In short

A Zener diode is engineered to undergo a sharp, non-destructive reverse breakdown at a precise voltage V_Z (typically 2–200 V). For |V| < V_Z it blocks. Beyond V_Z, it clamps the voltage across itself to V_Z no matter how much current flows, which is why it is the standard voltage regulator inside every Indian phone charger, inverter, and TV set-top box.

A photodiode is a reverse-biased p-n junction that generates a current proportional to the light intensity hitting its depletion region. A photon with energy h\nu > E_g (the semiconductor's band gap) breaks an electron out of a valence bond, the built-in field sweeps the electron-hole pair apart, and that is the photocurrent:

I_{ph} = \eta\, q\, \frac{P_\text{opt}}{h\nu}

where \eta is the quantum efficiency (fraction of photons that produce a charge pair), q is the electron charge, and P_\text{opt} is the optical power.

A light-emitting diode (LED) is a forward-biased p-n junction in a direct-band-gap semiconductor (gallium arsenide, gallium nitride, indium gallium nitride). When a forward-bias electron crosses the junction and falls into a hole on the p side, the energy E_g is released as a photon of wavelength

\lambda = \frac{hc}{E_g} = \frac{1240\ \text{nm·eV}}{E_g\ [\text{eV}]}.

A red LED (\lambda \approx 630 nm) needs E_g \approx 1.97 eV; a blue LED (\lambda \approx 465 nm) needs E_g \approx 2.67 eV; a white LED is a blue LED with a phosphor coating that down-converts some of the blue to yellow.

A solar cell is a photodiode designed for maximum area and maximum quantum efficiency. Sunlight generates electron-hole pairs throughout a large silicon wafer; the built-in junction field separates them and pushes current through an external load. In Indian sunlight (roughly 1000 W/m² at solar noon), a silicon cell delivers an open-circuit voltage of about V_{oc} \approx 0.6 V and a short-circuit current density of about 35 mA/cm², with conversion efficiencies of 18–22% for crystalline silicon. Connect sixty cells in series and you get the 350-watt panel that sits on a rooftop in Hyderabad.

All four devices are the same underlying object — a p-n junction — operated in four different regimes. The depletion region is the active volume; what changes is whether you pump charge carriers into it (LED), let photons create them (photodiode and solar cell), or drive the field hard enough to tear new carriers out of the atoms themselves (Zener).

Open a ₹20 USB charger bought at any Indian kirana shop and you will find four rectifier diodes in a bridge, a capacitor for smoothing, and tucked in the corner a small glass cylinder with a black stripe on one end — that is a Zener diode, and it is the reason the 5-volt output stays at 5 volts even when the wall voltage wanders between 200 and 240 V. Look up at the tube-light-style panel hanging from your bedroom ceiling and count the dots of light along the edge: each one is a light-emitting diode, a slab of gallium nitride the size of a grain of rice, converting electrons into photons at somewhere north of 60% efficiency. Walk up to the terrace of any new building in Pune or Chennai and you will see rectangular dark-blue panels tilted south — each one is about 60 solar cells wired in series, and each cell is a silicon p-n junction the size of a postcard, turning 20% of the sunlight that lands on it into electric current.

These four devices — Zener diode, photodiode, LED, solar cell — look like separate inventions. They are not. They are four things the same p-n junction does when you treat it differently. Understanding them means understanding which regime of operation each one sits in.

The four regimes of a p-n junction

Recall the p-n junction diode I-V curve: current is essentially zero until the forward bias reaches about V_0 \approx 0.7 V, then rises exponentially; in reverse bias, a tiny saturation current I_s of nanoamperes flows regardless of the reverse voltage — until the reverse voltage becomes large enough to cause breakdown, at which point the current suddenly shoots up.

The four operating regimes of a p-n junction on its I-V curveAn I-V curve with voltage on the horizontal axis, current on the vertical axis. Four regions are shaded and labelled: forward bias conducting (for LEDs and ordinary rectifier diodes), reverse bias dark (photodiode operating point with no light), reverse bias illuminated (photodiode and solar cell under light), and reverse breakdown (Zener region). V I 0 forward: LED diode conducts reverse: photodiode (dark current ≈ 0) reverse + light: photocurrent Zener breakdown V₀ ≈ 0.7 V −V_Z
The same p-n junction in four regimes. A rectifier diode lives in the forward region. An LED lives at the top of that forward region, where every injected carrier releases a photon. A photodiode lives on the solid reverse-bias segment, and the dashed curve below shows what happens when light hits it — the whole curve drops by the photocurrent $I_{ph}$. A Zener diode lives in the steep reverse-breakdown region on the left, where the current can climb vertically at essentially fixed voltage.

One device, four regimes. The job of each "special diode" is to engineer the junction so that one of these regimes becomes useful.

Zener diode — clamping a voltage

A standard rectifier diode, when reverse-biased past a few hundred volts, breaks down destructively: the built-up heat melts the silicon and the diode dies. A Zener diode is deliberately engineered to break down at a low, precise voltage — and to do so non-destructively, so that the breakdown is repeatable and reusable.

Why reverse breakdown happens

In reverse bias, the p side is held at a lower potential than the n side. The depletion region widens (look at the p-n junction article for the full derivation), and the electric field across it grows. At a reverse voltage of a few volts, the field in the depletion region can reach 10^8 V/m — enough to start ripping electrons out of the silicon atoms themselves. Two mechanisms can do the ripping, and a typical Zener uses a mix of both:

Zener tunnelling — at low breakdown voltages (V_Z \lesssim 5 V), the depletion region is so narrow that an electron in the valence band on the p side can quantum-mechanically tunnel directly into an empty conduction-band state on the n side. The tunnelling probability depends exponentially on the field, so once the field is strong enough, the current rises almost vertically.

Avalanche multiplication — at higher breakdown voltages (V_Z \gtrsim 7 V), the depletion region is wider and an individual electron accelerating across it can pick up enough energy to knock another electron out of a silicon atom (impact ionisation). That new electron is accelerated too, and it ionises another atom, and so on. The result is an electron avalanche — one original electron becomes thousands, and the current shoots up.

Why: both mechanisms produce the same I-V signature — a sharp, near-vertical rise at a well-defined V_Z — but the underlying physics differs. This is why you see "Zener diode" used as a generic name even when the diode is technically an avalanche diode. In most Indian CBSE and JEE textbooks, the distinction is skipped; "Zener" is used for any low-voltage breakdown diode.

The key engineering property is that the breakdown is non-destructive as long as the power dissipated (P = V_Z \cdot I) stays below the diode's rated limit. The Zener just needs a series resistor to keep the current sensible. When the resistor is chosen correctly, the diode can sit in breakdown indefinitely, and the voltage across it is pinned at V_Z regardless of small changes in supply voltage or load current.

The Zener voltage regulator — the working circuit

Here is the standard voltage regulator you will find in almost every piece of Indian electronics that runs off a variable DC supply: a Zener diode in parallel with the load, fed from the supply through a series resistor R_s.

Zener voltage regulator circuitA DC supply with variable voltage V_in on the left is connected through a series resistor R_s to a node. At this node, a Zener diode connects to ground with its cathode up (so that the diode is reverse-biased). In parallel with the Zener, a load resistor R_L also connects to ground. Arrows mark three currents: I_s flowing through the series resistor into the node, I_Z flowing down through the Zener, and I_L flowing down through the load. V_in (variable) R_s Z (V_Z) R_L V_out = V_Z I_s → I_Z ↓ I_L ↓
The standard Zener regulator. The Zener is reverse-biased so its cathode (the bar side) faces the positive rail. As long as the input voltage exceeds $V_Z$, the Zener sits in breakdown and holds $V_\text{out} = V_Z$ no matter how $V_\text{in}$ wanders.

How does it actually regulate? Apply Kirchhoff's current law at the node where R_s, the Zener, and R_L meet:

I_s = I_Z + I_L

Why: the current flowing in through R_s must equal the total flowing out — into the Zener plus into the load.

The load current is fixed by the output voltage and the load resistance: I_L = V_Z / R_L. The supply current is fixed by I_s = (V_\text{in} - V_Z)/R_s. So the Zener simply absorbs the difference:

I_Z = \frac{V_\text{in} - V_Z}{R_s} - \frac{V_Z}{R_L}.

If V_\text{in} suddenly rises — say the wall voltage swings from 220 V to 240 V, pushing the internal DC rail from 9 V to 10 V — I_s rises, but I_L is unchanged (because the output is still V_Z), so the extra current just flows through the Zener. The output voltage does not budge. If V_\text{in} drops by a similar amount, the Zener current drops, but as long as I_Z stays positive, the output voltage still sits at V_Z.

The regulation only fails when:

Between these two limits the Zener holds the output steady, typically to within about 1% for a well-chosen design. That is the whole secret of the 5 V on your phone charger's output port: a Zener diode, or a more modern IC that uses a Zener reference internally, clamping the voltage against variations.

Example 1: Designing a 5.1 V regulator for a phone charger's internal rail

A small charger has an internal DC rail that varies between 8 V and 12 V depending on the mains. You want to feed a 5.1 V logic controller that draws 20 mA, with the output voltage held to V_Z = 5.1 V by a 1 W Zener. Pick the series resistor R_s, and check the Zener's power dissipation in the worst case.

Step 1. The load current is I_L = V_Z / R_L, but you are told it directly: I_L = 20 mA.

Step 2. For regulation to hold at the lowest V_\text{in} = 8 V, the Zener must still carry some current — call it I_{Z,\min} = 5 mA (a typical rule: keep a few mA flowing so the diode stays in breakdown).

Step 3. At the lowest input, the series current must equal I_L + I_{Z,\min} = 25 mA. So

R_s = \frac{V_\text{in,min} - V_Z}{I_L + I_{Z,\min}} = \frac{8 - 5.1}{0.025} = 116\ \Omega.

Round up to a standard value: R_s = 120\ \Omega.

Why: size R_s so that at the lowest input voltage, enough current still flows to keep the Zener in breakdown. If you made R_s too large, the Zener would fall out of breakdown at low V_\text{in} and the output would sag.

Step 4. At the highest input V_\text{in,max} = 12 V, recompute:

I_s = \frac{12 - 5.1}{120} = 57.5\ \text{mA}.

The load still takes 20 mA, so the Zener absorbs I_{Z,\max} = 57.5 - 20 = 37.5 mA.

Step 5. Zener power dissipation at worst case:

P_Z = V_Z \cdot I_{Z,\max} = 5.1 \times 0.0375 = 0.19\ \text{W}.

Well below the 1 W rating. The design is safe.

Result: R_s = 120\ \Omega, with a 1 W, 5.1 V Zener absorbing up to 37.5 mA.

Load line for the Zener regulator exampleAn I-V curve for the Zener showing the vertical breakdown region at minus 5.1 volts. Two load lines crossing the breakdown: one for V_in equals 8 volts and one for V_in equals 12 volts. Their intersections with the Zener curve give the operating Zener currents — 5 mA and 37.5 mA respectively. V I (mA) −V_Z = −5.1 V V_in=8V V_in=12V I_Z=5 mA (min) I_Z=37.5 mA (max)
The two load lines correspond to the two extremes of the input voltage. Both intersect the Zener curve at exactly $-V_Z = -5.1$ V; only the Zener current changes. The output voltage, read off the horizontal intersection, is the same for both — that is the regulation.

What this shows: the voltage across the Zener is determined by the junction, not by the external circuit. The circuit can only push current through the junction; the junction decides how much voltage to drop. As long as you stay on the breakdown segment, that voltage is V_Z.

Every USB phone charger, every ₹200 bedside lamp with a USB port, every TV set-top box, every small WiFi router — all of them have a Zener somewhere, usually alongside a more sophisticated switching regulator but doing the same basic job. Three-terminal voltage regulator ICs (like the 7805 and LM317) have a Zener reference built inside them.

Photodiode — turning photons into current

A photodiode is the same p-n junction, reverse-biased, but now exposed to light. In the dark, the reverse current is just the tiny saturation current I_s — nanoamperes. When light with photon energy h\nu > E_g (the band gap of the semiconductor — 1.12 eV for silicon, 0.67 eV for germanium) falls on the junction, each absorbed photon breaks a covalent bond in the depletion region and creates an electron-hole pair.

The built-in electric field in the depletion region immediately separates them: the electron is swept toward the n side, the hole toward the p side. If there is an external circuit connecting the two sides, a current flows. This is the photocurrent.

Photodiode operation — photon generates an electron-hole pair that is swept apart by the depletion-region fieldA horizontal slab divided into a p region on the left and an n region on the right, with a dashed depletion region in the middle. A wavy arrow representing a photon enters the depletion region. Inside the depletion region, a plus-charge hole and a minus-charge electron are shown being pulled in opposite directions — the electron to the right into the n region, the hole to the left into the p region. An external wire connects the two sides through a resistor, and an arrow labelled I_ph shows conventional current flowing from n to p through the external circuit. p n depletion region photon (hν > E_g) + R_load V_R (reverse bias) ← I_ph
An incoming photon is absorbed inside the depletion region and creates an electron-hole pair. The built-in field (augmented by the external reverse bias) sweeps the hole into the p side and the electron into the n side. The resulting photocurrent $I_{ph}$ flows through the external circuit in the reverse direction and can be measured as a voltage across $R_\text{load}$.

From photon flux to photocurrent — the derivation

Suppose light of total optical power P_\text{opt} (watts) and wavelength \lambda falls on the photodiode's active area. Two steps turn this into a current.

Step 1. Number of photons per second. Each photon carries energy E_\gamma = h\nu = hc/\lambda. So the photon arrival rate is

\Phi = \frac{P_\text{opt}}{h\nu} = \frac{P_\text{opt} \lambda}{hc}.

Why: power is energy per second; divide by energy per photon to get photons per second.

Step 2. Fraction of photons that produce a collected charge pair. This is the quantum efficiency \eta (a dimensionless number between 0 and 1). Not every photon produces a usable pair — some are reflected at the surface, some pass through without being absorbed, some create a pair that recombines before the field can separate it. For a good silicon photodiode in the red, \eta \approx 0.8; for an ultra-violet photon hitting bare silicon, \eta drops because UV is absorbed so close to the surface that the pairs recombine before reaching the depletion region.

Each successful pair transports one electron's worth of charge through the circuit, so the photocurrent is

\boxed{\;I_{ph} = \eta\, q\, \Phi = \eta\, q\, \frac{P_\text{opt}}{h\nu} = \frac{\eta\, q\, \lambda}{hc}\, P_\text{opt}.\;}

Why: q is the charge per electron; multiplying by the pair-generation rate gives current. The linearity of I_{ph} in P_\text{opt} is the key feature — it is what makes photodiodes useful for light-intensity measurement over many orders of magnitude, from dim starlight to bright sunlight.

The responsivity R = I_{ph}/P_\text{opt} = \eta q \lambda/(hc) has units of A/W. For \lambda = 900 nm and \eta = 0.8, it is about 0.58 A/W — a silicon photodiode generates roughly 0.6 milliamps of current for every milliwatt of near-infrared light falling on it. This is why the TV remote in your drawing room (which emits at about 940 nm) can be detected by a small silicon photodiode from the 2 m away on the set-top box.

The spectral cutoff is set by the band gap: photons with wavelength longer than \lambda_c = hc/E_g do not have enough energy to break a bond, so they are not detected. For silicon (E_g = 1.12 eV), \lambda_c = 1240/1.12 \approx 1108 nm. That is why silicon photodiodes see the visible and near-infrared spectrum, but not the thermal infrared (10 µm) — thermal cameras use different materials (InGaAs or HgCdTe) with smaller band gaps.

Light-emitting diode — the reverse process

An LED takes the same p-n junction but flips the process. Instead of absorbing a photon to create an electron-hole pair, it starts with an electron and a hole, combines them, and emits a photon. This is radiative recombination.

Why direct-band-gap materials are required

In silicon, when an electron in the conduction band falls into a valence-band hole, the energy E_g is typically released as a lattice vibration (a phonon — heat), not as a photon. The reason is a quantum-mechanical selection rule: silicon is an indirect-band-gap semiconductor, meaning the conduction-band minimum and the valence-band maximum sit at different momentum values. An electron falling from one to the other must change both its energy and its momentum; photons carry very little momentum, so the transition typically needs a phonon to supply the momentum difference. That is a two-particle process — slow and inefficient.

In gallium arsenide (GaAs), gallium nitride (GaN), and indium gallium nitride (InGaN), the conduction-band minimum and the valence-band maximum sit at the same momentum. An electron can fall straight down from conduction band to valence band and emit a photon — a single-particle process that is fast and efficient. These are direct-band-gap semiconductors, and they are the materials from which all LEDs are made.

The photon wavelength — derived from the band gap

Forward-bias the junction. Electrons are injected from the n side into the p side; holes are injected from the p side into the n side. In the vicinity of the junction, an electron and a hole find each other. The electron falls from the conduction band edge to the valence band edge, losing energy E_g. In a direct-band-gap material, this energy comes out as a photon:

E_\text{photon} = h\nu = \frac{hc}{\lambda} = E_g.

Solving for \lambda:

\boxed{\;\lambda = \frac{hc}{E_g}.\;}

Why: conservation of energy. The electron gives up exactly E_g when it falls from the conduction band to the valence band, and a direct-band-gap material allows that energy to come out as a single photon rather than heat.

Plug in numbers. hc = 1240\ \text{eV·nm} is the useful shorthand (a number worth memorising). So \lambda in nm equals 1240 divided by E_g in eV. This gives the colour of every LED directly from its band gap:

Material E_g (eV) \lambda (nm) Colour
AlGaAs 1.97 630 Red
GaP 2.26 550 Green (yellowish)
InGaN (In-rich) 2.67 465 Blue
AlGaN (Al-rich) 3.4 365 Ultraviolet

A white LED — the kind in every bulb sold by Crompton or Bajaj or Havells — is a blue InGaN LED with a yellow phosphor (typically cerium-doped yttrium aluminium garnet, Ce:YAG) painted on the outside of the die. The blue light from the junction hits the phosphor, which absorbs it and re-emits a broader yellow spectrum. The blue-that-escapes plus the yellow-re-emitted adds up to something that looks white to your eyes — a trick borrowed from cathode-ray phosphors and adapted to LEDs. This is why a cheap white LED bulb sometimes looks bluish: the phosphor coating is thin, too much blue escapes, and the colour balance tips cold.

Why an LED needs a current-limiting resistor

The I-V curve of a forward-biased LED is nearly vertical once V > V_0 (the forward voltage — about 2 V for red, 3.2 V for white). If you connect an LED directly across a 3.3 V supply, a tiny increase in voltage (say from 3.2 V to 3.3 V) causes an enormous increase in current — potentially enough to burn the LED out in microseconds. The fix is a series resistor R that limits the current to the LED's rated value (typically 20 mA for a small indicator LED).

For a supply voltage V_s and an LED forward voltage V_F:

R = \frac{V_s - V_F}{I_\text{LED}}.

Why: the voltage across the resistor equals the supply minus the LED's forward drop; dividing by the desired current gives the resistor value. This is Ohm's law applied to the part of the circuit that is an ordinary resistor.

Example 2: Designing the resistor for a red indicator LED on an Arduino

You want to light a red LED (V_F = 2.0 V, I_\text{LED} = 10 mA) from a 5 V Arduino digital pin. What series resistor do you need? And how much energy per second does the LED convert to photons, if its internal quantum efficiency is 50%?

Step 1. Apply the current-limiting formula.

R = \frac{5.0 - 2.0}{0.010} = 300\ \Omega.

Round up to the standard value: R = 330\ \Omega (a safety margin of about 10% — always round up so the current is a little less than the rated maximum, not more).

Why: rounding up reduces the current, which extends the LED lifetime. Rounding down (say to 270 Ω) pushes the current slightly above 10 mA, which works but burns the LED hotter.

Step 2. Compute the actual LED current with the rounded resistor.

I_\text{actual} = \frac{5.0 - 2.0}{330} = 9.09\ \text{mA}.

Step 3. Power dissipated in the LED (electrical input):

P_\text{LED} = V_F \cdot I_\text{actual} = 2.0 \times 0.00909 = 18.2\ \text{mW}.

Step 4. Photon power out, at 50% internal quantum efficiency (meaning half the electrons recombine radiatively and half recombine non-radiatively, as heat):

P_\text{photon} = \eta_\text{IQE} \cdot P_\text{LED} = 0.5 \times 18.2 = 9.1\ \text{mW}.

Why: each radiatively recombining electron produces one photon of energy E_g \approx 2 eV ≈ V_F — the photon energy and the electrical energy per electron are the same. So the fraction of electrical power that becomes photon power is just the fraction of electrons that recombine radiatively.

Step 5. Photon arrival rate, using P_\text{photon} = \Phi \cdot h\nu with h\nu = 1240/630 eV = 1.97 eV = 3.15 \times 10^{-19} J:

\Phi = \frac{9.1 \times 10^{-3}}{3.15 \times 10^{-19}} \approx 2.9 \times 10^{16}\ \text{photons/s}.

Result: Use R = 330\ \Omega. The LED draws 9.1 mA and emits about 2.9 \times 10^{16} red photons every second. (Not all of these escape the die — the external quantum efficiency is lower because of internal reflection losses — but this is the number generated inside.)

Arduino output to red LED with current-limiting resistorA circuit with a 5 V source on the left connected through a 330 ohm resistor to a red LED and then to ground. Arrows and labels show the 9.1 mA current through the series loop, the 3 V drop across the resistor, and the 2 V drop across the LED. 5 V R = 330 Ω 3.0 V drop LED, V_F=2 V emits red photons I = 9.1 mA (loop)
The Arduino's 5 V drops across two elements in series: 3.0 V on the resistor, 2.0 V on the LED. The 9.1 mA loop current is the same through both. Of the 18 mW delivered to the LED, about half comes out as red photons.

What this shows: the resistor and the LED split the supply voltage. The resistor enforces the current; the LED uses the current to emit light. Every LED indicator you ever wire up follows this same pattern.

The reason an LED bulb is so efficient compared to an incandescent bulb is precisely this: in an incandescent, you heat a tungsten filament until it glows, and the glow is a broadband Planck spectrum peaking in the infrared — most of the energy leaves as heat, only a few percent as visible light. In an LED, each injected electron produces a single photon at the useful wavelength. There is no thermal spectrum to waste on. Modern white LED bulbs routinely achieve 100–200 lumens per watt, compared to 10–15 for incandescents.

Solar cell — the photodiode as a power source

A solar cell is a photodiode run without an external bias, connected to a load. When sunlight creates electron-hole pairs in the depletion region, the built-in junction field separates them, the carriers flow through the load, and electrical power is delivered from the cell to the circuit. The cell acts as a battery for as long as the sun shines.

The I-V curve under illumination — the derivation

The unilluminated junction obeys the Shockley diode equation (derived in the p-n junction article):

I_\text{dark} = I_s (e^{qV/(kT)} - 1).

Light adds a constant photocurrent I_{ph} flowing in the reverse direction (photon-generated pairs swept out by the built-in field). Using the sign convention that current out of the cell is positive:

\boxed{\;I = I_{ph} - I_s(e^{qV/(kT)} - 1).\;}

Why: the illuminated cell's current is just the dark Shockley current shifted downward by the photogenerated current. The light creates pairs that add to the reverse current regardless of what the applied voltage is doing. This is the single most important equation in photovoltaics.

Two limits of this equation define the cell's performance:

Short-circuit current I_{sc} — set V = 0 (short-circuit the cell). The exponential becomes 1, the bracket becomes zero, and

I_{sc} = I_{ph}.

Every photogenerated pair contributes to the external current. For a 10 cm × 10 cm silicon cell in 1000 W/m² sunlight, I_{sc} \approx 3.5 A.

Open-circuit voltage V_{oc} — set I = 0 (open-circuit the cell). Solve for V:

0 = I_{ph} - I_s(e^{qV_{oc}/(kT)} - 1)
e^{qV_{oc}/(kT)} = 1 + \frac{I_{ph}}{I_s}
V_{oc} = \frac{kT}{q}\,\ln\!\left(1 + \frac{I_{ph}}{I_s}\right).

Why: take the logarithm of both sides to isolate V_{oc}. For a silicon cell, I_{ph}/I_s is enormous (about 10^{10}), so V_{oc} \approx 25.85\ \text{mV} \times \ln(10^{10}) \approx 0.6 V. This is the fundamental reason silicon cells give about 0.6 V open-circuit: the ratio of photocurrent to saturation current is set by the band gap and the doping, and both are properties of silicon itself.

Between these two extremes, the I-V curve bends — there is a voltage called the maximum power point V_\text{mp} where the product P = IV is largest. That is the voltage a solar inverter (or a charge controller) tries to keep the cell operating at; it uses a technique called maximum power point tracking (MPPT) that you see advertised on every rooftop solar controller sold in India.

Solar cell I-V curves at three light intensitiesThree I-V curves for a solar cell, at 1000, 500, and 200 watts per square metre of illumination. Each curve starts at a short-circuit current on the vertical axis and bends down to an open-circuit voltage on the horizontal axis at around 0.6 volts. The maximum power point for the 1000 watt curve is marked at about 0.5 volts and 3.3 amperes. The knee of the curve is the sweet spot where a good solar charge controller operates. V (V) I (A) 0.2 0.4 0.6 3.5 2 0.75 1000 W/m² 500 W/m² 200 W/m² MPP (0.5 V, 3.3 A)
Three I-V curves of the same silicon cell under three light intensities. $I_{sc}$ grows proportionally with illumination (the photocurrent is linear in light), but $V_{oc}$ grows only logarithmically — a factor of 5 change in intensity shifts $V_{oc}$ by only $kT/q \cdot \ln 5 \approx 40$ mV. The knee of each curve is the maximum power point; a good charge controller keeps the panel operating there.

Indian numbers

A standard rooftop solar panel in India holds 60 cells in series. Each cell produces about 0.6 V open-circuit, 0.5 V at the maximum power point. Sixty in series gives about 30 V at MPP. With a cell area of 156 mm × 156 mm and a current density of about 35 mA/cm² at 1000 W/m², each cell in sunlight produces

I_\text{cell} = 0.035 \times 156 \times 15.6 / 10 \approx 9\ \text{A}.

(The cells are square with side 156 mm; the 15.6 comes from 156 mm = 15.6 cm, and dividing by 10 converts the mA to A.)

So a single 60-cell panel at noon in Hyderabad delivers about 30\ \text{V} \times 9\ \text{A} \approx 270 W. A 1-kW household installation is four of these panels, roughly 2.4 m² of roof area. A 5-kW system, which can meet most of an Indian household's daytime load (fans, lights, fridge, WiFi), is 20 panels over about 12 m² of roof — the size of a single bedroom floor.

Common confusions

If you just wanted to understand what these four diodes do and why, you can stop here — the four physical pictures above cover all of CBSE and the NEET/JEE conceptual questions. The rest is for readers who want a deeper view.

Temperature coefficient of the Zener voltage

For Zener diodes with V_Z \lesssim 5 V, the breakdown is dominated by tunnelling, and increasing temperature decreases V_Z (negative temperature coefficient). For V_Z \gtrsim 7 V, breakdown is dominated by avalanche multiplication, and increasing temperature increases V_Z (positive coefficient), because hotter atoms scatter carriers more, reducing their mean free path and raising the field needed to sustain the avalanche. Right around V_Z \approx 5.6 V, the two effects cancel, and the Zener has zero temperature coefficient — which is why precision voltage references in lab instruments are built from 5.6 V–6.2 V Zeners, and why the LM399 precision reference IC operates near that voltage.

The ideal solar cell efficiency — the Shockley-Queisser limit

A single-junction solar cell made of a material with band gap E_g has a thermodynamic efficiency ceiling, first derived in 1961, called the Shockley-Queisser limit. Two losses dominate:

  1. Below-gap photons — photons with h\nu < E_g are not absorbed; their energy is lost.
  2. Above-gap thermalisation — photons with h\nu > E_g are absorbed, but the excess energy h\nu - E_g is dumped as heat (the electron rapidly loses its extra kinetic energy to lattice vibrations before it can be extracted). All the voltage produced per photon is \sim E_g, regardless of the photon energy.

Balance these two losses and maximise power output against the solar spectrum. The result: for a single-junction cell in 1-sun AM1.5 sunlight (the Indian ground-level reference), the maximum possible efficiency is about 33.7%, occurring at E_g \approx 1.34 eV — which is between silicon (1.12 eV, theoretical limit 32%) and gallium arsenide (1.42 eV, theoretical limit 33.5%). Commercial silicon cells reach 22–24% in 2026; laboratory GaAs cells have demonstrated 29.1%.

You can beat the Shockley-Queisser limit with multi-junction cells — stack cells with decreasing band gaps on top of each other, each absorbing a different part of the spectrum. Space-grade triple-junction cells have reached 47% efficiency in concentrated sunlight. But they are expensive, and rooftop economics still favour single-junction silicon for now.

The ideality factor and why the Zener current does not grow to infinity

Writing I = I_s(e^{qV/(\eta kT)} - 1) with ideality factor \eta \approx 12 covers both the diffusion current regime (\eta = 1) and the recombination-in-depletion regime (\eta = 2) of a real diode. In reverse breakdown, the Zener I-V is not actually vertical — the curve has a small but non-zero slope, corresponding to the Zener impedance r_Z = dV/dI, typically a few ohms. This means the output voltage of a real Zener regulator moves by \Delta V \approx r_Z \cdot \Delta I as the load or input changes. For a r_Z = 5\ \Omega Zener carrying a 20 mA change, the output shifts by 100 mV — small, but not zero. Precision applications use either low-r_Z Zeners (a few tenths of an ohm) or a band-gap reference IC that uses feedback to crush the impedance even further.

Why is an LED "cold" but a solar cell "hot"?

An LED's surface stays relatively cool (you can usually touch a low-power LED indefinitely). A solar cell on a summer terrace in Rajasthan can reach 70 °C under full sun. Why?

Because the LED is a source of photons, its internal heat is generated only by the fraction of electrons that recombine non-radiatively — a small fraction if the internal quantum efficiency is high. The photons leave, taking their energy with them.

The solar cell, by contrast, absorbs all the incoming photons, extracts only a fraction of the energy as electrical output, and all the rest becomes heat in the cell. A 20% efficient cell dumps 80% of the incoming solar flux as heat. And higher temperature actually hurts a silicon cell's performance (the saturation current I_s rises sharply with T, and V_{oc} drops by about -2.3 mV/°C), which is why all rooftop solar farms in India worry about cell cooling.

Solar cells as detectors — the bridge back to photodiodes

If you run a silicon solar cell in reverse bias with a load resistor, it becomes a photodiode (with huge area and modest bandwidth). This is the point that unifies the two "different" devices: the same p-n junction, run in the photovoltaic quadrant (positive V, positive I out) is a power source; run in the photoconductive quadrant (negative V, positive I out) is a light sensor. The two devices are one physical object operated in two modes.

Where this leads next