Photodiode Speed & Bandwidth
RC, transit-time and diffusion-tail bandwidth, junction capacitance and thermal NEP vs photodiode area.
Responsivity
548.46 mA/W
Depletion Width W
10.54 µm
ε₀·ε_r / C''
Transit Limit
3.53 GHz
0.443·v/W, any area
RC BW @ 1 mm²
318.31 MHz
C = 10.0 pF, RC = 500.00 ps
Combined BW @ 1 mm²
317.02 MHz
RC-limited, drift carriers only
Drift Share
53.7 %
of DC photocurrent; 1/α = 18.7 µm
Diffusion −3 dB
13.59 MHz
intrinsic; τ = L²/D = 340 ns
Total −3 dB @ 1 mm²
13.47 MHz
drift + diffusion × transit × RC
Only 53.7 % of the photocurrent is generated inside W, so the response drops to that plateau (−5.4 dB) above the diffusion corner: the intrinsic −3 dB point is 13.59 MHz, and with the RC and transit limits the total at 1 mm² is 13.47 MHz, not the 317.02 MHz of the drift carriers alone. A thicker depletion region, a shorter wavelength or a thin epitaxial layer on a short-L substrate removes the tail.
Cj = C'' · A, depletion width W = ε₀εr / C''
fRC = 1 / (2π · R · Cj), ftr = 0.443 · v / W (carrier crossing the full width)
1/f3dB² = 1/fRC² + 1/ftr²
Drift share (1 − e−αW) / (1 − e−αW/(1 + αL)); diffusion current e−αW·αLω/(1 + αLω), Lω = L/√(1 + iωτ), τ = L²/D
ℛ = η · qλ / (hc) (responsivity)
NEPthermal = √(4kBT/RL · (π/2)·fRC) / ℛ at 300 K (Johnson noise of RL in the RC noise bandwidth)
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
RC limit with C ∝ area and the transit limit 0.443·v/W of one carrier crossing the full depletion width, combined as 1/f² = 1/f_RC² + 1/f_tr² (within 4 % of the exact response). Uniform generation with equal carrier speeds gives 0.553·v/W. Light absorbed below W diffuses from a semi-infinite field-free substrate: Gärtner's DC split with L replaced by L/√(1 + iωτ), τ = L²/D, and p = 0 at the depletion edge. At the Si 850 nm defaults (1/α 18.7 µm, W 10.5 µm, L 35 µm) only 53.7 % of the current drifts: the intrinsic −3 dB point is 13.6 MHz, and with the transit sinc and the 50 Ω RC pole the total at 1 mm² is 13.5 MHz. Back-surface and front-surface recombination, an undepleted top layer, a finite substrate and the depletion-width change with bias are not modelled.
- Bowers J. E., Burrus C. A. (1987). Ultrawide-band long-wavelength p-i-n photodetectors. J. Lightwave Technol. 5, 1339. Transit-time and RC limits of p-i-n bandwidth. doi:10.1109/JLT.1987.1075419
- Sze S. M., Ng K. K. (2007). Physics of Semiconductor Devices, 3rd ed. Wiley. p–n junction depletion capacitance (abrupt m = 1/2, linearly graded m = 1/3), n_i(T), generation and diffusion currents. doi:10.1002/0470068329
- Jacoboni C., Canali C., Ottaviani G., Alberigi Quaranta A. (1977). A review of some charge transport properties of silicon. Solid-State Electron. 20, 77–89. Hole saturation velocity v = 1.62e8·T^−0.52 cm/s, ≈ 8.4×10⁴ m/s at 300 K. doi:10.1016/0038-1101(77)90054-5
- Gärtner W. W. (1959). Depletion-layer photoeffects in semiconductors. Phys. Rev. 116, 84–87. Drift 1 − e^(−αW) and diffusion e^(−αW)·αL/(1 + αL) shares of the photocurrent. doi:10.1103/PhysRev.116.84
- Peter L. M. (1990). Dynamic aspects of semiconductor photoelectrochemistry. Chem. Rev. 90, 753–769. Modulated photocurrent of the Gärtner model. doi:10.1021/cr00103a005
- Bisquert J. (2002). Theory of the impedance of electron diffusion and recombination in a thin layer. J. Phys. Chem. B 106, 325–333. Frequency-domain diffusion–recombination with complex wavenumber √(1 + iωτ)/L. doi:10.1021/jp011941g
- Laird J. S., Ravishankar S., Rietwyk K. J., Mao W., Bach U., Smith T. A. (2022). Intensity modulated photocurrent microspectroscopy for next generation photovoltaics. Small Methods 6, 2200493. Diffusion–recombination transfer function following Peter and Bisquert (Eq. 15 of the open preprint arXiv:2201.10133). doi:10.1002/smtd.202200493