HP 50g Graphing, 48gII Graphing manual PN Step Junctions 13, Equations

PN Step Junctions (13, 1)

These equations for a silicon PNjunction diode use a “twosided stepjunction” model–the doping densi ty changes abruptly at the junction. The equation assume the current density is determined by minority carries injected across the depletion region and the PN junction is rectangular in its layout, The temperature should be between 77 and 500 K. (See “SIDENS” in Chapter 3.)

Equations:

	Vbi =	k-----⋅-----T⋅ LN --------NA---⋅---N-----D---
			q		ni	2 
xd =	2 ⋅ ε si ⋅	ε 0	⋅ (Vbi – Va) ⋅			 1		+	1	
	------------q-------------						N-----A---		N-----D---	

	Cj =		ε----s--i----⋅---ε----0-					Emax =	2-----⋅---(--V-----b---i---–-----V-----a---)
			xd						xd	q ⋅ Va
	ε si ⋅ ε 0 ⋅ E12								
BV =				⋅		1	+	1 		--k-----⋅---T----
	------------2----	⋅---	q-------------			N-----A---		--------	J = Js ⋅ e
									
								ND

Aj = (W + 2 ⋅ ΔW) ⋅ (L + 2 ⋅ ΔL)

π⋅ (W + L + 2 ⋅ ΔW + 2 ⋅ ΔL) ⋅ xj + 2 ⋅ π ⋅

I = J ⋅ Aj



– 1



xj2

Example:

Given: ND=1E22_cm^–3, NA=1E15_1/cm^3, T=26.85_°C, Js=1E–6_∝A/cm^2, Va=20_V, E1=3.3E5_V/cm, W=10_∝, W =1_∝, L=10_∝, L =1_∝, xj=2_∝.

Solution: Vbi=.9962_V, xd=5.2551_∝, Cj=2005.0141_pF/cm^2, Emax=79908.5240_V/cm, BV=358.0825_V, J= 1.0E–12_A/cm^2, Aj=3.1993E–6_cm^2, I= 3.1993E–15_mA.

552 Equation Reference