Question

Reverse Saturation Current of a Germanium Diode

The germanium pn junction described above is used to construct a diode with a cross-sectional area of A = (6) × 10⁻³ cm². The limiting reverse saturation current of a diode is given by:

Iₛ = A * e * nᵢ² * (Lₙ * Nₐ + Lₚ * Nᴰ)

where:
- e = 1.602 × 10⁻¹⁹ C is the charge of an electron,
- Dₙ and Dₚ are the diffusion coefficients for electrons and holes, respectively,
- Lₙ and Lₚ are the diffusion lengths for electrons and holes, respectively,
- Nₐ and Nᴰ are the concentrations of acceptor and donor atoms, respectively.

Germanium has an electron mobility of μₙ = 3600 cm²/V⋅s and a hole mobility of μₚ = 1800 cm²/V⋅s. Use diffusion lengths of Lₙ = Lₚ = 5 μm, and where necessary, use the same values from the previous questions.

What is the reverse saturation current of this pn junction?

Answer 1

We cannot calculate the reverse saturation current of the germanium diode without knowing the intrinsic carrier concentration, and the acceptor and donor atom concentrations, as these values are essential and not provided.

Step-by-step explanation:

To calculate the reverse saturation current (Is) of the germanium diode, we use the following formula:

Is = A * e * ni2 * (Ln * N∅ + Lp * ND)

It's given that e = 1.602 × 10−19 C. However, we need the intrinsic carrier concentration (ni), and the concentrations of acceptor (N∅) and donor (ND) atoms, as well as the diffusion coefficients (Dn and Dp) to proceed with this calculation. Without these values, which are typically determined empirically or provided in the question, we cannot calculate the current. The known values such as electron and hole mobilities, the charge of electron, and the cross-sectional area of the diode can be used when the missing quantities are provided.

The equation ties in various factors affecting the diode current, including physical constants and material properties that are critical in understanding semiconductor devices.