N Channel MOSFET level 3

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N Channel MOSFET level 3 mosn3 NSource NBulk NSource NBulk NSource NBulk NSource (a) (b) (c) (d) NBulk Figure 1: MOSFET Types Form: mosn3: instance name n 1 n n 3 n n 1 is the drain node, n is the gate node, n 3 is the source node, n is the bulk node. Parameters: parameter list Parameter Type Default value Required? gamma: Bulk threshold parameter (V 0.5 ) DOUBLE 0 no kp: Transconductance parameter (A/V ) DOUBLE 0.00001 no l: Device length (m) DOUBLE 0.00000 no w: Device width (m) DOUBLE 0.00005 no ld: Lateral diffusion length (m) DOUBLE 0 no wd: Lateral diffusion width (m) DOUBLE 0 no nsub:substrate doping (cm 3 ) DOUBLE 0 no phi: Surface inversion potential (V) DOUBLE 0.6 no tox: Oxide thickness (m) DOUBLE 1 10 7 no u0: Surface mobility (cm /V-s) DOUBLE 600 no vt0: Zero bias threshold voltage (V) DOUBLE 0 no kappa: Saturation field factor (m) DOUBLE 0. no t: Device temperature (degrees) DOUBLE 300.15 no tnom: Nominal temperature (degrees) DOUBLE 300.15 no nfs: Fast surface state density (cm ) DOUBLE 0 no eta: Static feedback on threshold voltage DOUBLE 0 no theta: Mobility modulation (1/V) DOUBLE 0 no tpg: Gate material type DOUBLE 0 no nss: Surface state density (cm ) DOUBLE 0 no vmax: Maximum carrier drift velocity (m/sec) DOUBLE 0 no xj: Metallurgical junction depth DOUBLE 0 no delta: Width effect on threshold voltage DOUBLE 0 no Example: mosn3:m1 3 0 0 l=1.u w=0u Description: f REEDA TM has the NMOS level 3 model based on the MOS level 3 model in SPICE. It uses the charge conservative Yang-Chatterjee model for modeling charge and capacitance. 1

DC Calculations: Constants used are: All parameters used are indicated in this font. Effective channel length and width: q = 1.601918 10 19 (As) (1) k = 1.38066 10 3 (J/K) () ɛ 0 = 8.85187 10 1 (F/m) (3) ɛ s = 11.7 ɛ 0 () E g = 1.16 7.0 10 T (V ) T + 1108 (5) C ox = ɛ 0 3.9 (F ) TOX (6) L eff = L LD (7) W eff = W WD (8) Depletion layer width coefficient Built in voltage: Square root of substrate voltage: ɛs X d = q NSUB 10 6 (9) V bi = VT0 GAMMA PHI (10) V BS 0 = SqV BS = PHI V BS PHI V BS > 0 = SqV BS = 1 + PHI 0.5 V BS(1 + PHI 0.75 V BS) Short-channel effect correction factor: In a short channel device, device threshold voltage tends to lower since part of the depletion charge in the bulk terminates the electric fields at the source and drain. The value of this correction factor is determined by the metallurgical depth XJ. (11) c 0 = 0.0631353 (1) c 1 = 0.80139 (13) c = 0.01110777 (1) T 1 = XJ (c 0 + c 1 X d SqV BS + c (X d SqV BS ) ) (15) F s = 1 LD + T 1 X d SqV BS 1 ( ) L eff XJ + X d SqV (16) BS Narrow channel effect correlation factor: The edge effects in a narrow channel cause the depletion charge to extend beyond the width of the channel. This has an effect of increasing the threshold voltage. F n = π ɛ s DELTA C ox W eff (17) Static feedback coefficient: The threshold voltage lowers because the charge under the gate terminal depleted by the drain junction field increases with V DS. This effect is Drain Induced Barrier Lowering (DIBL). σ = 8.1 10 ETA L eff 3 C ox (18)

Threshold voltage: V th = V bi σ V DS + GAMMA SqV BS F s + F n SqV BS Subthreshold operation: This variable is invoked depending on the value of the parameter NFS and is used only during subthreshold mode. X n = 1 + q NFS 10 C ox + F n + GAMMA Modified threshold voltage: This variable defines the limit between weak and strong inversion. Subthreshold gate voltage: Surface mobility: (19) F s SqV BS (0) NFS > 0 = V on = V th + k T q X n (1) NFS 0 = V on = V th () µ s = V gsx = MAX(V GS, V on ) (3) U0 10 1 + THETA (V gsx V th ) Saturation voltage: Calculation of this voltage requires many steps. The effective mobility is calculated as () µ eff = µ s F drain (5) where 1.0 F drain = 1 + µs V (6) DS VMAX L eff The Taylor expansion of coefficient of bulk charge is β = W eff L eff µ eff C ox (7) F B = GAMMA The standard value of saturation voltage is calculated as The final value of the saturation voltage depends on the parameter VMAX F s SqV BS + F n (8) V sat = V gsx V th 1 + F B (9) VMAX = 0 = V dsat = V sat (30) VMAX > 0 = V c = VMAX L eff µ s (31) V dsat = V sat + V c Vsat + Vc (3) Velocity saturation drain voltage: This ensures that the drain voltage does not exceed the saturation voltage. V dsx = MIN(V DS, V dsat ) (33) Drain Current: Linear Region: µ s I DS = β U0 10 F drain (V gsx V th 1 + F b V dsx ) V dsx (3) 3

Saturation region: Cutoff Region: I DS = β (V GS V th 1 + F b V dsat ) V dsat (35) I DS = 0 (36) Channel length modulation: As V DS increases beyond V dsat, the point where the carrier velocity begins to saturate moves towards the source. This is modeled by the term l. Xd l = X E p d + KAPPA (V DS V dsat ) E p Xd (37) where E p is the lateral field at pinch-off and is given by E p = VMAX µ s (1 F drain ) (38) The drain current is multiplied by a correction factor l fact. This factor prevents the denominator L eff l from going to zero. The corrected value of drain-source current is l 0.5 L eff = l fact = L eff L eff l (39) l > 0.5 L eff = l fact = l L eff (0) I DSnew = I DS l fact (1) Subthreshold operation: For subthreshold operation, if the fast surface density parameter NFS is specified and V GS V on, then the final value of drain-source current is given by I DSfinal = I DSnew e kt q V GS Von Xn () Yang-Chatterjee charge model This model ensures continuity of the charges and capacitances throughout different regions of operation. The intermediate quantities are: and V F B = V to GAMMA PHI PHI (3) C o = C ox W eff L eff () Accumulation region V GS V F B + V BS Cut-off region V F B + V BS < V GS V th Q d = 0 (5) Q s = 0 (6) Q b = C o (V GS V F B V BS ) (7) Q d = 0 (8) Q s = 0 (9) GAMMA Q b = C o { 1 + 1 + (V GS V F B V BS ) GAMMA } (50)

Saturation region V th < V GS V DS + V th Linear region V GS > V DS + V th Q d = 0 (51) Q s = 3 C o (V GS V th ) (5) Q b = C o (V F B PHI V th ) (53) V DS Q d = C o [ 8 (V GS V th V DS ) + V GS V th 3 V DS] (5) V DS Q s = C o [ (V GS V th V DS ) + V GS V th + 1 V DS] (55) Q b = C o (V F B PHI V th ) (56) The final currents at the transistor nodes are given by I d = I DSfinal + dq d dt I g = dq g dt I s = I DSfinal + dq s dt (57) (58) (59) 5

DC Characteristics Transient analysis 0.0008.5 Output 0.0007 0.0006 3.5 0.0005 3 Vds (V) 0.000 Vd (V).5 0.0003 1.5 0.000 1 0.0001 0.5 0 0 0.5 1 1.5.5 3 3.5.5 5 0 0 1e-09 e-09 3e-09 e-09 5e-09 6e-09 7e-09 8e-09 9e-09 1e-08 (a) Ids (A) Time (s) (b) Figure : Analysis results. Notes: This is the M element in the SPICE compatible netlist. Version: 00.08.01 Credits: Name Affiliation Date Links Nikhil Kriplani NC State University August 00 nmkripla@unity.ncsu.edu www.ncsu.edu 6

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