MOS Photo Sensitivity

For a p-type substrate under positive V_G, bands bend downward at the oxide-semiconductor interface and surface potential φ_s increases.

Weak inversion — φ_F < φ_s < 2φ_F. E_i crosses below E_F at the surface, so n_s = n_i·exp(qφ_s/kT) exceeds n_i but is still ≪ N_A. Sparse minority carriers, depletion width still growing with V_G.

Strong inversion — φ_s = 2φ_F. Now n_s = N_A: the surface is as n-type as the bulk is p-type. The inversion layer screens further V_G — all additional voltage drops across the oxide. Depletion width pins at:

Deep depletion — if V_G is pulsed beyond threshold faster than thermal generation can fill the inversion layer (τ_gen ~ ms), φ_s > 2φ_F and W > W_max. This non-equilibrium state is where the MOS cap is most photosensitive, and is the operating regime of every CCD pixel.

Accumulation (V_G < V_FB) — majority carriers at surface, no depletion, no field. Photogenerated pairs recombine. Essentially zero photoresponse.

Depletion (V_FB < V_G < V_T) — W grows as √φ_s. Photons absorbed within W or within one diffusion length L of the depletion edge generate e-h pairs swept by the field. Electrons → surface, holes → bulk. Sensitivity grows with V_G.

Strong inversion (equilibrium) — W pinned at W_max. Moderate but capped sensitivity. Inversion layer screens additional gate voltage.

Deep depletion (pulsed V_G ≫ V_T) — maximum sensitivity. W ≫ W_max, no inversion layer to screen the field. Photogenerated electrons drifting to the surface are the inversion charge — photons do the work thermal generation would eventually do.

Practical consequence: pulse V_G high → integrate photo-charge → read out before dark current fills the well. That’s the CCD clock cycle.

Two properties dominate: bandgap sets the long-λ cutoff (λ_max = hc/E_g), and absorption coefficient α(λ) determines required depletion width for efficient collection.

Direct bandgap (GaAs, InP, GaN, InGaAs): sharp absorption onset, α ~ 10⁴ cm⁻¹ at edge — 1 μm depletion captures most photons. Indirect (Si, Ge, SiC): phonon-assisted, α ~ 10² cm⁻¹ near E_g, needing 10–100 μm depletion for long-λ collection → low doping or deep depletion.

Short-λ cutoff: oxide transparency and surface recombination. SiO₂ transparent to ~150 nm. High-κ (HfO₂) absorbs below ~250 nm. Blue/UV has very high α → absorbed in first ~10 nm where S₀ is high → kills blue QE unless BSI.

Electron affinity χ sets the vacuum level offset E₀ = E_c + χ. Toggle “E₀ vacuum” to see how χ scales with material — notice 4H-SiC’s unusually small χ (3.17 eV), which is why SiC is attractive for electron emission and NEA devices.

Junction origin — PN diode has a built-in junction with φ_bi; depletion exists at equilibrium and widens with reverse bias. MOS cap depletion is entirely voltage-induced — no junction.

Operating mode — PN: steady-state, DC reverse bias, continuous photocurrent J_ph = qGW + diffusion terms. MOS cap: integrating detector in deep depletion (non-equilibrium). Photo-charge accumulates in surface potential well; must be clocked out. Current-mode vs charge-mode.

Speed — PN/PIN bandwidth set by τ_tr = W/v_sat and RC. GHz-capable. MOS cap “bandwidth” = integration time + charge transfer rate. Fine for video-rate imaging, not for telecom.

Dark current — both have J_dark ~ qn_iW/τ_g. MOS cap in deep depletion has W > W_max → worse dark current at equal doping/temperature. CCDs need cooling for long exposures.

QE — comparable at similar W. Deep depletion can exceed PN QE at long λ because W > W_max → larger collection volume.

Bottom line — PN = continuous current source → TIA → real-time sensing. MOS cap = charge bucket → fill with photons → read out. PN wins for speed. MOS cap wins for imaging arrays: every pixel is just a capacitor (compact, scalable, integrating). This is why CCDs worked and why CMOS APS still uses MOS depletion under the transfer gate — the 4T pixel architecture.