Chapter 39: Problem 2923

For the same density of impurity atoms, Zener voltage is (A) same for both Ge and Si (B) higher for Ge than for \(\mathrm{Si}\) (C) higher for silicon than for germanium (D) none of the above

Short Answer

Expert verified

The Zener voltage (\(V_Z\)) is higher for Silicon than for Germanium when the density of impurity atoms is the same. This is because Silicon has a higher critical electric field (\(E_c\)) than Germanium, and \(V_Z\) is directly proportional to the critical electric field. Therefore, the correct answer is (C) higher for silicon than for germanium.

Step by step solution

Start with the formula connecting Zener voltage and impurity density

In a Zener diode, the breakdown voltage (\(V_Z\)) is related to the density of impurity atoms (\(N_d\)) and the critical electric field (\(E_c\)) through the formula: \[V_Z = E_c \times w\] where \(w\) is the depletion layer width.

Consider the relationship between the width of the depletion layer and impurity density

The depletion layer width (w) is inversely proportional to the square root of the impurity density \(N_d\) and it can be expressed as: \[w \propto \frac{1}{\sqrt{N_d}}\]

Examine the critical electric field for both Ge and Si

Germanium has a lower critical electric field than Silicon. That means: \[E_c (\text{Ge}) < E_c (\text{Si})\]

Combine the relationships to compare Zener voltages for Ge and Si

Based on the relationships in steps 1-3, the Zener voltage is inversely proportional to the square root of the impurity density, while it is directly proportional to the critical electric field. So, we can write: \[V_Z (\text{Ge}) \propto \frac{E_c (\text{Ge})}{\sqrt{N_d}}\] \[V_Z (\text{Si}) \propto \frac{E_c (\text{Si})}{\sqrt{N_d}}\] Since both diodes have the same impurity density and critical electric fields are different, we can compare their Zener voltages. From step 3, we know that \(E_c(\text{Ge}) < E_c(\text{Si})\). Therefore, we can conclude that: \[V_Z (\text{Ge}) < V_Z (\text{Si})\]

Choose the correct answer option

Based on our comparison, the Zener voltage for Germanium is smaller than that for Silicon. So, the correct answer is: (C) higher for silicon than for germanium

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For the same density of impurity atoms, Zener voltage is (A) same for both Ge and Si (B) higher for Ge than for \(\mathrm{Si}\) (C) higher for silicon than for germanium (D) none of the above

Short Answer

Step by step solution

Start with the formula connecting Zener voltage and impurity density

Consider the relationship between the width of the depletion layer and impurity density

Examine the critical electric field for both Ge and Si

Combine the relationships to compare Zener voltages for Ge and Si

Choose the correct answer option

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