Unit 2: Diodes and its Application

1. p-n Junction as a Diode

A p-n junction is formed by bringing a p-type semiconductor into contact with an n-type semiconductor through a process like diffusion or epitaxial growth. This single crystal structure forms the basis of a semiconductor diode.

Formation of the Depletion Region

1. Initial State: The p-type material has a high concentration of holes (majority carriers) and a few thermally generated electrons (minority carriers). The n-type material has a high concentration of free electrons (majority carriers) and a few thermally generated holes (minority carriers). Both materials are initially electrically neutral.
2. Diffusion: Due to the concentration gradient at the junction, holes from the p-side diffuse into the n-side, and electrons from the n-side diffuse into the p-side.
3. Recombination: When a diffusing electron meets a diffusing hole, they recombine and annihilate each other near the junction.
4. Formation of Ions:
   • When an electron leaves the n-side, it leaves behind a positively charged donor ion (fixed in the crystal lattice).
   • When a hole leaves the p-side (i.e., an electron from a nearby atom fills the hole), it leaves behind a negatively charged acceptor ion (fixed in the crystal lattice).
5. Depletion Region (or Space Charge Region): This process creates a region on either side of the junction that is "depleted" of free charge carriers. This region contains only fixed positive ions on the n-side and fixed negative ions on the p-side.
6. Barrier Potential (V₀): The accumulation of these fixed ions creates a net positive charge on the n-side and a net negative charge on the p-side. This charge separation establishes an electric field (E-field) that points from the n-side to the p-side. This E-field opposes further diffusion of majority carriers. The potential difference created by this E-field is called the built-in potential, barrier potential, or contact potential (V₀).

The barrier potential is given by:
V₀ = V_T * ln( (N_A * N_D) / n_i² )
Where:

• V_T is the thermal voltage (kT/q). At room temperature (~300K), V_T ≈ 26 mV.
• k is Boltzmann's constant.
• T is the absolute temperature in Kelvin.
• q is the elementary charge.
• N_A and N_D are the acceptor and donor doping concentrations.
• n_i is the intrinsic carrier concentration.

For Silicon (Si), V₀ ≈ 0.7 V. For Germanium (Ge), V₀ ≈ 0.3 V.

2. Band structure of an Open-circuited p-n junction

An energy band diagram illustrates the energy levels of electrons in the material.

1. Separate p-type and n-type materials:
   • n-type: The Fermi level (E_Fn) is located near the conduction band (E_C).
   • p-type: The Fermi level (E_Fp) is located near the valence band (E_V).
2. At Equilibrium (Junction Formation): When the junction is formed and no external voltage is applied (open circuit), the system reaches thermal equilibrium. A key principle of thermal equilibrium is that the Fermi level must be constant throughout the entire material.
3. Band Bending: To align the Fermi levels (E_Fn and E_Fp), the energy bands of the p-type and n-type materials must shift relative to each other.
   • The energy bands on the n-side shift downwards.
   • The energy bands on the p-side shift upwards.
   • This results in a "bending" of the conduction and valence bands in the depletion region.
4. Built-in Potential in Band Diagram: The total amount of band bending is equal to the built-in potential energy, qV₀.
   • qV₀ = E_C(p-side) - E_C(n-side) = E_V(p-side) - E_V(n-side)
   • This potential energy barrier qV₀ prevents the net flow of majority carriers across the junction. An electron from the n-side's conduction band must gain at least qV₀ energy to overcome the barrier and move to the p-side's conduction band.

3. Current Components in a p-n Diode

In a p-n junction, two types of current flow:

1. Diffusion Current (I_diff):

   • Caused by the flow of majority carriers across the junction due to the concentration gradient.
   • Holes diffuse from p to n; electrons diffuse from n to p.
   • The direction of conventional diffusion current is from the p-side to the n-side.
   • This current is highly dependent on the applied bias voltage.

2. Drift Current (I_drift):

   • Caused by the flow of minority carriers driven by the electric field in the depletion region.
   • Minority electrons on the p-side are swept to the n-side.
   • Minority holes on the n-side are swept to the p-side.
   • The direction of conventional drift current is from the n-side to the p-side.
   • This current is largely independent of the applied bias but is highly dependent on temperature (as temperature generates more minority carriers).

Diode Biasing

• No Bias (Equilibrium): I_diff and I_drift are equal in magnitude and opposite in direction. The net current is zero.
  I_net = I_diff - I_drift = 0

• Forward Bias:

  • The positive terminal of a voltage source is connected to the p-side (anode) and the negative terminal to the n-side (cathode).
  • The applied voltage V opposes the built-in potential V₀, reducing the effective barrier height to (V₀ - V).
  • The depletion region width decreases.
  • Majority carriers can now easily diffuse across the junction, leading to a large diffusion current I_diff.
  • I_drift remains largely unchanged.
  • The net current I = I_diff - I_drift is large and flows from p to n.

• Reverse Bias:

  • The negative terminal of a voltage source is connected to the p-side and the positive terminal to the n-side.
  • The applied voltage V aids the built-in potential V₀, increasing the effective barrier height to (V₀ + V).
  • The depletion region width increases.
  • The large barrier almost completely stops the flow of majority carriers, so I_diff ≈ 0.
  • I_drift continues to flow, driven by the strong E-field. This small current is called the Reverse Saturation Current (I₀ or I_s).
  • The net current I = I_diff - I_drift ≈ -I₀ is very small and flows from n to p.

The Diode Current Equation (Shockley Equation)

This equation describes the overall current-voltage relationship of a diode:

I = I₀ * (e^(V / (η * V_T)) - 1)

Where:

• I = Total diode current
• I₀ = Reverse saturation current
• V = External voltage applied across the diode (+ for forward bias, - for reverse bias)
• η = Ideality factor (or emission coefficient). η = 1 for Germanium, η ≈ 2 for Silicon. It accounts for recombination in the depletion region.
• V_T = Thermal voltage (kT/q), approximately 26mV at 300K.

4. V-I Characteristics of a Diode

The V-I (Voltage-Current) characteristic is a graph of the current through the diode versus the voltage across it.

Forward Bias Region (V > 0)

• For small forward voltages (V < V_knee), the current is very small.
• Knee Voltage (or Cut-in/Threshold Voltage, V_knee): This is the forward voltage at which the diode current begins to increase rapidly.
  • For Si: V_knee ≈ 0.6 - 0.7 V
  • For Ge: V_knee ≈ 0.2 - 0.3 V
• Beyond the knee voltage, the current increases exponentially with voltage. The diode acts like a closed switch.

Reverse Bias Region (V < 0)

• When a reverse voltage is applied, a very small reverse saturation current I₀ (in the range of µA or nA) flows.
• This current is nearly constant and independent of the reverse voltage, up to a certain point.
• The diode acts like an open switch.

Breakdown Region (V < -V_BR)

• Breakdown Voltage (V_BR): If the reverse voltage is increased to a large enough value, a phenomenon called reverse breakdown occurs.
• At this voltage, the current increases drastically, and without a current-limiting resistor, this can permanently damage the diode.
• Mechanisms of Breakdown:
  1. Zener Breakdown: Occurs in heavily doped diodes at low reverse voltages (< 5V). The strong electric field is sufficient to pull electrons directly from the valence band to the conduction band (tunneling). It has a negative temperature coefficient.
  2. Avalanche Breakdown: Occurs in lightly doped diodes at higher reverse voltages (> 5V). Minority carriers accelerated by the strong E-field gain enough kinetic energy to collide with atoms in the lattice and create new electron-hole pairs. These new carriers are also accelerated, creating more pairs in a cascading "avalanche" effect. It has a positive temperature coefficient.

5. Temperature Dependence of Diode Parameters

Temperature significantly affects a diode's behavior.

1. Reverse Saturation Current (I₀):

   • I₀ is primarily due to thermally generated minority carriers.
   • I₀ is highly sensitive to temperature. It approximately doubles for every 10°C rise in temperature.
   • I₂(T) = I₁(T) * 2^((T₂ - T₁) / 10)

2. Forward Voltage Drop (V_F):

   • For a constant forward current, the required forward voltage V_F decreases as temperature increases.
   • The temperature coefficient is negative: dV/dT ≈ -2.5 mV/°C for both Si and Ge.
   • This is because the increased thermal energy helps carriers overcome the potential barrier more easily.

3. Breakdown Voltage (V_BR):

   • Zener Breakdown: Has a negative temperature coefficient (V_BR decreases as T increases).
   • Avalanche Breakdown: Has a positive temperature coefficient (V_BR increases as T increases).

6. Diode Resistance

1. Static (DC) Resistance (R_DC):

   • The resistance of the diode at a specific operating point (Q-point) on the V-I curve.
   • It is the simple ratio of voltage to current at that point.
   • R_DC = V_D / I_D (where V_D and I_D are the DC voltage and current at the Q-point).
   • It is not constant and varies with the operating point.

2. Dynamic (AC or Differential) Resistance (r_d):

   • The resistance offered by the diode to a small AC signal superimposed on a DC operating point.
   • It is the reciprocal of the slope of the V-I curve at the Q-point.
   • r_d = dV_D / dI_D
   • By differentiating the Shockley equation, we get the widely used formula:
     r_d = η * V_T / I_D
   • This shows that the dynamic resistance is inversely proportional to the DC current I_D. At low currents, r_d is high; at high currents, r_d is very low.

7. Transition and Diffusion Capacitance

A diode exhibits two types of capacitance, which are significant in high-frequency applications.

1. Transition Capacitance (C_T) (or Depletion/Space-Charge Capacitance):

   • Dominates under reverse bias.
   • The p and n regions act as the two plates of a capacitor, and the depletion region acts as the dielectric insulating them.
   • The width of the depletion region (W) changes with the applied reverse voltage. A larger reverse voltage leads to a wider W and thus a smaller capacitance.
   • C_T = εA / W
   • Where ε is the permittivity of the semiconductor, A is the junction area, and W is the depletion width.
   • C_T is voltage-dependent: C_T ∝ (V_R + V₀)^(-n), where V_R is the reverse voltage and n is a grading coefficient (1/2 for abrupt junction, 1/3 for linear junction).
   • This effect is utilized in varactor diodes.

2. Diffusion Capacitance (C_D) (or Storage Capacitance):

   • Dominates under forward bias.
   • It arises from the storage of injected minority carriers near the junction. When the forward voltage changes, the amount of stored charge changes, which is analogous to the charging/discharging of a capacitor.
   • C_D = dQ / dV = τ * (dI / dV) = τ / r_d
   • Where τ is the mean lifetime of the minority carriers.
   • C_D is directly proportional to the forward current I_D (since r_d is inversely proportional to I_D).
   • C_D is typically much larger than C_T.

8. p-n Diode Switching Times

When a diode is switched from one state to another (e.g., from ON to OFF), it does not respond instantaneously due to the capacitive effects.

Turn-ON Time

The time required for the forward current to reach a steady-state value after a forward voltage is applied. It is usually very small and often neglected.

Turn-OFF Time (Reverse Recovery Time, t_rr)

This is the more significant parameter. It is the time it takes for a diode to switch from the forward-biased (ON) state to the reverse-biased (OFF) state.

t_rr = t_s + t_t

1. Storage Time (t_s):

   • When the diode is switched to reverse bias, the stored minority charge in the neutral regions must first be removed.
   • During this time, the diode continues to conduct a significant reverse current (I_R) as the junction clears out these stored carriers. The voltage across the diode remains near its forward-biased value.
   • t_s is the time from the application of the reverse voltage until the stored minority charge concentration at the junction drops to zero.

2. Transition Time (t_t):

   • After the stored charge is removed, the diode begins to behave like a capacitor (C_T).
   • The reverse current then decays to the steady-state reverse saturation level (I₀).
   • t_t is the time taken for the reverse current to fall from I_R to approximately 10% of I_R.

• t_rr is a critical parameter for high-frequency applications. Standard rectifier diodes have t_rr in microseconds (µs), while fast-recovery diodes have t_rr in nanoseconds (ns).

9. Special Diodes

a. Zener Diode

• Principle: A heavily doped p-n junction diode designed to operate specifically in the reverse breakdown region. The breakdown is sharp, predictable, and non-destructive if the current is limited.

• Symbol:

• V-I Characteristic: Similar to a normal diode but with a very sharp, vertical breakdown at a specific reverse voltage known as the Zener Voltage (V_Z).

• Application: Primarily used as a voltage regulator. When placed in parallel with a load, it maintains a nearly constant voltage V_Z across the load despite variations in input voltage or load current, as long as the diode remains in breakdown.

b. LED (Light Emitting Diode)

• Principle: A forward-biased p-n junction that emits light through a phenomenon called electroluminescence. When electrons from the n-side recombine with holes on the p-side, they release energy. In specific semiconductor materials (direct bandgap), this energy is released in the form of photons (light).

• Symbol:

• Materials & Color: The color of the emitted light depends on the bandgap energy of the material used.

  • Gallium Arsenide (GaAs): Infrared
  • Gallium Arsenide Phosphide (GaAsP): Red or Yellow
  • Gallium Nitride (GaN): Blue, Green

• Operation: Requires a forward voltage of ~1.5V to 3.5V to operate. A series current-limiting resistor is essential to prevent damage from excessive current.

c. Tunnel Diode

• Principle: Based on the quantum mechanical effect called tunneling. It is made from very heavily doped p and n materials, resulting in an extremely thin depletion region (<10 nm).

• Symbol:

• V-I Characteristic: Exhibits a unique negative differential resistance (NDR) region. As the forward voltage increases from zero, the current first rises to a peak (I_P), then decreases to a valley (I_V), and finally increases again like a normal diode.

• Application: The negative resistance property allows it to be used in very high-frequency (microwave) applications like oscillators, amplifiers, and high-speed switching circuits.

d. p-i-n Diode

• Structure: Consists of a wide, undoped or lightly doped intrinsic (i) semiconductor layer sandwiched between heavily doped p-type and n-type regions.
• Symbol: Same as a standard diode.
• Operation:
  • Reverse Bias: The wide intrinsic layer results in a very wide depletion region. This leads to extremely low transition capacitance (C_T). It acts as a very good open switch or insulator.
  • Forward Bias: A large number of carriers are injected into the i-region, drastically reducing its resistance. It acts as a good conductor or closed switch.
• Application: Its low capacitance and ability to switch between high and low impedance states make it ideal for use as an RF/Microwave switch, attenuator, and high-speed photodetector.

10. Applications: Rectifiers, Clippers, and Clampers

a. Rectifiers

A rectifier is a circuit that converts alternating current (AC) into direct current (DC).

Half-Wave Rectifier (HWR)

• Circuit: A single diode in series with the load resistor R_L.
• Operation: During the positive half-cycle of the AC input, the diode is forward-biased and conducts, allowing current to flow through the load. During the negative half-cycle, the diode is reverse-biased and blocks current.
• Waveforms: The output is a series of positive pulses.
• Parameters:
  • V_dc = V_m / π
  • I_dc = I_m / π
  • V_rms = V_m / 2
  • Ripple Factor (γ): γ = 1.21 (very high ripple)
  • Efficiency (η): η = 40.6% (low)
  • Peak Inverse Voltage (PIV): The maximum reverse voltage the diode must withstand is PIV = V_m.

Full-Wave Rectifier (FWR)

• Operation: Converts both positive and negative half-cycles of the AC input into a pulsating DC output.

1. Center-Tapped FWR

• Circuit: Requires a transformer with a center-tapped secondary winding and two diodes.
• Operation: Diode D1 conducts during the positive half-cycle, and D2 conducts during the negative half-cycle. The current through the load is always in the same direction.
• PIV: PIV = 2V_m (a major disadvantage).

2. Bridge FWR

• Circuit: Uses four diodes arranged in a bridge configuration. Does not require a center-tapped transformer.

• Operation: During the positive half-cycle, diodes D1 and D2 conduct. During the negative half-cycle, diodes D3 and D4 conduct. The load current remains unidirectional.

• PIV: PIV = V_m (more efficient use of diodes).

• Parameters for FWR (both types):

  • V_dc = 2V_m / π
  • I_dc = 2I_m / π
  • V_rms = V_m / √2
  • Ripple Factor (γ): γ = 0.482 (much better than HWR)
  • Efficiency (η): η = 81.2% (much better than HWR)

b. Clipping Circuits (Limiters)

Clippers are circuits that remove or "clip off" a portion of an input waveform that lies above or below a certain reference level.

• Series Clipper: Diode is in series with the load.
• Parallel Clipper: Diode is in parallel with the load.
• Unbiased Clipper: Clips at 0V (or +/- 0.7V considering the diode drop).
• Biased Clipper: A DC voltage source (V_ref) is added in series with the diode to set the clipping level to V_ref +/- 0.7V.

Example: Positive Parallel Clipper
A diode is placed in parallel with the load, with its cathode connected to the input and anode to ground.

• During positive half-cycle: When V_in > 0.7V, the diode turns ON and shorts the output to 0.7V. V_out = 0.7V.
• During negative half-cycle: The diode is OFF (open circuit). No current flows through it, so V_out = V_in.
• Result: The positive part of the waveform above 0.7V is clipped off.

c. Clamping Circuits (DC Restorers)

Clampers are circuits that add a DC level to an AC signal, shifting the entire waveform up or down without changing its shape. The circuit uses a capacitor, a diode, and a resistor.

• Positive Clamper: Shifts the waveform upwards, clamping the negative peak at or near 0V.
• Negative Clamper: Shifts the waveform downwards, clamping the positive peak at or near 0V.

Example: Negative Clamper
A capacitor is in series with the input. A diode is in parallel with the load, with its anode connected to the output and cathode to ground.

1. First Positive Half-Cycle: The diode turns ON. The capacitor charges up quickly to the peak voltage of the input (V_m), with polarity opposing the source. V_out is clamped at 0V (ideal diode) or -0.7V (practical diode).
2. Subsequent Cycles: When V_in goes below V_m, the diode turns OFF. The capacitor now acts like a DC voltage source of value V_m. The output voltage becomes V_out = V_in - V_c = V_in - V_m.
3. Result: The entire waveform is shifted downwards by V_m. The positive peak is now at 0V, and the negative peak is at -2V_m.

11. Understanding the Datasheet of Diodes 1N4001-1N4007

The 1N400x series is a family of popular general-purpose 1A silicon rectifier diodes. The main difference between the models is their reverse voltage rating.

Key Absolute Maximum Ratings

These are limits that, if exceeded, may cause permanent damage to the device.

• V_RRM: This is the most critical specification and the primary differentiator. It's the maximum reverse voltage the diode can block repeatedly. A 1N4004 can handle up to 400V, while a 1N4007 can handle 1000V. You must choose a diode with a V_RRM greater than the PIV of your circuit.
• I_O: The maximum average DC current the diode can pass continuously without overheating. For all models, it is 1.0 A.
• I_FSM: The maximum current the diode can handle for a very short, non-repetitive pulse (like the initial turn-on surge of a capacitor).

Electrical Characteristics (at T = 25°C unless otherwise noted)

• V_F: The forward voltage drop across the diode when it is conducting 1.0 A. This is important for power dissipation calculations (P_D = V_F * I_F). The datasheet specifies a maximum of 1.1V.
• I_R: The reverse saturation current (leakage current) at the maximum rated reverse voltage. Note how it increases significantly with temperature (from 5 µA at 25°C to 50 µA at 100°C), as predicted by theory.
• t_rr: The reverse recovery time. A value of 2.0 µs (microseconds) means these are standard recovery diodes, unsuitable for high-frequency switching applications (e.g., above a few tens of kHz), but perfectly fine for 50/60 Hz mains rectification.