Fundamental Physics Concepts: Semiconductors and Optics

Posted on Mar 14, 2026 in Physics

PN Junction: Diffusion, Drift, and Barrier Potential

1. Diffusion Current: Due to the concentration gradient, majority carriers move across the junction (holes from the p-side to the n-side and electrons from the n-side to the p-side). This motion constitutes the diffusion current.

2. Drift Current: The electric field in the depletion region causes minority carriers to move across the junction (holes from the n-side to the p-side and electrons from the p-side to the n-side). This is called drift current.

3. Barrier Potential: The accumulation of positive and negative ions on either side of the junction creates an internal electric field. The potential difference associated with this field that opposes further diffusion is called the barrier potential.

Galvanometer Sensitivity and Enhancement

1. Current Sensitivity (Is): It is defined as the deflection produced per unit current flowing through the galvanometer.
Is = Φ / I = NAB / k

2. Voltage Sensitivity (Vs): It is defined as the deflection produced per unit voltage applied across the galvanometer.
Vs = Φ / V = NAB / (kR) (where R is resistance).

Method to Increase Current Sensitivity

To increase current sensitivity, one can increase the number of turns (N) in the coil or increase the magnetic field (B) using a strong permanent magnet.

Laws of Reflection via Huygen’s Principle

Consider a plane wavefront AB incident on a reflecting surface MN at an angle i. Let v be the speed of light. In time t, the disturbance from B reaches C, so BC = v × t. During this time, a secondary spherical wavelet from A spreads to D, where AD = v × t.

In ΔABC and ΔADC:

  • AC = AC (Common)
  • BC = AD = vt
  • ∠ABC = ∠ADC = 90°

The triangles are congruent (RHS), so ∠BAC = ∠DCA. Therefore, ∠i = ∠r (Angle of incidence = Angle of reflection).

Snell’s Laws of Refraction via Huygen’s Principle

Consider a plane wavefront AB incident on a refracting surface at an angle i. Let v1 and v2 be the speeds of light in medium 1 and 2. The time taken for the disturbance to travel from B to C is t = BC / v1. In the same time t, the secondary wavelet from A travels to E in medium 2, so AE = v2t.

  • From ΔABC: sin i = BC / AC = v1t / AC
  • From ΔAEC: sin r = AE / AC = v2t / AC

Dividing the two: sin i / sin r = (v1t / AC) / (v2t / AC) = v1 / v2 = constant (1μ2). This proves Snell’s Law.

Forward and Reverse Bias in P-N Junction Diodes

1. Forward Bias Characteristics

  • Connection: The P-side is connected to the positive terminal and the N-side to the negative terminal of the battery.
  • Effect: The applied voltage opposes the potential barrier, causing the depletion layer width to decrease.
  • Current: Majority charge carriers cross the junction easily. After a certain voltage called Knee Voltage, the current increases exponentially (measured in mA).

2. Reverse Bias Characteristics

  • Connection: The P-side is connected to the negative terminal and the N-side to the positive terminal.
  • Effect: The applied voltage supports the potential barrier, causing the depletion layer width to increase.
  • Current: Majority carriers are blocked. A very small current flows due to the drift of minority carriers, known as Reverse Saturation Current. If voltage is increased excessively, Breakdown occurs.

Working Principle of a Moving Coil Galvanometer

Principle: A current-carrying coil placed in a uniform magnetic field experiences a torque.

Working: When current I flows through the coil of N turns and area A, it experiences a deflecting torque τd = NIAB sin θ. In a radial magnetic field, θ = 90°, so τd = NIAB. This torque is balanced by a restoring torque τr = kφ produced in the spring (where k is the torsional constant and φ is the deflection).

In equilibrium: kφ = NIAB ⇒ φ = (NAB / k) I. Therefore, φ ∝ I, meaning the deflection is directly proportional to the current.

Ohm’s Law Limitations and Wheatstone Bridge

(i) Limitations of Ohm’s Law

  1. Non-linear V-I relationship: In many devices (like vacuum tubes or semiconductor diodes), the relationship between Voltage (V) and Current (I) is not a straight line.
  2. Directional Dependence: The relation between V and I depends on the sign of V. In a p-n junction diode, reversing the voltage does not produce the same current magnitude.
  3. Non-uniqueness: There may be more than one value of voltage for the same current. For example, in Gallium Arsenide (GaAs), there is a region of negative resistance.

(ii) Derivation of Wheatstone Bridge Condition

A Wheatstone bridge consists of four resistors P, Q, R, and S connected to form a quadrilateral ABCD. A galvanometer G is connected between B and D, and a battery is connected between A and C.

Balanced Condition: The bridge is balanced when the potential at B equals the potential at D. No current flows through the galvanometer (Ig = 0).

Applying Kirchhoff’s Laws: Let I1 be the current through P and I2 be the current through R. Under balanced conditions, the current through Q is I1 and through S is I2.

  1. Loop ABDA: -I1P + I2R = 0 ⇒ I1P = I2R (Eq. 1)
  2. Loop BCDB: -I1Q + I2S = 0 ⇒ I1Q = I2S (Eq. 2)

Dividing Eq. 1 by Eq. 2: P / Q = R / S.

Solar Energy and Nuclear Binding Energy

1. Source of Solar Energy: Proton-Proton (P-P) Cycle

The source of energy in the sun is nuclear fusion. In the sun’s core, hydrogen nuclei (protons) fuse to form helium nuclei. The overall reaction is:
4 11H + 2e– → 42He + 2ν + 6γ + 26.7 MeV

Mass defect is converted into energy according to E = Δm c2.

2. Binding Energy Calculation for 147N

Given Data: Z=7, N=7, mp=1.00783 amu, mn=1.00867 amu, MN=14.00307 amu.

  • Mass of constituents: (7 × 1.00783) + (7 × 1.00867) = 7.05481 + 7.06069 = 14.1155 amu
  • Mass Defect (Δm): 14.1155 – 14.00307 = 0.11243 amu
  • Total Binding Energy (B.E.): 0.11243 × 931 MeV ≈ 104.67 MeV
  • B.E. per Nucleon: 104.67 / 14 ≈ 7.48 MeV/nucleon

Coherent Sources and Young’s Double Slit Experiment

(i) Definitions

  • Coherent Sources: Sources that emit light waves of the same frequency and have a zero or constant phase difference over time.
  • Incoherent Sources: Sources that emit light waves with frequent and random changes in phase difference (e.g., two independent bulbs).

(ii) Effects on Fringes in YDSE

Fringe width β = λD / d

  1. Screen moved away (D increases): The fringe width β increases. The pattern becomes wider.
  2. Source slit moved closer: If the source is too close, the angular size increases, the condition for interference is violated, and fringes overlap and disappear.
  3. White light source: The central fringe is white. Nearby fringes are colored (violet inner edge, red outer edge). Further out, the pattern becomes uniform white illumination.

Dielectrics and Dipole Potential Energy

(i) Dielectrics

Dielectrics are non-conducting substances (insulators) that permit the development of an induced electric field due to polarization when placed in an external field (e.g., Mica, Glass).

(ii) Change in Capacitance

When a dielectric with constant K is inserted, the capacitance increases by a factor of K: C = KC0.

(iii) Potential Energy of an Electric Dipole

Consider a dipole moment p in a uniform field E at an angle θ.

  1. Torque: τ = pE sin θ
  2. Work Done (dW): dW = τ dθ = pE sin θ dθ
  3. Total Potential Energy (U): Integrating from θ1 to θ2:
    W = pE [-cos θ]. For θ1 = 90° to θ2 = θ, U = -pE cos θ = -p · E.