Question 6 of 7: Photodiode and Phototransistor Light Sensing

Question 6: Photodiode and Phototransistor Light Sensing (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.

a) Incident photons with energy at or above the semiconductor's bandgap generate electron-hole pairs within (or diffusing into) the reverse-biased junction's depletion region; the strong electric field there — built-in plus the applied reverse bias — sweeps the photo-generated carriers across the junction, adding a photocurrent that flows in the SAME direction as the diode's normal reverse leakage current. It is the depletion-region field doing the carrier COLLECTION, not forward-bias carrier injection, which is why the device is operated reverse-biased for sensing.

b) Even with zero incident light, a reverse-biased junction still carries a small "dark current" from (i) thermally generated minority carriers being continuously swept across the junction by the same depletion-region field, and (ii) surface leakage current along the junction's exposed edges. This dark current sets the photodiode's fundamental noise floor and minimum detectable signal.

c) Cool the photodiode — thermally generated dark current follows an Arrhenius-type exponential temperature dependence, so cooling drastically reduces it (the basis for cooled detectors in low-light imaging and spectroscopy); choose a lower-leakage device (smaller junction area, a wider-bandgap semiconductor with a lower intrinsic thermal generation rate); minimize the reverse bias voltage, since the surface-leakage component of dark current increases with reverse bias; and ensure good surface passivation to suppress the surface-leakage contribution specifically.

d) A phototransistor uses the photocurrent generated at its base-collector junction — which behaves exactly like a bare photodiode — as the BASE current driving an integral bipolar transistor. That transistor supplies its own current gain $\beta$ (typically 100-1000$\times$) to the photocurrent, so the phototransistor's collector current is approximately $\beta$ times larger than the same illumination would produce from the bare photodiode alone — at the cost of a slower response (larger effective junction capacitance/longer carrier transit time through the amplifying structure) and reduced linearity compared to the photodiode by itself.

e) For the sensing-resistor circuit shown, increasing $V_{exc}$ increases the voltage headroom available to drop across the sensing/feedback resistor for a given photocurrent, and for a phototransistor specifically a higher collector-emitter bias modestly widens the depletion region and can slightly raise the effective photocurrent gain. The DOMINANT effect on the circuit's output sensitivity, however, is the value of the sensing/feedback resistor itself — exactly the same transimpedance (current-to-voltage) sensitivity relationship already derived for the thermistor voltage divider in Q5(a): raising the sensing resistor raises $dV_{out}/dI_{photo}$ directly, while $V_{exc}$ mainly sets the available dynamic range/headroom before saturation rather than the fundamental sensitivity slope.

f) A photodetector's quantum efficiency (fraction of incident photons that generate a collected electron-hole pair) is governed by two competing, wavelength- dependent effects: the photon energy must exceed the material's bandgap (setting a long-wavelength cutoff below which photons simply are not absorbed), and the photon's absorption DEPTH in the semiconductor (set by the material's wavelength-dependent absorption coefficient) must be well matched to the depth of the depletion/collection region — too short a wavelength is absorbed very near the surface, where recombination losses are high before carriers can be collected, while too long a wavelength penetrates past the depletion region entirely. Every detector material therefore has a characteristic spectral-response curve peaking at some intermediate wavelength and falling off toward both the UV and IR ends.

g) A photomultiplier tube converts incident photons striking a photocathode into photoelectrons via the photoelectric effect; these primary electrons are accelerated by a strong field toward a first "dynode" (a specially coated electrode) where each impacting electron knocks loose several secondary electrons; that multiplied burst is accelerated toward a second dynode, multiplied again, and so on through a cascade of typically 8-14 dynode stages, each stage multiplying the electron count by roughly 3-6$\times$. The CUMULATIVE gain (the product of every stage's individual gain) can reach $10^6$-$10^8$, so even a SINGLE detected photon produces a large, easily measurable current pulse at the final anode — this enormous internal gain, combined with a very low intrinsic dark current, is what lets a PMT resolve individual photons that a simple photodiode cannot pull out of its own noise floor.

h) At very low light levels the number of photons collected per pixel over the exposure is small, so the fundamental photon-counting shot noise (Poisson statistics, SNR $\propto\sqrt{N}$) becomes comparable to, or larger than, the signal itself; on top of that, the CCD's own read noise (from the charge-to-voltage readout amplifier, roughly constant regardless of signal level) becomes a significant or even dominant fraction of the total signal. Together these appear in the finished image as visible pixel-to-pixel brightness/colour fluctuations ("graininess"), reduced effective dynamic range and lost shadow detail, and a more visible fixed-pattern component (dark- current non-uniformity) relative to the weak true signal — an overall grainy, low-contrast, noisy-looking low-light image. This is why low-light imaging favours longer exposures, pixel binning, or cooled sensors: each increases the photon count relative to the fixed read-noise floor.