Reverse bias

A p-n junction is under reverse bias when the external voltage makes the p side negative with respect to the n side. The applied voltage adds to the built-in potential, the depletion region widens, and only a small leakage current flows until the junction breaks down. Most semiconductor photodetectors and many modulators operate this way. A PIN photodiode for telecom receivers is typically held at a few volts, often in the range −1 to −5 V depending on the design; an avalanche photodiode runs close to breakdown, at tens of volts in InGaAs and often hundreds in silicon.

What the bias does in a photodiode

A photodiode can work at zero bias (photovoltaic mode), but reverse bias improves it in three ways. The depletion region, where photogenerated carriers are collected by drift, becomes wider; the junction capacitance falls; and the electric field across the absorber rises, so carriers drift out at close to their saturated velocity instead of diffusing slowly. The photocurrent flows in the reverse direction, from n to p through the device, and adds to the reverse leakage.

For an abrupt one-sided junction with doping $N$ on the lightly doped side, the depletion width is

$$W = \sqrt{\frac{2\varepsilon\,(V_\text{bi} + V_R)}{qN}}$$

where $V_\text{bi}$ is the built-in voltage and $V_R$ the reverse bias, so $W$ grows as the square root of the total voltage: four times the voltage gives twice the width. For silicon with $N = 10^{15}$ cm⁻³ and $V_\text{bi} = 0.7$ V, $W$ is 0.95 µm at zero bias and 2.7 µm at 5 V reverse bias. The capacitance per unit area is $\varepsilon/W$, so a 1 mm² junction falls from about 109 pF to 38 pF over the same change.

In a PIN diode the lightly doped intrinsic layer is depleted at a small bias, after which $W$ is fixed by the layer thickness and further bias mainly raises the field. A 30 µm diameter InGaAs PIN with a 1 µm depleted layer ($\varepsilon_r \approx 13.9$) has a capacitance of about 87 fF, an RC limit of 37 GHz into 50 Ω before parasitics. The transit limit for the same layer is roughly $0.4\,v/W$; with the hole saturation velocity of InGaAs, about $5 \times 10^6$ cm/s, this gives about 20 GHz, and accounting for the faster electrons and for absorption spread through the layer raises it to about 30 GHz. In InGaAs the slower holes set the transit time, which the UTC photodiode design avoids. At 2 V across 1 µm, plus the built-in voltage, the field is about 27 kV/cm, in the range where drift velocities approach saturation.

Costs of more bias

Dark current rises with reverse bias: generation current grows with the depleted volume, and at high fields tunneling and edge leakage add more. More bias also raises the dissipated power at high photocurrent. At high optical power, the photogenerated charge in the depletion region screens the applied field, and the response slows and saturates; extra bias pushes this space-charge limit to higher current, which is why high-power photodiodes are often run at larger bias than small-signal ones.

Beyond a certain voltage the junction breaks down by impact ionization or tunneling. An APD is designed to operate just below that point to gain internal multiplication, and a single-photon avalanche diode a few volts above it. For an ordinary PIN, the datasheet's maximum reverse voltage is an absolute limit.

Reverse bias in modulators

Silicon depletion modulators place a p-n junction across the waveguide. Reverse bias widens the depletion region inside the optical mode, removing free carriers and raising the refractive index through the plasma dispersion effect. Because no minority carriers are injected, the response is limited by RC time rather than carrier lifetime, which allows bandwidths of tens of GHz; the cost is a phase that varies nonlinearly with voltage, following the square-root growth of $W$. An electro-absorption modulator uses reverse bias to shift its absorption edge onto the signal wavelength.

Practical points and pitfalls

Biasing is usually done through a resistor and decoupling capacitor, or a bias tee at high frequency, and noise on the bias supply couples directly to the output. When the diode is measured with a source-measure unit, a current compliance limit protects it if the bias is accidentally applied in the forward direction or the device breaks down. Sign conventions vary: some datasheets quote reverse bias as a positive number, others as a negative cathode-to-anode voltage, so the polarity should be checked before the first connection.

Common questions

Why are photodiodes reverse biased?

To widen the depletion region, lower the capacitance and raise the internal field, which together give higher speed and a more linear response. Zero bias is preferred when the lowest dark current and noise matter more than speed.

What happens to capacitance under reverse bias?

It falls as the depletion region widens, as $1/\sqrt{V_\text{bi}+V_R}$ for an abrupt junction, and stops falling once a PIN diode's intrinsic layer is fully depleted.

Does reverse bias increase responsivity?

Only slightly in most PIN diodes, through a wider collecting region and fewer carriers lost to recombination. In an avalanche photodiode biased near breakdown it increases strongly through gain.

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); G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), chapter 4.