < Vgsn – Vtn0Vdsn = Vgsn – Vtn0Vdsn > Vgsn – Vtn0
The resistance of the pinch-off point is higher than the channel.
The flow rate of the water does not depend on the waterfall.
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4.1.3 Mathematical expression of I-V characteristics
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Shape and size of MOSFETpoly-Si (G)
S Dcontact contact
n-activep-well
W
LL: Gate length (ゲート長）W: Gate width （ゲート幅）Leff: Effective channel lengthWeff: Effective channel widthxj: Junction depthtox: Gate oxide thickness （ゲート酸化膜厚）toxf: Field oxide thicknesstm: Poly-Si thickness
contact
substratep-well
n+n+
xj
toxf
Leff
Shallow Trench Isolation
GD
SB
p+
D
STISTI
toxtm
poly
-Si
p-w
ell
subs
trate
Weff
G
STI
STI
p-active
B
Note: p+ and n+ mean the highly-doped semiconductors.
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Parameters of MOSFETPara-meter
Description Typical values in 0.5um technology
Responsibility
L Gate length 0.5um DesignerW Gate width > 3um DesignerLeff Effective gate length Leff < L ManufacturerWeff Effective gate width Weff < W Manufacturerxj Junction depth 0.2um Manufacturertox Thickness of gate oxide 10nm (100Å) Manufacturertoxf Thickness of field oxide 1um Manufacturertm Thickness of gate 0.5um Manufacturer
Note: Strictly speaking, the electrical characteristics of MOSFET depends on Leff, Weff, and tOX. Leff and Weff can be approximated by L and W, respectively.
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Ids-Vds characteristic of MOSFET
Linear region Saturation region
Sub-threshold region (Exponential)
0tngsndsn VVV 0tngsndsn VVV
0tngsn VV
0tngsndsn VVV
Vdsn
I dsn
Linear region(Quadratic)
Saturation region(Constant)
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Ids-Vgs characteristic of MOSFET
Linear region(Linear)
Saturationregion(Quadratic)
Sub-thresholdregion（Exponential）
Vgsn
I dsn
Vtn0
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Mathematical expression of linear region
}21){(
}21){(
20
20
dsndsntngsnn
dsndsntngsnOnn
ndsn
VVVV
VVVVCLWI
Linear region (Gradual Channel Approximation*)
Linear function of Vgsn Quadratic function of Vdsn
* See appendix for more information.
(1)
𝜇 :𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦 𝑚 /𝑉𝑠𝐶 :𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑎 𝑔𝑎𝑡𝑒 𝑜𝑥𝑖𝑑𝑒 𝐹/𝑚2
𝑉 :𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑎𝑡 𝑉 0𝑉
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Boundary of the regions
0tngsndsn VVV
0}){( 0 dsntngsnndsn
dsn VVVdVdI
0tngsndsn VVV
Peak of the curve in linear region
Vdsn
I dsn
0tngsn VV
Linear Saturation
(1)
Boundary of linear region and saturation region (Overdrive voltage)
0tngsndsn VVV
(2)
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Mathematical expression of saturation region
20
2000
)(2
})(21)(){(
tngsnn
tngsntngsntngsnndsn
VV
VVVVVVI
Saturation region (Gradual Channel Approximation)
Quadratic function of Vgsn
Constant for Vdsn
Overdrive voltage
(3)
𝑉 𝑉 𝑉 𝑉
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4.1.4 Improved model of MOSFET
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Channel length modulation0V Vgsn Vdsn
0tndsngsn VVV
Gate
DrainSourcep
n n
ΔL
0tndsngsn VVV Saturation region
Channel length = Leff – ΔL (ΔL is proportional to Vdsn0.5 )
The channel length is decreased with increasing Vdsn and the Idsn is gradually increased with increasing Vdsn.
Channel length modulation parameter
Eq. (3)Vdsn
I dsn
Eq. (3)Eq. (4)
(4)
Leff
𝐼𝛽2 𝑉 𝑉 1 𝜆 𝑉 𝑉
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Body effect 1
MOSFET typically operates under the condition that the body potential VB = GND potential, but the substrate voltage Vbsn isnot equal to zero, when the source potential VS ≠ GND potential.
)2(212 0 bsnfpArO
fpFBtn VNqCVV
Substrate voltageImpurity concentration in channel region
When Vbsn< 0, The threshold voltage Vth0 is increased. (See next slide.)
gsn
dsn
bsn
(5)
VB
VS
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Body effect 2
Vgsn
I dsn
Vbsn < 0
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Short channel MOSFET
1. Short channel effect– A threshold voltages Vtn0 and |Vtp0| are decreased with decreasing a
gate length L.
2. Velocity saturation of carrier– In a long channel MOSFET, a drift velocity of a carrier is
proportional to an electric field. On the other hand, a drift velocity of a carrier is constant in a high electric field of a short channel MOSFET.
– As the result, Ids-Vgs characteristic in a saturation region is not expressed by a quadratic function, but a linear function.
Short channel MOSFET (L < 0.3μm)
A device model incorporated in circuit simulators takes the short channel effects into account.
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4.1.5 Summary of MOSFET model
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Summary of n-ch MOSFET modelRegion Model equation
Linear region
Saturation region
Onn
nn
dsndsntngsnndsn
CLW
VVVVI
}21){( 20
0tngsndsn VVV
20
20
)(2
)1()(2
tngsnn
dsntngsnn
dsn
VV
VVVI
0tngsndsn VVV
Ln and Wn are determined by the circuit designer.CO is controlled by the semiconductor manufacturer.
OXSiOO t
C 120
Capacitance of a gate oxide(F/m2)
n：Electron mobility (m2/Vs）An electron mobility is a material constant.
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Summary of p-ch MOSFET modelRegion Model equation
Linear region
Saturation region
Opp
pp
dspdsptpgsppdsp
CLW
VVVVI
}21){( 20
|||| 0tpgspdsp VVV
20
20
)(2
)1()(2
tpgspp
dsptpgspp
dsp
VV
VVVI
|||| 0tpgspdsp VVV
Note: Vgsp, Vdsp, Idsp < 0
OXSiOO t
C 120
Capacitance of a gate oxide(F/m2)
n：Electron mobility (m2/Vs）An electron mobility is a material constant.
Ln and Wn are determined by the circuit designer.CO is controlled by the semiconductor manufacturer.
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p-ch and n-ch MOSFET
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n-chIds
VgsVtn0
Ids
Vds
Ids: A current flowing from a drain to a source is positive.
Vdsn =Vgsn –Vtn0
Vtp0
p-chVdsp =Vgsp –Vtp0
n-ch
p-ch
The polarity of the voltage and the current of a p-ch MOSFET and a n-ch MOSFET are opposite each other.
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Reference potential of MOSFET
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p-ch MOSFET
n-ch MOSFET
Reference level of p-ch MOSFET
Reference level of n-ch MOSFET
Vgsp < 0
Vgsn > 0
Vdsp < 0
Vdsn > 0
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Type of MOSFET
FBBBFBBOX
BASitn VVC
qNV
222
22 00
n-chIds
Vgs
Vtn0> 0
Vtp0< 0
p-ch
Vtn0< 0
Vtp0> 0
The threshold voltage is controlled by VFB (Flat-band voltage) and NA(Acceptor concentration).
n-chVtn0 > 0 Enhancement modeVtn0 < 0 Depletion mode
p-chVtp0 > 0 Depletion modeVtp0 < 0 Enhancement mode
The enhancement mode MOSFET isused both of logic and analog circuits.
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