# MOSFET I-V characteristics: general mosfet i-v and c-v.pdf¢ MOSFET capacitance-voltage...

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The channel current is: I = V (q nS μ W) /L = V q μ W (ci/q) × (VGS – VT) /L

MOSFET I-V characteristics: general consideration

The current through the channel is VI

R =

where V is the DRAIN – SOURCE voltage

Here, we are assuming that V

2

Key factors affecting FET performance (for any FET type):

In most MOSFET applications, an input signal is the gate voltage VG and the output is the drain current Id. The ability of MOSFET to amplify the signal is given by the output/input ratio: the transconductance, gm = dI/dVGS.

MOSFET transconductance

L I and gm

High carrier mobility μ and short gate length L are the key features of FETs

I = μ W ci × (VGS – VT) V /L

gm = V μ W ci /L

(V is the Drain – Source voltage)

From this:

μ I and gm

3

Modern submicron gate FET

V-groove quantum wire transistor

Source Drain

Gate

Operating frequency – up to 300 GHz

2 μm

4

When no drain voltage V is applied, the entire channel has the same potential as the Source, i.e. VCH = 0. In this case, as we have seen, nS = (ci/q) × (VGS – VT)

Drain current saturation in MOSFET

- + G

Semiconductor

The gate length L

DS

+ -

V

VGS

where VGS is the gate – source voltage and VT is the threshold voltage

When the drain voltage V is applied, the channel potential changes from VCH = 0 on the Source side to VCH= V on the drain side. In this case, the induced concentration in the channel also depends on the position.

5

Drain current saturation in MOSFET

- + G

Semiconductor

The gate length L

DS

+ -

V

VGS

With the drain voltage V is applied, the actual induced concentration in any point x of the channel depends on the potential difference between the gate and the channel potential V(x) at this point. This is because this local potential difference defines the voltage that charges the elementary gate – channel capacitor. On the source end of the channel (x=0, VCH=0): nS(0) = (ci/q) × (VGS – VT). On the drain end of the channel (x=L, VCH= V): nS(L) = (ci/q) × (VGS – VT - V) < nS(0) At any point between source and drain,

nS(L) < nS(x) = (ci/q) × [VGS – VT – V(x)] < nS(0)

6

L

nS

V=0

VGS > VT

x

Drain current saturation in MOSFET

V1 > 0

V2 > V1

V3 = VGS-VT

G

Semiconductor

DS

VVGS

Id

V

7

MOSFET Modeling

1. Constant mobility model

Assuming a constant electron mobility, μn, using the simple charge control model the absolute value of the electron velocity is given by,

vn = μnF = μn dV dx

With the gate voltage above the threshold, the drain current, Id, is given by

Id = Wqμn dV dx

ns Where W is the device width

Rewriting, Where VGT = VGS – VT.

d

n i GT

I dV dx

W c V V( )μ =

−

dV vs dx dependence represents a series connection of the elementary parts of MOSFET channel (for the series connection, voltages add up whereas current is the same).

8

Integrating along the channel, from x=0 (V=0) to x=L (V=VDS), we obtain:

Id = W μn ci

L VGT VDS

Id = Wμnci

L VGT −

VDS 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟ VDS

For, VDS

9

Channel pinch off and current saturation Pinch off occurs when VG – VCH = VT at the drain end;

nS (L) =0; the current Id saturates

When,

VDS = VSAT = VGS − VT

where VSAT is the saturation voltage.

The saturation (pinch off) current,

Id = Isat = Wμnci

2L VGT

2

Id = Wμnci

L VGT −

VDS 2

⎛ ⎝ ⎜

⎞ ⎠ ⎟ VDS

From the Id – V dependence, at VDS=VSAT = VGT,

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Transconductance

Defined as

gm = dId

dVGS VDS From the equations for the drain current, Id, derived above, we find that

gm = βVDS , for VDS VSAT

⎧ ⎨ ⎩ β = μnci

W Lwhere

High transconductance is obtained with high values of the low field electron mobility, thin gate insulator layers (i.e., larger gate insulator capacitance ci = εi/di), and large W/L ratios.

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2. Velocity saturation model

In semiconductors, electric field F accelerates electrons, i.e. the drift velocity of electron increases: v=μF

However, at high electric fields this velocity saturates

In modern short channel devices with channel length of the order of 1 µm or less, the electric field in the channel can easily exceed the characteristic electric, Fs field of the velocity saturation

Fs = vs μ n

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Electric field in the channel

the electric field in the channel in the direction parallel to the semiconductor- insulator interface

F = Id

qμ nns V( )W

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

P ot

en tia

l ( V

)

Distance (µm)

1

1.2

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5

E le

ct ric

F ie

ld (k

V /c

m )

Distance (µm)

1

1.2

0 1 2 3 4 5S ur

fa ce

C on

ce nt

ra tio

n (1

01 2

1/ cm

2 )

Distance (µm)

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Potential, electric field, and surface electron concentration in the channel of a Si MOSFET for VDS = 1 and 1.2 V. L = 5 µm, di = 200 Å, µn = 800 cm2/Vs, VGS = 2 V, VT = 1 V.

vn = μnF = μn dV dx

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Once the electric field at the drain side of the channel (where the electric field is the highest) exceeds Fs, the electron velocity saturates, leading to the current saturation. In short-channel MOSFETs, this occurs at the drain bias smaller than the pinch-off voltage VDS = VGT.

Field at drain

Saturation condition, Fs = ISAT

μ nci VGT − VSAT( )W

d

n i GT

I dV dx

W c V V( )μ =

−

d x L

n i GT DS

IdVF L dx W c V V

( ) ( )μ=

= = −

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Saturation current versus gate-to-source voltage for 0.5 µm gate and 5 µm gate MOSFETs. Dashed lines: constant mobility model, solid lines: velocity saturation model.

15

MOSFET saturation current accounting for velocity saturation:

Isat = gchVGT

1 + 1 + VGT VL

⎛

⎝ ⎜

⎞

⎠ ⎟

2

where VL = FsL and the channel conductance gch = q µn ns W / L, where ns=ci VGT/q

When FS L >> VGT (MOSFET with long gate or no velocity saturation):

Isat = gchVGT

1 + 1 + VGT VL

⎛

⎝ ⎜

⎞

⎠ ⎟

2 2 ch

sat GT g

I V≈ Id = Isat = Wμnci

2L VGT

2

(Expression obtained before on slide 9)

When FS L

16

Source and drain series resistances. Source and drain parasitic series resistances, Rs and Rd, play an important role, especially in short channel devices where the channel resistance is smaller.

Gate

DrainSource

I R s I Rd+ V +DS

R s R

d

ddV =ds

VGS = Vgs − Id Rs

VDS = Vds − Id Rs + Rd( )

17

The measured transconductance (extrinsic)

gm = dId dVgs Vds =const

The intrinsic transconductance (VGS and VDS being intrinsic voltages)

gmo = dId

dVGS VDS=const

Where gd0 is the drain conductance gdo = dId

dVDS VGS =const

These parameters are related as gm = gmo

1 + gmo Rs + gdo R s + Rd( )

Similarly, extrinsic drain conductance can be written as,

gd = gdo

1 + gmo Rs + gdo Rs + Rd( )

In the current saturation region (VDS > VSAT), gd0 ≈ 0

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The saturation current in MOSFET with parasitic resistances:

Isat = gchoVgt

1 + gchoRs + 1 + 2gchoRs + Vgt / VL( )2

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2 2.5

D ra

in C

ur re

nt (m

A )

Drain-to-Source Voltage (V)

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2 2.5

D ra

in C

ur re

nt (m

A )

Drain-to-Source Voltage (V)

MOSFET output characteristics calculated for zero parasitic resistances and parasitic resistances of 5 Ω. Gate length is 1 µm

where VL = FsL and gcho = ciVgtµnW/L.

19

MOSFET capacitance-voltage characteristics

To simulate MOSFETs in electronic circuits, we need to have models for both the current-voltage and the capacitance-voltage characteristics. As MOSFETs is a three terminal device, we need three ca

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