Solar cell and its characteristics

1. What a Solar Cell Is

Solar cell / photovoltaic cell = p-n junction that converts light to electrical power via photovoltaic effect: photons $hν≥E_g$ create electron-hole pairs in/near depletion region, separated by built-in field ⇒ current to external load. No external bias needed (operates in 4th quadrant of I-V, power delivered).

Related to photodiode but optimized for power (large area, anti-reflection, texturing) vs detection (speed).

2. Construction (Si dominant)

Top: grid metal contact (allows light) + anti-reflection coating (SiN) + n+ emitter thin (≈0.5 µm)
Middle: p-n junction (n emitter on p base, or p on n)
Bottom: back contact (metal)
Textured surface (pyramids) traps light by multiple reflection.

3. Working — Photovoltaic Effect Steps

Photon absorption in Si:

hν ≥E_g (1.12 eV ⇒ λ≤1100 nm)

creates $e-h$ pair (excess carriers).
2. Pairs generated within diffusion length of depletion diffuse to junction, field separates: electrons to n-side, holes to p-side.
3. Charge separation ⇒ photovoltage $V_{oc}$ forward biases junction; current flows through load ⇒ power $P=V·I$ .

Band diagram: built-in $V_{bi}$ tilts bands; light splits quasi-Fermi levels.

4. I-V Characteristics (illuminated p-n)

Dark diode:

I_{dark}=I_0(e^{eV/kT}-1)

Under illumination shift down by photocurrent $I_{ph} (≈ I_{sc})$ :

I = I_0(e^{eV/kT}-1) - I_{ph}

Key points:

Short-circuit current $I_{sc}=I_{ph} ∝$ light intensity (at $V=0$ ).
Open-circuit voltage $V_{oc}= (kT/e) ln(I_{ph}/I_0 +1)$ (~0.6 V for Si).
Maximum power point $(V_m,I_m)$ where $P_m=V_m I_m$ maximal, rectangle inside I-V.
Fill factor

FF = V_m I_m/(V_{oc} I_{sc})

(~70–83% good).

Efficiency

η = P_m/(P_{light}·Area)= V_{oc}I_{sc}FF/(P_{in})

Si commercial ~15–22%, lab >26%.

5. Worked Illustration

Si cell area 10 cm², P_in=1000 W/m² ⇒ 1 W incident, I_sc=3 A, V_oc=0.6 V, FF=0.8 ⇒ P_m=1.44 W? Wait 3·0.6·0.8=1.44 W >1 W impossible ⇒ realistic I_sc~0.3 A for 10 cm² (30 mA/cm²) ⇒ P_m≈0.144 W ⇒ η≈14% ✓

Spectral: Si absorbs λ<1100 nm (visible + near IR), loses sub-bandgap photons and excess above Eg as heat.

6. Exam Points

Explain photovoltaic effect $hν≥E_g → e-h → separated by junction field — 5-7 marks, very frequent (almost certain).
Draw structure and band diagram — 5 marks, frequent.
Sketch illuminated I-V with $I_{sc}, V_{oc}, FF$ , and give

FF, η

— 5-7 marks, very frequent.

Compare photodiode (detector, reverse bias) vs solar (power, zero bias) — 3 marks.

Solar cell and its characteristics