[Type text] [Type text] Dr. D. V. Kamath

MOS Basics

Characteristics BJT MOS

Current conduction

Bipolar

Unipolar

Noise MOSFETs are less noisy than BJTs. Hence, MOSFETs are more

suitable for signal processing applications

Source Type

Current Controlled Current Source

(CCCS)

Voltage Controlled Current

Source (VCCS)

Input Impedance

Low

High

Characteristic

parameter

β (ℎ𝐹𝐸)

𝑔𝑚

Current

𝐼𝑐 = 𝐼𝑠 𝑒𝑉𝐵𝐸 𝑉𝑇⁄

𝐼𝑑𝑠 =µ𝑛𝐶𝑜𝑥

2

𝑊

𝐿(𝑉𝑔𝑠 − 𝑉𝑡ℎ)

2

Transconductance

𝑔𝑚 = 𝐼𝑐 𝜂𝑉𝑇⁄

𝑔𝑚 = √2𝛽𝐼𝑑𝑠

Current driving

capability

High Low

Package density Low High

Bandwidth

MOSFETS have higher bandwidth compared to BJTs. It is relatively easy to control device geometries and scaling in MOS

devices when compared with BJT circuits.

***

[Type text] [Type text] Dr. D. V. Kamath

NMOS Device

LD (lateral diffusion) - Level 2 SPICE model parameter

DL (delta length) - BSIM model parameter ***

MOS parameters

Parameter Description Equation Unit

µ𝑛 Surface mobility of carrier - cm2 Vsec⁄

𝑊 𝐿⁄ Channel aspect ratio - -

𝐶𝑔 Gate-to-channel capacitance 𝐶𝑔 =

ɛ𝑖𝑛𝑠ɛ𝑜𝑊𝐿

𝐷

pF

𝐶𝑜𝑥 Gate capacitance per unit area 𝐶𝑜𝑥 =𝐶𝑔

𝑊𝐿=

ɛ𝑖𝑛𝑠ɛ𝑜

𝐷

𝑝𝐹 µ𝑚2⁄

𝐾𝑛 Process transconductance

parameter

𝐾𝑛 = µ𝑛𝐶𝑜𝑥

= µ𝑛

ɛ𝑖𝑛𝑠ɛ𝑜

𝐷

𝐴 𝑉2⁄

β Beta 𝛽𝑛 = 𝐾𝑛

𝑊

𝐿

𝐴 𝑉2⁄

𝛥𝑉 Overdrive potential 𝛥𝑉 = 𝑉𝑔𝑠 − 𝑉𝑡h

V

[Type text] [Type text] Dr. D. V. Kamath

Enhancement-type nMOS transistor in non-conducting condition

***

Enhancement-type nMOS transistor with 𝑽𝑮𝑺 > 𝑽𝑻𝑯 and 𝑽𝑫𝑺 = 0

***

Enhancement-type nMOS transistor with 𝑽𝑮𝑺 > 𝑽𝑻𝑯 and a small 𝑽𝑫𝑺

***

[Type text] [Type text] Dr. D. V. Kamath

Increasing VDS

causes the channel to acquire a tapered shape

***

MOS drain characteristics

Drain characteristics of depletion type NMOS

[Type text] [Type text] Dr. D. V. Kamath

Drain characteristics of enhancement type NMOS ***

Ids versus Vds relationship

Charge induced below the thinox layer between drain and source is dependent on Vgs

Drain current Ids is

thus

dependent on both Vds and Vgs

[Type text] [Type text] Dr. D. V. Kamath

Electron transit time computation

Ids versus Vds relationship for MOS in non-saturation region

Voltage along the channel varies linearly with distance X from the source due to the IR

drop in the channel, the average value is Vds/2

Effective gate voltage is Vgs -

Vth

[Type text] [Type text] Dr. D. V. Kamath

Alternate expressions of Ids for MOS in non-saturation region

[Type text] [Type text] Dr. D. V. Kamath

Ids expression for MOS in saturation region

Substituting limiting condition Vds = Vgs –Vth

in (1), we get Ids expression for saturation region

Drain current equations for NMOS

Region of operation Equation Condition

Cut-off

𝐼𝑑𝑠𝑛 = 0

𝑉𝑔𝑠𝑛 < 𝑉𝑡ℎ𝑛

Ohmic

𝐼𝑑𝑠𝑛 =𝛽𝑛

2𝑉𝑑𝑠{2(𝑉𝑔𝑠𝑛 − 𝑉𝑡ℎ𝑛) − 𝑉𝑑𝑠𝑛}

𝑉𝑔𝑠𝑛 > 𝑉𝑡ℎ𝑛

𝑉𝑑𝑠𝑛 < 𝑉𝑔𝑠𝑛 − 𝑉𝑡ℎ𝑛

Saturation

𝐼𝑑𝑠𝑛 =𝛽𝑛

2(𝑉𝑔𝑠𝑛 − 𝑉𝑡ℎ𝑛)

2

𝑉𝑔𝑠𝑛 > 𝑉𝑡ℎ𝑛

𝑉𝑑𝑠𝑛 ≥ 𝑉𝑔𝑠𝑛 − 𝑉𝑡ℎ𝑛

Drain current equations for PMOS

Region of

operation

Equation Condition

Cut-off

𝐼𝑑𝑠𝑝 = 0

𝑉𝑠𝑔𝑝 < |𝑉𝑡ℎ𝑝| or

|𝑉𝑔𝑠𝑝| < |𝑉𝑡ℎ𝑝|

Ohmic 𝐼𝑠𝑑𝑝 =

𝛽𝑝

2𝑉𝑠𝑑{2(𝑉𝑠𝑔𝑝 − |𝑉𝑡ℎ𝑝|) − 𝑉𝑠𝑑𝑝}

or

−𝐼𝑑𝑠𝑝 = 𝐼𝑠𝑑𝑝 =𝛽𝑝

2𝑉𝑑𝑠𝑝{2(𝑉𝑔𝑠𝑝 − 𝑉𝑡ℎ𝑝)

− 𝑉𝑑𝑠𝑝}

|𝑉𝑔𝑠𝑝| > |𝑉𝑡ℎ𝑝|

|𝑉𝑑𝑠𝑝| < |𝑉𝑔𝑠𝑝| − |𝑉𝑡ℎ𝑝|

[Type text] [Type text] Dr. D. V. Kamath

Saturation 𝐼𝑠𝑑𝑝 =

𝛽𝑝

2(𝑉𝑠𝑔𝑝 − |𝑉𝑡ℎ𝑝|)

2

or

−𝐼𝑑𝑠𝑝 = 𝐼𝑠𝑑𝑝 =𝛽𝑝

2(𝑉𝑔𝑠𝑝 − 𝑉𝑡ℎ𝑝)

2

|𝑉𝑔𝑠𝑝| > |𝑉𝑡ℎ𝑝|

|𝑉𝑑𝑠𝑝| > |𝑉𝑔𝑠𝑝| − |𝑉𝑡ℎ𝑝|

***

Deep Ohmic region

Region of

operation

Description Equation

Deep ohmic

𝐼𝑑𝑠 = 𝛽(𝑉𝑔𝑠 − 𝑉𝑡ℎ)𝑉𝑑𝑠

𝑅𝑜𝑛 =1

𝛽(𝑉𝑔𝑠−𝑉𝑡ℎ)

𝑉𝑔𝑠 > 𝑉𝑡ℎ

𝑉𝐷𝑆 ≪ 2(𝑉𝐺𝑆 − 𝑉𝑇𝐻)

***

MOS transconductance

𝑔𝑚 =𝜕𝐼𝐷

𝜕𝑉𝐺𝑆|𝑉𝑑𝑠,𝑐𝑜𝑛𝑠𝑡

𝐼𝑑𝑠 =𝛽

2(𝑉𝑔𝑠 − 𝑉𝑡ℎ)

2 𝑓𝑜𝑟 𝑀𝑂𝑆 𝑖𝑛 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛

𝑔𝑚 = 𝛽(𝑉𝑔𝑠 − 𝑉𝑡ℎ)

𝑔𝑚 = √2𝛽𝐼𝑑𝑠

***

[Type text] [Type text] Dr. D. V. Kamath

Basic MOS small-signal model (at low frequencies)

𝑖𝑑 = 𝑔𝑚𝑣𝑔𝑠

MOS device is basically characterized by transconductance 𝑔𝑚

MOS device is modeled by VCCS

MOS output conductance 𝒈𝒅𝒔

The output conductance 𝑔𝑑𝑠 is expressed as

gds =δIds

δVds= λ𝐼𝑑𝑠

λ α 1

L and Ids α

1

L

gds α 1

L2

The output conductance 𝑔𝑑𝑠 is strongly dependent on the channel length

MOS transistor figure of merit 𝝎𝑶

The parameter 𝜔𝑂 is used as a measure of frequency response or switching speed ωO = 1 τsd⁄

ωO =gm

Cg=

µnCoxWL

(Vgs − Vth)

CoxWL=

µn(Vgs − Vth)

L2=

1

τsd

A fast switching speed requires that 𝑔𝑚 be as high as possible

The switching speed depends on effective gate voltage and on carrier mobility and inversely as

the square of channel length

***

vm

v

G D

ids

v g

- -

gs

+

S

+

dsgs