Q.Can the potential barrier across a p-n junction be measured by simply connecting a voltmeter across the junction?

No, it cannot. The key idea is that the potential barrier exists only at the junction itself, not across the entire device terminals.

Reasoning:

1. At the p-n junction, diffusion of majority carriers creates a depletion region with an internal electric field, giving rise to a built-in potential barrier $V_0$ (typically ~0.7 V for silicon).

2. When you connect a voltmeter across the p and n terminals, you complete an external circuit. The voltmeter measures the net potential difference between its probes. …

Why the Question Matters

This is a classic trick question in semiconductor physics. Many students assume that since a p-n junction has a potential barrier (typically 0.3–0.7 V for silicon), you should be able to read that voltage directly with a voltmeter. But that assumption misses a subtle but crucial point: the voltmeter itself becomes part of the circuit, and the physics of contacts between different materials changes everything.

Let’s understand why.

The Core Concept: Contact Potentials

When you connect a voltmeter to a p-n junction, you are not just touching the p-side and n-side with identical wires. You are creating a chain of different materials:

• Metal wire (say copper) from voltmeter terminal → contact with p-type silicon
• p-type silicon → n-type silicon (the junction itself)
• n-type silicon → contact with another metal wire → back to voltmeter

Every junction between two different materials develops its own contact potential (also called built-in potential or work-function difference). The voltmeter reads the net voltage around the entire loop, not just the p-n junction barrier.

Step-by-Step Reasoning

1. The p-n junction at equilibrium has a built-in potential $V_0$ across its depletion region. This potential arises because diffusion of majority carriers across the junction leaves behind fixed ionized impurities, creating an electric field that opposes further diffusion. At equilibrium, the net current is zero.

2. Now consider what happens when you attach metal probes. Each metal-semiconductor contact also forms a junction with its own built-in potential. For a metal with work function $\phi_m$ contacting a semiconductor with electron affinity $\chi$, the contact potential is $V_{ms} = (\phi_m - \chi)/q$ (plus doping-dependent corrections).

3. The complete circuit forms a closed loop. Going around: metal₁ → p-Si → n-Si → metal₂ → voltmeter → back to metal₁. Kirchhoff’s voltage law says the sum of all potential differences around this loop must be zero at equilibrium (no external battery).

4. The voltmeter reads the net voltage across its terminals. That net voltage is the sum of:

   • Contact potential at metal₁–p-Si junction
   • Built-in potential of p-n junction ($V_0$)
   • Contact potential at n-Si–metal₂ junction
   • Any potential drops in the wires (negligible)

5. Here’s the key insight: At equilibrium, the sum of all these contact potentials exactly cancels the p-n junction barrier. The net voltage around the loop is zero. The voltmeter reads zero.

Method: Following the Complete Measurement Loop, Not Just the Junction Being Probed

The instinct is to think a voltmeter simply "reads" whatever voltage exists at the junction -- the method here is to recognise that attaching probes creates a CLOSED LOOP with its own additional junctions, and to sum everything around that whole loop rather than looking at the p-n junction in isolation.

Step 1 -- Note where the built-in potential actually lives.

The p-n junction's built-in potential $V_0$ exists only across its own depletion region, established by carrier diffusion and recombination there, at equilibrium (zero net current).

Step 2 -- Recognise what attaching a voltmeter actually adds to the circuit.

Connecting metal probes to the p-side and n-side does not just "tap into" the junction -- it introduces two NEW junctions of its own: a metal-to-p-type contact and a metal-to-n-type contact, one at each probe. Every contact between two different materials develops its own contact (built-in) potential, just as the p-n junction does.

Step 3 -- Trace the complete closed loop.

The full measurement path runs: metal probe 1 $\to$ p-side $\to$ (the p-n junction, contributing $V_0$) $\to$ n-side $\to$ metal probe 2 $\to$ voltmeter $\to$ back to metal probe 1. This is a single closed loop containing THREE potential steps, not one.

Step 4 -- Apply equilibrium to the whole loop. …