Conductivity and Resistivity:

Charge Concentration and Current:

In the case of intrinsic semiconductors

• Mobility: $\eta_{h}=\eta_{e}$
• In P type: $\eta_{\mathrm{h}} \gg \eta_{\mathrm{e}}$
• Current: $i=i_e+i_h$
• Mass Action Law: $\eta_{\mathrm{e}} \eta_{\mathrm{n}}=\eta_{\mathrm{i}}^{2}$
• Number of electrons moving from valence band to conduction band:

$\eta=A T^{3 / 2} e^{-E g / 2 k T}$

where: A is positive constant

• Hall Effect equation: $\sigma=e\left(\eta_e \mu_e+\eta_n \mu_n\right)$

For p-type: $\eta_{\mathrm{n}} \gg \eta_{\mathrm{e}}$

For n-type $\eta_{e} \gg \eta_{h}$

• Dynamic Resistance of P-N junction in forward biasing: $R=\frac{\Delta V}{\Delta I}$

Transistor

• CB amplifier

(i) ac current gain: $\alpha_c=\frac{\text { Small change in collector current }\left(\Delta i_c \right)}{\text { Small change in emitter current }\left(\Delta i_e\right)}$

(ii) dc current gain: $\alpha_{d c}=\frac{\text { Collector current }\left(i_c \right)}{\text { Emitter current }\left(i_e\right)}$

Value of $\alpha_{dc}$ lies between 0.95 to 0.99.

(iii) Voltage gain: $A_{v}=\frac{\text { Change in output voltage }\left(\Delta V_{0}\right)}{\text { Change in input voltage }\left(\Delta V_{f}\right)}$

A_{v}=a_{ac} \times \text{Resistance gain}

(iv) Power gain: $dB =\frac{\text { Change in output power }\left(\Delta P_{0}\right)}{\text { Change in input power }\left(\Delta P_C \right)}$

$\Rightarrow$ Power gain, $dB = 10 \log_{10}(\mathrm{a}^{2} \times \text{Resistance gain})$

(v) Phase difference (between output and input) : 0 degrees

(vi) Application : For High Frequencies

CE Amplifier

(i) ac current gain: $\beta_{ac}=\left(\frac{\Delta i_C}{\Delta i_b}\right) \text{ at } V_{CE}= \text{constant}$

(ii) dc current gain: $\beta_{dc}=\frac{i_c}{i_b}$

(iii) Voltage gain : $A_v=\frac{\Delta V_0}{\Delta V_i}=\beta_{ac} \times \text{Resistance gain}$

(iv) Power gain: $dB = 10 \log_{10} \left(\frac{P_0}{P_i}\right) = \beta^2 \times \text{Resistance}$

(v) Transconductance $\left(g_{m}\right)$ : The ratio of the change in collector current to the change in emitter base voltage is called trans conductance i.e. $g_{m}=\frac{\Delta i_{c}}{\Delta V_{E B}}$

Also, $g_{m}=\frac{A_{V}}{R_{L}}$ $R_{L}= \text{Load resistance}$

• Relation between $\alpha$ and $\beta$:

$\beta=\frac{\alpha}{1-\alpha}$

$\alpha=\frac{\beta}{1+\beta}$

GATE: