characteristics

characteristics

1. What Characteristics Means (Diode I-V)

Diode I-V characteristic = graph of current $I$ vs voltage $V$ across p-n junction, showing rectifying (unilateral, non-linear) behaviour: low resistance forward, high resistance reverse.

2. Ideal vs Practical Characteristic

Forward bias ($V>0$, p positive, n negative, $V$ opposes $V_{bi}$):

• Below $V_γ$ (cut-in, ~0.3V Ge, 0.7V Si): tiny current (recombination).
• Above $V_γ$: exponential rise:

where

= reverse saturation (pA–nA),

at 300K. Rapid increase after knee.

• Dynamic resistance $r_d = V_T/I$ small (~tens of Ω at mA).

Reverse bias ($V<0$, p negative, n positive, aids $V_{bi}$):

• Small leakage $I≈-I_0$ (constant, nA–µA) due to minority drift, voltage-independent until breakdown.
• Breakdown at $V_{BR}$: two mechanisms (next topics) — Zener (tunneling, $V<6V$, sharp) and Avalanche (impact ionization, $V>6V$), current shoots up, can destroy if unlimited.

3. Ideal Diode Model

• Ideal: $I=0$ for $V<0$, $V=0$ for $I>0$ (zero $V$ drop when on, zero $I$ when off) — used for rough analysis.
• Constant voltage model: $V=0.7V$ when on (Si) — better.

4. Worked Checks

(a) Si diode at V=0.7V, I=10mA, I0=1nA: check I=1e-9(e^{0.7/0.026}-1)≈1e-9·4.8e11=0.48A? Actually 0.7/0.026≈26.9, e^{26.9}≈4.8e11 ⇒ 0.48A, but high-level injection reduces? Approx shows exponential rise.

(b) Reverse V=-5V: I≈ -1nA (leakage) until -50V breakdown ⇒ -1A.

(c) Need to find dynamic r at I=10mA: r_d=26mV/10mA=2.6Ω.

(d) Temperature: I0 doubles every 10°C, Vγ drops 2mV/°C.

(e) Real diode: forward drop ~0.7V at rated current, reverse leakage increases with T.

5. Exam Points

• Sketch I-V with forward exponential, reverse leakage, breakdown, mark $V_γ$ (0.7 Si) — 7 marks, very frequent (the most common diode characteristic question).
• Write Shockley equation $I=I_0(e^{V/V_T}-1)$ — 3-5 marks, very frequent.
• Mention reverse $I_0$ and breakdown at $V_{BR}$ — 3-5 marks, frequent.
• Show ideal vs practical model — 3 marks.