5.1 Internal, extraction, external, and power efficiencies

The active region of an ideal LED emits one photon for every electron injected. Each charge quantum-particle (electron) produces one light quantum-particle (photon). Thus the ideal active region of an LED has a quantum efficiency of unity. The internal quantum efficiency is defined as

П _ number of photons emitted from active region per second _ PJnt / (h v) (51)

nint number of electrons injected into LED per second I / e

where Pint is the optical power emitted from the active region and I is the injection current.

Photons emitted by the active region should escape from the LED die. In an ideal LED, all photons emitted by the active region are also emitted into free space. Such an LED has unity extraction efficiency. However, in a real LED, not all the power emitted from the active region is emitted into free space. Some photons may never leave the semiconductor die. This is due to several possible loss mechanisms. For example, light emitted by the active region can be reabsorbed in the substrate of the LED, assuming that the substrate is absorbing at the emission wavelength. Light may be incident on a metallic contact surface and be absorbed by the metal. In addition, the phenomenon of total internal reflection, also referred to as the trapped light phenomenon, reduces the ability of the light to escape from the semiconductor. The light extraction efficiency is defined as

П ^ _ number of photons emitted into free space per second _ P / (h v) (52)

nextraction number of photons emitted from active region per second Pint/(h v)

where P is the optical power emitted into free space.

The extraction efficiency can be a severe limitation for high-performance LEDs. It is quite difficult to increase the extraction efficiency beyond 50% without resorting to highly

number of photons emitted into free space per second _ P / (h v)

number of electrons injected into LED per second I / e

The external quantum efficiency gives the ratio of the number of useful light particles to the number of injected charge particles.

The power efficiency is defined as

npower

where IV is the electrical power provided to the LED. Informally, the power efficiency is also called the wallplug efficiency.

Exercise: LED efficiency. Consider an LED with a threshold voltage of Vth = Eg / e = 2.0 V with a differential resistance of Rs = 20 Q, so that the I-V characteristic in the forward direction is given by V = Vth + I Rs. When the device is operated at 20 mA it emits a light power of 4 mW of energy h v = Eg. Determine the internal quantum efficiency, the external quantum efficiency, and the power efficiency, assuming that the extraction efficiency is 50%.