Solar cell comparison + equations

What are the properties of Si solar cells: BG, absorption, mobilities, diffusion length, lifetime, defect tolerance, thickness, architecture, processing, screening

indirect BG, alpha~10³/cm (low), mu_e =1000 cm²/V/s (high), mu_h=450 (high), L=100um (long), t=um-ms (long), poor defect tolerance, 200um thick, pn junction, high T many step processing, high screening er~20

What are the properties of Organic solar cells: BG, absorption, mobilities, diffusion length, lifetime, defect tolerance, thickness, architecture, processing, screening

direct BG, alpha~10^4/cm (high), mu_e and mu_h<1cm²/V/s (low), L=10nm(exciton),100nm(free) (short), t~ns (short), decent defect tolerance, 100-150nm thick (thin), bulk heterojunction, low T solution or thermal evaporation, v low screening er~3

What are the properties of Perovskite solar cells: BG, absorption, mobilities, diffusion length, lifetime, defect tolerance, thickness, architecture, processing, screening

direct BG, alpha~10^4-5/cm (high), mu_e/mu_h = 60cm²/V/s (moderate), L=10um (moderate), t=100ns-10us (medium high), high defect tolerance, ~500nm thick (thin), pin/nip, low T solution or thermal evaporation, high screening er~20

Lifetime tau=

1/k1

k1 =

NRR constant, variable w defect density, small=wide Ef splitting

k2 =

RR constant, material property

Optical density OD =

-log(I(L)/I_0) = alphaL/ln(10)

Beer’s Law

I(z) = I_0 e^-alphaz

Power conversion efficiency PCE =

(V_oc .J_sc.FF)/Power in = J_mp.V_mpp/P_in

Fill factor FF =

J_mpp.V_mpp/J_sc.V_oc

Energy =

hc/lambda = 1240eVnm/lambda(nm)

Hydrogen ionisation energy E_n=

-13.6eV/n²

External quantum efficiency

extracted Pelectrons / incident photons

Photoluminescence quantum yield PLQY =

photons emitted / photons absorbed, tells us how much RR vs NRR

How does Voc change with alpha

increases with alpha but more slowly due to log dependence on no of e

How does Jsc vary with alpha

increases with alpha, goes from not being able to absorb any photons to absorbing all of them

How does FF vary with alpha

roughly constant, small rise when carriers generated optimally in depletion region, dip after where more photons absorbed too far away from the junction

List in order to largest to smallest affect, the different causes of fermi level splitting

transport layer/interfaces, surface NRR, bulk NRR, TT

Why do surface defects only affect V_oc (not so much Jsc and FF)

at Jsc, high V, carriers moving quickly to interfaces, less time spent at surface; at Voc, low V, low/little charge movement , charges spend longer at interfaces and recombine

Describe the relationship between QFLS, V_oc, QFLS_rad, E_g

E_g>QFLS_rad>QFLS>V_oc,; E_g: full bandgap energy; QFLS_rad: unavoidable RR and entropy; QFLS: NRR defects, traps, all reducing carrier population below radiative limit; V_oc: device losses, interface recomb, QFL bending at contacts

How does poor mobility affect V_oc, Jsc and FF

Voc decreases as more recomb can occur, Jsc only affected for very low mobility due to high E field at short circuit, FF decreases

What is the difference between Frenkel and Wannier Mott excitons

Frenkel = high energy, localised excitons due to low dielectric constant; WM = low energy, delocalised excitons due to high dielectric constant; WM easier to dissociate = more current

What is the condition for excitons to form

E>kT