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Semiconductors formulas

Master Semiconductors through 30 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Semiconductors, every formula

30 formulas, typeset and free. Print it, or keep it open beside your practice.

Intrinsic carrier concentration
$n_{e} = n_{h} = n_{i}$
Q1MCQIntrinsic
In an intrinsic semiconductor, the electron and hole concentrations satisfy:
- A
  $n_e=n_h=n_i$
- B
  $n_e\gg n_h$
- C
  $n_h\gg n_e$
- D
  $n_e=0$
Mass-action law
$n_{e} n_{h} = n_{i}^{2}$
all types
Q1MCQMass action
For any semiconductor, $n_e\,n_h$ equals:
- A
  $n_i^{2}$
- B
  $n_i$
- C
  $2n_i$
- D
  $0$
p-type semiconductor
$n_{h} ≫ n_{e}$
trivalent doping
Q1MCQp-type
A p-type semiconductor is formed by doping with a:
- A
  trivalent atom
- B
  pentavalent atom
- C
  tetravalent atom
- D
  noble gas
n-type semiconductor
$n_{e} ≫ n_{h}$
pentavalent doping
Q1MCQn-type
An n-type semiconductor is formed by doping with a:
- A
  pentavalent atom
- B
  trivalent atom
- C
  tetravalent atom
- D
  noble gas
Total current
$i = i_{e} + i_{h}$
Q1MCQTotal current
The total current in a semiconductor is:
- A
  $i_e+i_h$
- B
  $i_e-i_h$
- C
  $i_e$
- D
  $i_h$
Conductivity
$σ = e (n_{e} μ_{e} + n_{h} μ_{h})$
Q1MCQConductivity
The conductivity of a semiconductor is:
- A
  $e(n_e\mu_e+n_h\mu_h)$
- B
  $e n_e\mu_e$
- C
  $e n_h\mu_h$
- D
  $e(n_e-n_h)$
n-type conductivity
$σ = e n_{e} μ_{e}$
Q1MCQn-type conductivity
For an n-type semiconductor, the conductivity is dominated by:
- A
  $e n_e\mu_e$
- B
  $e n_h\mu_h$
- C
  $e(n_e+n_h)$
- D
  $0$
p-type conductivity
$σ = e n_{h} μ_{h}$
Q1MCQp-type conductivity
For a p-type semiconductor, the conductivity is dominated by:
- A
  $e n_h\mu_h$
- B
  $e n_e\mu_e$
- C
  $e(n_e+n_h)$
- D
  $0$
Mobility
$μ = \frac{v _{d}}{E}$
Q1MCQMobility
The mobility of a charge carrier is:
- A
  $\dfrac{v_d}{E}$
- B
  $v_d E$
- C
  $\dfrac{E}{v_d}$
- D
  $eE$
Carrier generation
$n = A T^{3/2} e^{- E_{g} /2 k T}$
Q1MCQCarrier generation
The number of carriers excited across the gap varies as:
- A
  $T^{3/2}e^{-E_g/2kT}$
- B
  $e^{E_g/2kT}$
- C
  $T^{2}$
- D
  $e^{-kT}$
Dynamic resistance of a diode
$R = \frac{Δ V}{Δ I}$
Q1MCQDynamic resistance
The dynamic resistance of a diode is:
- A
  $\dfrac{\Delta V}{\Delta I}$
- B
  $\dfrac{\Delta I}{\Delta V}$
- C
  $VI$
- D
  $\dfrac{V}{I}$
Emitter current
$i_{e} = i_{b} + i_{c}$
CB dc current gain
$α = \frac{i _{c}}{i _{e}}$
0.95–0.99
CB ac current gain
$α_{a c} = \frac{Δ i _{c}}{Δ i _{e}}$
Q1MCQCB ac gain
The CB ac current gain is:
- A
  $\dfrac{\Delta i_c}{\Delta i_e}$
- B
  $\dfrac{\Delta i_c}{\Delta i_b}$
- C
  $\dfrac{i_c}{i_b}$
- D
  $\dfrac{i_e}{i_c}$
CE dc current gain
$β = \frac{i _{c}}{i _{b}}$
CE ac current gain
$β_{a c} = \frac{Δ i _{c}}{Δ i _{b}}$
Q1MCQCE ac gain
The CE ac current gain is:
- A
  $\dfrac{\Delta i_c}{\Delta i_b}$
- B
  $\dfrac{\Delta i_c}{\Delta i_e}$
- C
  $\dfrac{i_e}{i_c}$
- D
  $\dfrac{i_b}{i_c}$
β in terms of α
$β = \frac{α}{1 - α}$
Q1MCQβ from α
The relation between $\beta$ and $\alpha$ is:
- A
  $\beta=\dfrac{\alpha}{1-\alpha}$
- B
  $\beta=\dfrac{1-\alpha}{\alpha}$
- C
  $\beta=1-\alpha$
- D
  $\beta=\alpha$
α in terms of β
$α = \frac{β}{1 + β}$
Q1MCQα from β
The relation for $\alpha$ in terms of $\beta$ is:
- A
  $\alpha=\dfrac{\beta}{1+\beta}$
- B
  $\alpha=\dfrac{1+\beta}{\beta}$
- C
  $\alpha=1+\beta$
- D
  $\alpha=\beta$
Voltage gain (CE)
$A_{v} = β_{a c} \times resistance gain$
Q1MCQVoltage gain
The voltage gain of a CE amplifier is:
- A
  $\beta_{ac}\times\text{resistance gain}$
- B
  $\alpha_{ac}\times\text{resistance gain}$
- C
  $\beta_{ac}^{2}$
- D
  $\text{resistance gain}$
Power gain (CE)
$A_{p} = β_{a c}^{2} \times resistance gain$
Q1MCQPower gain
The power gain of a CE amplifier is:
- A
  $\beta_{ac}^{2}\times\text{resistance gain}$
- B
  $\beta_{ac}\times\text{resistance gain}$
- C
  $\beta_{ac}$
- D
  $\alpha_{ac}^{2}$
Transconductance
$g_{m} = \frac{Δ i _{c}}{Δ V _{E B}} = \frac{A _{v}}{R _{L}}$
Q1MCQTransconductance
The transconductance is:
- A
  $\dfrac{\Delta i_c}{\Delta V_{EB}}$
- B
  $\dfrac{\Delta V_{EB}}{\Delta i_c}$
- C
  $\dfrac{i_c}{i_b}$
- D
  $A_v R_L$
OR gate
$Y = A + B$
Q1MCQOR gate
The output of an OR gate is:
- A
  $A+B$
- B
  $A\cdot B$
- C
  $\bar A$
- D
  $A\oplus B$
AND gate
$Y = A \cdot B$
Q1MCQAND gate
The output of an AND gate is:
- A
  $A\cdot B$
- B
  $A+B$
- C
  $\bar A$
- D
  $\overline{A\cdot B}$
NOT gate
$Y = \overset{ˉ}{A}$
Q1MCQNOT gate
The output of a NOT gate is:
- A
  $\bar A$
- B
  $A$
- C
  $A+B$
- D
  $A\cdot B$
NAND gate
$Y = \overline{A \cdot B}$
Q1MCQNAND gate
The output of a NAND gate is:
- A
  $\overline{A\cdot B}$
- B
  $A\cdot B$
- C
  $\overline{A+B}$
- D
  $A+B$
NOR gate
$Y = \overline{A + B}$
Q1MCQNOR gate
The output of a NOR gate is:
- A
  $\overline{A+B}$
- B
  $A+B$
- C
  $\overline{A\cdot B}$
- D
  $A\cdot B$
XOR gate
$Y = A \oplus B$
Q1MCQXOR gate
The output of an XOR gate is:
- A
  $A\oplus B$
- B
  $A+B$
- C
  $A\cdot B$
- D
  $\bar A$
De Morgan's first theorem
$\overline{A + B} = \overset{ˉ}{A} \cdot \overset{ˉ}{B}$
Q1MCQDe Morgan 1
De Morgan's first theorem states:
- A
  $\overline{A+B}=\bar A\cdot\bar B$
- B
  $\overline{A+B}=\bar A+\bar B$
- C
  $\overline{A\cdot B}=\bar A\cdot\bar B$
- D
  $\overline{A+B}=A\cdot B$
De Morgan's second theorem
$\overline{A \cdot B} = \overset{ˉ}{A} + \overset{ˉ}{B}$
Q1MCQDe Morgan 2
De Morgan's second theorem states:
- A
  $\overline{A\cdot B}=\bar A+\bar B$
- B
  $\overline{A\cdot B}=\bar A\cdot\bar B$
- C
  $\overline{A+B}=\bar A+\bar B$
- D
  $\overline{A\cdot B}=A+B$
Absorption law
$A + A B = A$
Q1MCQAbsorption law
The Boolean absorption law states $A+AB$ equals:
- A
  $A$
- B
  $B$
- C
  $AB$
- D
  $A+B$

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Semiconductors formulas

Semiconductors, every formula

Intrinsic carrier concentration

Mass-action law

p-type semiconductor

n-type semiconductor

Total current

Conductivity

n-type conductivity

p-type conductivity

Mobility

Carrier generation

Dynamic resistance of a diode

Emitter current

CB dc current gain

CB ac current gain

CE dc current gain

CE ac current gain

β in terms of α

α in terms of β

Voltage gain (CE)

Power gain (CE)

Transconductance

OR gate

AND gate

NOT gate

NAND gate

NOR gate

XOR gate

De Morgan's first theorem

De Morgan's second theorem

Absorption law

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