ece-1109 ECE-1109 Introduction to ECE

Semiconductor Physics and Diode Fundamentals

Final Consolidated Summary: Semiconductor Physics and Diodes

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Part 1: Band Theory and Semiconductor Classification

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 [1-4].	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 [7-9].	No energy gap [7-9].	Electrons easily move into higher unoccupied energy levels within the same band upon applying an electric field .
Insulator	Bands are separated .	Very large, nearly $\le 15\text{ eV}$ .	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 $\le 2\text{ eV}$ .	Acts like an insulator at low temperatures; conductivity increases as temperature increases .

3. Carrier Generation and Movement

• Carrier Generation: At $T=0\text{ K}$, covalent bonding positions are filled . When temperature increases, valence electrons gain thermal energy to overcome the band gap, becoming free electrons (negative carriers) in the CB, leaving behind positive empty states called holes [12-15].

• 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 .

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 $E$ .	$J_n=en{\mu }_{n}E$ . Current flows opposite to electron flow .	$J_p=ep{\mu }_{p}E$ . Current flows in the direction of hole flow .	$J=en{\mu }_{n}E+ep{\mu }_{p}E$ .
Diffusion Current	Motion due to a concentration gradient (carriers move from high to low concentration regions) [20-23].	$J_n=e{D}_n\frac{dn}{dx}$. Current flows opposite to electron flow .	$J_p=e{D}_p\frac{dp}{dx}$. Current flows in the same direction as hole flow .	N/A

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Part 2: Extrinsic Semiconductors and Junctions

1. Extrinsic Material Characteristics

Type	Doping Impurity	Doping Group	Carrier Generation	Majority Carrier
Extrinsic	Specific impurities (trivalent or pentavalent) are added (doping) to create carriers [11, 24-26].	N/A	N/A	N/A
N-type	Donor impurity (P, As, Sb) [27-30].	Group V (Pentavalent) .	Fifth valence electron is loosely bound and easily breaks free, creating an electron without creating a corresponding hole .	Electrons (have preponderance over holes) . Minority carriers are holes .
P-type	Acceptor impurity (B, Al, Ga, In) .	Group III (Trivalent) .	Accepts a valence electron, leading to the creation of a hole without generating an electron .	Holes (have preponderance over electrons) . Minority carriers are electrons .
Electrical Neutrality	Both N-type and P-type semiconductors remain neutral because the charge of ionized donor/acceptor atoms balances the charge of the free carriers [35-38].	N/A	N/A	N/A

2. 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) [39-42].

   ◦ If holes $>$ electrons, $E_F$ is closer to the VB (P-type) [39-42].

• Carrier Concentration in Extrinsic Material:

   ◦ Fundamental relationship: $n_0{p}_0=n_i^2$ .

   ◦ For N-type ($n\gg p$): $n_0\approx N_D$, and $p_0=n_i^2/N_D$ .

   ◦ For P-type ($p\gg n$): $p_0\approx N_A$, and $n_0=n_i^2/N_A$ . .

3. 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 [49-52].
Depletion Width ($W$)	Higher doping concentration (increased $N_A$ or $N_D$) decreases the depletion region width ($W$ decreases) . Lower doping concentration increases $W$ .	$W\propto 1/\text{Doping concentration}$ .

4. 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 [55-58].	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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Part 3: Diode Characteristics and Advanced Topics

1. Diode I-V Characteristics and Temperature Effects

• Diode Equation: The theoretical relationship between voltage and current is $I_D=I_s\left(e^{V_D/\eta V_T}-1\right)$ .

   ◦ Forward: For positive $V_D$, current increases exponentially [64-67].

   ◦ Reverse: For negative $V_D$, the exponential term quickly approaches zero, leaving $I_D\approx -I_s$ (leakage current) .

• Temperature Effects:

   ◦ The required forward bias voltage decreases as temperature increases .

   ◦ The reverse leakage current ($I_s$) is strongly temperature dependent . $I_s$ approximately doubles for every $5^{\circ }\text{ C}$ or $10^{\circ }\text{ C}$ rise in temperature .

2. Reverse Breakdown

Mechanism	Doping Level	Characteristics
Breakdown Voltage	Critical reverse bias voltage at which the current increases sharply, and relatively large current can flow with little increase in voltage [68-71].	Reverse voltage breakdown occurs by two mechanisms .
Avalanche Breakdown	Low doped diode .	Occurs at high reverse voltage. Carriers gain kinetic energy and break covalent bonds via collision, creating more electron-hole pairs, which continues until diode burnout [70-73].
Zener Breakdown	Highly doped diode .	Occurs at low reverse voltage because the thin depletion region creates a strong electric field, accelerating electrons across the barrier .

3. Diode Resistance and Capacitance

Characteristic	Condition	Formula / Behavior
DC / Static Resistance ($R_{DC}$)	Steady-state operation point.	$R_{DC}=V_D/I_D$. High in reverse bias, decreases as current increases past the knee voltage .
AC / Dynamic Resistance ($r_d$ or $r_p$)	Defines the specific change in current/voltage around an operating point (slope of the tangent) .	$r_d=\frac{d{V}_D}{d{I}_D}=\frac{\eta V_T}{I_D}$. (If $\eta =1,V_T=26\text{ mV}$, then $r_p=26\text{ mV}/I_D$) .
Transition Capacitance ($C_T$)	Reverse-biased junction .	The depletion region (free of carriers) acts as the insulator between the p-type and n-type regions (plates) [78-81]. $C_T$ decreases as reverse bias increases because depletion width increases ($C\propto 1/d$) .
Diffusion Capacitance ($C_D$)	Forward-biased junction .	Occurs due to the accumulation of stored minority charge carriers near the junction . $C_D$ increases as forward bias voltage increases because the stored charge increases .
Reverse Recovery Time ($t_{rr}$)	Time required to switch from forward-biased (conducting) to reverse-biased (blocking) state .	$t_{rr}$ is the sum of storage time ($t_s$) and transition time ($t_t$) .

4. 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 .

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