Key Concepts of Energy Band Diagrams

Why This Matters

Energy band diagrams are the foundation for understanding why materials conduct electricity differently—and more importantly, how we engineer semiconductors to build every electronic device you use. When you're tested on semiconductor physics, you're really being asked to explain the relationship between band structure, charge carriers, and device behavior. Questions will probe whether you understand how doping shifts the Fermi level, why junctions create built-in electric fields, and what happens to band diagrams under bias conditions.

These concepts connect directly to carrier transport, junction physics, and device operation—the core principles that appear repeatedly in FRQs about diodes, transistors, and photovoltaic cells. Don't just memorize that silicon has a band gap of $1.1 \, \text{eV}$—know what that means for thermal excitation, doping effectiveness, and device applications. If you can sketch a band diagram and explain what's happening to electrons and holes, you've mastered the conceptual core of semiconductor physics.

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Band Gap Classification: What Determines Conductivity

The band gap—the energy separation between the valence and conduction bands—determines whether a material is an insulator, semiconductor, or conductor. This single parameter controls whether electrons can be thermally excited into conducting states.

Insulators

• Large band gap (> 4 eV)—electrons cannot gain enough thermal energy to jump to the conduction band at room temperature
• Tightly bound electrons remain localized in the valence band, resulting in negligible electrical conductivity
• Common examples include glass, rubber, and ceramics—materials chosen specifically because they block current flow

Conductors

• Overlapping or zero band gap—the valence and conduction bands merge, allowing electrons to move freely without energy input
• Abundant free charge carriers (typically $10^{22}-10^{23}$ electrons per $\text{cm}^3$) enable efficient current flow
• Metals like copper and silver are preferred for wiring due to their high carrier density and mobility

Semiconductors

• Moderate band gap (1–3 eV)—small enough for thermal excitation but large enough for controlled conductivity
• Tunable properties through temperature, doping, or applied fields make these materials the foundation of electronics
• Silicon ($E_g = 1.1 \, \text{eV}$) and germanium ($E_g = 0.67 \, \text{eV}$) are the workhorses of the semiconductor industry

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Intrinsic vs. Extrinsic: Engineering Carrier Concentrations

Pure semiconductors have limited conductivity, but doping—intentionally adding impurities—lets us control carrier type and concentration. This is how we transform a mediocre conductor into a precisely engineered electronic material.

Intrinsic Semiconductors

• Pure, undoped material—conductivity arises solely from thermally generated electron-hole pairs
• Equal concentrations of electrons ($n$) and holes ($p$), where $n = p = n_i$ (the intrinsic carrier concentration)
• Temperature-dependent conductivity—carrier concentration follows $n_i \propto T^{3/2} e^{-E_g/2k_BT}$, doubling roughly every 10°C for silicon

N-Type Semiconductors

• Donor doping with Group V elements (phosphorus, arsenic) adds electrons to the conduction band
• Majority carriers are electrons—the Fermi level shifts upward toward the conduction band edge
• Enhanced conductivity is controlled by dopant concentration, typically $10^{15}-10^{18} \, \text{cm}^{-3}$

P-Type Semiconductors

• Acceptor doping with Group III elements (boron, gallium) creates holes in the valence band
• Majority carriers are holes—the Fermi level shifts downward toward the valence band edge
• Hole conduction dominates, though electrons still exist as minority carriers

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Junction Physics: Where Band Diagrams Get Interesting

When different materials meet, band bending occurs to equalize the Fermi level across the junction. This creates built-in electric fields and the depletion regions that make devices work.

P-N Junction

• Depletion region forms at the interface as electrons and holes diffuse across and recombine, leaving behind ionized dopants
• Built-in potential ($V_{bi}$) creates an electric field opposing further diffusion—typically $0.6-0.7 \, \text{V}$ for silicon
• Foundation of diodes, transistors, and solar cells—understanding this junction is essential for all semiconductor device physics

Forward Bias

• External voltage (P positive, N negative) reduces the built-in potential barrier
• Depletion region narrows—majority carriers can now diffuse across the junction, enabling exponential current flow
• Current follows $I = I_0(e^{qV/k_BT} - 1)$, the ideal diode equation you'll need for quantitative problems

Reverse Bias

• External voltage (P negative, N positive) adds to the built-in potential barrier
• Depletion region widens—majority carrier flow is blocked, leaving only tiny reverse saturation current ($I_0$)
• Breakdown occurs at high reverse voltages through avalanche or Zener mechanisms—important for voltage regulation

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Metal-Semiconductor Contacts: Beyond P-N Junctions

Not all junctions involve two semiconductors. Metal-semiconductor interfaces create their own unique band structures with distinct advantages for certain applications.

Metal-Semiconductor Junction (Schottky Barrier)

• Barrier height ($\phi_B$) forms at the interface, determined by the metal work function and semiconductor electron affinity
• Majority carrier device—current flows via thermionic emission over the barrier, not minority carrier injection
• Fast switching and low forward drop ($\sim 0.3 \, \text{V}$)—ideal for high-frequency rectifiers, RF mixers, and solar cells

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Quick Reference Table

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Self-Check Questions

1. What feature of the band diagram distinguishes an N-type semiconductor from a P-type semiconductor, and how does this relate to majority carrier type?

2. Compare the depletion region width under forward bias versus reverse bias—what happens to the built-in electric field in each case?

3. If an FRQ shows a band diagram with the Fermi level very close to the conduction band, what can you conclude about the doping type and approximate dopant concentration?

4. Why does a Schottky diode switch faster than a P-N junction diode? Explain in terms of the charge carriers involved in each device.

5. Two semiconductors have band gaps of $0.7 \, \text{eV}$ and $1.4 \, \text{eV}$. Which would have higher intrinsic carrier concentration at room temperature, and how would this affect their conductivity without doping?