This document discusses channel length modulation in MOSFETs. It explains that in saturation, the channel length decreases with increasing drain voltage due to the depletion region extending farther into the channel. This effectively reduces the channel length and increases the drain current. The document derives an expression for drain current that includes a channel length modulation coefficient to model this effect, showing that current increases with higher drain voltages due to the reduced channel length.

1. Channel Length
Modulation of MOSFET
By Prof. Hitesh Dholakiya
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VLSI Lecture series
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2. Outlines
❖ Basics of Channel Length Modulation
❖ Channel length Modulation in MOSFET
❖ Derivation of drain current for channel length modulation
❖ Characteristics of MOSFET with channel length modulation
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3. Basics of Channel length Modulation
❖ In saturation region of working with MOSFET, there is channel length
Modulation with MOSFET.
❖ In that channel length will change with respect to drain voltage of
MOSFET.
❖ Channel length will decrease with respect to increase in drain
voltage in saturation region.
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4. Channel Length Modulation in MOSFET
𝑽𝑮𝑺 > 𝑽𝑻𝟎
Depletion Region
Inversion Layer (Channel)
𝑽𝑫 small
𝑽𝑫 = 𝑽𝑫𝑺𝑨𝑻
Pinch Off Point
𝑽𝑫 > 𝑽𝑫𝑺𝑨𝑻
Pinch Off Point
L
L’ ∆L
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5. ❖ Total charge density in channel is given by
𝑸𝑰(𝒀) = −𝑪𝑶𝑿 𝑽𝑮𝑺 − 𝑽𝑪 𝒀 − 𝑽𝑻𝑶
❖ Inversion layer charge at source (Y=0) end is given by
𝑸𝑰(𝒀 = 𝟎) = −𝑪𝑶𝑿 𝑽𝑮𝑺 − 𝑽𝑻𝑶
❖ Inversion layer charge at Drain end (Y=L) end is given by
𝑸𝑰(𝒀 = 𝑳) = −𝑪𝑶𝑿 𝑽𝑮𝑺 − 𝑽𝑫𝑺 − 𝑽𝑻𝑶
❖ At the edge of saturation 𝑽𝑫𝑺 = 𝑽𝑫𝑺𝑨𝑻
𝑽𝑫𝑺 = 𝑽𝑫𝑺𝑨𝑻 = 𝑽𝑮𝑺 − 𝑽𝑻𝑶
❖ Inversion layer charge at Drain end (Y=L) in saturation
region is given by
𝑸𝑰(𝒀 = 𝑳) ≈ 𝟎
❖ Effective channel length in saturation region will become
𝑳′ = 𝑳 − ∆𝑳
❖ At pinch off point of channel, channel voltage will be 𝑽𝑫𝑺𝑨𝑻
❖ Gradual channel approximation is only valid in channel,
as per that drain current in deep saturation is given by
∴ 𝑰𝑫(𝒔𝒂𝒕) =
𝝁𝒏. 𝑪𝑶𝑿
𝟐
.
𝑾
𝑳′
. (𝑽𝑮𝑺 − 𝑽𝑻𝑶)𝟐
∴ 𝑰𝑫(𝒔𝒂𝒕) =
𝝁𝒏. 𝑪𝑶𝑿
𝟐
.
𝑾
(𝑳 − ∆𝑳)
. (𝑽𝑮𝑺 − 𝑽𝑻𝑶)𝟐
∴ 𝑰𝑫(𝒔𝒂𝒕) =
𝟏
𝟏 −
∆𝑳
𝑳
𝝁𝒏. 𝑪𝑶𝑿
𝟐
.
𝑾
𝑳
. (𝑽𝑮𝑺 − 𝑽𝑻𝑶)𝟐
❖ Here,
∆𝑳 ∝ 𝑽𝑫𝑺 − 𝑽𝑫𝑺𝑨𝑻
❖ To simplify this drain current equation, we will take λ
(Channel length modulation coefficient)
∴ 𝟏 −
∆𝑳
𝑳
= 𝟏 − 𝝀𝑽𝑫𝑺 ⇒
𝟏
𝟏 −
∆𝑳
𝑳
= 𝟏 + 𝝀𝑽𝑫𝑺
❖ So drain current is given by
∴ 𝑰𝑫 𝒔𝒂𝒕 =
𝝁𝒏. 𝑪𝑶𝑿
𝟐
.
𝑾
𝑳
. 𝑽𝑮𝑺 − 𝑽𝑻𝑶
𝟐. (𝟏 + 𝝀𝑽𝑫𝑺)
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6. ❖ Drain current is given by
∴ 𝑰𝑫 𝒔𝒂𝒕 =
𝝁𝒏. 𝑪𝑶𝑿
𝟐
.
𝑾
𝑳
. 𝑽𝑮𝑺 − 𝑽𝑻𝑶
𝟐. (𝟏 + 𝝀𝑽𝑫𝑺)
Drain Current
Drain Voltage
𝑽𝑮𝑺𝟏 with λ=0
𝑽𝑮𝑺𝟐 with λ=0
with λ ≠ 0
with λ ≠ 0
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