1.1 Semiconductor Theory, PN Junction & Conduction

1.1 Semiconductor Theory, PN Junction & Conduction

Modern aircraft avionics, flight guidance computers, engine full-authority digital engine controls (FADEC), and electrical power generation systems depend fundamentally on solid-state semiconductor electronics. Under the European Aviation Safety Agency (EASA) Part-66 Module 04 syllabus, certifying maintenance engineers must master the atomic architecture, physical transport phenomena, and conduction characteristics of semiconductor materials. This section explores atomic lattices, donor and acceptor doping, PN junction formation, barrier potentials, forward and reverse bias dynamics, and breakdown mechanisms.

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Atomic Structure & The Semiconductor Crystal Lattice

All electrical materials are classified according to their atomic electron configuration and energy band structure into conductors, insulators, and semiconductors:

• Conductors (e.g., copper, silver, aluminum) possess overlapping valence and conduction bands, allowing valence electrons to drift freely under minimal electric fields.
• Insulators (e.g., mica, Teflon, glass) feature a wide forbidden energy gap ($E_g > 5\text{ eV}$), preventing valence electrons from reaching the conduction band under standard operating conditions.
• Semiconductors possess a moderate forbidden energy gap ($E_g \approx 0.6\text{ to } 1.5\text{ eV}$) that can be overcome by thermal, optical, or electrical energy.

The two foundational semiconductor elements in electronics are Silicon and Germanium:

1. Silicon ($Z = 14$): Its electron configuration is $1s^2 2s^2 2p^6 3s^2 3p^2$ (shells: 2, 8, 4). The four electrons in the outermost $M$-shell constitute its valence electrons. At $300\text{ K}$ ($25^\circ\text{C}$), pure silicon has an energy bandgap of $E_g = 1.12\text{ eV}$.
2. Germanium ($Z = 32$): Its electron configuration is $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^2$ (shells: 2, 8, 18, 4). The four electrons in the outermost $N$-shell constitute its valence electrons. At $300\text{ K}$, germanium has an energy bandgap of $E_g = 0.67\text{ eV}$.

graph LR
    subgraph DiamondLattice["Covalent Crystal Lattice Structure"]
        A["Si Core (+4)"] --- B["Shared Valence Pair (2e-)"]
        B --- C["Si Core (+4)"]
        C --- D["Shared Valence Pair (2e-)"]
        D --- E["Si Core (+4)"]
    end

In an intrinsic (chemically pure) crystal, each tetravalent atom shares its four valence electrons with four neighboring atoms in a diamond cubic lattice via covalent bonding. At absolute zero ($0\text{ K}$), all valence electrons are locked within these covalent bonds, the conduction band is completely empty, and the crystal behaves as a perfect electrical insulator.

As ambient temperature rises, thermal vibrations impart sufficient energy to rupture a small fraction of covalent bonds. An electron absorbing energy greater than the bandgap ($E_g$) transitions across the forbidden gap into the conduction band, becoming a free electron. The vacancy left behind in the valence band behaves as an effective positive charge of magnitude $+q$ ($1.602 \times 10^{-19}\text{ C}$) and is termed a hole ($h^+$). Under an applied electric field, conduction occurs simultaneously through free electrons moving in the conduction band and valence electrons hopping between vacancies, which appears macroscopically as holes migrating in the opposite direction.

Because thermal excitation generates electrons and holes in identical quantities, intrinsic carrier concentrations are equal ($n = p = n_i$). Intrinsic semiconductors exhibit a Negative Temperature Coefficient (NTC) of resistance: as temperature increases, carrier density increases exponentially, causing electrical resistance to drop sharply.

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Extrinsic Semiconductors: Doping Principles

Because the intrinsic carrier concentration of pure silicon is extraordinarily low at room temperature ($n_i \approx 1.5 \times 10^{10}\text{ cm}^{-3}$ out of $\approx 5 \times 10^{22}\text{ atoms/cm}^3$), intrinsic silicon is a poor conductor. To control conductivity, deliberate impurities are introduced in tiny, precisely measured concentrations (typically 1 part in $10^6$ to $10^8$) through a process termed doping, creating extrinsic semiconductors.

N-Type Semiconductor (Pentavalent Doping)

When pure silicon or germanium is doped with a pentavalent element from Group 15 of the periodic table—such as Phosphorus ($Z=15$), Arsenic ($Z=33$), or Antimony ($Z=51$):

• Four of the impurity atom's valence electrons form covalent bonds with adjacent silicon atoms.
• The fifth valence electron cannot fit into the covalent bond structure and remains loosely bound to the impurity nucleus with an ionization energy of only $\approx 0.05\text{ eV}$ in silicon (and $\approx 0.01\text{ eV}$ in germanium).
• At room temperature ($300\text{ K}$), thermal energy is more than sufficient to ionize virtually all donor atoms, promoting their fifth electrons into the conduction band.
• The impurity atoms are termed donor atoms because they donate conduction electrons without creating corresponding valence holes.
• Upon releasing an electron, the donor atom becomes an immobile, positively charged ion ($D^+$) locked into the crystal lattice.

In N-type material:

• Majority Carriers: Free electrons ($n_n \approx N_D$).
• Minority Carriers: Thermally generated holes ($p_n = n_i^2 / N_D$).
• Electrical Neutrality: The bulk crystal remains electrically neutral because the total number of positive charges (protons in silicon and donor nuclei) exactly balances the total number of negative charges (valence and conduction electrons).

P-Type Semiconductor (Trivalent Doping)

When intrinsic silicon is doped with a trivalent element from Group 13 of the periodic table—such as Boron ($Z=5$), Gallium ($Z=31$), or Indium ($Z=49$):

• The three valence electrons form covalent bonds with three adjacent silicon atoms, leaving an incomplete bond (a vacancy) with the fourth neighbor.
• This vacancy readily accepts a valence electron from an adjacent silicon-silicon bond with very little thermal activation energy ($\approx 0.05\text{ eV}$ in silicon).
• When an electron jumps into the vacancy, a new hole is created in the valence band, allowing charge transport.
• The impurity atoms are termed acceptor atoms.
• Upon capturing an electron, each acceptor atom becomes an immobile, negatively charged ion ($A^-$) bound firmly within the crystal lattice.

In P-type material:

• Majority Carriers: Holes ($p_p \approx N_A$).
• Minority Carriers: Thermally generated free electrons ($n_p = n_i^2 / N_A$).
• Electrical Neutrality: The crystal remains strictly neutral because negative acceptor ions balance mobile positive holes.

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Formation of the PN Junction & The Depletion Region

When P-type and N-type semiconductor regions are joined within a single continuous crystal lattice, a PN junction is formed. Because a steep concentration gradient exists across the metallurgical boundary, mobile majority carriers immediately begin to diffuse across the junction:

1. Free electrons in the N-region diffuse across the interface into the P-region.
2. Holes in the P-region diffuse across the interface into the N-region.
3. Upon crossing the junction, diffusing electrons recombine with nearby holes, neutralizing both mobile carriers.

graph TD
    subgraph Equilibrium["PN Junction in Thermal Equilibrium"]
        P["P-Region<br/>Majority: Mobile Holes (h+)<br/>Fixed: Negative Ions (A-)"]
        DEP["Depletion Region (Space Charge)<br/>No Mobile Carriers<br/>Uncompensated Ions: [ A- | D+ ]<br/>Built-in Electric Field E (N -> P)"]
        N["N-Region<br/>Majority: Mobile Electrons (e-)<br/>Fixed: Positive Ions (D+)"]
    end
    P -->|"Hole Diffusion"| DEP
    N -->|"Electron Diffusion"| DEP
    DEP -->|"Built-in Potential V0<br/>Opposes Further Diffusion"| P

As recombination continues, the mobile carriers disappear from the vicinity of the boundary, leaving behind uncompensated, fixed ionic cores locked in the lattice:

• Positively charged donor ions ($D^+$) on the N-side of the boundary.
• Negatively charged acceptor ions ($A^-$) on the P-side of the boundary.

This zone adjacent to the junction is completely stripped of mobile charge carriers and is called the depletion region (or space charge region). The separated positive and negative ionic charges establish an internal, built-in electric field ($\vec{E}$) directed from the positive donor ions (N-side) toward the negative acceptor ions (P-side).

This built-in electric field opposes further majority carrier diffusion. Dynamic equilibrium is reached when the electric field becomes strong enough that the drift current (minority carriers swept across the junction by the field) exactly balances the diffusion current (majority carriers climbing the potential barrier). The electrostatic potential difference across the depletion region at thermal equilibrium is the barrier potential ($V_0$ or $V_K$, also known as the contact potential or knee voltage):

• Silicon (Si): $V_0 \approx 0.7\text{ V}$ at $25^\circ\text{C}$ ($300\text{ K}$).
• Germanium (Ge): $V_0 \approx 0.3\text{ V}$ at $25^\circ\text{C}$ ($300\text{ K}$).

The barrier potential has a negative temperature coefficient: it decreases by approximately $2\text{ mV/}^\circ\text{C}$ as junction temperature increases, due to enhanced intrinsic carrier thermal generation.

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Forward Bias Dynamics & Conduction

A PN junction is forward biased when an external DC voltage source ($V_F$) is connected with its positive terminal to the P-type material (anode) and its negative terminal to the N-type material (cathode):

1. The external positive potential repels positive holes in the P-region toward the junction, while the negative terminal repels free electrons in the N-region toward the junction.
2. The applied external electric field directly opposes the built-in space-charge electric field, reducing the net potential barrier and narrowing the physical width of the depletion region.
3. As long as $V_F < V_0$, the barrier remains sufficient to restrict current to a negligible level.
4. When the external bias reaches and exceeds the barrier threshold ($V_F \ge 0.7\text{ V}$ for silicon, $0.3\text{ V}$ for germanium), the potential barrier is eliminated. Majority carriers flood across the junction in enormous numbers, recombining and establishing a large forward current ($I_F$).

The forward current-voltage relationship is governed by the Shockley diode equation:

$I_D = I_S \left( e^{\frac{q V_D}{\eta k T}} - 1 \right) = I_S \left( e^{\frac{V_D}{\eta V_T}} - 1 \right)$

Where:

• $I_S$ is the reverse saturation leakage current.
• $q$ is the elementary electron charge ($1.602 \times 10^{-19}\text{ C}$).
• $V_D$ is the voltage across the diode junction.
• $k$ is Boltzmann's constant ($1.381 \times 10^{-23}\text{ J/K}$).
• $T$ is absolute temperature in Kelvin (K).
• $\eta$ is the ideality factor ($\approx 1$ for germanium; $\approx 1\text{ to } 2$ for silicon).
• $V_T = \frac{k T}{q}$ is the thermal voltage, equal to approximately $25.86\text{ mV} \approx 26\text{ mV}$ at room temperature ($300\text{ K}$).

Above the knee voltage, the current increases exponentially. To prevent destructive overcurrent, a forward-biased diode must always operate in series with a current-limiting load or resistor. The dynamic (AC) forward resistance ($r_d$) of the diode is the reciprocal of the slope of the VI curve:

$r_d = \frac{d V_D}{d I_D} \approx \frac{\eta V_T}{I_D}$

At a forward current of $26\text{ mA}$ (with $\eta = 1$), the dynamic resistance of a silicon diode junction is only $r_d \approx 26\text{ mV} / 26\text{ mA} = 1\ \Omega$.

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Reverse Bias Dynamics & Leakage Current

A PN junction is reverse biased when an external DC voltage source ($V_R$) is connected with its positive terminal to the N-type material (cathode) and its negative terminal to the P-type material (anode):

1. The external positive terminal attracts free electrons in the N-region away from the junction; simultaneously, the negative terminal attracts holes in the P-region away from the junction.
2. This majority carrier withdrawal exposes additional donor and acceptor ions, widening the depletion region and increasing the height of the internal potential barrier to $(V_0 + V_R)$.
3. Majority carrier diffusion across the junction is completely halted.
4. However, the widened electric field aids the transit of thermally generated minority carriers (electrons in the P-region, holes in the N-region) that drift into the depletion zone. The electric field sweeps these minority carriers across the junction, creating a minute reverse saturation current ($I_S$).

Because minority carrier concentration depends strictly on thermal bond breakage rather than the magnitude of reverse voltage, $I_S$ remains almost completely constant as reverse voltage increases, up to the point of breakdown. However, $I_S$ is exceptionally sensitive to operating temperature:

[!NOTE] The 10°C Thermal Doubling Rule: In both silicon and germanium PN junctions, the reverse saturation leakage current ($I_S$) approximately doubles for every $10^\circ\text{C}$ rise in junction temperature: $I_S(T_2) = I_S(T_1) \cdot 2^{\frac{T_2 - T_1}{10}}$

At $25^\circ\text{C}$, the reverse leakage of a typical small-signal silicon diode is on the order of $1\text{ nA to } 10\text{ nA}$, whereas an equivalent germanium diode exhibits $1\text{ }\mu\text{A to } 10\text{ }\mu\text{A}$—roughly 1,000 times greater. When installed in aircraft engine bays or unconditioned avionics compartments where temperatures reach $+85^\circ\text{C}$ to $+125^\circ\text{C}$, germanium leakage escalates to hundreds of microamperes, triggering severe signal degradation and risk of thermal runaway.

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Reverse Breakdown: Zener vs. Avalanche Mechanisms

If the reverse bias voltage is increased beyond a critical threshold known as the breakdown voltage ($V_{BR}$), the reverse current escalates abruptly. If the current is not constrained by external circuit impedance, excessive power dissipation will destroy the component. Two distinct physical mechanisms produce reverse breakdown:

graph TD
    subgraph BreakdownMechanisms["Reverse Breakdown Comparison"]
        ZENER["Zener Breakdown<br/>• Heavily Doped PN Junctions<br/>• Thin Depletion Region (&lt; 5-6 V)<br/>• Intense Field (> 3x10^5 V/cm)<br/>• Quantum Mechanical Tunneling<br/>• Negative Temp Coefficient (NTC)"]
        AVAL["Avalanche Breakdown<br/>• Lightly Doped PN Junctions<br/>• Wide Depletion Region (> 6 V)<br/>• High Kinetic Acceleration<br/>• Impact Ionization & Multiplication<br/>• Positive Temp Coefficient (PTC)"]
    end

1. Zener Breakdown (Field Emission / Tunneling)

• Doping Level: Occurs in junctions that are heavily doped with impurity atoms on both P and N sides.
• Depletion Region Geometry: High doping creates an extremely narrow depletion layer (often less than $10\text{ nm}$). Consequently, even a modest reverse voltage (below $5\text{ V}$ to $6\text{ V}$) generates an intense electric field exceeding $3 \times 10^5\text{ V/cm}$ ($30\text{ MV/m}$).
• Mechanism: The immense electric field exerts direct electrostatic force on valence electrons, tearing them out of their covalent bonds. These electrons tunnel directly across the narrow forbidden bandgap from the valence band of the P-type material into the conduction band of the N-type material (quantum mechanical tunneling).
• Temperature Coefficient: Negative. As junction temperature increases, crystal lattice thermal energy excites valence electrons to higher energy states, narrowing the effective bandgap; therefore, a lower reverse voltage is required to initiate tunneling.

2. Avalanche Multiplication (Impact Ionization)

• Doping Level: Occurs in lightly to moderately doped junctions.
• Depletion Region Geometry: Lower doping results in a comparatively wide depletion region. Breakdown occurs at higher reverse voltages (typically above $6\text{ V}$).
• Mechanism: Thermally generated minority carriers entering the wide depletion region are accelerated by the high electric field over relatively long mean free paths, acquiring substantial kinetic energy. When an energetic electron collides with a stationary silicon lattice atom, it knocks a valence electron out of its covalent bond (impact ionization), creating a new electron-hole pair. The liberated carriers are in turn accelerated by the field, colliding with additional lattice atoms to liberate further carriers in a geometric chain reaction (avalanche multiplication).
• Temperature Coefficient: Positive. As temperature rises, lattice atoms vibrate more violently. Moving carriers collide with vibrating lattice atoms much more frequently, reducing their mean free path and preventing them from accumulating ionizing kinetic energy unless a higher electric field (higher reverse voltage) is applied.

[!WARNING] Avionics Thermal Runaway: Exceeding a semiconductor's maximum junction operating temperature ($T_{j,max} \approx 175^\circ\text{C}$ to $200^\circ\text{C}$ for silicon, but only $85^\circ\text{C}$ to $100^\circ\text{C}$ for germanium) causes thermally generated intrinsic carriers to overwhelm the dopant carrier concentration. The device loses all PN junction rectification, conducting uncontrollably in both directions until permanent thermal destruction occurs.

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Diode Symbols, Polarity Marking & Package Identification

Every diode symbol is built from the same two elements: a solid triangle, which is the anode (A), pointing at a bar, which is the cathode (K). Conventional current flows in the direction the triangle points, and only when the device is forward biased. Modifications to the bar or added leads identify the device family:

[!NOTE] Reading Polarity on the Physical Part: The cathode is always the marked end. On glass and plastic axial diodes it is a painted band; on metal stud rectifiers the case is usually the cathode; on surface-mount packages it is a printed stripe or a bevelled corner; on an LED the cathode is the shorter lead and the flat on the moulding. The PCB silkscreen repeats the band on the component outline, so a diode fitted against the printed band is reversed. Fitting an axial rectifier or freewheeling diode backwards places a forward-biased short across the aircraft bus.

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Diode Parameters on the Datasheet

The Part-66 syllabus names six diode parameters explicitly. All six appear on a standard rectifier datasheet; the figures below are for the very common 1N4007 silicon rectifier:

Two of these are routinely misapplied in service:

• Frequency is a real limit, not a formality. A general-purpose $2\ \mu\text{s}$ recovery rectifier such as the 1N4007 is perfectly happy on a $400\text{ Hz}$ aircraft bus, where the half-cycle lasts $1.25\text{ ms}$. Fit the same part in a $50\text{ kHz}$ switch-mode converter (half-cycle $10\ \mu\text{s}$) and it conducts backwards for a fifth of every half-cycle, overheating and destroying itself. Switch-mode stages need fast-recovery ($t_{rr} < 100\text{ ns}$) or Schottky ($t_{rr} < 1\text{ ns}$) parts.
• $I_{F(AV)}$ is an average, not a peak. In a capacitor-input filter the diodes conduct in short, tall pulses; the peak repetitive current can be five to ten times the average. Size against $I_{FSM}$ for switch-on inrush as well as $I_{F(AV)}$ for steady state.

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Diodes in Series and in Parallel

Where a single device cannot meet the required blocking voltage or current, diodes are connected in series or in parallel. Neither connection shares perfectly on its own, because no two junctions are identical.

Series Connection - Increasing the Blocking Voltage

Series-connected diodes divide the reverse voltage between them, but the division follows leakage current, not the ratings. In reverse bias the string carries one common current, so the diode with the lowest leakage must develop the highest reverse voltage to pass that current - and it is the first to avalanche.

The cure is a voltage-equalising (sharing) resistor connected across each diode, sized so that the resistor current swamps the leakage mismatch. Fast transients are shared by adding a small capacitor across each diode, because reverse-recovery charge differs between devices even when steady leakage is matched. Note also that the forward drops add: two silicon diodes in series drop about $1.4\text{ V}$.

Worked example - equalising resistors. Two $600\text{ V}$ rectifiers are placed in series to block $800\text{ V}$ on a high-voltage radar supply. At operating temperature their reverse leakages are $I_{L1} = 5\ \mu\text{A}$ and $I_{L2} = 25\ \mu\text{A}$ (a mismatch of $\Delta I_L = 20\ \mu\text{A}$). Choose equalising resistors so the resistor current is roughly ten times the mismatch:

$I_R \ge 10 \cdot \Delta I_L = 10 \times 20\ \mu\text{A} = 200\ \mu\text{A} \quad \Longrightarrow \quad R = \frac{800\text{ V} / 2}{200\ \mu\text{A}} = \frac{400\text{ V}}{2.0 \times 10^{-4}\text{ A}} = 2.0\text{ M}\Omega$

The residual imbalance is then $\Delta V = \Delta I_L \cdot R = 20\ \mu\text{A} \times 2.0\text{ M}\Omega = 40\text{ V}$, so the two diodes block $420\text{ V}$ and $380\text{ V}$ - both comfortably inside the $600\text{ V}$ rating. Each resistor dissipates only $P = V^2 / R = (400)^2 / 2.0 \times 10^6 = 0.08\text{ W}$.

Parallel Connection - Increasing the Current Capacity

Parallel diodes share the load current, but the forward voltage drop of a silicon junction has a negative temperature coefficient of about $-2\text{ mV/}^\circ\text{C}$. The diode that happens to run hottest therefore drops slightly less voltage, takes a larger share of the current, heats further, and takes more current still. This regenerative process is called current hogging and ends in thermal runaway of one device followed by cascade failure of the rest.

Three standard countermeasures are used on aircraft Transformer Rectifier Units and generator rectifier banks:

1. Small series ballast (sharing) resistors in each diode leg, typically dropping $0.2\text{ V}$ to $0.5\text{ V}$ at rated current, so the resistive drop dominates the junction mismatch.
2. Matched devices from the same production batch, selected for forward voltage within a few millivolts.
3. A common heat sink, so all the paralleled junctions run at the same temperature and the negative temperature coefficient cannot create an imbalance in the first place.

Paralleling does not reduce the forward drop - the string still drops about $0.7\text{ V}$ - and it does nothing for the PIV rating, which remains that of a single device.

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Silicon vs. Germanium Comparison

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Worked Numerical Calculation: Forward Diode DC Circuit

An aircraft cockpit annunciator panel contains an indicator circuit energized from an avionics DC supply rail of $V_S = 14.0\text{ V DC}$. A silicon diode operates in series with a current-limiting resistor $R_S = 330\ \Omega$ to provide reverse-polarity protection.

  +14.0V DC o----[ RS = 330 Ω ]----( Anode >| Cathode )----o GND (0V)
                                      Silicon Diode

Step 1: Calculate Voltage Across the Series Resistor

Applying Kirchhoff's Voltage Law (KVL) around the closed loop: $V_S - V_R - V_D = 0$ $V_R = V_S - V_D$ Assuming a standard forward voltage drop of $V_D = 0.70\text{ V}$ for silicon: $V_R = 14.0\text{ V} - 0.70\text{ V} = 13.30\text{ V}$

Step 2: Determine Loop Current ($I_D$)

Applying Ohm's law to the current-limiting resistor: $I_D = \frac{V_R}{R_S} = \frac{13.30\text{ V}}{330\ \Omega} = 0.04030\text{ A} = 40.30\text{ mA}$

Step 3: Calculate Diode Forward Power Dissipation ($P_D$)

$P_D = V_D \cdot I_D = 0.70\text{ V} \times 40.30\text{ mA} = 28.21\text{ mW}$

Step 4: Calculate Resistor Power Dissipation ($P_R$)

$P_R = V_R \cdot I_D = 13.30\text{ V} \times 0.04030\text{ A} = 0.5360\text{ W} = 536.0\text{ mW}$

Engineering Conclusion: The diode dissipates only $28.2\text{ mW}$, operating well within standard $250\text{ mW}$ limits. However, the series resistor dissipates $0.536\text{ W}$, meaning a standard $0.5\text{ W}$ resistor would be over-stressed; a technician or designer must install a resistor rated for at least $1.0\text{ W}$ to guarantee aerospace reliability.