Important Diodes Notes FE Sem 2 Semiconductor Physics | MU

An ordinary p-n diode only lets current flow one way, but by changing the doping, the bias or the material we get diodes with very special talents: one that senses light, one that turns light into power, one that holds a voltage steady, one that behaves like a voltage-controlled capacitor, and one that oscillates at microwave frequencies. This module of the Semiconductor Physics elective covers the working and applications of the photodiode, the solar cell, the Zener diode, the varactor diode and the Gunn diode. It maps to course outcome CO3 (plot the I-V characteristics and understand the applications of special diodes).

Summary

Photodiode: A photodiode is a p-n (or p-i-n) junction designed to detect light, operated in reverse bias. Construction: a junction close to the surface with a window or lens so light reaches the depletion region; often a wide intrinsic layer between p and n (PIN photodiode) to increase the absorbing region and reduce capacitance. Working: in darkness only a tiny reverse current flows, called the dark current (due to thermally generated minority carriers). When light of energy \(h\nu \geq E_g\) falls on the junction, photons create electron-hole pairs in and near the depletion region. The strong reverse-bias field sweeps electrons to the n side and holes to the p side, increasing the reverse current. This photocurrent is proportional to the light intensity over a wide range. Characteristics: plots of reverse current against reverse voltage for different illumination levels are nearly horizontal lines, spaced in proportion to intensity; the current is almost independent of the reverse voltage. Two modes: photoconductive (reverse biased; fast, linear, used in communication) and photovoltaic (zero bias; low noise, used in light meters). The responsivity \(R = I_p/P = \eta e\lambda/hc\) (A/W), where η is the quantum efficiency. Avalanche photodiodes (APDs) are biased near breakdown so that each photo-generated carrier is multiplied, giving internal gain for very weak light. Applications: optical fibre receivers, light meters, smoke detectors, barcode scanners, CD/DVD players, remote-control receivers, pulse oximeters, position sensors and light-operated switches.

Solar cell: A solar cell is a large-area p-n junction operated without external bias that converts light into electrical power by the photovoltaic effect. Construction: a thin heavily doped n layer on a thicker p-type wafer, a top finger grid, a full back contact and an anti-reflection coating. Working: photons absorbed near the junction create electron-hole pairs; the built-in field separates them, electrons to n and holes to p; this produces an open-circuit voltage (about 0.5 to 0.6 V for Si) and drives current through an external load. The illuminated diode equation is \(I = I_L - I_0(e^{V/\eta V_T} - 1)\), where \(I_L\) is the light-generated current. The I-V characteristic lies in the fourth quadrant of the diode curve (drawn flipped for convenience): it meets the current axis at the short-circuit current \(I_{sc} \approx I_L\) and the voltage axis at the open-circuit voltage \(V_{oc} = \eta V_T\ln(I_L/I_0 + 1)\). Maximum power \(P_m = V_mI_m\) occurs at the knee; fill factor \(FF = V_mI_m/(V_{oc}I_{sc})\); efficiency \(\eta = P_m/P_{in}\). Difference from a photodiode: a solar cell is large, unbiased and delivers power, while a photodiode is small, reverse biased and senses light. Applications: rooftop and utility solar power, satellites, calculators, street lights, solar pumps, chargers.

Zener diode: A Zener diode is a heavily doped silicon p-n junction designed to operate in the reverse breakdown region without damage. Heavy doping makes the depletion region very thin, so a reverse voltage of only a few volts creates a field of about \(10^8\) V/m, strong enough to pull electrons out of covalent bonds directly by quantum tunnelling (Zener effect). For breakdown voltages above about 6 V the mechanism is mostly avalanche multiplication; both are used in "Zener" diodes. Characteristics: in forward bias it behaves like an ordinary diode; in reverse bias the current is tiny until the Zener voltage \(V_Z\), after which the current rises sharply while the voltage stays almost constant at \(V_Z\). Parameters: Zener voltage \(V_Z\) (available from about 2.4 V to over 100 V), minimum (knee) current \(I_{ZK}\), maximum current \(I_{ZM}\) set by power rating \(P_Z = V_ZI_{ZM}\), and the small dynamic resistance \(r_z = \Delta V_Z/\Delta I_Z\). Application as a voltage regulator: the Zener diode is connected in reverse across the load, with a series resistor R_s from the supply. If the supply voltage or load current changes, the Zener current changes to absorb the difference while the load voltage stays at \(V_Z\): \(I_S = (V_S - V_Z)/R_s\), \(I_L = V_Z/R_L\), \(I_Z = I_S - I_L\). Other uses: reference voltages, over-voltage protection, wave clipping and shaping, meter protection. Symbol: a diode with bent (Z-shaped) bar.

Varactor diode: A varactor (varicap, voltage-variable capacitor) diode is a p-n junction designed to be used in reverse bias as a capacitor whose value is controlled by voltage. In reverse bias, the depletion region acts as the insulating dielectric between the conducting p and n regions, which act as the plates. The junction capacitance is \(C_T = \varepsilon A/W\). Increasing the reverse voltage widens the depletion region W, which lowers the capacitance. For an abrupt junction \(W \propto (V_0 + V_R)^{1/2}\), so \(C_T = \dfrac{K}{(V_0 + V_R)^{1/2}}\); for a hyperabrupt junction (special doping profile) the exponent is larger (about 1 to 2), giving a wider tuning range. Typical capacitances are a few pF to a few hundred pF. Characteristic: C_T versus V_R is a falling curve. Applications: electronic tuning of radio and TV receivers (replacing mechanical gang capacitors), voltage-controlled oscillators (VCOs) in phase-locked loops and mobile phones, frequency modulators, automatic frequency control, parametric amplifiers and frequency multipliers. In an LC circuit \(f = 1/(2\pi\sqrt{LC})\), so changing the bias voltage tunes the frequency.

Gunn diode: A Gunn diode, or transferred electron device (TED), is not a p-n junction at all: it is a piece of n-type GaAs (or InP) with heavily doped n⁺ contacts at both ends (n⁺-n-n⁺). It is named after J. B. Gunn, who in 1963 observed microwave current oscillations when a steady voltage above a threshold was applied to GaAs. Principle (transferred electron effect, explained by the Ridley-Watkins-Hilsum theory): the conduction band of GaAs has a lower valley (Γ) where electrons have small effective mass and high mobility, and an upper satellite valley (L) about 0.3 eV higher where electrons have larger effective mass and much lower mobility. At low fields electrons stay in the lower valley, and current rises with voltage (Ohm's law). When the field exceeds a threshold of about 3.2 to 3.5 kV/cm, electrons gain enough energy to transfer to the upper valley, where they slow down; the average drift velocity then decreases as the field increases. This gives a region of negative differential resistance (current falls as voltage rises). Oscillation: in this region the uniform field is unstable; a high-field region called a domain (an accumulation of slow electrons followed by depleted region) forms near the cathode and travels to the anode at about the saturation drift velocity (about \(10^5\) m/s). While a domain exists the current drops; when it reaches the anode it disappears, the current rises, and a new domain forms at the cathode. The current therefore pulses at the transit-time frequency \(f = v_d/L\), where L is the length of the active region; for L = 10 μm, f ≈ 10 GHz. Applications: microwave oscillators and sources (1 to 100 GHz) for radar speed guns, police radars, automatic door openers, intruder alarms, collision-avoidance radar, microwave transmitters, local oscillators in receivers, and test equipment.

Mind map

Zener diode as a voltage regulator

Important definitions

Formulas

Key points to remember

• Photodiode: reverse bias, photocurrent proportional to light, almost independent of voltage.
• Solar cell: no bias, works in the fourth quadrant, gives power.
• Zener: heavily doped, used in reverse breakdown; keeps voltage constant over a wide current range.
• Zener mechanism dominates below about 5 V, avalanche above about 6 V.
• Varactor: reverse bias increases depletion width and reduces capacitance.
• For an abrupt junction, capacitance halves when (V0 + VR) becomes four times larger.
• Gunn diode has no p-n junction; it uses two conduction band valleys of GaAs.
• Gunn threshold field is about 3.2 to 3.5 kV/cm; frequency f = vd/L.
• Silicon cannot make a Gunn diode because it lacks the required valley structure.

Solved examples

Example 1. A Zener regulator has VS = 20 V, Rs = 500 Ω, VZ = 10 V and RL = 1 kΩ. Find IS, IL, IZ and the Zener power.

\(I_S = (20 - 10)/500 = 0.02\) A \(= 20\) mA. \(I_L = 10/1000 = 10\) mA. \(I_Z = 20 - 10 = 10\) mA. \(P_Z = 10\times0.01 = 0.1\) W.

Example 2. An abrupt-junction varactor has a capacitance of 20 pF at 4 V reverse bias. Neglecting V0, find its capacitance at 16 V. If used with a 10 μH coil, find the tuning range.

\(C \propto V_R^{-1/2}\): \(C_2 = 20\sqrt{4/16} = 10\) pF. \(f_1 = 1/(2\pi\sqrt{10\times10^{-6}\times20\times10^{-12}}) = 11.25\) MHz; \(f_2 = 1/(2\pi\sqrt{10\times10^{-6}\times10\times10^{-12}}) = 15.92\) MHz. Changing the bias from 4 V to 16 V tunes the circuit from about 11.3 MHz to 15.9 MHz.

Example 3. A photodiode has quantum efficiency 0.8 at 850 nm. Find its responsivity and the photocurrent for 50 μW of incident light.

\(R = \dfrac{\eta e\lambda}{hc} = \dfrac{0.8\times1.6\times10^{-19}\times850\times10^{-9}}{6.63\times10^{-34}\times3\times10^{8}} = 0.547\) A/W. \(I_p = RP = 0.547\times50\times10^{-6} = 2.74\times10^{-5}\) A \(= 27.4\) μA.

Example 4. A solar cell of area 0.01 m² has Isc = 2 A, Voc = 0.6 V and FF = 0.75 under 1000 W/m². Find the maximum power and efficiency.

\(P_m = FF\,V_{oc}I_{sc} = 0.75\times0.6\times2 = 0.9\) W. \(P_{in} = 1000\times0.01 = 10\) W. \(\eta = 0.9/10 = 9\%\).

Example 5. A solar cell has IL = 3 A and I0 = 1 nA at 300 K (η = 1). Find Voc.

\(V_{oc} = 0.02585\ln(3/10^{-9} + 1) = 0.02585\times21.82 = 0.564\) V.

Example 6. A GaAs Gunn diode has an active length of 10 μm and the domain velocity is 10^5 m/s. Find the oscillation frequency and the threshold voltage (Eth = 3.3 kV/cm).

\(f = v_d/L = 10^{5}/10^{-5} = 10^{10}\) Hz \(= 10\) GHz (X band). \(E_{th} = 3.3\) kV/cm \(= 3.3\times10^{5}\) V/m. \(V_{th} = 3.3\times10^{5}\times10\times10^{-6} = 3.3\) V.

Important questions and answers

Q1. Explain the working of a photodiode with its characteristics. (5 marks)

Symbol: diode with two arrows pointing in. Circuit: photodiode in reverse bias with a series resistor and a battery; output taken across the resistor. In dark, only dark current flows (nA). When light falls on the junction, photons with \(h\nu \geq E_g\) generate electron-hole pairs in the depletion region; the reverse field separates them, adding to the minority carrier current, so the reverse current rises in proportion to the illumination. Characteristics: I_R versus V_R for different intensities are almost horizontal lines, equally spaced for equal steps of intensity; I_R versus intensity is a straight line. PIN structure widens the absorption region for faster, more sensitive detection; APD adds internal gain. Applications: optical communication, light meters, smoke detectors, barcode readers, remote control receivers, medical sensors.

Q2. Explain the working of a solar cell and its I-V characteristics. (5 marks)

Construction and working as in the summary: thin n layer on p wafer, light absorbed near the junction, pairs separated by built-in field, voltage generated without bias, current through the load. I-V curve: the dark diode curve shifted down by I_L into the fourth quadrant; plotted flipped, it begins at I_sc on the current axis, stays flat, bends at the knee and drops to zero at V_oc. Mark V_m, I_m and the maximum power rectangle. Define fill factor and efficiency. Note that I_sc is proportional to intensity while V_oc grows logarithmically.

Q3. What is a Zener diode? Explain its characteristics and its use as a voltage regulator. (6 marks)

A Zener diode is a heavily doped Si p-n junction designed for reverse breakdown operation. Characteristics: forward like an ordinary diode (cut-in 0.7 V); reverse current tiny until V_Z, then a sharp, almost vertical rise with nearly constant voltage. Mechanism: thin depletion layer, very high field, tunnelling (Zener effect) for low V_Z; avalanche for higher V_Z. Regulator: series resistor R_s from supply, Zener in reverse across load. Explain line regulation (V_S changes, I_Z adjusts, V_L constant) and load regulation (R_L changes, I_Z adjusts). Conditions: \(V_S > V_Z\), \(I_{ZK} < I_Z < I_{ZM}\). Draw the circuit and the reverse characteristic with V_Z, I_ZK and I_ZM marked.

Q4. Explain the varactor diode and its applications. (5 marks)

A varactor is a reverse-biased p-n junction used as a variable capacitor. The p and n regions act as plates and the depletion region as dielectric; \(C_T = \varepsilon A/W\). As reverse voltage increases, W increases as \((V_0 + V_R)^{1/2}\) for an abrupt junction, so \(C_T \propto (V_0 + V_R)^{-1/2}\) decreases. Hyperabrupt junctions give a larger variation. Graph: C_T falling with V_R. Symbol: diode with a capacitor symbol. Applications: electronic tuning in radio and TV receivers, VCOs in PLLs and mobile phones, FM modulators, automatic frequency control, frequency multipliers and parametric amplifiers. Advantages: small, no moving parts, tuned electronically and remotely.

Q5. Explain the working of a Gunn diode. (6 marks)

Structure: n⁺-n-n⁺ GaAs with ohmic contacts; no p-n junction. Energy band: GaAs conduction band has a lower valley with light, fast electrons and an upper valley about 0.3 eV higher with heavy, slow electrons. Below the threshold field electrons are in the lower valley, current rises with voltage. Above about 3.3 kV/cm, electrons transfer to the upper valley, their average velocity falls, giving negative differential resistance. Graph: drift velocity (or current) versus field rising to a peak at E_th and then falling. In the NDR region, a high-field domain forms at the cathode, drifts to the anode at about \(10^5\) m/s and disappears, then a new one forms; the current pulses with period equal to the transit time, \(f = v_d/L\). With a resonant cavity the frequency can be tuned. Applications: microwave oscillators (1 to 100 GHz) for radar speed guns, door openers, burglar alarms, collision-avoidance and microwave communication.

Q6. Compare a photodiode and a solar cell. (3 marks)

Photodiode: reverse biased; small area; detects light; output is a current signal proportional to intensity; fast response; works in the third quadrant. Solar cell: no external bias; large area; converts light to power; output is power to a load; slower; works in the fourth quadrant. Both use the generation of electron-hole pairs by light at a p-n junction.

Q7. Why are Zener diodes heavily doped? (2 marks)

Heavy doping makes the depletion region very thin, so a small reverse voltage produces a very strong field, causing breakdown at a low, sharp and stable voltage. The doping level is chosen to set the desired V_Z.

Exam tips

• Learn the symbol, bias condition, principle, characteristic and two applications of each diode; this covers most questions.
• In Zener numericals check that I_Z is positive and within limits; if negative, the diode is not regulating.
• For varactor numericals note whether V₀ is given; if not, use C ∝ V_R^−1/2.
• For the Gunn diode, draw the two-valley band diagram and the v versus E curve; this is the core of the answer.
• Use 1.24/λ(μm) for photon energy in eV in photodiode numericals.

FAQs

Can an LED be used as a photodiode?

Yes, weakly. An LED produces a small photocurrent when light of energy above its band gap falls on it, but it is less sensitive than a purpose-built photodiode.

Why is the Gunn diode called a diode if it has no junction?

It has two terminals (anode and cathode) and is used like a diode in circuits, so the name stuck, though transferred electron device is the more accurate name.

Why must a Zener regulator have a series resistor?

In breakdown the Zener voltage stays nearly constant while the current can rise enormously. The series resistor limits the current and absorbs the difference between supply and Zener voltage.

Is a varactor capacitance large enough for power supplies?

No. Varactors give only picofarads to a few hundred picofarads, which suits high-frequency tuning circuits but not filtering in power supplies.

These notes follow the University of Mumbai first-year engineering syllabus (NEP 2020, Semiconductor Physics, Semester II) and were prepared with AI help and checked.