Chapter 7. Diode
Recommended Article: 【Circuit Theory】 Circuit Theory Table of Contents
2. Diode
1. Semiconductor
⑴ Overview
① Faraday first reported semiconductors.
② Semiconductors have conductivity between conductors and insulators, which can be controlled by factors like temperature and purity.
① Definition: Theory analyzing the potential energy for bound atoms rather than free particles
② Classification of energy bands
○ Energy band: A continuous range where states exist
○ Forbidden band gap: A continuous range where states don’t exist
○ Energy gap: Energy required to move an electron from valence band to conduction band
○ Energy bands further categorized into valence band and conduction band
③ Fermi level
○ Definition: The highest energy level electrons can have at 0 K
○ Fermi level defined this way leads to a half probability of electron occupancy at any temperature
○ Fermi-Dirac distribution: Probability of an energy level E being filled by particles at temperature T
○ Conductor: Fermi level located at the boundary of the valence band and conduction band
○ Insulator: Fermi level located in the middle of valence band and conduction band
○ Semiconductor: Fermi level located in the middle of valence band and conduction band
④ Free electron (conduction electron)
○ Electrons that gain energy and become free to move after breaking shared bonds
○ Concentration of free electrons (n)
⑤ Hole
○ A location where an electron was present but is now vacant
○ Concentration of holes (p)
⑥ Size of energy gap determines electrical conductivity and resistance
Figure 1. Energy bands of insulators, semiconductors, and conductors
○ Conductor: Valence band and conduction band overlap
○ Electrons capable of free movement between atoms at room temperature
○ Example 1: Silver’s resistance is ρ = 1.59 × 10-6 Ω·cm
○ Example 2: Copper’s resistance is ρ = 1.67 × 10-6 Ω·cm
○ Semiconductor: Narrow band gap
○ Example 1: Germanium’s resistance is ρ = 50 Ω·cm
○ Example 2: Silicon’s resistance is ρ = 250,000 Ω·cm. Energy gap is 1.12 eV
○ Insulator: Wide band gap
○ Example 1: Diamond’s resistance is ρ = 1012 Ω·cm
○ Example 2: Tungsten’s resistance is ρ = 9 × 1012 Ω·cm
⑶ Intrinsic Semiconductor
① Definition: Semiconductor made of pure crystals of elements like Si, Ge with 4 outer electrons
② Silicon crystal
○ Silicon unit cell is cubic. One side is 5.43 Å
○ Each silicon atom is neighbored by 4 silicon atoms
③ Temperature increase → Entropy increase → Generation of free electrons and holes
○ Number of free electrons = Number of holes
○ At 300 K, electron density in silicon ni = 1.5 × 1010 cm-3 (relatively low)
④ Resistance variation with temperature
Figure 2. Resistance variation with temperature for conductors, semiconductors, and insulators[Note:2]
○ Conductor: Temperature increase → Increased atomic vibration → Increased resistance
○ Semiconductor: Temperature increase → Increased free electrons and holes → Reduced resistance
○ Insulator: Temperature increase → Electrons separate from atoms → Reduced resistance
○ In semiconductors and insulators, resistance reduction due to increased atomic vibration is greater than the effect of increased resistance, unlike conductors
○ Semiconductor components like computer parts show increased current due to temperature: Reason for needing cooling systems
⑤ Current flow in semiconductors
○ Type 1: Drift current: Movement of free electrons due to electric field in conductors
○ μn: Electron mobility ≈ 1350 cm2/(V·s)
○ μp: Hole mobility ≈ 480 cm2/(V·s)
○ Viscosity unit is N·s/m2, similar to inverse mobility
○ Intrinsic semiconductor
○ Drift current can saturate, so equation needs some modification
Figure 3. Saturated drift current
○ Type 2: Diffusion current: Current due to diffusion motion or convection motion of charge carriers
○ Apply Fick’s Law of Diffusion inference
○ Einstein relationship
⑷ Impurity Semiconductor
Figure 4. Energy levels in impurity semiconductors
(가) is Intrinsic Semiconductor, (나) is N-type Semiconductor, (다) is P-type Semiconductor
① Doping: Adding impurities to intrinsic semiconductors to increase electrical conductivity
② P-type Semiconductor
○ Group 14 elements (Si, Ge) (4 valence electrons) + Group 13 elements (B, Al, Ga, In) (3 valence electrons)
○ Reaction equation: Na represents acceptor density
○ Acceptor level created between conduction band and valence band, reducing band gap
○ Acceptor level is close to valence band
○ P-type semiconductors generally have electrons filled in acceptor levels
○ More holes in valence band than free electrons in conduction band, so current mainly due to holes
③ N-type Semiconductor
○ Group 14 elements (Si, Ge) (4 valence electrons) + Group 15 elements (P, As, Sb) (5 valence electrons)
○ Reaction equation: Nd represents donor density
○ Donor level created between conduction band and valence band, reducing band gap
○ Donor level is close to conduction band
○ More free electrons in conduction band than holes in valence band, so current mainly due to electrons
④ Fermi level
○ P-type Semiconductor: Fermi level formed close to valence band due to acceptor levels
○ N-type Semiconductor: Fermi level formed close to conduction band due to donor levels
⑤ Charge numbers in impurity semiconductors
○ Similarity with equilibrium constant (a): Regarding electron density n, hole density p, energy gap Eg,
○ Charge equilibrium equation (b)
○ Number of holes (in P-type semiconductor): Simultaneous equations (a) and (b)
○ Generally, concentration of majority carriers closely matches impurity density introduced
⑥ Process of creating impurity semiconductor devices
○ 1st. Melt silicon to a high temperature to form a highly pure liquid state
○ 2nd. Gradually cool while mixing small amounts of impurities
○ 3rd. Form a cylindrical crystal mass called an ingot
○ 4th. Form a thin wafer by thinly slicing the cross-section of the ingot
⑦ Example 1: ni = 1015 (1/cm3), Na = 1017 (1/cm3)
⑧ Example 2: Electrical conductivity of silicon at room temperature
⑨ Example 3: Electrical conductivity of p-type semiconductor with one indium-doped silicon atom among 107 silicon atoms at room temperature
2. Diode
⑴ Definition: State where P-type and N-type semiconductors are joined. Permits current flow in only one direction
① Anode: P-type semiconductor region
② Cathode: N-type semiconductor region
③ Current flows only from anode to cathode direction: Doesn’t flow from cathode to anode
⑵ Equilibrium: State where no voltage is applied to PN junction
① Depletion region
Figure 5. Depletion region
○ Definition: Area near PN junction with no free electrons and holes
○ 1st. Electrons from N-type semiconductor move to P-type semiconductor due to diffusion force
○ 2nd. Recombination: Conduction band’s free electrons and valence band’s holes meet and annihilate
○ 3rd. Atoms lose electrons in N-type semiconductor form (+) pole, atoms gain electrons in P-type semiconductor form (-) pole
○ 4th. Electric field force forms: Additional movement of electrons inhibited by polarized atoms
○ 5th. Equilibrium reached when diffusion and electric field forces balance
② Built-in voltage
○ Electric field forms from N-type to P-type semiconductor → Potential difference occurs → Inhibition of electrons and holes moving towards N-type and P-type
○ Built-in voltage: Potential difference at equilibrium. Also known as potential barrier, contact potential, etc.
○ pn: Density of holes in N-type semiconductor
○ pp: Density of holes in P-type semiconductor
○ nn: Density of electrons in N-type semiconductor
○ np: Density of electrons in P-type semiconductor
○ Generally assumed to be 0.6 ~ 0.7 V in silicon diode problems
○ In equilibrium, carrier density with respect to distance from PN junction is assumed constant, unlike biasing
○ Equations such as pn(x) ≈ pn, np(x) ≈ np are valid.
○ To distinguish from bias, the carrier concentration in equilibrium is denoted as pn0, np0, etc.
③ Width of the depletion region
○ The wider the depletion region, the larger the built-in voltage: Reverse bias applies
⑶ Bias: State where voltage is applied to the PN junction
Figure 6. Bias
① Principle: Only contributes to current flow by minority carriers
○ Majority carriers do not significantly affect current flow
○ In P-type semiconductor, electrons diffuse to form current
○ In N-type semiconductor, holes diffuse to form current
② Forward Bias: Forward conducting state. Current allowed
○ Definition: State where the anode (P-type semiconductor) is connected to the positive terminal of the battery and the cathode (N-type semiconductor) is connected to the negative terminal of the battery
○ 1st. Understanding 1. Voltage applied in the direction of increased diffusion force: Electric field due to the potential barrier opposes the electric field due to the battery
○ Electric field due to the battery goes from (+) terminal to (-) terminal
○ Electric field due to charges goes from (+) charge to (-) charge
○ 1st. Understanding 2. Additional movement of electrons and holes to the depletion region narrows it
○ Battery voltage provides holes to P-type semiconductor → Holes move from P-type end to PN junction
○ Battery voltage provides electrons to N-type semiconductor → Electrons move from N-type end to PN junction
○ 2nd. Depletion region narrows, leading to excessive minority carriers – excess electrons and excess holes
○ 3rd. Excess electrons move to P-type semiconductor end. Excess holes move to N-type semiconductor end (estimated)
○ Concentration: Minority carrier concentration increases towards the junction
○ 4th. Diffusion current flows: Depletion region doesn’t hinder current flow
Figure 7. Concentration distribution in forward bias [Footnote: 6]
○ Dotted lines represent equilibrium concentration
○ Some figures indicate a gap equal to the width of the depletion layer at the junction
○ Current doesn’t always flow under forward bias; additional energy beyond the threshold barrier is needed
○ Formulation
③ Reverse Bias: Reverse blocking state. Current blocked
○ Definition: State where the anode (P-type semiconductor) is connected to the negative terminal of the battery and the cathode (N-type semiconductor) is connected to the positive terminal of the battery
○ 1st. Understanding 1. Voltage applied in the direction of decreased diffusion force: Electric field due to the potential barrier and electric field due to the battery are in the same direction
○ Electric field due to the battery goes from (+) terminal to (-) terminal
○ Electric field due to charges goes from (+) charge to (-) charge
○ 1st. Understanding 2. Additional movement of electrons and holes to the depletion region widens it
○ Circuit voltage provides electrons to P-type semiconductor
○ Circuit voltage provides holes to N-type semiconductor
○ Consequently, depletion region widens
○ 1st. Understanding 3. Battery voltage moves electrons to N-type end and holes to P-type end
○ 2nd. Depletion region widens
○ 3rd. Current doesn’t flow
○ Concentration: Fewer holes near the depletion region → Current doesn’t flow
Figure 8. Concentration distribution in reverse bias [Footnote: 7]
○ Dotted lines represent equilibrium concentration
○ Some figures indicate a gap equal to the width of the depletion layer at the junction
○ Formulation: IS is referred to as reverse saturation current
⑷ Diode Current-Voltage Characteristics
① Ideal diode
○ Formulation
○ Forward (P-type → N-type current) is like a zero-resistance wire (short)
○ Reverse (N-type → P-type current) blocks all current (open)
○ Generally, ideal diodes are represented as filled diodes
○ In practice, diodes are usually represented as empty diodes
② Real diode: Horizontal axis is diode voltage VD, vertical axis is diode current ID
Figure 9. Real diode current-voltage characteristics [Footnote: 8]
③ Threshold voltage (VF): Represented by VF
○ Definition: Voltage at which current flows but is small since it cannot overcome the potential barrier. Diode acts like a large resistance
○ Model 1. Based on the Fermi-Dirac distribution function
○ Actual diode characteristic curve is exponential
○ Useful to approximate this exponential function for two identical diodes in parallel connection
○ Thermal voltage is typically about 0.0253 V (25.3 mV)
○ Model 2. Piecewise Linear Model: Reflects only the threshold voltage, interprets the rest similar to an ideal diode
○ Generally, threshold voltage is about 0.6 to 1 V
○ Silicon junction threshold voltage: 0.7 V
○ Germanium junction threshold voltage: 0.3 V
○ Gallium arsenide junction threshold voltage (used in semiconductor lasers): 1.6 V
○ (Note) Threshold voltage and thermal voltage are unrelated
○ With current-voltage characteristics and threshold voltage, operating point can be determined
Figure 10. System of equations for current-voltage characteristics and piecewise linear model
(Example: V = 1, R = 1, a = 0.25, b = 1, vD = 0.5, iD = 0.4)
○ Equivalent circuit in threshold voltage problem
Figure 11. Equivalent circuit in threshold voltage problem
○ Current-voltage characteristics and threshold voltage characteristics are different terms
○ Model 3. Incremental method (small signal method): Diode can be treated as a single resistor for small changes in bias point (VD, ID)
Figure 12. Case where diode is approximated as a variable resistor
○ General formula
○ Example
④ Breakdown voltage
○ Definition: Maximum reverse voltage a diode can withstand
○ Avalanche breakdown
○ In practice, diodes have a very small leakage current (tens of mA) under reverse voltage
○ Reason: Electrons are present in P-type semiconductor and holes are present in N-type semiconductor as minority carriers
○ 1st. Electrons entering the depletion region gain sufficient kinetic energy due to the intensified electric field from the reverse bias
○ 2nd. These electrons separate electron-hole pairs in combined states
○ 3rd. Separated electrons initiate further chain reactions
○ 4th. Ultimately, the entire depletion region is neutralized → Current flows
○ A diode that undergoes avalanche breakdown is damaged
○ Even in the presence of a depletion region under forward bias, diode’s resistance effect appears: nonlinear
○ When avalanche breakdown occurs, the depletion region is eliminated, making the diode equivalent to a wire: piecewise linear
○ (Note) Junction destruction can be thought of as turning a diode into a reverse voltage source
○ Zener breakdown
○ Junction with heavily doped semiconductor → Increased diffusion → Reduced depletion region → Frequent quantum tunneling → Current flows
○ 1st. Electrons on the P-side valence band have higher energy than electrons on the N-side conduction band
○ 2nd. Adequate reverse voltage for direct movement results in current flow ( quantum tunneling )
⑤ Rated current
○ Definition: Maximum current a diode can allow to flow forward without being destroyed
○ Diodes must always be accompanied by a series-connected resistor for overcurrent protection
⑸ Special Diodes
① Zener Diode
○ Definition: Device utilizing the phenomenon where a constant voltage is formed when Zener breakdown occurs
Figure 13. Zener diode and Zener breakdown [Footnote: 9]
○ Under forward bias, the threshold voltage is constant, and the current-voltage characteristics are nonlinear
○ Under reverse bias, the breakdown voltage changes due to doping, and the current-voltage characteristics are piecewise linear
○ Zener diodes have high doping levels and have well-controlled breakdown voltages of 3 to 8 V
○ While breakdown durability of Zener diodes is enhanced, overcurrent still needs to be prevented
○ Example of voltage regulator circuit
○ Strategy: Assume Zener diode is absent
Figure 14. Example of voltage regulator circuit
○ For RL = 1.2 kΩ
○ For RL = 4 kΩ
② Light Emitting Diode (LED)
○ Under forward bias, carriers recombine near the junction, resulting in light emission
Figure 15. Principle of LED emission [Footnote: 10]
A is P-type semiconductor, and B is N-type semiconductor
○ (Note) N-type semiconductors have lower energy levels than P-type but have a higher conduction band
○ LED emits light corresponding to the band gap size
○ (Note) Most diodes convert energy to heat, not light
○ Silicon (Si) semiconductor, Germanium (Ge) semiconductor: Convert energy to heat, not light
○ Gallium arsenide (GaAs) semiconductor, Gallium phosphide (GaP) semiconductor: Emit light
○ High efficiency: Energy savings of up to 90% possible
③ Photodiode
○ Definition: Device that converts light energy into electrical energy by absorbing light energy
○ Similar Photovoltaic Effect
○ When light energy reaches the depletion region, electron-hole pairs are generated, resulting in current flow
○ In other words, electrons in P-type semiconductor transition to the conduction band of N-type semiconductor, simultaneously generating holes and free electrons
○ Functions as a sensor: Photocurrent depends only on the amount of light, independent of reverse bias voltage ( ∵ photocurrent is proportional to the number of electrons, which is proportional to the amount of light)
○ Reverse bias circuit
○ Meaning 1. To enhance light sensitivity, reverse bias is applied to increase the depletion region (raising the threshold)
○ Meaning 2. To prevent current flow in a solar charging battery when not under sunlight, connect the charging battery in reverse bias
○ (Note) Dark current: Current that flows without light exposure
○ Example 1. CD player, fire alarm, remote control receiver
○ Example 2. Solar Cells
Figure 16. Circuit of a solar cell
ⓐ: Direction of electrons, ⓑ: Direction of current, X is an n-type semiconductor
○ Example 3. Digital Camera Image Sensor (CCD)
Figure 17. Image sensor of a digital camera
○ Path of light: Lens → CCD → Converted to current signal → Detected light provides brightness, color, and coordinate information based on intensity and position
○ Must operate in visible light range, so threshold frequency should be lower than that of visible light
○ Example 4. Multi-channel Photodetector (Photodiode Array Spectrophotometer)
○ Measures dispersed light at different wavelengths simultaneously
○ Mainly uses an array of 1024 or 2048 silicon photodiodes
○ Advantages: Fast speed, excellent reproducibility, simultaneous measurement at multiple wavelengths
○ Disadvantages: Low resolution (1 ~ 3 nm) (0.1 nm possible for dispersive type), errors due to light source intensity and detector sensitivity
○ Used in real-time spectrophotometers
○ Example 5. pn Photodiode, pin Photodiode, Avalanche Photodiode, Phototransistor, PSD, 1D and 2D Arrays
⑹ Applications
① Crystal Radio Receiver (Cat’s Whisker): First commercialized diode circuit
② Light Emitting Diode (LED): CD players, fire alarms, remote control receivers, solar cells, CCD
③ Maximum output of input voltage
Figure 18. Maximum output of input voltage using diodes
④ Rectifier
3. Rectifier
⑴ Rectification: Process of converting AC voltage to DC voltage
⑵ Half-wave rectifier circuit
① Circuit Diagram
Figure 19. Half-wave rectifier circuit and load voltage curve for ideal diode
○ For forward bias, diode resistance is 0, so power supply voltage is directly transmitted to the load
○ For reverse bias, diode resistance is ∞, so power supply voltage is 0
② Actual diode
Figure 20. Half-wave rectifier circuit and load voltage curve for real diode
○ Real diode can be approximated as connected to a reverse-biased constant voltage similar to an ideal diode
○ Power supply voltage can be considered shifted downward by the reverse-biased voltage Vd
○ Load voltage can be considered as only the positive portion
② Half-wave rectifier circuit with capacitor
Figure 21. Half-wave rectifier circuit with capacitor circuit diagram
Figure 22. Half-wave rectifier circuit with capacitor
○ Segment 1. 0 ~ ¼ T
○ Capacitor charges quickly based on power supply voltage
○ Time constant is RC, so assumption is equivalent to assuming C is small
○ C = ∞ represents a short circuit, C = 0 represents an open circuit
○ In reality, capacitor voltage doesn’t follow power supply voltage perfectly as long as C is not zero
○ Segment 2. ¼ T ~
○ Capacitor discharges as power supply voltage is lower
○ Discharge follows an exponential curve, decreasing slower than power supply voltage
○ Larger load resistance leads to less discharge and flatter curve
○ Segment 3. ~ ¾ T
○ Rising capacitor voltage meets descending power supply voltage
○ After meeting, capacitor voltage starts rising along with power supply voltage
○ Segment 4. ¾ T ~
○ Power supply voltage decreases faster than capacitor voltage
○ Capacitor voltage starts to discharge and decreases following an exponential curve
○ Conclusion: Capacitor presence flattens voltage curve
⑶ Full-wave rectifier circuit
① Disadvantages of half-wave rectifier circuit
○ Half of the current is blocked in half-wave rectifier
○ Longer discharge time for capacitor in half-wave rectifier
② Full-wave rectifier: Utilizes all input energy
③ Type 1. Bridge full-wave rectifier circuit: Uses 4 diodes
○ Circuit diagram
Figure 23. Circuit diagram
○ Voltage drop is doubled compared to the circuit with ideal diodes
○ Adding a capacitor in parallel with the resistor yields smoother output than a half-wave rectifier
Figure 24. Load voltage of bridge full-wave rectifier circuit
④ Type 2. Center-tap full-wave rectifier circuit: Uses 2 diodes
○ Circuit diagram
Figure 25. Center-tap full-wave rectifier circuit diagram
○ Center-tap full-wave rectifier circuit with capacitor
Figure 26. Center-tap full-wave rectifier circuit with capacitor
⑷ Clipping circuit (Limiting circuit): Distribution of resistance and diode
① Definition: Circuit that clips the input voltage to not exceed a certain value
Figure 27. Clipping circuit
○ Case 1. VOUT ＜ VBIAS + 0.7: VOUT = VIN ( ∵ Reverse bias)
○ Case 2. VOUT ＞ VBIAS + 0.7: VOUT = VBIAS + 0.7 ( ∵ Forward bias)
○ Analyze cases for VOUT by reversing logical order
○ 0.7 V represents the threshold voltage
② Bidirectional simultaneous control is possible
Figure 28. Bidirectional simultaneous control of clipping circuit
○ Case 1. VOUT ＜ -6 - 0.7: VOUT = -6 - 0.7 = -6.7
○ Case 2. -6 - 0.7 ＜ VOUT ＜ 4 + 0.7 **: **VOUT = VIN
○ Case 3. VOUT ＞ 4 + 0.7: VOUT = 4.7
⑸ Clamping circuit: Distribution of capacitor and diode
① Definition: Circuit that shifts input signal waveform to a certain level without changing its shape
② Circuit diagram
Figure 29. Clamping circuit
○ Top left potential is input voltage, top right potential is output voltage
○ Assumption 1. R = ∞: Connecting a sufficiently large resistor in parallel with diode is practical for certain reasons
○ Assumption 2. Large C: Capacitor has a large time constant, voltage changes slowly. Functions like a secondary power supply
○ Interpret circuit based on equilibrium state
○ In equilibrium, capacitor is considered connected to a power supply corresponding to maximum voltage
○ Negative clamper: P-type semiconductor of diode is output potential, N-type semiconductor is grounded. This figure represents this case
○ Case 1 is only valid for points, not segments, making it distinct from Case 2
○ Case 1 is important because it derives VC and constant
○ All clamping circuits can be solved using case-based approach
○ Positive clamper: N-type semiconductor of diode is output potential, P-type semiconductor is grounded
○ Considering the scenario where diode is flipped in this figure: Input voltage remains the same
○ All clamping circuits can be solved using case-based approach
○ Clamping circuit operates as a clamping circuit for the input signal after the capacitor is fully charged
Figure 30. Capacitor charging status and clamping circuit
○ (Note) Implementing clamping circuit in practice is very challenging
⑹ Bridge rectifier: Uses a bridge circuit for rectification
4. Real Rectifiers
Input: 2018.01.27 08:55
Modification: 2022.09.11 20:22