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Chapter 7. Diode (diode)

Recommended Article: 【Circuit Theory】 Circuit Theory Table of Contents


1. Semiconductor

2. Diode

3. Rectifier circuit

4. Actual rectifier


a. Diode Experiment



1. Semiconductor

⑴ Overview

① Faraday first observed semiconductors

② Semiconductors have conductivity between conductors and insulators, which can be controlled by factors like temperature and purity

Band Gap Theory

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

Free electron (conduction electron)

○ Electrons that gain energy and become free to move after breaking shared bonds

○ Concentration of free electrons (n)

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[Note:1]

○ 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[Note:3]

(가) is Intrinsic Semiconductor, (나) is N-type Semiconductor, (다) is P-type Semiconductor

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

Example 1: ni = 1015 (1/cm3), Na = 1017 (1/cm3)

Example 2: Electrical conductivity of silicon at room temperature

Example 3: Electrical conductivity of p-type semiconductor with one indium-doped silicon atom among 107 silicon atoms at room temperature



2. Diode (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

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

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]

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

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 )

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

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

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

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