Transit time

Transit time is the time a charge carrier needs to cross a region of a device. For drift at velocity $v$ across a layer of width $W$ it is simply $t = W/v$. In a reverse-biased photodiode the region is the depletion region, the field is high enough that carriers move near their saturated velocities, and the transit time of the slower carrier is one of the two main limits on bandwidth, the other being RC time. In InGaAs, with saturated velocities of about $6.5 \times 10^6$ cm/s for electrons and $4.8 \times 10^6$ cm/s for holes, crossing a 1 µm layer takes 15 ps for an electron and 21 ps for a hole.

Transit-limited bandwidth

Photocurrent flows in the external circuit for as long as carriers are moving in the depletion region, so a finite crossing time spreads each photocurrent pulse. Sze and Ng give the resulting 3 dB frequency as $2.4/(2\pi t)$, or

$$f_\text{tr} \approx \frac{0.4\,v}{W}$$

the form used in the reverse bias entry. The prefactor depends on where the light is absorbed and on how the electron and hole contributions combine, and other treatments quote values from about 0.4 to 0.55; the photodetector characterization article uses 0.45. With the InGaAs hole velocity, $W$ = 1 µm gives 19 GHz, about 20 GHz, and 0.5 µm gives 38 GHz; the 0.45 prefactor gives 22 GHz for 1 µm, and electrons alone would give 26 GHz. The article's 27 GHz uses 0.45 with a single velocity of 6 × 10⁶ cm/s, between the electron and hole values; weighting both carriers and absorption spread through the layer gives about 30 GHz, the upper figure in the reverse-bias entry. The hole-only value of 19 GHz is the conservative bound used below.

Trade-off with RC time

A thinner depletion layer shortens transit but raises the junction capacitance $C = \varepsilon A/W$, so the RC limit $f_\text{RC} = 1/(2\pi R C)$ falls as $W$ shrinks. Combining the two as

$$\frac{1}{f_\text{3dB}^2} = \frac{1}{f_\text{tr}^2} + \frac{1}{f_\text{RC}^2}$$

gives an optimum width where the two limits are equal. For a 30 µm diameter InGaAs PIN photodiode into 50 Ω ($\varepsilon_r \approx 13.9$), with $f_\text{tr} = 0.4\,v_h/W$, the optimum is $W$ = 0.72 µm, where both limits are 26.5 GHz and the combined bandwidth is 18.7 GHz; at 1 µm the RC limit is 37 GHz, the transit limit 19 GHz, and the combined value 17 GHz. Shrinking the diameter to 10 µm moves the optimum to 0.24 µm and the bandwidth to 56 GHz, but a 0.24 µm absorber with $\alpha \approx 0.7 \times 10^4$ cm⁻¹ absorbs only about 15% of the light in one pass, against 40% at 0.72 µm. Waveguide illumination avoids this trade: light travels along the absorber while carriers cross only its thin dimension. Parasitic capacitance and inductance in the package, ignored here, lower all these figures.

Holes, electrons and the UTC design

Because holes are slower in InGaAs, they set the transit limit of a PIN, and at high photocurrent their space charge also screens the field first. The UTC photodiode absorbs light in a thin p-doped layer where holes are majority carriers and relax without traveling, and only electrons cross the depleted InP collector. Electrons in InP can briefly exceed their steady-state velocity, reaching about $4 \times 10^7$ cm/s, so a 0.3 µm collector can be crossed in under 1 ps. The diffusion of electrons out of the absorber then usually dominates the response time, and bandwidths beyond 300 GHz have been demonstrated.

Carriers generated outside the depletion region have no drift field and must diffuse, which can take nanoseconds and produces the slow tail described in the depletion region entry. Measured bandwidths that improve with bias, or responses that fall off at low frequency, are signs of incomplete depletion or diffusion.

Transit time in lasers

In a quantum-well laser, injected carriers must cross the undoped separate-confinement layers before the wells capture them. The diffusion time across a layer of thickness $d$ is of order $d^2/2D$; for $d$ = 0.1 µm and an assumed ambipolar diffusion coefficient of 5 cm²/s it is about 10 ps. This transport delay adds a low-pass term to the laser's small-signal response and effectively reduces the differential gain seen by the relaxation oscillations, which lowers the modulation bandwidth.

Common questions

How is transit time calculated?

Divide the width of the region by the carrier velocity. For a 1 µm InGaAs depletion region, holes at $4.8 \times 10^6$ cm/s take 21 ps and electrons at $6.5 \times 10^6$ cm/s take 15 ps.

Is a photodiode limited by transit time or by RC time?

Both contribute, combined approximately in quadrature. Large-area detectors are usually RC limited and small, thick ones transit limited; an optimized design makes the two roughly equal.

Does more reverse bias reduce the transit time?

Only until the field is high enough for the carriers to approach saturated velocity, of order tens of kV/cm in InGaAs. Beyond that, extra bias does not speed the crossing, though it helps the field resist space-charge screening at high photocurrent.

References: S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); T. Ishibashi and H. Ito, J. Appl. Phys. 127, 031101 (2020); R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels and J. E. Bowers, IEEE J. Quantum Electron. 28, 1990 (1992); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012).