Semiconductor Physics and Diode Fundamentals

Final Consolidated Summary: Semiconductor Physics and Diodes

1. Energy Band Fundamentals

Concept	Definition/Mechanism	Key Principle
Energy Band	A set of closely-spaced energy levels formed when multiple atoms are brought near one another, causing the individual energy levels to split .	According to the Pauli Exclusion Principle, an isolated atom’s energy level can occupy no more than two electrons .
Forbidden Band / Energy Gap	Regions of energy values that electrons cannot possess, separating non-overlapping energy bands .	The size of this gap separates different types of solids .
Valence Band (VB)	The band of energy occupied by the outermost electrons (valence electrons) .	May be completely filled or partially filled .
Conduction Band (CB)	The band of next higher permitted energy, normally located above the VB .	Normally empty. Electrons here (conduction electrons) can move freely .

2. Classification of Solids

Solid Type	CB & VB Relationship	Energy Gap ( $E_{g}$ ) Size	Conduction Behavior
Conductor	Bands overlap .	No energy gap .	Electrons easily move into higher unoccupied energy levels within the same band upon applying an electric field .
Insulator	Bands are separated .	Very large, nearly $\leq 15 eV$ .	Impossible for electrons to conduct electric current without a very strong field that causes the element to break down .
Semiconductor	Bands are separated .	Very small, nearly $\leq 2 eV$ .	Acts like an insulator at low temperatures; conductivity increases as temperature increases .

3. Direct and Indirect Semiconductors

Semiconductor Type	Momentum Relationship	Light Emission Property
Direct	Maximum of VB and minimum of CB occur at the same momentum value .	Electron transition does not require momentum change . The corresponding wavelength of irradiated energy lies in the visible light region. Used for LED/laser production .
Indirect	Maximum of VB and minimum of CB occur at different momentum values .	Electron requires additional energy for the change in momentum. Not generally used for LED/laser production .

4. Carrier Generation

Table 1: Carrier Generation Mechanisms

Mechanism	Semiconductor Type	Process/Generation	Resulting Carrier Concentration
Thermal Generation	Intrinsic (Pure)	Valence electrons gain sufficient thermal energy to cross the band gap, leaving behind holes. This creates electron-hole pairs (EHPs).	The number of electrons (n) in the conduction band is exactly equal to the number of holes (p) in the valence band: n=p=ni.
Doping Generation	Extrinsic (Impurity-Added)	A small and controlled amount of impurity atoms (dopants) is added. This process increases conductivity by introducing extra charge carriers.	Carrier density is much higher than thermal generation and depends on the doping level. Electron and hole concentrations are not equal.

• Conduction Mechanism: When an electric field is applied, electrons in the CB move toward the positive terminal, and the motion of electrons filling holes makes it appear as if a positive charge (hole) is moving toward the negative terminal. Current flow is opposite to electron flow and in the same direction as hole flow .

5. Career Movements

Current Type	Cause/Mechanism	Electron Current Density ( $J_{n}$ )	Hole Current Density ( $J_{p}$ )	Total Drift Current Density ( $J$ )
Drift Current	Motion due to an applied electric field ( $E$ ) . Electrons move opposite to $E$ . Holes move in the direction of $E$ .	$J_{n} = e n μ_{n} E$ . Current flows opposite to electron flow .	$J_{p} = e p μ_{p} E$ . Current flows in the direction of hole flow .	$J = e n μ_{n} E + e p μ_{p} E$ .
Diffusion Current	Motion due to a concentration gradient (carriers move from high to low concentration regions) .	$J_{n} = e D_{n} \frac{d n}{d x}$ . Current flows opposite to electron flow .	$J_{p} = e D_{p} \frac{d p}{d x}$ . Current flows in the same direction as hole flow .	N/A

6. Extrinsic Material Characteristics

Table 01: Extrinsic Semiconductor Types

Feature	n-type Semiconductor	p-type Semiconductor
Dopant Type	Pentavalent impurity (Donor atoms, Group V, e.g., P, As, Sb).	Trivalent impurity (Acceptor atoms, Group III, e.g., B, Ga, In).
Generation Mechanism	Donor atoms easily release an extra free electron into the conduction band. This atom’s fifth valence electron is loosely bound.	Trivalent atoms create a deficiency of one electron, leading to the formation of a hole in the valence band. Acceptor atoms accept a valence electron, creating holes without generating free electrons.
Carrier Roles	Electrons are the majority carriers; holes become minority carriers.	Holes are the majority carriers; electrons are minority carriers.
Dopant Energy Level	Creates a Donor level (Ed) very near the conduction band.	Creates an empty Acceptor level near the valence band.
Fermi Level	Closer to the Conduction Band.	Closer to the Valence Band.
Electrical State	Remains electrically neutral, as the positive charge from the ionized donor atom balances the free electron.	Remains electrically neutral, as the negative charge from the ionized acceptor atom balances the positive charge of the hole.
Both N-type and P-type semiconductors remain neutral because the charge of ionized donor/acceptor atoms balances the charge of the free carriers

7. Fermi Level and Carrier Concentration

• Intrinsic Semiconductor: The probability/number of electrons in the CB is equal to the probability/number of holes in the VB . The Fermi level ( $E_{F}$ ) is in the middle of the energy gap .

• Extrinsic Fermi Level:

◦ If electrons $>$ holes, $E_{F}$ is closer to the CB (N-type)

◦ If holes $>$ electrons, $E_{F}$ is closer to the VB (P-type)

• Carrier Concentration in Extrinsic Material:

◦ Fundamental relationship: $n_{0} p_{0} = n_{i}^{2}$ .

◦ For N-type ( $n ≫ p$ ): $n_{0} \approx N_{D}$ , and $p_{0} = n_{i}^{2} / N_{D}$ .

◦ For P-type ( $p ≫ n$ ): $p_{0} \approx N_{A}$ , and $n_{0} = n_{i}^{2} / N_{A}$ .

8. p-n Junction (No Bias)

Phenomenon	Description	Effect
Formation	Holes diffuse from the p-side to the n-side, and electrons diffuse from the n-side to the p-side, due to large carrier concentration gradients .	Leaves behind uncompensated fixed positive donor ions (n-side) and negative acceptor ions (p-side) .
Depletion Region	The region depleted of mobile charge carriers (electrons and holes), containing only the fixed ions .	An electric field appears across the junction, tending toward the positive charge .
Built-in Potential ( $V_{0}$ )	The electric field creates a potential difference across the junction (potential barrier), which increases until equilibrium occurs .	At equilibrium, the net current flow is zero: drift current exactly cancels diffusion current .
Depletion Width ( $W$ )	Higher doping concentration (increased $N_{A}$ or $N_{D}$ ) decreases the depletion region width ( $W$ decreases) . Lower doping concentration increases $W$ .	$W \propto 1/ Doping concentration$ .

9. p-n Junction Biasing

Bias Condition	External Voltage Polarity (P to N)	Effect on Barrier/Width	Current Flow Mechanism
Forward Bias	Positive to P, Negative to N ( $V_{D}$ ) .	Applied field opposes the built-in field . Potential barrier decreases to $(V_{0} - V_{D})$ . Depletion width decreases.	Diffusion Current (Majority Carriers): Electrons diffuse n to p, holes diffuse p to n, resulting in a large current .
Reverse Bias	Positive to N, Negative to P ( $V_{R}$ ) .	Applied field adds to the built-in field . Potential barrier increases to $(V_{0} + V_{R})$ . Depletion width increases .	Drift Current (Minority Carriers): The electric field sweeps minority carriers across the junction, generating a very small, constant current called leakage current .

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BJT Circuit Analysis Assignment