Two-photon photovoltaic effect (TPP effect) is an energy collection method based on two-photon absorption (TPA). The TPP effect can be thought of as the nonlinear equivalent of the traditional photovoltaic effect involving high optical intensities. This effect occurs when two photons are absorbed at the same time resulting in an electron-hole pair.
Background
TPA is typically several orders of magnitude weaker than linear absorption at low light intensities. It differs from linear absorption in that the optical transition rate due to TPA depends on the square of the light intensity, thus it is a nonlinear optical process and can dominate over linear absorption at high intensities. Therefore, the power dissipation from the TPA and the resulting free carrier scattering are harmful problems in semiconductor devices which operate based on the nonlinear optical interactions such as the Kerr and Raman effects, when dealing with high intensities. The TPP effect is studied as a possible solution to this double crisis on energy efficiency.
Although some improvements and theoretical investigation on the field have been done in the past, the concrete application of the effect was numerically and experimentally analysed for the first time by Bahram Jalali and colleagues in 2006 in Silicon.
Physics
TPP effect devices are based on waveguides with lateral p–n junction diodes, in which the pump power is nonlinearly lost due to TPA and free-carrier absorption (FCA) along the z-direction, perpendicular to the junction x-y cross-section.
Coupled optical intensity is governed by the following equation:
where: is the linear absorption coefficient; the TPA coefficient; and is called the FCA coefficient which is given by Soref´s expression.
Carrier photogeneration rate is defined by:
where is the energy of the photon and the factor is due to the fact that there are two photons involved in the process.
Photocurrent per unit length: , where is the effective area of the waveguide and is the electron charge. For a waveguide of length , we have
We define as the coupled pump intensity at . Therefore, we obtain the following expression:
This last expression is called the effective length which is the nonlinear equivalent to the interaction length defined in optical fibers. Contribution to carrier injection and recombination to the total current need to be considered as well so that the total photodiode current is expressed as:
The Shockley equation gives I–V (current-voltage) characteristic of an idealized diode:
The value of is called the reverse bias saturation current and is defined by:
where and are defined in Fig. 1 and the remaining parameters have the usual meaning defined in reference Sze's Physics of semiconductor devices.
The Shockley equation is valid since photogeneration in the N and P doped regions is negligible in the p–n diode. This contrasts the conventional solar cell theory, where photogeneration predominantly occurs in the N and P doped regions as shown in Fig. 2.
Due to PIN structure (Figure 2) we have to take into account the recombination current which we approximate by Shockley–Read–Hall recombination given by :
where is defined in Fig.1, is the effective carrier density along and and are the electron and hole bulk recombination lifetimes, respectively.
In a circuit, power dissipation refers to the rate at which energy is lost due to resistive elements and is defined traditionally as follows:
We now define collection efficiency, which is number of carriers/photons consumed by TPA:
This is appropriate for such devices as amplifiers and wavelength converters where energy harvesting is a useful byproduct but not the main functionality of the device itself. If the TPP effect is intended to be used in a photovoltaic cell, then the power efficiency should be considered.
First, external quantum efficiency is given by , where refers to the coupling efficiency of the light into the waveguide and
which can be approximated to:
Finally, power efficiency is given by: