Semiconductor
Conductivity and Resistivity:
Category | $\mathrm{P}(\pi-\mathrm{m})$ | $\rho\left(\pi^{-1} \mathrm{~m}^{-1}\right)$ |
---|---|---|
Conductors | $10^{-2}-10^{-6}$ | $10^{2}-10^{8}$ |
semiconductors | $10^{-5}-10^{-6}$ | $10^{5}-10^{-6}$ |
Insulators | $10^{11}-10^{19}$ | $10^{-11}-10^{-19}$ |
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:
PYQ-2023-Semiconductors-Q2, PYQ-2023-Semiconductors-Q6, PYQ-2023-Semiconductors-Q7, PYQ-2023-Semiconductors-Q8
P | Q | AND (Λ) | OR (v) | NAND (¬Λ) | NOR (¬v) | XOR (⊕) | Conditional (⇒) | Bi-conditional (⇔) |
---|---|---|---|---|---|---|---|---|
T | T | T | T | F | F | F | T | T |
T | F | F | T | T | F | T | F | F |
F | T | F | T | T | F | T | T | F |
F | F | F | F | T | T | F | T | T |