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N Channel MOSFET level 1 mosn1

NDrain

NSource

NGate

NBulk

NDrain

NSource

NGate

NBulk

NDrain

NSource

NGate

NBulk

NDrain

NSource

NGate

NBulk

(a) (b) (c) (d)

Figure 1: N Channel MOSFET Level 1 model

Form:

mosn1:instance name n1 n2 n3 n4 parameter listinstance name is the model name,

n1 is the drain node,n2 is the gate node,n3 is the source node,n4 is the bulk node.

Parameters:

Parameter Type Default value Required?vt0: Zero bias threshold voltage (V) DOUBLE 0 no

kp: Transconductance parameter (A/V2) DOUBLE 2 105 nogamma: Bulk threshold parameter (V0.5) DOUBLE 0 nophi: Surface inversion potential (V) DOUBLE 0.6 nolambda: Channel-length modulation (1/V) DOUBLE 0 nopb: Bulk junction potential (V) DOUBLE 0.8 no

tox: Oxide thickness (m) DOUBLE 1 107 nold: Lateral diffusion length (m) DOUBLE 0 nou0: Surface mobility (cm2/V-s) DOUBLE 600 nofc: Forward bias junction fit parameter DOUBLE 0.5 nonsub: Substrate doping (cm3) DOUBLE 1 1015 notpg: Gate material type DOUBLE 1 nonss: Surface state density (cm2) DOUBLE 0 notnom: Nominal temperature (C) DOUBLE 27 not: Device temperature (C) DOUBLE 27 nol: Device length (m) DOUBLE 2 106 now: Device width (m) DOUBLE 50 106 noalpha: Impact ionization current coefficient DOUBLE 0 no

Example:

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mosn1:m1 2 3 0 0 l=1.2u w=20u

Description:

FreeDa has the NMOS level 1 model based on the MOS level 1, Schichman-Hodges model inSPICE. The model uses the charge conservative Yang-Chatterjee model for modeling chargeand capacitance.

The physical constants used in the model evaluation are

k Boltzmanns constant 1.38062261023 J/Kq electronic charge 1.60219181019 C0 free space permittivity 8.854214871 10

12 F/mSi permittivity of silicon 11.70OX permittivity of silicon dioxide 3.90ni intrinsic concentration of silicon @ 300 K 1.451016 m3

Standard Calculations

Absolute temperatures (in kelvins, K) are used. The thermal voltage

VT H(TNO M) =kTNO M

q. (1)

The silicon bandgap energy

EG(TN OM) = 1.16 0.000702 4T2

NO M

TNO M + 1108. (2)

The difference of the gate and bulk contact potentials

MS = GATE BULK. (3)

The gate contact potential

GATE =

3.2 TP G = 03.25 NMOS & TP G = 13.25 + EG NMOS & TP G = 1

. (4)

The contact potential of the bulk material

BULK = 3.25 + EG for NMOS (5)

The capacitance per unit area of the oxide is

COX =OXTOX

. (6)

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The effective length LEF F of the channel is reduced by the amount LD of the lateral diffusionat the source and drain regions:

LEF F = L

2LD (7)

Similarly the effective length WEF F of the channel is reduced by the amount WD of thelateral diffusion at the edges of the channel.

WEF F = W 2WD (8)

Process Oriented Model

If omitted, device parameters are computed from process parameters using defaults if nec-essary provided that both TOX and NSUB are specified. If either TOX or NSUB is not specifiedthen the critical device parameters must be specified.

If KP is not specified in the model statement then

KP = 0/COX (9)

If PHI is not specified, then it is evaluated as

PHI = 2B = 2VT H(TNO M) lnNSUB

ni(10)

If GAMMA is not specified in the model statement then

GAMMA = =

2SiqNSUB

COX(11)

If VTO is not specified in the model statement then it is evaluated as

VTO = VF B +

2B + 2B (12)

where VF B is

VF B = MS q NSSCOX

(13)

Temperature Dependence

Temperature effects are incorporated as follows where T and TNOM are absolute temperaturesin Kelvins (K).

VT H =kT

q(14)

KP(T) = KP(TNO M/T)3/2 (15)

(T) = 0(TNO M/T)3/2 (16)

2B(T) = 2BT

TNO M 3VT H ln T

TNO M+ EG(TNO M EG(T) (17)

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DC Current Calculations

The Schichman-Hodges model computes the current of the MOS device in only three regions,cutoff, linear and saturation. The regions are defined as:

cutoff region: VGS < VTlinear region: VGS > VT and VDS < VGS VTsaturation region: VGS > VT and VDS > VGS VT

where the threshold voltage is

VT =

VF B + 2B +

2B VBS VBS 2B

VF B + 2B VBS < 2B(18)

Then

ID =

0 cutoff region

WEF FLEF F

KP2 (1 + VDS)VDS [2(VGS VT) VDS] linear region

WEF FLEF F

KP2 (1 + VDS) [VGS VT]

2saturation region

(19)

Yang-Chatterjee ChargeModel

Once the DC channel current has been calculated, the charge at each terminal of the MOSdevice is computed. The charge values are used to compute the AC current flow through

each terminal according to the Yang-Chatterjee model. This model ensures continuity ofthe charges and capacitances throughout different regions of operation. The intermediatequantities are:

VF B = Vto

2B 2B (20)and

Co = COX Weff Leff (21)

The charge is computed for for each of the four regions of operation, accumulation, cut-off,saturation and linear.

Accumulation region VGS VF B + VBS

Qd = 0 (22)Qs = 0 (23)

Qb = Co (VGS VF B VBS) (24)4

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Cut-off region VF B + VBS < VGS VthQd = 0 (25)

Qs = 0 (26)

Qb = Co GAMMA2

2{1 +

1 +

4 (VGS VF B VBS)GAMMA2

} (27)

Saturation region Vth < VGS VDS + VthQd = 0 (28)

Qs = 23

Co (VGS Vth) (29)Qb = Co (VF B PHI Vth) (30)

Linear region VGS > VDS + Vth

Qd = Co [ V2

DS

8 (VGS Vth VDS2 )+ VGS Vth

2 3

4VDS] (31)

Qs = Co [ V2

DS

24 (VGS Vth VDS2 )+

VGS Vth2

+1

4VDS] (32)

Qb = Co (VF B PHI Vth) (33)

The final currents at the transistor nodes are given by

Id = ID +dQd

dt(34)

Ig =dQg

dt(35)

Is = ID + dQsdt

(36)

Notes:

This is the M element in the SPICE compatible netlist. The unmodified Yang-Chatterjeecharge model has a charge partition scheme in the saturation region that sets the draincharge to zero. This results in a loss of the high-frequency current roll-off at the drain nodein saturation.

Credits:Name Affiliation Date LinksAaron Walker NC State University August 2002 www.ncsu.edunmkripla@unity.ncsu.edu www.ncsu.edu

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