Properties of Crystalline Silicon

The lattice structure of crystalline silicon is cubic diamond, and has long range order and symmetry.  Different cuts can be made across and through the lattice to see different planes (see diagram above).  For the (100) surface, whose normal points in the [100] direction, the plane has 2 valence electrons pointing to the front.  For the (111) surface, the plane has 1 valence electron pointing in the direction of the normal to the plane.

The electronic band dispersion diagram (see diagram above) shows the indirect band gap of silicon.  The vertical axis shows the energy level of the valence and conduction bands, while the horizontal axis shows the crystal momentum (momentum of the charge carriers), the lattice momentum in various directions.  To get excited into the conduction band, electrons in the valence band require a change in energy and momentum.  The band gap of silicon as shown magnified in the diagram below, consists of the lowest point of the conduction band at x, which is indicative of the [100] direction, and the highest energy value of the valence band at gamma.

The indirect band gap energy required is the difference between the energy levels at x and gamma and equals 1.12eV or a maximum wavelength of 1107nm.  There can also be direct transition of electrons, where the direct band gap energy required is found at gamma.  The value is 3.4eV or a maximum wavelength of 364nm, which is the blue spectral part.  Hence, it is more difficult to excite electrons into the conduction band for silicon, as compared to direct band gap materials like GaAs and InP.  This also means that the absorption coefficient is much lower (see diagram below).

Germanium is also an indirect band gap material, but it has a low band gap of 0.67eV, so it starts absorbing light at wavelengths below 1850nm, with direct transitions at lower wavelengths at certain momentum-space directions.

Referring to the diagram above, assuming a EQE of 1, a silicon band gap of 1.12eV corresponding to a wavelength of 1107nm will lead to a theoretical maximum J_sc of about 45mA/cm².  This is the spectral utilisation consideration.

Referring to the diagram above, using Lambert-Beer's law, it can be seen that to absorb a higher wavelength of 970nm, a longer absorption path length of 230 microns is required to absorb 90% of all incident light.  This is a typical thickness of silicon wafer and shows the importance of light trapping techniques for crystalline silicon absorber layers for wavelengths above 900nm.

Finally, consider band gap utilisation as determined by recombination losses, where only Auger and SRH recombination are considered due to silicon's indirect band gap transitions.  Here, 2 types of silicon have to be considered: monocrystalline silicon (single crystalline) and polycrystalline silicon (polysilicon).  Single crystalline has an unbroken crystalline lattice up to the edges.  Polysilicon consists of many small crystalline grains in random orientations, meaning that there's many grain boundaries (see diagram below).

Hence, polysilicon has many lattice mismatches, which leads to defects at the grain boundaries, so the lifetime of charge carriers is shorter than single crystalline.  There is a lot of SRH recombinations.  Generally, the larger the grain size, the charge carrier lifetimes will be longer.  This means that band gap utilisation is better, and the V_oc will be larger.



Reference:
4.1 Properties of Crystalline Silicon, Delft University of Technology, https://www.youtube.com/watch?v=rPeBUO_08GE