Conductivity and Resistivity:

Charge Concentration and Current:

In 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 reaching from valence bond to conduction bond:

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

where: A is positive constant

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

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: $$\alpha_c=\frac{\text { Samll change incollector current }\left(\Delta i_c \right)}{\text { Samll change incollector current }\left(\Delta i_e\right)}$$

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

$\Rightarrow A_{v}=a_{a c} \times$ Resistance gain

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

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

(v) Phase difference (between output and input) : same phase

(vi) Application : For High frequency

CE Amplifier

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

(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: $$dB = \frac{\Delta P_0}{\Delta P_i}=\beta^2 ac \times \text{Resistance}$$

(v) Transconductance $\left(g_{m}\right)$ : The ratio of the change in collector 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: