# Lecture 3: Nonideal Transistor Theory. CMOS VLSI DesignCMOS VLSI Design 4th Ed. 4: Nonideal Transistor Theory2 Outline  Nonideal Transistor Behavior

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### Text of Lecture 3: Nonideal Transistor Theory. CMOS VLSI DesignCMOS VLSI Design 4th Ed. 4: Nonideal...

PowerPoint PresentationLecture 3:
Outline
Ideal Transistor I-V
Ideal vs. Simulated nMOS I-V Plot
65 nm IBM process, VDD = 1.0 V
4: Nonideal Transistor Theory
ON and OFF Current
Saturation
Cutoff
Electric Fields Effects
Attracts carriers into channel
Long channel: Qchannel Evert
Long channel: v = mElat
4: Nonideal Transistor Theory
Coffee Cart Analogy
Vds is how long you have been up
Your velocity = fatigue × mobility
Vgs is a wind blowing you against the glass (SiO2) wall
At high Vgs, you are buffeted against the wall
At high Vds, you scatter off freshmen, fall down, get up
Velocity saturation
4: Nonideal Transistor Theory
Collisions with oxide interface
4: Nonideal Transistor Theory
Velocity Saturation
Velocity reaches vsat
Electrons: 107 cm/s
Better model
Example 1
Calculate the effective carrier mobilities of nMOS and pMOS transistors when fully ON. Assume Vgs = 1 V, Vt = 0.3 V and tox = 1.05 nm
4: Nonideal Transistor Theory
Example 2
Find the critical voltage for nMOS and pMOS transistors that are fully ON, using the values obtained in example 1 and L = 50nm.
(Hint Vc = EcL)
4: Nonideal Transistor Theory
Vel Sat I-V Effects
Velocity-saturated ON current increases with VDD
Real transistors are partially velocity saturated
Approximate with a-power law model
Ids VDDa
4: Nonideal Transistor Theory
a-Power Model
Channel Length Modulation
Region between n and p with no carriers
Width of depletion Ld region grows with reverse bias
Leff = L – Ld
Ids increases with Vds
Chan Length Mod I-V
not feature size
4: Nonideal Transistor Theory
Threshold Voltage Effects
Vt is Vgs for which the channel starts to invert
Ideal models assumed Vt is constant
Really depends (weakly) on almost everything else:
Body voltage: Body Effect
4: Nonideal Transistor Theory
Body Effect
Vsb affects the charge required to invert the channel
Increasing Vs or decreasing Vb increases Vt
fs = surface potential at threshold
Depends on doping level NA
And intrinsic carrier concentration ni
g = body effect coefficient
4: Nonideal Transistor Theory
Body Effect Cont.
4: Nonideal Transistor Theory
DIBL
Electric field from drain affects channel
More pronounced in small transistors where the drain is closer to the channel
Drain-Induced Barrier Lowering
High drain voltage causes current to increase.
4: Nonideal Transistor Theory
Short Channel Effect
In small transistors, source/drain depletion regions extend into the channel
Impacts the amount of charge required to invert the channel
And thus makes Vt a function of channel length
Short channel effect: Vt increases with L
Some processes exhibit a reverse short channel effect in which Vt decreases with L
4: Nonideal Transistor Theory
Leakage
Simulated results
What differs?
4: Nonideal Transistor Theory
Leakage Sources
Subthreshold conduction
Dominant source in contemporary transistors
Gate leakage
Junction leakage
4: Nonideal Transistor Theory
Subthreshold Leakage
n is process dependent
S ≈ 100 mV/decade @ room temperature
4: Nonideal Transistor Theory
Gate Leakage
Exponentially sensitive to tox and VDD
A and B are tech constants
Greater for electrons
Negligible for older processes (tox > 20 Å)
Critically important at 65 nm and below (tox ≈ 10.5 Å)
From [Song01]
Junction Leakage
Ordinary diode leakage
Band-to-band tunneling (BTBT)
Diode Leakage
At any significant negative diode voltage, ID = -Is
Is depends on doping levels
And area and perimeter of diffusion regions
Typically < 1 fA/mm2 (negligible)
4: Nonideal Transistor Theory
Band-to-Band Tunneling
Especially sidewall between drain & channel
when halo doping is used to increase Vt
Increases junction leakage to significant levels
Xj: sidewall junction depth
Gate-Induced Drain Leakage
Occurs at overlap between gate and drain
Most pronounced when drain is at VDD, gate is at a negative voltage
Thwarts efforts to reduce subthreshold leakage using a negative gate voltage
4: Nonideal Transistor Theory
Temperature Sensitivity
Increasing temperature
Reduces mobility
Reduces Vt
So What?
They still behave like switches.
But these effects matter for…
Supply voltage choice
Parameter Variation
Process: Leff, Vt, tox of nMOS and pMOS
Vary around typical (T) values
Fast (F)
Leff: short
Vt: low
tox: thin
for nMOS and pMOS
4: Nonideal Transistor Theory
Environmental Variation
Fast:
Process Corners
Process corners describe worst case variations
If a design works in all corners, it will probably work for any variation.
Describe corner with four letters (T, F, S)
nMOS speed
pMOS speed
Important Corners
Purpose
nMOS
pMOS
VDD
Temp
Example 3
Consider an nMOS transistor manufactured in 65nm process, with nominal threshold voltage equal to 0.3 V and doping levels of 8x10^17 cm^(-3). The substrate is connected to ground with a contact. What will be the change in the treshold voltage at room temperature if the sourse is at 0.6V instead of 0V?
(Assume tox = 1.05 nm, q=1.6x10^(-19) Cb, vT = kT/q = 26mV, ni = 1.45x10^10 cm^(-3), εox = 3.9x8.85x10^(-14) F/cm, εSi = 11.7x8.85x10^(-14) F/cm)
4: Nonideal Transistor Theory
Example 4
An nMOS transistor has a threshold voltage of 0.4V and Vdd = 1.2V. A designer considers reducing the threshold voltage by 100 mV in order to increase transistor speed
(i) By how much would the saturation current increase (for Vgs=Vds=Vdd) if the transistors were ideal?
(ii) By how much would the subthreshold leakage current increase in room temperature for Vgs=0; Assume n=1.4
(iii) By how much would the subthreshold leakage current increase at 120°C?
Assume that Vt is constant.
k=1.380 6504(24)×10−23 J/K
4: Nonideal Transistor Theory
Example 5
Find the subthreshold leakage current of an inverter at room temperature if the input A=0. Let βn=2βp = 1mA/V^2., n=1.4, and ABS(Vt)=0.4V. Assume the body effect and DIBL coefficients are zero.
4: Nonideal Transistor Theory
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