Microelectronics and Semiconductor Devices - Comprehensive Notes

Microelectronics

• Microelectronics is the study and manufacture of very small electronic components and circuits.
• Key components include:
  • Semiconductors
  • Transistors: BJT (Bipolar Junction Transistor) & MOS (Metal-Oxide-Semiconductor)
  • Optoelectronics
• Reference book:
  • Fundamentals of Microelectronics, Behzad Razavi (any edition)

Applications of Microelectronics

• Microelectronics is used in a wide variety of applications, including:
  • Wireless charging
  • Batteries
  • Cameras
  • Power management ICs
  • Lenses
  • AMOLED displays
  • Memory
  • Microprocessors
  • Computer systems
  • Operating systems
  • Artificial Intelligence (AI)
  • Sensors
  • Communications modules
  • 5G
  • IoT (Internet of Things)

Circuits

• Examples of circuits include:
  • AC Power Supply
  • Stepdown Transformer with specifications: Primary 230V, Secondary 12V, 1A
  • Integrated Amplifier

Circuit Components

• Passive Components:
  • Resistors: Denoted by R, $R = \frac{V}{I}$. Series: $R<em>T = R</em>1 + R<em>2$. Parallel: $\frac{1}{R</em>T} = \frac{1}{R<em>1} + \frac{1}{R</em>2}$
  • Capacitors: Denoted by C, $C = \frac{Q}{V}$. Series: $\frac{1}{C<em>T} = \frac{1}{C</em>1} + \frac{1}{C<em>2}$. Parallel: $C</em>T = C<em>1 + C</em>2$
  • Inductors: Denoted by L, $V<em>L = L \frac{di}{dt}$. Series: $L</em>T = L<em>1 + L</em>2$. Parallel: $\frac{1}{L<em>T} = \frac{1}{L</em>1} + \frac{1}{L_2}$

Mesh Analysis

• Mesh analysis is a method for solving circuits with multiple loops.
• Steps:
  • Identify the meshes and assign variables (e.g., $i<em>1$, $i</em>2$).
  • Apply Kirchhoff's Voltage Law (KVL) to each mesh.
  • Solve the resulting system of equations.
• Example:
  • Mesh 1: $-15 + 5i<em>1 + 10(i</em>1 - i_2) + 10 = 0$
  • Mesh 2: $6i<em>2 + 4i</em>2 + 10(i<em>2 - i</em>1) - 10 = 0$
  • Simplified equations:
    • $15i<em>1 - 10i</em>2 = 5$
    • $-10i<em>1 + 20i</em>2 = 10$
  • Solving by elimination:
    • $i_1 = 1A$
    • $i_2 = 1A$
    • $I<em>1 = i</em>1 = 1A, I<em>2 = i</em>2 = 1A, I<em>3 = i</em>1 - i_2 = 0A$
  • Solving by Cramer’s rule:
    • System of equations in matrix form:
      • $\begin{bmatrix} 15 & -10 \ -10 & 20 \ \end{bmatrix} \begin{bmatrix} i<em>1 \ i</em>2 \ \end{bmatrix} = \begin{bmatrix} 5 \ 10 \ \end{bmatrix}$
    • Determinants:
      • $\Delta = \begin{vmatrix} 15 & -10 \ -10 & 20 \ \end{vmatrix} = 200$

Passive vs. Active Devices

• Passive Devices:
  • Components such as resistors, capacitors, and inductors.
  • Cannot control current by means of another electrical signal.
• Active Devices:
  • Have the ability to electrically control electric charge flow.
  • Examples: vacuum tubes and transistors.
  • Transistors (BJTs and MOSFETs) are built from semiconductor pn junctions.

Semiconductor Fundamentals

• Semiconductor devices serve as the heart of microelectronics.
• The PN junction is the most fundamental semiconductor device.

Semiconductors

• Semiconductors have conductivities between those of metals and insulators.
• The conductivity can be varied over several orders of magnitude by adding controlled amounts of impurity atoms (doping).
• The ability to control and change the conductivity of semiconductors allows for the design of a variety of semiconductor devices.

Charge Carriers in Semiconductors

• To understand PN junction IV characteristics, it is important to understand charge carriers’ behavior in solids, how to modify carrier densities, and different mechanisms of charge flow.

Periodic Table

• Elements with three to five valence electrons are relevant to semiconductors, with Si (Silicon) being the most important.

Silicon

• Si has four valence electrons; can form covalent bonds with four neighbors.
• When temperature increases, electrons in the covalent bond can become free.
  • A valence electron is an electron in the outer shell associated with an atom.

Electron-Hole Pair Interaction

• With free electrons breaking off covalent bonds, holes are generated.
• Holes can be filled by absorbing other free electrons, so effectively there is a flow of charge carriers.

Energy Band

• Electrons in a solid exhibit different energy levels.
• The grouping of these different energy levels is known as the energy band.

Metals

• In metals, the bands either overlap or are partially filled.
• Electrons and empty energy states are intermixed within the bands so that electrons can move freely under the influence of an electric field.
• Electrons in the conduction band contribute to the conduction process.

Semiconductors and Band Gap

• A band gap is the distance between the valence band of electrons and the conduction band.
• It represents the minimum energy required to excite an electron to a state in the conduction band where it can participate in conduction.
• The difference between semiconductors and insulators is the much smaller size of the bandgap.
• Example: Si has a bandgap of ~1.1 eV compared with ~5eV for diamond.
• This allows for excitation of electrons from the valence band to the conduction band by reasonable amounts of thermal or optical energy.

Insulators

• Insulators have a filled valence band separated from an empty conduction band by a bandgap containing no allowed energy states.
• There can be no charge transport within the valence band since no empty states are available into which electrons can move.

Doping (N type)

• Pure Si can be doped with other elements to change its electrical properties.
• If Si is doped with P (phosphorous), it has more electrons, becoming type N (electron).
• Concentration of donor atoms: $N_D / cm^3$

Doping (P type)

• If Si is doped with B (boron), it has more holes, becoming type P.
• Concentration of acceptor atoms: $N_A / cm^3$

Properties of Semiconductor Types in Silicon

• N-type (negative):
  • Dopant: Group V (e.g., Phosphorus).
  • Bonds: Excess Electrons.
  • Majority Carriers: Electrons.
  • Minority Carriers: Holes.
• P-type (positive):
  • Dopant: Group III (e.g., Boron).
  • Bonds: Missing Electrons (Holes).
  • Majority Carriers: Holes.
  • Minority Carriers: Electrons.

PN Junction

• A PN junction is formed when N-type and P-type semiconductors are joined together.

Boolean Algebra

• Boolean algebra was formulated by George Boole, an English mathematician (1815-1864).
  • Describes propositions whose outcome would be either true or false.
• In computer work:
  • Used in addition to describe circuits whose state can be either 1 (true) or 0 (false).

Examples of Boolean Algebra

• Simplification examples:
  • $Z = BC + BE + A B C$
  • $Z = BC + B (C + AC)$
  • $Z = BC + B (C + A)$
  • $Z = BC + BC + AB$

Boolean Algebra and Transistor Circuits

• Boolean algebra can be physically realized by transistor circuits.
• Any operation that can be described in Boolean algebra can be turned into a simple transistor circuit called a gate.
• Gates are the building blocks of computers.

OR Gate

• A simple logic gate.
• Implements the OR operation from Boolean algebra.

PN Junction (Diode)

• When N-type and P-type dopants are introduced side-by-side in a semiconductor, a PN junction or a diode is formed.

Diode's Three Operation Regions

• Equilibrium, reverse bias, and forward bias.

Diode in Reverse Bias

• When the N-type region of a diode is connected to a higher potential than the P-type region, the diode is under reverse bias.
• There is a built-in electric field across the junction that blocks current flow.
• Behaves as an open circuit.

Diode in Forward Bias

• When the N-type region of a diode is at a lower potential than the P-type region, the diode is in forward bias.
• The built-in electric field decreases.
• In forward bias, a current flows through the pn junction which depends on the forward bias voltage $V_F$

IV Characteristic of PN Junction

• The current and voltage relationship of a PN junction is exponential in the forward bias region and relatively constant in the reverse bias region.
• $I<em>D = I</em>S (exp(\frac{V<em>D}{V</em>T}) - 1)$
  • thermal voltage $V_T = \frac{kT}{q} \approx 26mV$
  • saturation current $I_S \approx 10^{-12} A$

Logic Gates

• NOT gate: Output is the inverse of the input.
• AND gate: Output is 1 only if both inputs are 1.
• NAND gate: Output is 0 only if both inputs are 1.
• OR gate: Output is 1 if either input is 1.
• NOR gate: Output is 0 if either input is 1.
• XOR gate: Output is 1 only if the inputs are different.
• XNOR gate: Output is 1 only if the inputs are the same.

Diode Logic: OR GATE

• Diodes together with resistors can be used to implement digital logic functions.
• Diodes connected to 5V inputs (logic 1) will conduct (forward biased).
• Current from the source flows to the resistor, so $V_Y = 5V$.
• Keeps the diodes whose inputs are low (logic 0) in reverse bias.
• Thus, Y=A OR B OR C.
• Diode logic can only implement OR and AND because inverters (NOT gates) require an active device.

Active Devices

• Active devices have the ability to electrically control electric charge flow.
• Vacuum tubes and transistors are examples of active devices.
• Transistors (BJTs and MOSFETs) are built from semiconductor pn junctions.

Structure and Symbol of Bipolar Transistor

• A bipolar transistor can be thought of as a sandwich of three doped Si regions.
• The outer two regions are doped with the same polarity, while the middle region is doped with opposite polarity.

Forward Active Region

• $V<em>{BE} > 0, V</em>{BC} < 0$

Input-Output Characteristics of Bipolar Transistor

• When an “input” signal is applied at the base ($V<em>{BE}$), an “output” current flows at the collector ($I</em>C$).

Transconductance “gain”

• Transconductance, $g_m$, shows a measure of how well the transistor converts voltage to current.
• It is one of the most important parameters in circuit design.
• $g<em>m$ can be visualized as the slope of $I</em>C$ versus $V_{BE}$.
• A large $I<em>C$ has a large slope and therefore a large $g</em>m$.

PNP Transistors

• With the polarities of emitter, collector, and base reversed, a PNP transistor is formed.
• All the principles that applied to NPN's also apply to PNP’s, with the exception that the emitter is at a higher potential than the base and the base at a higher potential than the collector.

Example: NOT Logic Gate

• When the input is LOW, the transistor $Q_1$ turns OFF.
• Current flows through $R_1$ to the output, thus the output is HIGH.
• When the input is HIGH, the transistor $Q_1$ turns ON.
• Current flows through the collector-emitter junction to GND, causing the output to go LOW.

Parallel-Plate Capacitor

• The capacitor consists of 2 conducting plates separated with a dielectric (nonconducting) material.

Metal-Oxide-Semiconductor (MOS) Capacitor

• The MOS structure can be thought of as a parallel-plate capacitor, with the top plate being the positive plate, the oxide being the dielectric, and the Si substrate being the negative plate (assuming P-substrate).

Structure and Symbol of n-MOSFET

• This device is symmetric, so either of the $n^+$ regions can be source or drain.

Formation of Channel in nMOS

• First, a positive potential is applied to the metal gate and a negative potential to the n-doped Drain and Source.

MOSFET Characteristics

• A potential is applied between the Drain and Source ($V<em>D$) to generate an output drain current $I</em>D$.
• The output drain current $I<em>D$ varies with a varying input voltage $V</em>G$ while keeping $V_D$ constant.

PMOS Transistor

• It is possible to create a MOS device where holes are the dominant carriers. This is called the PMOS transistor.
• It behaves like an NMOS device with all the polarities reversed.

CMOS

• CMOS stands for “Complementary Metal Oxide Semiconductor.”
• In CMOS technology, both N-type and P-type transistors are used to design logic functions.
• The same signal which turns ON a transistor of one type is used to turn OFF a transistor of the other type.
• This is the dominant semiconductor technology for microprocessors, microcontroller chips, memories like RAM, ROM, EEPROM, and application-specific integrated circuits (ASICs).

CMOS Technology

• It is possible to grow an n-well inside a p-substrate to create a technology where both NMOS and PMOS can coexist.
• This is known as CMOS, or “Complementary MOS.”

Comparison of Bipolar and MOS Transistors

• Bipolar devices have a higher $g_m$ than MOSFETs for a given bias current due to their exponential IV characteristics.
• CMOS devices have low static power utilization and huge noise immunity, allowing for integrating logic functions with high density on an integrated circuit.

Moore’s Law

• Moore's Law is a term used to refer to the observation made by Gordon Moore in 1965 that the number of transistors in a dense integrated circuit (IC) doubles about every two years.
• The future of Moore's Law is uncertain.
• Eventually, miniaturization will lead to the atomic level.
• At that point, the law cannot be sustained.

Optoelectronics

• Optoelectronics is the study and application of electronic devices that source, detect, and control light.

Revisiting the bandgap

• The bandgap dictates whether a material will behave like a metal, semiconductor or insulator.

Optical Absorption

• The excitation of an electron from the valence band to the conduction band requires a minimum energy of $E_g$.
• When an incident photon of energy >$E_g$ interacts with an electron in the valence band, the electron absorbs the incident photon and gains sufficient energy to surmount the energy bandgap to reach the conduction band.

Recombination and Luminescence

• When an electron and hole recombine, the electron drops from an energy level in the conduction band to an energy level in the valence band, resulting in the generation of photons (light) or phonons (lattice vibrations).

LEDs: Application of (Electro)Luminescence

• Light-emitting diodes (LEDs) are p-n junction devices.
• The junction in an LED is forward biased, and when electrons cross the junction from the n- to the p-type material, the electron-hole recombination process produces some photons in the IR or visible spectrum in a process called electroluminescence.
• An exposed semiconductor surface can then emit light.