Unit 2: Fundamental of semiconductor devices

1. PN Junction Diode

A PN junction diode is the most fundamental semiconductor device, formed by joining a P-type semiconductor with an N-type semiconductor. This junction forms the basis for many other electronic devices.

1.1. Formation and Working Principle

• P-type Semiconductor: Doped with trivalent impurities (e.g., Boron, Gallium), resulting in an excess of "holes" (positive charge carriers).
• N-type Semiconductor: Doped with pentavalent impurities (e.g., Phosphorus, Arsenic), resulting in an excess of free electrons (negative charge carriers).
• Formation of Depletion Region:
  1. When a P-type and N-type material are joined, free electrons from the N-side diffuse across the junction to combine with holes on the P-side due to the concentration gradient.
  2. Similarly, holes from the P-side diffuse to the N-side.
  3. This recombination of charge carriers near the junction leaves behind immobile ions: positive donor ions on the N-side and negative acceptor ions on the P-side.
  4. This region, depleted of mobile charge carriers, is called the depletion region or space charge region.
  5. The accumulation of these immobile ions creates an electric field and a potential barrier (or built-in potential, V₀), which opposes further diffusion of charge carriers. For silicon, V₀ is approximately 0.7V; for germanium, it is 0.3V.

1.2. Biasing a PN Junction Diode

Biasing refers to applying an external voltage across the diode.

a) Forward Bias

• Connection: The positive terminal of the external voltage source is connected to the P-side (anode), and the negative terminal is connected to the N-side (cathode).
• Working:
  1. The applied voltage opposes the built-in potential barrier.
  2. If the applied voltage is greater than the potential barrier (e.g., > 0.7V for Si), the barrier is overcome.
  3. The depletion region width decreases significantly.
  4. Majority carriers (holes from P-side, electrons from N-side) can now easily cross the junction.
  5. This results in a large current flow from the P-side to the N-side. The diode is said to be "ON".
• Resistance: The diode offers very low resistance to current flow.

b) Reverse Bias

• Connection: The negative terminal of the external voltage source is connected to the P-side (anode), and the positive terminal is connected to the N-side (cathode).
• Working:
  1. The applied voltage aids the built-in potential barrier, increasing its height.
  2. The depletion region width increases.
  3. Majority carriers are pulled away from the junction, preventing them from crossing.
  4. A very small current, called the reverse saturation current (I₀), flows due to the movement of minority carriers. This current is typically in the order of microamperes (μA) or nanoamperes (nA) and is largely independent of the reverse voltage. The diode is said to be "OFF".
• Resistance: The diode offers very high resistance to current flow.
• Breakdown: If the reverse voltage is increased to a critical value called the breakdown voltage (Vbr), a large reverse current flows, which can permanently damage the diode. This is due to effects like Zener breakdown or Avalanche breakdown.

1.3. V-I Characteristics of a PN Junction Diode

The V-I (Voltage-Current) characteristic curve shows the relationship between the voltage applied across the diode and the current flowing through it.

• Forward Characteristic:
  • The current is negligible until the applied voltage exceeds the cut-in voltage or knee voltage (approx. 0.7V for Si).
  • Beyond the knee voltage, the current increases exponentially with the applied voltage.
• Reverse Characteristic:
  • In the reverse bias region, a very small, almost constant reverse saturation current (I₀) flows.
  • At the breakdown voltage (Vbr), the current increases sharply.

1.4. Applications of PN Junction Diode

The primary application stems from its ability to allow current flow in only one direction.

• Rectifiers: Convert Alternating Current (AC) to Direct Current (DC).
  • Half-Wave Rectifier: Uses a single diode to pass only the positive (or negative) half-cycles of the AC input waveform. It is simple but inefficient.
  • Full-Wave Rectifier: Uses multiple diodes to convert both half-cycles of the AC input.
    • Center-Tapped Transformer Rectifier: Uses two diodes and a center-tapped transformer.
    • Bridge Rectifier: Uses four diodes in a bridge configuration. It is the most common type as it does not require a center-tapped transformer and has a higher efficiency.
• Clippers and Clampers: Wave-shaping circuits.
• Voltage Regulators: Zener diodes, which are designed to operate in the breakdown region, are used to provide a constant output voltage.
• Switches: A forward-biased diode acts as a closed switch, and a reverse-biased diode acts as an open switch.

2. Bipolar Junction Transistor (BJT)

A BJT is a three-terminal semiconductor device that can be used for amplification and switching applications. It is a "current-controlled" device, where a small current at one terminal controls a much larger current between the other two.

2.1. Structure and Types

A BJT consists of three alternating layers of P-type and N-type semiconductor material.

• Terminals:

  1. Emitter (E): Heavily doped. Its function is to inject a large number of majority charge carriers into the base.
  2. Base (B): Very thin and lightly doped. Its function is to pass most of the injected carriers from the emitter to the collector.
  3. Collector (C): Moderately doped and is the largest of the three regions in physical size (to dissipate heat). Its function is to collect the charge carriers from the base.

• Types:

  1. NPN Transistor: Consists of a P-type base sandwiched between an N-type emitter and an N-type collector. Majority carriers are electrons.
  2. PNP Transistor: Consists of an N-type base sandwiched between a P-type emitter and a P-type collector. Majority carriers are holes.

(Note: The arrow on the emitter indicates the direction of conventional current flow.)

2.2. Working Principle (NPN Transistor in Active Region)

For a BJT to work as an amplifier, it must be operated in the active region. This requires specific biasing:

• Emitter-Base (EB) Junction: Must be forward-biased.
• Collector-Base (CB) Junction: Must be reverse-biased.

Operation Steps:

1. The forward-biased EB junction causes the emitter to inject a large number of electrons into the thin, lightly doped P-type base.
2. Because the base is very thin and lightly doped, only a very small percentage of these electrons (typically <5%) recombine with the holes in the base. This small recombination current flows out of the base terminal as the base current (Iₑ).
3. The vast majority of electrons (typically >95%) are swept across the reverse-biased CB junction into the collector region due to the strong electric field.
4. These electrons flow out of the collector terminal, constituting the collector current (Iₑ).
5. The total current leaving the emitter, emitter current (Iₑ), is the sum of the base and collector currents.

Key Relationship:
Iₑ = Iₑ + Iₑ

The crucial aspect is that a small base current Iₑ controls a much larger collector current Iₑ. The ratio of these currents is the current gain (β).

β = Iₑ / Iₑ (β, or hFE, is typically between 50 and 400)

Since Iₑ is very small compared to Iₑ, we can approximate Iₑ ≈ Iₑ.

2.3. Operating Regions

3. MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor)

A MOSFET is another type of transistor used for amplifying and switching electronic signals. Unlike the BJT, it is a voltage-controlled device. It has a very high input impedance, making it ideal for many digital and analog circuits.

3.1. Structure and Types

• Terminals:

  1. Source (S): The terminal from which charge carriers (electrons or holes) enter the channel.
  2. Drain (D): The terminal through which charge carriers leave the channel.
  3. Gate (G): The control terminal. The voltage applied to the gate controls the conductivity of the channel between the source and drain. The gate is electrically insulated from the channel by a thin layer of silicon dioxide (SiO₂).
  4. Substrate or Body (B): The semiconductor material on which the MOSFET is built.

• Types: MOSFETs are broadly classified into two main categories.

a) Enhancement-Mode MOSFET (E-MOSFET)

• The device is normally OFF when the gate-source voltage (Vgs) is zero.
• A channel must be "induced" or "enhanced" by applying a suitable Vgs.
• N-Channel E-MOSFET: A positive Vgs attracts electrons to the region under the gate, forming a conductive N-type channel between the source and drain. Current flows when Vgs > Vth (threshold voltage).
• P-Channel E-MOSFET: A negative Vgs attracts holes to form a P-type channel. Current flows when Vgs < Vth (threshold voltage is negative).

b) Depletion-Mode MOSFET (D-MOSFET)

• The device is normally ON when Vgs is zero because a physical channel is manufactured between the source and drain.
• The channel conductivity can be controlled by Vgs.
  • Depletion Mode: Applying a voltage of the opposite polarity (negative Vgs for N-channel) repels charge carriers from the channel, "depleting" it and reducing current flow.
  • Enhancement Mode: Applying a voltage of the same polarity (positive Vgs for N-channel) attracts more charge carriers, "enhancing" the channel and increasing current flow.

3.2. Applications

• Digital Logic Gates: MOSFETs (especially CMOS technology, using both N-channel and P-channel) are the building blocks of modern digital electronics like microprocessors and memory chips. They act as highly efficient electronic switches.
• Analog Amplifiers: Used in various amplifier configurations.
• Power Electronics: Power MOSFETs are used in power supplies, motor controls, and high-power switching applications.
• Memory Cells: Used in RAM and flash memory.

4. Operational Amplifier (Op-Amp)

An Operational Amplifier is a very high-gain, direct-coupled differential amplifier integrated circuit (IC). It is a fundamental building block in analog electronics.

4.1. Ideal Features (Characteristics)

An ideal op-amp has the following properties:

1. Infinite Open-Loop Voltage Gain (Aᵥ = ∞): The gain of the op-amp without any feedback is infinite. This means even a tiny difference in voltage between its inputs produces a very large output voltage.
2. Infinite Input Impedance (Zᵢₙ = ∞): It draws no current from the input source. (In reality, it's very high, in the MΩ range).
3. Zero Output Impedance (Zₒᵤₜ = 0): The output voltage does not change with the load current. It can supply any amount of current to the load. (In reality, it's very low, a few ohms).
4. Infinite Bandwidth (BW = ∞): The gain is constant for all frequencies, from DC to the highest AC frequencies.
5. Zero Offset Voltage: When the input voltages are equal (V+ = V-), the output voltage is exactly zero.

4.2. The Virtual Ground Concept

This is the single most important concept for analyzing op-amp circuits with negative feedback.

• An op-amp with negative feedback (where a portion of the output is fed back to the inverting - input) will always try to make the voltage difference between its two inputs (V+ and V-) equal to zero.
• V_differential = V+ - V- ≈ 0 or V+ ≈ V-
• This is due to the infinite open-loop gain. If there were any significant difference between V+ and V-, the output would saturate to its maximum or minimum supply voltage. The feedback mechanism prevents this by forcing the inputs to be equal.

Virtual Ground:

• If the non-inverting terminal (V+) is connected to ground (0V), then due to the negative feedback action, the inverting terminal (V-) will also be at 0V.
• This point (V-) is called a virtual ground because it is at 0V potential but is not physically connected to the ground. Because the input impedance is infinite, no current flows into the op-amp terminal, but current can flow through this node to other parts of the circuit.

4.3. Op-Amp Configurations

a) Inverting Amplifier

In this configuration, the output signal is 180° out of phase with the input signal.

• Analysis:

  1. The non-inverting input (V+) is connected to ground, so V+ = 0V.
  2. Due to the virtual ground concept, the inverting input (V-) is also at 0V. V- = 0V.
  3. Because the op-amp has infinite input impedance, no current flows into the V- terminal.
  4. Apply Kirchhoff's Current Law (KCL) at the V- node: Current entering = Current leaving.
     Iᵢₙ = Iբ
  5. Using Ohm's law:
     (Vᵢₙ - V-) / Rᵢₙ = (V- - Vₒᵤₜ) / Rբ
  6. Substitute V- = 0V:
     (Vᵢₙ - 0) / Rᵢₙ = (0 - Vₒᵤₜ) / Rբ
  7. Simplify to find the voltage gain (Aᵥ):
     Vᵢₙ / Rᵢₙ = -Vₒᵤₜ / Rբ
Vₒᵤₜ / Vᵢₙ = -Rբ / Rᵢₙ

• Closed-Loop Gain (Aᵥ):
  

  TEXT

      Aᵥ = -Rբ / Rᵢₙ
      

  
  The gain is determined solely by the external resistors Rբ and Rᵢₙ. The negative sign indicates the 180° phase inversion.

b) Non-Inverting Amplifier

In this configuration, the output signal is in phase with the input signal.

• Analysis:

  1. The input signal Vᵢₙ is applied directly to the non-inverting terminal (V+). So, V+ = Vᵢₙ.
  2. Due to negative feedback, V- is forced to be equal to V+. Therefore, V- = Vᵢₙ.
  3. No current flows into the V- terminal. The current through Rᵢₙ is the same as the current through Rբ.
  4. The voltage at the V- node can be found using the voltage divider rule for Rᵢₙ and Rբ:
     V- = Vₒᵤₜ * (Rᵢₙ / (Rᵢₙ + Rբ))
  5. Substitute V- = Vᵢₙ:
     Vᵢₙ = Vₒᵤₜ * (Rᵢₙ / (Rᵢₙ + Rբ))
  6. Rearrange to find the voltage gain (Aᵥ):
     Vₒᵤₜ / Vᵢₙ = (Rᵢₙ + Rբ) / Rᵢₙ
Vₒᵤₜ / Vᵢₙ = 1 + (Rբ / Rᵢₙ)

• Closed-Loop Gain (Aᵥ):
  

  TEXT

      Aᵥ = 1 + (Rբ / Rᵢₙ)
      

  
  The gain is always greater than or equal to 1 and is positive, indicating no phase inversion.