Semiconductor Devices — MHT-CET Physics Formulas and Traps

Energy Bands and Doping

Conductors, Insulators and Semiconductors

Intrinsic semiconductor

n_e = n_h = n_i

n-type and p-type Doping

Mass-action law

n_e\,n_h = n_i^2

Common traps

A semiconductor's valence band is 'completely filled'

Only at absolute zero. At room temperature some electrons have left it, so the valence band is partly EMPTY and the conduction band partly FILLED. The 'completely filled' options describe an insulator.

n-type means negatively charged

The 'n' names the majority CARRIER, not the charge of the crystal: every donor electron came with a donor atom, so the crystal is neutral.

The p-n Junction: Depletion Layer and Biasing

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The Depletion Layer and Its Field

Barrier

\vec E_{\text{junction}}: \; n \to p, \qquad V_n > V_p

Forward and Reverse Bias

Bias rule

V_p > V_n \Rightarrow \text{forward}, \qquad V_p < V_n \Rightarrow \text{reverse}

Common traps

The p-side is at the higher potential

The p-side LOST holes and holds negative ions, so it sits LOWER. The field runs from n to p; the options reverse both.

Comparing the sizes of negative voltages

−1.0 V is HIGHER than −1.5 V. A drawing with −1.0 V on the p-side and −1.5 V on the n-side is forward biased; the minus signs are there to trip the eye.

Diode Circuits and Rectifiers

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Circuits With Diodes

Silicon diode in series

I = \frac{V - 0.7}{R}

Half-Wave and Full-Wave Rectifiers

Output frequency

f_{\text{half}} = f, \qquad f_{\text{full}} = 2f

Common traps

Including a reverse-biased branch

A reverse-biased ideal diode carries NO current, so everything in series with it vanishes from the circuit. Adding its resistor in parallel is the most common wrong answer.

Full-wave keeps the input frequency

Each half-cycle becomes a pulse, so a 50 Hz input gives 100 pulses a second. Answering 50 Hz for both rectifiers is the planted option.

Special-Purpose Diodes: Zener, LED, Photodiode and Solar Cell

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The Zener Regulator

Zener current

I_Z = \frac{V_{\text{in}} - V_Z}{R_s} - \frac{V_Z}{R_L}

LED, Photodiode and Solar Cell

Band gap and wavelength

E_g = \frac{hc}{\lambda}, \qquad \lambda\,(\text{nm}) \approx \frac{1240}{E_g\,(\text{eV})}

Common traps

Giving the Zener the whole series current

The series current splits: the load takes

\frac{V_Z}{R_L}

and only the rest flows in the Zener. 20 mA through the resistor with 15 mA in the load leaves 5 mA, not 20.

Detecting light in forward bias

In forward bias the large diffusion current hides the small change that light makes; a photodiode must be REVERSE biased, where the whole current is the light-made minority carriers.

The Transistor and the Common-Emitter Amplifier

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Current Ratios α and β

Current gains

\alpha = \frac{I_C}{I_E}, \quad \beta = \frac{I_C}{I_B}, \quad \beta = \frac{\alpha}{1 - \alpha}

The Common-Emitter Amplifier

CE amplifier

A_V = \beta\,\frac{R_L}{R_{\text{in}}}, \qquad A_P = \beta\,A_V

n-p-n and p-n-p Transistors

Currents

I_E = I_B + I_C

Common traps

Calling the collector fraction β

'90% reach the collector' is α = 0.9, and β is

\frac{0.9}{0.1} = 9

— not 90. The options offer α and β both ways round.

Squaring β in the voltage gain

Voltage gain has ONE factor of β; power gain has two.

78 \times \frac{6.5}{1.3} = 390

is the voltage gain;

78^2 \times 5

would be the power gain.

Drawing the diodes pointing inward

An n-p-n's base is p-type, so the diode arrows point OUT from the base to E and C. Arrows pointing into the base describe a p-n-p.

Logic Gates and Boolean Algebra

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The Basic Gates and Their Truth Tables

NAND and NOR

\text{NAND: } Y = \overline{A\cdot B}, \qquad \text{NOR: } Y = \overline{A + B}

Which Single Gate Is a Combination Equal To?

De Morgan's laws

\overline{A\cdot B} = \overline{A} + \overline{B}, \qquad \overline{A + B} = \overline{A}\cdot\overline{B}

Output and Boolean Expression of a Circuit

Absorption

A + \overline{A}B = A + B, \qquad A(A + B) = A

Common traps

Reading one row and stopping

(0, 0) → 1 fits NAND, NOR and XNOR alike. Check a second row before choosing: (0, 1) → 1 rules out NOR.

Missing the bubble

A small circle on a gate's output (or input) is a NOT. Reading a NAND as an AND flips every answer that follows; check each gate's output for a bubble before writing its expression.

Trusting the pattern, not the gates

Circuits that LOOK alike on paper can differ by one bubble, and a NAND–NAND pair gives a different answer from an AND–NAND pair. Carry the 0s and 1s through every gate yourself rather than matching the picture to one seen before.

Semiconductor Devices formulas

Energy Bands and Doping

Conductors, Insulators and Semiconductors

n-type and p-type Doping

Common traps

The p-n Junction: Depletion Layer and Biasing

The Depletion Layer and Its Field

Forward and Reverse Bias

Common traps

Diode Circuits and Rectifiers

Circuits With Diodes

Half-Wave and Full-Wave Rectifiers

Common traps

Special-Purpose Diodes: Zener, LED, Photodiode and Solar Cell

The Zener Regulator

LED, Photodiode and Solar Cell

Common traps

The Transistor and the Common-Emitter Amplifier

Current Ratios α and β

The Common-Emitter Amplifier

n-p-n and p-n-p Transistors

Common traps

Logic Gates and Boolean Algebra

The Basic Gates and Their Truth Tables

Which Single Gate Is a Combination Equal To?

Output and Boolean Expression of a Circuit

Common traps

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