HP 48gII Graphing, 50g Graphing manual Nmos Transistors 13, Vds

NMOS Transistors (13, 2)

These equations for a silicon NMOS transistor use a twoport network model. They include linear and no nlinear regions in the device characteristics and are based on a gradualchannel approximation (the electric f ields in the direction of current flow are small compared to those perpendicular to the flow). The drain current and transconductance calculations differ depending on whether the transistor is in the linear, saturated, or cutoff region. The equations assume the physical geometry of the device is a rectangle, secondorder lengthparameter effects are negligible, shotchannel, hotcarrier, and velocity saturation effects are negligible, and subthreshol d currents are negligible. ( See “SIDENS” in Chapter 3.)

Equations:

We = W – 2 ⋅ ΔW		Le = L – 2 ⋅ ΔL	Cox =		ε----o---x---	⋅	--ε---0-
		(VGS – Vt) ⋅ VDS – V-----D-----S2			tox
IDS = Cox ⋅ ∝ n ⋅  W------e--	⋅ 			⋅ (1 + λ ⋅		VDS)
 Le 		2	

γ =	2 ⋅ ε si ⋅ ε 0 ⋅ q ⋅ NA
	----------------C----o----x---------------------

Vt = Vt0 + γ ⋅ ( 2 ⋅ ABS(φ p) – ABS(VBS) – 2 ⋅ ABS( φ p))

φ p =	–k ⋅ T		 NA		gds = IDS ⋅ λ
	-------------	⋅ LN --------
	q		ni
gm = Cox ⋅ ∝ m ⋅			 We	⋅ (1 + λ ⋅ VDS) ⋅ 2 ⋅ IDS
			--------
			 Le

VDsat = VGS – Vt

Example:

Given: tox=700_Å, NA=1E15_1/cm^3, ∝n=600_cm^2/ (V∗s), T=26.85_°C, Vt0=0.75_V, VGS=5_V, VBS=0_V, VDS=5_V, W=25_∝, W =1_∝, L=4_m, L =0.75_∝, λ=0.05_1/V.

Solution: We=23_∝, Le=2.5_∝, Cox=49330.4750_pF/cm^2, γ =0.3725_V^.5, φp= .2898_V, Vt=0.75_V, VDsat=4.25_V, IDS=3.0741_mA, gds=1.5370E–4_S, gm=1.4466_mA/V.

Equation Reference 553