Question

For an unbiased Silicon \(n\text{-}p\text{-}n\) transistor in thermal equilibrium, which one of the following electronic energy band diagrams is correct? (\(E_c\) = conduction band minimum, \(E_v\) = valence band maximum, \(E_F\) = Fermi level.) 

 

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Hint:

At thermal equilibrium in any semiconductor junction, the Fermi level remains constant throughout the material.

Answer 1

The Correct Option is B

Step 1: Understanding n-p-n transistor structure:

An n-p-n transistor consists of three regions:

• Emitter (n-type): heavily doped n-type semiconductor
• Base (p-type): lightly doped p-type semiconductor (thin middle layer)
• Collector (n-type): moderately doped n-type semiconductor

Step 2: Band diagram characteristics for unbiased n-p-n transistor:

At n-p junctions: Built-in potential creates band bending at both junctions (emitter-base and base-collector)

Fermi level: In thermal equilibrium, the Fermi level $E_F$ must be constant (flat) throughout the entire structure - this is the key condition for thermal equilibrium

Band bending:

• At emitter-base junction: Bands bend downward going from n (emitter) to p (base)
• At base-collector junction: Bands bend upward going from p (base) to n (collector)

Energy relationships:

• In n-type regions: $E_F$ is closer to $E_c$ (conduction band)
• In p-type region: $E_F$ is closer to $E_v$ (valence band)

Step 3: Analyzing the options:

(A): Shows $E_F$ varying across the structure - incorrect (violates thermal equilibrium)

(B):

• Shows flat/constant $E_F$ throughout (dashed line)
• Shows proper band bending at both junctions
• $E_c$ dips down in the middle (p-region)
• $E_v$ rises up in the middle (p-region)
• This correctly represents thermal equilibrium

(C): Shows flat bands with no bending - incorrect (doesn't show junction effects)

(D): Shows $E_F$ varying significantly - incorrect (violates thermal equilibrium)

Answer: (B)