“n gives negatives, p gives positives”
Which dopant makes which type
Pentavalent doping gives spare electrons, so n-type. Trivalent doping leaves holes, so p-type. The letter tells you the majority carrier's sign.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Semiconductor Electronics formulas
The last chapter of the course, and often the most scoring, because the questions repeat. Doping, the p-n junction, the two rectifiers and the logic gates account for nearly every mark, and none of them need heavy algebra.
19 formulas, 4 memory hooks, and the 5 mistakes that cost the most marks.
Semiconductors
| What | Formula | Symbols and notes |
|---|---|---|
| Intrinsic semiconductor | ne = nh = ni | pure silicon or germanium |
| Mass action law | nenh = ni² | holds for doped material too |
| n-type | pentavalent dopant, electrons are the majority carriers | phosphorus, arsenic, antimony |
| p-type | trivalent dopant, holes are the majority carriers | boron, aluminium, indium |
| Energy gap | Si about 1.1 eV, Ge about 0.7 eV | an insulator's gap is far larger |
| Conductivity | σ = e(neμe + nhμh) | μ is the mobility |
The p-n junction
| What | Formula | Symbols and notes |
|---|---|---|
| Barrier potential | about 0.7 V for silicon, 0.3 V for germanium | the knee voltage of the diode |
| Forward bias | p to positive, depletion layer narrows, current flows | resistance is low |
| Reverse bias | p to negative, depletion layer widens, tiny leakage only | resistance is high |
| Half wave rectifier | output frequency = input frequency | uses one diode, efficiency about 40.6% |
| Full wave rectifier | output frequency = 2 × input frequency | uses two or four diodes, efficiency about 81.2% |
| Ripple factor | half wave 1.21, full wave 0.48 | lower is smoother |
| Zener diode | works in reverse breakdown as a voltage regulator | heavily doped, thin depletion layer |
Logic gates
| What | Formula | Symbols and notes |
|---|---|---|
| OR | Y = A + B | output 1 if any input is 1 |
| AND | Y = A·B | output 1 only if all inputs are 1 |
| NOT | Y = Ā | the inverter |
| NAND | Y = (A·B)‾ | AND followed by NOT; a universal gate |
| NOR | Y = (A + B)‾ | OR followed by NOT; also universal |
| XOR | Y = AB̄ + ĀB | output 1 when the inputs differ |
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Memory hooks
How to remember this chapter.
“Forward is narrow, reverse is wide”
The depletion layer
Forward bias narrows the depletion layer and current flows. Reverse bias widens it and the current nearly stops.
“Full wave doubles”
Rectifier output frequency
A half wave rectifier passes 50 Hz through as 50 Hz; a full wave gives 100 Hz, and it is smoother because it uses both halves of the cycle.
“NAND and NOR build everything”
Universal gates
Either one alone can be wired to make every other gate, which is why whole chips are built from them.
Where marks go
The mistakes that cost the most.
- Saying a doped semiconductor is charged. Doping adds carriers but the material stays electrically neutral.
- Thinking a diode conducts in reverse bias. Only a tiny leakage current flows, until breakdown.
- Giving the full wave rectifier the same output frequency as the input. It is doubled.
- Forgetting that a semiconductor's resistance falls as temperature rises, unlike a metal's.
- Connecting a Zener diode in forward bias for regulation. It regulates in reverse breakdown.
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