Question 2 of 7: PIN Photodiode — Structure, Photocurrent and Responsivity

Question 2: PIN Photodiode — Structure, Photocurrent and Responsivity (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. Parts (a)–(b) are structural/qualitative (device cross-section, internal fields, and the governing photocurrent relation); part (c) has one numeric result — the silicon absorption band edge — found from the given bandgap; part (d) is a qualitative explanation of the two competing time constants that set a PIN diode's bandwidth.

Part (a) — structure, internal fields and operation

A PIN photodiode inserts a wide, lightly-doped (nominally intrinsic) layer between a heavily doped $p^+$ anode and $n^+$ cathode. Under reverse bias the depletion region punches through the entire intrinsic layer (it is "fully depleted"), so essentially all of the applied reverse voltage drops across the $i$-region and the electric field there is close to uniform — unlike a simple $pn$ junction, where the field is triangular and largely confined to the narrow, lightly-doped side. The fixed space charge is concentrated in two thin sheets at the $p^+$/$i$ and $i$/$n^+$ boundaries (ionized acceptors on the $p^+$ side, ionized donors on the $n^+$ side), with essentially zero net charge density through the bulk of the $i$-region since free-carrier density there is negligible at reverse bias.

When light with photon energy $h\nu>E_g$ is incident (through a thin, lightly-doped window layer so absorption happens mainly in the $i$-region), each absorbed photon can generate one electron–hole pair. The strong, uniform field in the $i$-region sweeps the electron toward the $n^+$ side and the hole toward the $p^+$ side at (near) their saturation drift velocities, producing an external photocurrent proportional to the incident optical power. Because the absorbing region is fully depleted, there is essentially no slow diffusion component to the response — this drift-dominated collection is what makes PIN diodes fast compared to a simple $pn$ photodiode.

Part (b) — photocurrent equation, operating mode, and I–V curve

Under reverse bias, the total diode current is the (negligible) reverse dark/saturation current minus the photogenerated current, essentially independent of the exact reverse voltage once the diode is fully depleted: $$I = -I_{dark} - I_{ph}, \qquad I_{ph}=R\,P_{in}=\frac{\eta q}{h\nu}P_{in},$$ where $R$ is the diode's responsivity (A/W) and $P_{in}$ the incident optical power; the load resistor $R_L$ simply converts $I_{ph}$ to an output voltage $V_{out}=I_{ph}R_L$ and does not enter the photocurrent relation itself. This bias condition — diode reverse biased, output current controlled by incident light rather than forward-bias carrier injection — is called the photoconductive mode (as opposed to the unbiased photovoltaic mode used in solar cells).

Part (c) — responsivity curve shape and band-edge wavelength

The responsivity of an ideal photodiode would rise linearly with wavelength ($R=\eta q\lambda/hc$, since each photon carries less energy at longer $\lambda$ but still contributes one electron per absorbed photon at fixed $\eta$). In a real silicon detector the curve instead rises from the UV, peaks somewhere in the near-IR (limited by how efficiently photons are absorbed within the depletion width at each wavelength — silicon's absorption coefficient falls as $\lambda$ increases), and then drops sharply to zero once the photon energy falls below the bandgap and the material becomes transparent. That cutoff, the band edge wavelength, is fixed purely by $E_g$: $$\lambda_g=\frac{hc}{E_g}=\frac{(6.626\times10^{-34})(2.998\times10^8)}{(1.11)(1.602\times10^{-19})} =\boxed{1117\ \text{nm}}$$ using the paper's own $\text{Si}\ E_g=1.11$ eV.

Part (d) — response-time terms and the optimum intrinsic width

$\tau_{RC}$ is the electrical (Miller-type) time constant set by the junction capacitance $C_j$ (which scales inversely with intrinsic-region width $w$, since $C_j\propto\varepsilon A/w$) charging into the external circuit impedance $R_L$: $\tau_{RC}\approx R_LC_j$. $\tau_{drift}$ is the carrier transit time across the intrinsic region at the saturation drift velocity $v_{sat}$: $\tau_{drift}\approx w/v_{sat}$, which grows directly with $w$. Because $\tau_{RC}$ decreases with wider $w$ (smaller capacitance) while $\tau_{drift}$ increases with wider $w$ (longer transit distance), the two error sources trade off against each other; minimizing $\tau=\sqrt{\tau_{RC}^2+\tau_{drift}^2}$ over $w$ therefore yields a single optimum intrinsic-layer thickness rather than "as thin/thick as possible" in either direction — too thin and RC charging dominates, too thick and transit time dominates.