Photodiodes

A photodiode is a p-n junction device designed to convert incident light into an electrical current. It operates under reverse bias, where the generated photocurrent is directly proportional to the intensity of the incoming light. Photodiodes are fundamental in optical communication receivers, light meters, and medical imaging systems.

Core Concept of Photodiode Operation

A photodiode is essentially a reverse-biased p-n junction. Under reverse bias, the depletion region widens, and the dark current (reverse saturation current) is very small, typically in the nanoampere range. When photons with energy greater than the band gap energy of the semiconductor strike the junction, they generate electron-hole pairs through the process of photogeneration. These electron-hole pairs are swept across the depletion region by the built-in electric field, creating a net current called photocurrent.

The condition for photogeneration is that the photon energy must satisfy hf >= Eg, where h is Planck's constant, f is the photon frequency, and Eg is the semiconductor band gap. For silicon (Eg = 1.12 eV), this corresponds to wavelengths shorter than approximately 1100 nm, covering the visible and near-infrared spectrum. Germanium and InGaAs photodiodes extend this range further into the infrared.

The reason reverse bias is preferred over forward bias is that in reverse bias, the depletion region is wide, so most photogenerated carriers are created inside or very near the depletion region. This ensures fast and efficient collection of the carriers before they recombine. Forward bias would narrow the depletion region and reduce collection efficiency significantly.

Mathematical Expression and Responsivity

The total current in a photodiode under reverse bias and illumination is described by a modified diode equation. The responsivity R is the most important figure of merit and is defined as the photocurrent generated per unit optical power incident on the device. Mathematically, R = I_ph / P_opt, with units of amperes per watt (A/W). Responsivity depends on the quantum efficiency and the wavelength of the incident light.

The quantum efficiency (eta) represents the fraction of incident photons that successfully generate a collected electron-hole pair. It accounts for reflection losses at the surface, absorption outside the depletion region, and recombination before collection. The relationship between responsivity and quantum efficiency is given by R = (eta * q * lambda) / (h * c), where q is the electron charge, lambda is the wavelength, h is Planck's constant, and c is the speed of light.

Another important parameter is the response time of the photodiode, which determines how fast the device can follow a modulated optical signal. The response time is limited by the transit time of carriers across the depletion region and the RC time constant of the device. A wider depletion region improves quantum efficiency but increases transit time, creating a fundamental design tradeoff in high-speed photodiode design.

Practical Understanding of Photodiode Parameters

In real photodiode circuits, the device is operated in one of two modes. In photoconductive mode, a reverse bias is applied, giving faster response and wider dynamic range but introducing shot noise from the dark current. In photovoltaic mode, no external bias is applied and the photodiode acts like a small current source, which minimizes dark current and noise, making it suitable for precision low-light measurements such as in medical equipment.

The dark current is the reverse leakage current that flows even in the absence of light. It is generated by thermally excited minority carriers near the depletion region. At room temperature, silicon photodiodes have dark currents in the range of 1 to 10 nA. This current sets the noise floor for detection and limits the minimum detectable optical power of the device.

For GATE and university examinations, it is useful to remember that the photocurrent is independent of the reverse bias voltage (within a wide operating range) and depends linearly on the incident optical power. This linearity over several decades of optical power is one of the major advantages of photodiodes over photoresistors (LDRs), which have a non-linear response.

Given:
Wavelength of incident light: lambda = 850 nm = 850 x 10^-9 m
Quantum efficiency: eta = 0.75
Incident optical power: P_opt = 200 uW = 200 x 10^-6 W
q = 1.6 x 10^-19 C, h = 6.626 x 10^-34 J.s, c = 3 x 10^8 m/s

Why this formula applies:
Responsivity R = (eta * q * lambda) / (h * c) gives A/W from quantum efficiency and wavelength.
Photocurrent I_ph = R * P_opt

Formula:
R = (eta * q * lambda) / (h * c)
I_ph = R * P_opt

Substitution:
R = (0.75 * 1.6e-19 * 850e-9) / (6.626e-34 * 3e8)
R = (1.02e-28) / (1.988e-25)

Calculation:
R = 0.5132 A/W
I_ph = 0.5132 * 200e-6

Final Answer:
Responsivity R = 0.513 A/W
Photocurrent I_ph = 102.6 uA

Exam Tip: In GATE problems, if wavelength and quantum efficiency are given, always compute responsivity first using R = (eta * q * lambda)/(hc), then multiply by optical power. A common trap is forgetting to convert wavelength from nm to meters before substituting.

• Photons with energy hf >= Eg generate electron-hole pairs (EHPs) in all three regions of the photodiode.
• EHPs generated inside the depletion region are immediately swept to opposite sides by the strong built-in electric field, contributing directly to photocurrent.
• EHPs generated within a diffusion length of the depletion region edge in p or n regions also contribute, as minority carriers diffuse to the junction.
• The photocurrent flows in the reverse direction (from n to p externally) and adds to the small dark (reverse saturation) current.
• The speed of response is limited by transit time across the depletion region and the RC time constant formed by junction capacitance and load resistance.

Quick Revision

• Photodiodes operate under reverse bias; photons generate EHPs that are swept by the depletion region electric field to create photocurrent.
• Condition for photogeneration: hf >= Eg (photon energy must exceed semiconductor band gap).
• Responsivity formula: R = (eta * q * lambda) / (h * c), units A/W. Directly proportional to wavelength and quantum efficiency.
• Photocurrent: I_ph = R * P_opt. It is linear with optical power and independent of reverse bias over a wide range.
• Photoconductive mode (reverse biased): faster, wider dynamic range, more noise. Photovoltaic mode (zero bias): less noise, slower.
• Dark current sets the noise floor; typical silicon dark current is 1-10 nA at room temperature.
• Common GATE trap: forgetting to convert lambda from nm to meters in the responsivity formula, or confusing responsivity (A/W) with quantum efficiency (dimensionless).