Semiconductor Physics and Electronic Circuit Analysis

Posted on Feb 22, 2026 in Electrical Engineering

Hall Effect Fundamentals

The Hall effect is the phenomenon in which a transverse electric field (and hence a potential difference called Hall voltage) is developed across a current-carrying conductor or semiconductor when it is placed in a magnetic field perpendicular to the direction of current.

The Hall Field

The Hall field (E_H) is the electric field produced across the width of the conductor due to charge separation caused by the magnetic force on moving charge carriers. It acts perpendicular to both the current and the magnetic field.

Physical Origin of the Hall Effect

Consider a conductor carrying current I along the x-direction. A magnetic field B is applied perpendicular to the current (for example, along the z-direction). The charge carriers (electrons or holes) move with drift velocity v_d.

Each moving charge experiences a Lorentz force:
F = q(v_d × B)

This force pushes charge carriers toward one side of the conductor, causing charge accumulation. The accumulation creates an electric field (Hall field) that opposes further charge separation. Equilibrium is reached when:
qE_H = qv_dB
or
E_H = v_dB

Thus, the Hall effect originates from the magnetic force acting on moving charge carriers, leading to a transverse electric field.

Applications of the Hall Effect

• Determination of the nature of charge carriers: Identifying whether a material is an n-type or p-type semiconductor.
• Measurement of carrier concentration: Used to find the number density of charge carriers.
• Measurement of magnetic field: Hall probes are used to measure magnetic field strength.
• Determination of mobility of charge carriers.
• Hall sensors: Used in speed sensors, current sensors, proximity sensors, and position-sensing devices.

Difference Amplifiers Using Op-Amps

A basic differential amplifier circuit using an operational amplifier (Op-Amp) has two inputs, V_in1 and V_in2. The output voltage (V_out) is proportional to the difference between these two inputs.

• Circuit Diagram: The circuit typically uses an Op-Amp with four resistors, two connected to the inverting input and two to the non-inverting input, often configured with a feedback loop.
• Output Voltage Expression:
  V_out = (R₄ / R₃)(V_in2 – V_in1)
  For a balanced amplifier where R₁ = R₃ and R₂ = R₄, the expression simplifies to:
  V_out = (R₂ / R₁)(V_in2 – V_in1)

Advantages of Using Op-Amps

• Very High Gain: They have an extremely high open-loop voltage gain, often treated as infinite in ideal cases.
• High Input Impedance: Ideally, infinite input impedance means they draw negligible current from the input source.
• Low Output Impedance: Ideally, zero output impedance allows them to drive various loads effectively.
• High CMRR: A high Common-Mode Rejection Ratio (CMRR) means they are excellent at amplifying only the difference between two signals while rejecting common noise.
• Versatility: With external feedback components, they can be configured for applications including integrators, differentiators, and filters.

Classification of MOSFET Types

MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors) are broadly classified into two main categories:

1. Enhancement-type MOSFET (E-MOSFET): Normally OFF devices with no conductive channel at zero gate-source voltage (V_GS = 0). A voltage must be applied to the gate to create a channel.
2. Depletion-type MOSFET (D-MOSFET): Normally ON devices that have a physically fabricated channel. A voltage is applied to the gate to deplete the channel and turn the device OFF.

Both types come in two polarities: n-channel and p-channel.

Structure and Working of P-Channel E-MOSFET

• Structure: A P-EMOSFET consists of a lightly doped n-type substrate into which two heavily doped p-type regions (source and drain) are diffused. A thin layer of silicon dioxide (SiO₂) insulation is grown over the region between the source and drain, and a metal gate electrode is placed on top. The substrate is typically connected to the source terminal.
• Working: When a negative voltage is applied to the gate, it repels electrons in the n-type substrate and attracts minority holes. If the negative gate voltage exceeds the threshold voltage (V_th), enough holes accumulate to form a conductive p-channel. A voltage applied between the drain and source then causes holes to flow, with the current magnitude controlled by the gate voltage.

Transistor Definitions and Calculations

A transistor is a three-terminal semiconductor device used for amplifying signals or as an electronic switch. It controls a larger current flow between two terminals using a smaller current or voltage applied to a third terminal.

Current Gain Calculation

Note: Given I_C = 7 mA and I_E = 7.125 mA. We calculate I_B, α, and β.

Step 1: Calculate Base Current (I_B)
The fundamental relationship is I_E = I_C + I_B.
I_B = I_E – I_C = 7.125 mA – 7 mA = 0.125 mA

Step 2: Calculate Common-Base Current Gain (α)
α = I_C / I_E = 7 mA / 7.125 mA ≈ 0.9825

Step 3: Calculate Common-Emitter Current Gain (β)
β = I_C / I_B = 7 mA / 0.125 mA = 56

Common-Drain FET Amplifier Analysis

• Circuit Diagram: A common-drain FET amplifier (source follower) has the input applied to the gate and the output taken from the source. The drain is connected to the DC supply (AC ground). It includes a source resistor (R_S) and a gate resistor for biasing.
• Voltage Gain: The voltage gain (A_v) is given by:
  A_v = (g_mR_S) / (1 + g_mR_S)
  Since g_m and R_S are positive, the denominator is always greater than the numerator, meaning A_v < 1. This circuit is used as a buffer due to high input and low output impedance.
• Analogous Configuration: The analogous BJT configuration is the common-collector (CC) amplifier, also known as an emitter follower.