PN Step Junctions (13, 1)
These equations for a silicon PN-junction diode use a “two-sided step-junction” model–the doping density 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 N-----A------⋅---N-----D--- |
| | | | | | | | | | q | | | ni | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | |
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| 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---- | |
--------------- | -⋅---------------- | | ----- | --- | ----- | | | | J = Js ⋅ e | | – 1 |
| 2 | q | | | NA | | | | | | | | | | | | |
| | | | | ND | | | | | | | | | |
| Aj = | | ( | W + 2 | ⋅ | | W | ) ⋅ ( | L + 2 | ⋅ | L | ) | | | | | | | | |
| | | | | | | | | | | | | | | |
| | | | | π ⋅ ( | W + L + 2 | ⋅ | W + 2 | ⋅ | | L | ) ⋅ | xj + 2 | ⋅ π ⋅ | xj | 2 |
| | | | | | |
| | | | | | | | | | | |
| | | | | | | | | | I = J | ⋅ | Aj | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | |
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_∝, ΔW=1_∝, L=10_∝, ΔL=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.
5-52 Equation Reference
