Solid State Basics (Compact)

ece-1109 ECE-1109 Introduction to ECE

I. Semiconductor Basics

• Materials:
  • Conductor: Supports charge flow (e.g., Cu, Al). Resistivity $\rho \approx 10^{-6}\Omega \text{cm}$.
  • Insulator: No conductivity (e.g., Mica, Wood). $\rho \approx 10^{12}\Omega \text{cm}$.
  • Semiconductor: Conductivity between conductors and insulators. Examples: Silicon (Si, $E_g=1.1$ eV) and Germanium (Ge, $E_g=0.67$ eV).
• Charge Carriers:
  • Intrinsic: Pure semiconductor; $n=p=n_i$.
  • Extrinsic (Doped):
    • n-type: Pentavalent impurity (P, As, Sb). Electrons are majority carriers ($n\approx N_D$).
    • p-type: Trivalent impurity (B, Ga, In). Holes are majority carriers ($p\approx N_A$).
• Key Formulas:
  • Mass Action Law: $np=n_i^2$.
  • Charge Neutrality: $N_D+p=N_A+n$.
  • Conductivity ($\sigma$): $\sigma =(n{\mu }_n+p{\mu }_p)e$. Current Density $J=\sigma E$.
  • Resistivity ($\rho$): $\rho =1/\sigma$.

II. PN Junction Diode

• Biasing:
  • Forward Bias: P-terminal (+), N-terminal (-). Depletion width ($W_d$) decreases; diffusion current flows.
  • Reverse Bias: P-terminal (-), N-terminal (+). $W_d$ increases; only minority drift current ($I_s$) flows.
• Barrier Potential ($V_b$): Built-in voltage preventing diffusion. $V_b=\frac{kT}{e}\ln (\frac{N_A{N}_D}{n_i^2})$. Typically 0.7V for Si, 0.3V for Ge.
• Diode Current Equation: $I_D=I_S(e^{\frac{k{V}_D}{T_K}}-1)$, where $k=11600/\eta$.
• Resistance Levels:
  • DC (Static): $R_D=V_D/I_D$.
  • AC (Dynamic): $r_d=\frac{26\text{mV}}{I_D}$.
  • Average AC: $R_{avg}=\Delta V_d/\Delta I_d$.
• Equivalent Models:
  • Piece-wise Linear: Includes $V_b$ and resistance $R_D$.
  • Constant Voltage Drop: Ideal diode + $V_b$ (0.7V or 0.3V).
  • Ideal: Switch (Short in forward, Open in reverse).

III. Diode Rectifiers

• Half-Wave Rectifier:
  • $V_{avg}(DC)=V_m/\pi$.
  • $V_{rms}=V_m/2$.
  • Efficiency $\eta =40.56$.
  • Ripple Factor $r=1.21$.
  • PIV $\ge V_m$.
• Full-Wave Rectifier (Center-Tapped & Bridge):
  • $V_{avg}(DC)=2V_m/\pi$.
  • $V_{rms}=V_m/\sqrt{2}$.
  • Efficiency $\eta =81.1$.
  • Ripple Factor $r=0.48$.
  • PIV: Bridge $\ge V_m$; Center-Tapped $\ge 2V_m$.
• Form Factor: $F.F=V_{rms}/V_{avg}$. (1.57 for Half-Wave; 1.11 for Full-Wave).

IV. Zener Diode

• Operation: Operates in reverse breakdown (Avalanche) to regulate voltage ($V_Z$).
• Voltage Regulator Analysis:
  • Load ($R_L$) fixed, $V_i$ fixed: Check if $V_{th}=\frac{R_L{V}_i}{R+R_L}\ge V_Z$. If yes, Zener is ON ($V_L=V_Z$).
  • $R_L$ Minimum Condition: $R_{L(min)}=\frac{V_{Z}R}{V_i-V_Z}$.
  • $V_i$ Range ($R_L$ fixed):
    • $V_{i(min)}=\frac{V_Z(R+R_L)}{R_L}$.
    • $V_{i(max)}=I_{R_{max}}R+V_Z$ (limited by $P_{ZM}$).
• Power: $P_Z=I_Z{V}_Z$. Maximum power $P_{ZM}$ determines max current.

V. Bipolar Junction Transistor (BJT)

• Structure: Emitter (E), Base (B), Collector (C). Doping: $E>C>B$. Width: $C>E>B$.
• Active Mode: J1 (Emitter-Base) Forward Biased, J2 (Collector-Base) Reverse Biased.
• Current Relationships:
  • $I_E=I_C+I_B$.
  • $I_C=\beta I_B$ (ignoring leakage $I_{CEO}$).
  • $I_C=\alpha I_E$ (ignoring leakage $I_{CBO}$).
• Parameters:
  • $\alpha$ (Common Base Gain): $0.95-0.98$. $\alpha =\frac{\beta }{1+\beta }$.
  • $\beta$ (Common Emitter Gain): Typical amplification factor. $\beta =\frac{\alpha }{1-\alpha }$.
• Biasing Configurations:
  1. Fixed Bias: $I_B=\frac{V_{CC}-V_{BE}}{R_B}$.
  2. Emitter Bias: Stabilized by $R_E$. $I_B=\frac{V_{CC}-V_{BE}}{R_B+(\beta +1)R_E}$.
  3. Collector Feedback: $I_B=\frac{V_{CC}-V_{BE}}{(\beta +1)R_C+R_B}$.