Gold nanoparticles introduced ZnO/Perovskite/Silicon heterojunction solar cell

t
p
are the Fresnel coefficients for parallel 
polarized light, 
β 
is the angle of incident light,
 γ
is the angle of 
refracted light. 
After determining the optical properties in TMM, the 
generation coefficient is calculated using the quantum yield 
function. The quantum yield is a logic function that takes 1 if 
the photon energy is greater than or equal to the material's 
bandgap, and 0 otherwise. 
There are mainly 3 types of recombination in 
semiconductors [42]: Radiative, Shockley-Read-Hall (SRH) 
and Auger. Since silicon is an indirect semiconductor, it 
mainly has SRH and Auger recombination, Radiative 
recombination is almost absent. ZnO and perovskite are direct 
semiconductors, they have three types of recombination. 
Therefore, separate recombination models were used for each 
region in the modeling. For example, since the emitter region 
is made of ZnO or Perovskite, all three recombinations have 
been declared to exist, and since the base is made of silicon, 
only SRH and Auger recombinations have been declared to 
exist. SRH recombination due to defects is calculated using 
formula 3 [43]. 
(
)
(
)
2
,
1
1
n p i eff
SRH
net
p
n
n
p
np
n
R
n
n
p
p
 




−
=
+
+
+
(3)
Here: n is the electron concentration, p is the hole 
concentration, γ
n
,γ
p
are the coefficients, τ
n
,τ
p
are the electron 
and the hole lifetime, n
1
,p
1
are the electron and the hole 
concentration on the trap. 
Auger recombination is calculated using formula 4 [44] and 
is also called three particles recombination. Accordingly, as 
the concentration of charge carriers increases, so does its 
portion in the total recombination. An increase in the input 
concentration causes an increase in the concentration of charge 
carriers. Therefore, after the input concentration reaches a 
certain critical value, Auger recombination begins to 
dominate. 
(
)(
)
2
,
A
net
n
p
i eff
R
C n C p np n
=
+
−
(4)
Here: C
n
,C
p
are Auger coefficients. n
i,eff
is the intrinsic 
carrier concentration. 
The electrostatic field formed around the charge carriers 
and ionized impurities and the electric potential are calculated 
using the Poisson equation in formula 5 [45]. 
(
)
D
A
q
p
n
N
N


 = −
− −
+
(5)
Here: 
ε 
is the permittivity, 
N
D
and 
N
A
are the concentrations 
of donor and acceptor, 
q
is the charge. 
The internal electric field created by the ions in the p-n 
junction separates the electron-hole pairs and help to reach 
them to the contacts. So, unlike the diode, the drift movement 
of charge carriers plays the main role in the solar cell. The 
Masetti formula is given in formula 6 [46] was used to 
calculate the mobility of charge carriers. Because in the 
Masetti model, the effect of electron-phonon scattering, input 
concentration and temperature are also considered. 
Consequently, this model is suitable for estimating the 
mobility of charge carriers in nanoparticle-incorporated solar 
cells. 
min 2
min1
,0
,0
,0
,0
1
,0
,0
exp
1 ((
) / )
1 (
/ (
))