Basic Electronics - Semiconductors and Diode Applications

Course Information and Learning Objectives

• Course Name: Basic Electronics

• Course Code: EC 1001

• Lecture Number: 01

• Credits: 3

• Academic Year: 2020-2021

• Faculty: Dr. Vishal Das, Manipal University Jaipur

• Primary Session Outcome: Recall the fundamental concepts of semiconductors.

• Program Outcome Mapping (PO1): Apply principles of physics to describe the working of semiconductor devices. Demonstrate and apply knowledge of mathematics, science, and engineering to classical and recent problems of electronic design and communication systems.

• Assessment Criteria:

  • Assignments

  • Quizzes

  • Mid-term Examination I

  • Mid-term Examination II

  • End-term Examination

Fundamental Properties of Semiconductors

• Definition: Semiconductors are materials whose electrical properties lie between those of conductors and insulators. They are a special class of elements characterized by their conductivity levels and their position on the periodic table.

• Outer Shell Configuration: The definition of a semiconductor is often based on the number of electrons in its outer valence shell.

• Classification of Semiconductor Materials:

  • Single Crystal: These consist of a single element throughout the structure. Examples include Germanium $(Ge)$ and Silicon $(Si)$.

  • Compound: These consist of two or more different elements combined. Examples include Gallium Arsenide $(GaAs)$, Cadmium Sulfide $(CdS)$, Gallium Nitride $(GaN)$, and Gallium Arsenide Phosphide $(GaAsP)$.

• Primary Elements in Electronics: The three most frequently used semiconductors in the construction of electronic devices are $(Ge)$, $(Si)$, and $(GaAs)$.

Atomic Structure and Energy Levels

• Energy and Proximity: The farther an electron is from the nucleus, the higher its energy state.

• Energy Level Hierarchy:

  • Nucleus: The center of the atom.

  • Inner Shells: Third level, second level, etc., moving outward.

  • Valence Level: The outermost shell of the atom.

• Energy Gaps: Electrons are separated from higher energy bands by energy gaps. To move from the valence band to becoming a free carrier in the conduction band, an electron must absorb energy.

• Free Carriers: These are free electrons generated only by external causes, such as potential differences or applied electric fields established by voltage sources.

• Material Comparison: An electron in the valence band of silicon $(Si)$ must absorb more energy than one in the valence band of germanium $(Ge)$ to become a free carrier.

Intrinsic and Extrinsic Semiconductor Electronics

• Carrier Types in N-Type Materials:

  • Majority Carriers: Electrons.

  • Minority Carriers: Holes.

• Carrier Types in P-Type Materials:

  • Majority Carriers: Holes.

  • Minority Carriers: Electrons.

• Mobility Values ($m^2/Vs$):

  • Silicon (Si): Electron mobility $\mu_n = 0.135$, Hole mobility $\mu_p = 0.048$.

  • Germanium (Ge): Electron mobility $\mu_n = 0.39$, Hole mobility $\mu_p = 0.19$.

• Carrier Density and Mass Action Law:

  • Intrinsic Silicon at 300K: Intrinsic carrier density $n_i = 1.5 \times 10^{16}/m^3$.

  • Mass Action Law Equation: $n_0 p_0 = n_i^2$.

  • Extrinsic Silicon Doped with Arsenic (As): If typical concentration is $10^{21}\text{ atoms/m}^3$, then majority carriers $n_0 = 10^{21}\text{ electrons/m}^3$.

  • Minority Carrier Calculation: $p_0 = \frac{(1.5 \times 10^{16})^2}{10^{21}} = 2.25 \times 10^{11}\text{ holes/m}^3$.

• Conductivity Calculation ($\sigma$):

  • Majority Carriers (n-type): $\sigma_n = n_0 \times \mu_n \times q$

  • Example Calculation: $\sigma_n = 10^{21} \times 0.135 \times 1.6 \times 10^{-19} = 0.216\,(\Omega\,cm)^{-1}$.

  • Minority Carriers (p-type): $\sigma_p = p_0 \times \mu_p \times q$

  • Example Calculation: $\sigma_p = 2.25 \times 10^{11} \times 0.048 \times 1.6 \times 10^{-19} = 0.173 \times 10^{-10}\,(\Omega\,cm)^{-1}$.

  • Total Conductivity: $\sigma_{total} = \sigma_n + \sigma_p \approx 0.216\,(\Omega\,cm)^{-1}$.

The P-N Junction and Depletion Region

• Formation of the Junction:

  • Conduction-band electrons on the n-type side are attracted to valence-band holes on the p-type side.

  • As electrons diffuse from the n-region to the p-region, they leave behind positively charged donor atoms.

  • As holes diffuse from the p-region to the n-region, they uncover negatively charged acceptor atoms.

• Space Charge Region (SCR) / Depletion Region:

  • The net positive and negative charges induce an electric field ($\epsilon$) directed from the n-region to the p-region.

  • All mobile electrons and holes are swept out of this region by the electric field, thus it is "depleted" of mobile charge.

• Force Balance in Thermal Equilibrium:

  • Diffusion Force: Produced by the density gradients of majority carriers at the edges of the SCR.

  • Electric Field Force: Produced by the SCR electric field, acting in the opposite direction to the diffusion force.

  • In thermal equilibrium, these two forces exactly balance each other.

Diode Principles and Operating Conditions

• Structure: A diode is a two-terminal device consisting of an Anode (P-side) and a Cathode (N-side).

• Ideal Function: Ideally, a diode conducts current in only one direction.

• Three Operating Conditions:

  • No Bias: $V_D = 0\,V$, $I_D = 0\,A$. Only a modest depletion region exists.

  • Forward Bias: External voltage matches the polarity of the p- and n-type materials (Positive to P, Negative to N). This causes the depletion region to narrow. Electrons and holes are pushed toward the junction and gain sufficient energy to cross it.

  • Reverse Bias: External voltage is applied in opposite polarity (Negative to P, Positive to N). This causes the depletion region to widen. Electrons in n-type are attracted to the positive terminal, and holes in p-type are attracted to the negative terminal.

• Forward Bias Voltage Thresholds ($V_γ$):

  • Germanium (Ge): $\approx 0.3\,V$ ($0.2\,V$ to $0.3\,V$ range).

  • Silicon (Si): $\approx 0.7\,V$ ($0.6\,V$ to $0.7\,V$ range).

  • Gallium Arsenide (GaAs): $\approx 1.2\,V$.

Mathematical Modeling of Diodes

• The Diode Equation: $I_D = I_s (e^{\frac{V_D}{n V_T}} - 1)$

  • $I_s$: Reverse saturation current.

  • $V_D$: Applied forward-bias voltage.

  • $n$: Ideality factor (ranges between 1 and 2; assume $n=1$ unless noted).

  • $V_T$: Thermal voltage, calculated as $V_T = \frac{kT}{q}$.

• Physical Constants:

  • Boltzmann’s Constant ($k$): $1.38 \times 10^{-23}\,J/K$.

  • Temperature ($T$): Measured in Kelvins ($273 + \text{Celsius}$).

  • Electron Charge ($q$): $1.6 \times 10^{-19}\,C$.

• V-I Characteristics:

  • Cut-in or Knee Voltage: The point where current begins to increase rapidly under forward bias.

  • Reverse Saturation current: Small current flowing during reverse bias, usually in the micro-ampere ($\mu A$) range.

  • Breakdown: The point where reverse voltage causes a sharp increase in current.

• Temperature Dependence:

  • Reverse Saturation Current ($I_s$): Approximately doubles for every $10^{\circ}C$ rise in temperature. Formula: $I_{o2} = I_{o1} 2^{\frac{T_2 - T_1}{10}}$.

  • Cut-in Voltage: Decreases with an increase in temperature.

Diode Circuit Analysis and Applications

• Load-Line Analysis:

  • Used to analyze diode circuits using actual device characteristics.

  • A straight load line is defined by the network parameters. Maximum $I_D = \frac{E}{R}$, and maximum $V_D = E$.

  • Q-point (Quiescent Point): The intersection of the load line and the characteristic curve, identifying the operating $I_D$ and $V_D$.

• Clippers (Limiters):

  • Goal: To "clip" away a portion of an input signal without distorting the remaining waveform.

  • Series Clippers: Diode is in series with the load.

  • Parallel Clippers: Diode is in parallel with the load. The diode clips any voltage that forward biases it.

  • Biased Clippers: A DC battery is added in series with the diode to change the clipping level.

• Clampers:

  • Goal: To shift a waveform to a different DC level.

  • Components: Constructed of a diode, a resistor ($R$), and a capacitor ($C$).

  • Design Requirement: The resistor is chosen such that the discharge period $5\tau = 5RC$ is much larger than the period $T/2$. This ensures the capacitor holds its charge.

  • Functionality: During the diode "on" state, the capacitor charges. During the "off" state, the output is the sum of the input and the capacitor voltage.