Unit 1: Semiconductor and its application

1. Intrinsic and Extrinsic Semiconductors

Semiconductors are materials whose electrical conductivity lies between that of a conductor (e.g., copper) and an insulator (e.g., glass). In robotics, they form the foundational building blocks for microcontrollers, sensors, and motor drivers.

Intrinsic Semiconductors

• Definition: A pure semiconductor material with no significant impurities (e.g., pure Silicon or Germanium).
• Characteristics:
  • At absolute zero (0 K), it acts as a perfect insulator.
  • At room temperature, thermal energy breaks some covalent bonds, creating electron-hole pairs.
  • The number of free electrons () exactly equals the number of holes (). (intrinsic carrier concentration).
  • Conductivity is very low and thus not practically useful for manufacturing electronic devices.

Extrinsic Semiconductors

• Definition: An intrinsic semiconductor doped with specific impurities to increase its conductivity.
• N-Type Semiconductor:
  • Created by adding pentavalent impurities (Phosphorus, Arsenic, Antimony).
  • These atoms have 5 valence electrons. Four form covalent bonds, leaving one weakly bound electron free to conduct.
  • Majority carriers: Electrons.
  • Minority carriers: Holes.
• P-Type Semiconductor:
  • Created by adding trivalent impurities (Boron, Gallium, Indium).
  • These atoms have 3 valence electrons, creating a vacancy (a "hole") in the covalent bond structure.
  • Majority carriers: Holes.
  • Minority carriers: Electrons.

2. The P-N Junction Diode

When a P-type and an N-type semiconductor are joined at the atomic level, they form a P-N junction, the basis of the diode.

The Unbiased Diode

• When initially joined, free electrons from the N-side diffuse across the junction to fill holes on the P-side.
• Depletion Region: This recombination creates a region near the junction devoid of free charge carriers.
• Barrier Potential: The N-side becomes slightly positive (loss of electrons) and the P-side slightly negative (gain of electrons). This creates an electric field that opposes further diffusion.
  • Silicon (Si) barrier potential
  • Germanium (Ge) barrier potential

The Biased Diode

Applying an external voltage across the P-N junction is called biasing.

• Forward Bias (FB):
  • Positive terminal connected to P-type, negative to N-type.
  • The external voltage opposes the barrier potential.
  • The depletion region narrows. Once the external voltage exceeds the barrier potential (0.7V for Si), majority carriers cross the junction, and significant current flows.
• Reverse Bias (RB):
  • Positive terminal connected to N-type, negative to P-type.
  • The external voltage aids the barrier potential.
  • The depletion region widens. Majority carrier flow is blocked.
  • Only a tiny leakage current flows due to minority carriers (thermally generated).

The Ideal Diode

A theoretical construct used to simplify circuit analysis.

• Forward Bias: Acts as a perfect short circuit (0V drop, resistance).
• Reverse Bias: Acts as a perfect open circuit ( current, infinite resistance).
• Application in Robotics: Used for quick mental math when designing reverse polarity protection for robot battery inputs.

3. Diode Equation, Characteristics, and Temperature Dependence

The Diode Equation (Shockley Equation)

The mathematical relationship between the current through a diode and the voltage across it:

Where:

• = Diode current
• = Reverse saturation current (leakage current)
• = Voltage applied across the diode
• = Ideality factor (1 for Germanium, 2 for Silicon)
• = Thermal voltage ( at room temperature, )

V-I Characteristics

The Voltage-Current (V-I) curve visually represents diode behavior:

1. Forward Region (1st Quadrant): Current is effectively zero until the voltage reaches the knee voltage (0.7V for Si). After this, current increases exponentially.
2. Reverse Region (3rd Quadrant): Very small, constant reverse saturation current () flows.
3. Breakdown Region: If the reverse voltage exceeds the Peak Inverse Voltage (PIV), avalanche/zener breakdown occurs, causing a massive rush of current that can destroy a standard diode.

Temperature Dependence

Semiconductors are highly sensitive to temperature changes.

• Barrier Potential: Decreases by approximately 2.5 mV for every 1°C rise in temperature ().
• Reverse Saturation Current (): Approximately doubles for every 10°C rise in temperature. This can lead to thermal runaway if not managed in robot power electronics.

4. Special Purpose Diodes

Zener Diode

• A heavily doped P-N junction designed specifically to operate safely in the reverse breakdown region.
• Zener Breakdown: Occurs in heavily doped diodes at lower voltages (< 6V). The intense electric field pulls electrons directly out of covalent bonds.
• Avalanche Breakdown: Occurs in lightly doped diodes at higher voltages (> 6V). High-velocity minority carriers collide with atoms, knocking free more electrons.

Zener Diode as a Voltage Regulator

A Zener diode maintains a constant output voltage () across a load, despite variations in input voltage or load current.

• Circuit Setup: The Zener is placed in reverse bias, strictly in parallel with the load. A series resistor () is placed between the unregulated source and the Zener.
• Working Principle:
  
  (Source current equals Zener current plus Load current).
  If input voltage increases, increases. The Zener absorbs the excess current (), keeping and the voltage across the load () perfectly constant.

Light Emitting Diode (LED)

• A heavily doped forward-biased P-N junction that emits light via electroluminescence.
• When electrons cross the junction and recombine with holes, they drop from the conduction band to the valence band, releasing energy in the form of photons.
• Standard Silicon/Germanium release heat. LEDs use direct bandgap materials like Gallium Arsenide (GaAs) for infrared, or Gallium Arsenide Phosphide (GaAsP) for visible light.
• Application: Status indicators on robotic control boards, opto-isolators, and optical encoders for motor speed tracking.

5. Diode Applications: Rectifiers

Rectification is the process of converting Alternating Current (AC) to Direct Current (DC).

Half-Wave Rectifier (HWR)

• Design: A single diode in series with an AC source and a load resistor.
• Operation: During the positive half-cycle, the diode is forward-biased and conducts. During the negative half-cycle, it is reverse-biased and blocks current.
• Metrics:
  • Maximum Efficiency:
  • Ripple Factor (): $1.21$ (121% - highly inefficient)
  • Peak Inverse Voltage (PIV): (Peak source voltage)

Full-Wave Rectifier (FWR)

Converts both half-cycles of the AC input into pulsating DC.

1. Center-Tapped FWR:

• Uses a center-tapped transformer and two diodes.
• Diode conducts during the positive half, during the negative half.
• PIV =

2. Bridge Rectifier:

• Uses four diodes arranged in a bridge topology. No center-tapped transformer needed.
• During the positive half, and conduct. During the negative half, and conduct.
• PIV =

FWR Metrics:

• Maximum Efficiency:
• Ripple Factor (): $0.48$ (48% - much smoother than HWR)

6. Diode Applications: Wave Shaping

Clippers (Limiters)

Circuits used to "clip" or remove portions of an AC waveform (above or below a certain reference voltage) without distorting the remaining part.

• Series Clipper: The diode is in series with the load.
• Shunt (Parallel) Clipper: The diode is in parallel with the load.
• Biased Clipper: A DC battery is placed in series with the diode to raise or lower the clipping threshold.
• Application in Robotics: Protecting sensitive ADC (Analog-to-Digital) pins on microcontrollers from voltage spikes (e.g., clipping signals to exactly 5V or 3.3V).

Clampers (DC Restorers)

Circuits used to shift the entire AC waveform positively or negatively along the DC axis without changing its shape or peak-to-peak amplitude.

• Components: Capacitor, Diode, and Resistor.
• Operation: The capacitor charges to the peak voltage of the input signal during the diode's forward-biased cycle. During the reverse-biased cycle, the capacitor acts like a battery in series with the input, shifting the waveform.
• Application in Robotics: Shifting sensor signals (e.g., a radar or sonar echo swinging between -2V and +2V shifted to 0V and 4V) to be read by a unipolar microcontroller.

7. Power Supply Design

A reliable DC power supply is critical for robotics. Designing a linear power supply follows a standard block diagram:

1. Transformer: Steps down mains AC voltage (e.g., 120V/220V to 12V AC).
2. Rectifier: (Usually a Bridge Rectifier) Converts the stepped-down AC into pulsating DC.
3. Filter: Smooths the pulsating DC.
   • A large Electrolytic Capacitor placed in parallel with the load charges on peaks and discharges during troughs, significantly reducing the ripple factor.
4. Voltage Regulator: Uses a Zener diode circuit or dedicated ICs (like the LM7805 for 5V output) to remove remaining ripples and provide a flat, stable DC voltage regardless of load changes.

8. Data Sheet of a Diode

When designing robotic circuits (such as selecting a "flyback" diode to protect microcontrollers from motor back-EMF), engineers must interpret diode datasheets. Key parameters include:

• (Maximum Repetitive Peak Reverse Voltage): The maximum reverse voltage the diode can withstand without breaking down. (e.g., 1000V for a 1N4007).
• (Average Rectified Forward Current): The maximum continuous current the diode can safely pass without overheating. (e.g., 1A for 1N4007).
• (Non-Repetitive Peak Forward Surge Current): The maximum brief spike in current the diode can survive (usually for 8.3ms).
• (Forward Voltage Drop): The actual voltage lost across the diode when conducting rated current (often around 1V to 1.1V for power diodes, rather than the ideal 0.7V).
• (Reverse Leakage Current): The small current that escapes when the diode is reverse-biased (typically measured in ).
• (Reverse Recovery Time): The time it takes for a diode to turn off (stop conducting) after the voltage switches from forward to reverse.
  • Standard diodes (1N400x) have slow and are used for 50/60Hz AC rectification.
  • Fast switching diodes (1N4148) or Schottky diodes have very low (nanoseconds) and are critical for high-frequency PWM motor control in robotics.

Example Extract: 1N4007 Datasheet (Typical Values)
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VRRM (Peak Repetitive Reverse Voltage) : 1000 V
V(RMS) (RMS Reverse Voltage)           : 700 V
I_O (Average Rectified Current)        : 1.0 A
I_FSM (Forward Surge Current)          : 30 A
V_F (Maximum Forward Voltage @ 1A)     : 1.1 V
I_R (Maximum DC Reverse Current @ 25C) : 5.0 µA