A germanium specimen is doped with aluminum. The concentration of acceptor | PGMN Solutions

A germanium specimen is doped with aluminum. The concentration of acceptor atoms is 〖10〗^21/m^3. The intrinsic concentration of electron hole pairs is 〖10〗^19/m^3. The concentration of electrons in the specimen is
(A) 〖10〗^2/m^3
(B) 〖10〗^4/m^3
(C) 〖10〗^15/m^3
(D) 〖10〗^17/m^3




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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Semiconductor Devices
📌 Topic: Doping and Carrier Concentration in Semiconductors

🔹 Step 1: Understand what happens when germanium is doped with aluminum
Germanium is an intrinsic semiconductor. When it is doped with aluminum, which is a trivalent element, it becomes a p-type semiconductor. This means the acceptor atoms create holes (majority carriers), and the electrons become minority carriers.

🔹 Step 2: Recall the key relationship
In an extrinsic semiconductor, the product of electron and hole concentration remains equal to the square of the intrinsic concentration.
So, electron concentration multiplied by hole concentration equals intrinsic concentration squared.

🔹 Step 3: Use the given data
Intrinsic concentration is ten raised to nineteen per meter cube.
Acceptor concentration (hole concentration) is ten raised to twenty-one per meter cube.

Now, using the concept,
Electron concentration = (intrinsic concentration squared) divided by hole concentration
= (ten raised to thirty-eight) divided by (ten raised to twenty-one)
= ten raised to seventeen per meter cube.

🔹 Step 4: Conceptual conclusion
Since the specimen is heavily p-type, the number of electrons (minority carriers) will be much less, and that is exactly what this relation shows.

✅ Final Answer: (D) ten raised to seventeen per meter cube 🚀
🔥 Pro Tip: Always use the rule n multiplied by p equals ni squared to find minority carrier concentration in doped semiconductors—it saves time and gives accurate results!

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