### Semiconductor Characteristics: Table Overview #### Table Details The images provide two tables detailing semiconductor characteristics for both p-side and n-side regions of a diode. --- #### Table 1: Material Properties | **p-side** | | | **n-side** | | | | | | | |-------------|----|----|-------------|----|----|----|----|----| | \( N_A \) | \( D_n \) | \( L_n \) | \( N_D \) | \( D_p \) | \( L_p \) | \( V_0 \) | \( \varepsilon_{\text{max}} \)(V) | \( J_s \) | Area | \( J(V) \) | | \( \text{cm}^{-3} \) | \( \text{cm}^2/\text{s} \) | cm | \( \text{cm}^{-3} \) | \( \text{cm}^2/\text{s} \) | cm | V | V/cm | A/cm\(^2\) | cm\(^2\) | A/cm\(^2\) | | \( 1 \times 10^{18} \) | | | \( 6 \times 10^{15} \) | | | | | | | \( 1 \times 10^{-7} \) | * **\( N_A \) and \( N_D \):** Doping concentrations for p-type and n-type respectively. * **\( D_n \), \( D_p \):** Diffusion coefficients for electrons and holes. * **\( L_n \), \( L_p \):** Diffusion lengths for electrons and holes. * **\( V_0 \):** Built-in voltage. * **\( \varepsilon_{\text{max}}(V) \):** Maximum electric field. * **\( J_s \):** Saturation current density. * **\( J(V) \):** Current density. --- #### Table 2: Electrical Properties | **p-side** | | **n-side** | | | | | | | |-------------|----|-------------|----|---|---|---|----|----| | \( \sigma_p \) | \( R_p \) | \( \ ## Educational Content: Abrupt Junction Diode Analysis ### Problem Statement **Given:** A long base, silicon p⁺n abrupt junction diode with the following parameters: - **n-side (ND):** 6E15 cm⁻³ - **p-side (NA):** 1E18 cm⁻³ - **Minority carrier lifetimes:** τₚ = τₙ = 10 ns = 1E-8 seconds - **Junction area (A):** 1E-7 cm² - **Distance from junction to applied V contacts:** - \( W_n = W_p = 25 \mu m = 2.5E-3 cm \) **Alert:** \( W = x_n + x_p \) is not the space charge width. Refer to the diagram. ### Diagram Description The diagram depicts a silicon p⁺n abrupt junction diode: - The p⁺ side has an acceptor concentration \( N_A \). - The n side has a donor concentration \( N_D \). - Regions \( W_p \) and \( W_n \) indicate distances related to carrier movement with \( x_p \) and \( x_n \) representing depletion region widths. ### Tasks #### a. Forward Bias Validation With a forward bias \( V = 0.6 \) volts, confirm low-level injection (LLI) applicability: - Show: \( \Delta p(x_n) = p_{n0} \left[ \exp\left(\frac{qV}{kT}\right) - 1 \right] \ll n_n \approx N_D \) #### b. Parameter Calculation Utilize given values to compute parameters for the diode with forward bias \( V = 0.6 \) volts: - **Minority carrier parameters:** - \( \sigma_n = q\mu_nN_D \) - \( \sigma_p = q\mu_pN_A \) - **Electric field at metallurgical junction:** \( \mathcal{E}_{max} \) - **Carrier concentration ratio:** \( R = R_p + R_n = W_p/(A \cdot \sigma_p) + W_n/(A \cdot \sigma_n) \) #### c. Expression for \( J_p(x) \) Determine \( J_p(x) \) on the n-side: - Evaluate at contact:

### Semiconductor Characteristics: Table Overview #### Table Details The images provide two tables detailing semiconductor characteristics for both p-side and n-side regions of a diode. --- #### Table 1: Material Properties | p-side | | | n-side | | | | | | | |-------------|----|----|-------------|----|----|----|----|----| | \( N_A \) | \( D_n \) | \( L_n \) | \( N_D \) | \( D_p \) | \( L_p \) | \( V_0 \) | \( \varepsilon_{\text{max}} \)(V) | \( J_s \) | Area | \( J(V) \) | | \( \text{cm}^{-3} \) | \( \text{cm}^2/\text{s} \) | cm | \( \text{cm}^{-3} \) | \( \text{cm}^2/\text{s} \) | cm | V | V/cm | A/cm\(^2\) | cm\(^2\) | A/cm\(^2\) | | \( 1 \times 10^{18} \) | | | \( 6 \times 10^{15} \) | | | | | | | \( 1 \times 10^{-7} \) | * \( N_A \) and \( N_D \): Doping concentrations for p-type and n-type respectively. * \( D_n \), \( D_p \): Diffusion coefficients for electrons and holes. * \( L_n \), \( L_p \): Diffusion lengths for electrons and holes. * \( V_0 \): Built-in voltage. * \( \varepsilon_{\text{max}}(V) \): Maximum electric field. * \( J_s \): Saturation current density. * \( J(V) \): Current density. --- #### Table 2: Electrical Properties | p-side | | n-side | | | | | | | |-------------|----|-------------|----|---|---|---|----|----| | \( \sigma_p \) | \( R_p \) | \( \ ## Educational Content: Abrupt Junction Diode Analysis ### Problem Statement Given: A long base, silicon p⁺n abrupt junction diode with the following parameters: - n-side (ND): 6E15 cm⁻³ - p-side (NA): 1E18 cm⁻³ - Minority carrier lifetimes: τₚ = τₙ = 10 ns = 1E-8 seconds - Junction area (A): 1E-7 cm² - Distance from junction to applied V contacts: - \( W_n = W_p = 25 \mu m = 2.5E-3 cm \) Alert: \( W = x_n + x_p \) is not the space charge width. Refer to the diagram. ### Diagram Description The diagram depicts a silicon p⁺n abrupt junction diode: - The p⁺ side has an acceptor concentration \( N_A \). - The n side has a donor concentration \( N_D \). - Regions \( W_p \) and \( W_n \) indicate distances related to carrier movement with \( x_p \) and \( x_n \) representing depletion region widths. ### Tasks #### a. Forward Bias Validation With a forward bias \( V = 0.6 \) volts, confirm low-level injection (LLI) applicability: - Show: \( \Delta p(x_n) = p_{n0} \left[ \exp\left(\frac{qV}{kT}\right) - 1 \right] \ll n_n \approx N_D \) #### b. Parameter Calculation Utilize given values to compute parameters for the diode with forward bias \( V = 0.6 \) volts: - Minority carrier parameters: - \( \sigma_n = q\mu_nN_D \) - \( \sigma_p = q\mu_pN_A \) - Electric field at metallurgical junction: \( \mathcal{E}_{max} \) - Carrier concentration ratio: \( R = R_p + R_n = W_p/(A \cdot \sigma_p) + W_n/(A \cdot \sigma_n) \) #### c. Expression for \( J_p(x) \) Determine \( J_p(x) \) on the n-side: - Evaluate at contact: