Channel length modulation

1. Channel Length
Modulation of MOSFET
By Prof. Hitesh Dholakiya
Engineering Funda
VLSI Lecture series
Engineering Funda
Engineering Funda Android App VLSI YT Playlist

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
Engineering Funda
Engineering Funda Android App VLSI YT Playlist

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.
Engineering Funda
Engineering Funda Android App VLSI YT Playlist

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
Engineering Funda

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)
Engineering Funda

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
Engineering Funda