
Research Article


Simulation of n_{1}p_{2} Microcrystalline Silicon Tunnel Junction with AMPS1D in aSi :H/μcSi :H Tandem Solar Cells 

Abbas Belfar
and
Rachida Mostefaoui



ABSTRACT

The electrical properties of aSi:H/μcSi:H micromorph tandem solar cells was studied with computer simulation. In this study, AMPS (Analysis of microelectronic and photonic structure)1D is used to study the output parameters, Short circuit current (J_{sc }), opencircuit Voltage (V_{oc}), Fill Factor (FF) and Efficiency (η) of single (aSi:H, μcSi:H) and (aSi:H/μcSi:H) double junction solar cells. The carrier transport at the junction between the two pin subcells is simulated with the help of a thin heavily defective Recombination Layer (RL) with a reduced mobility gap. The comparison between the output parameters of the above different types solar cells is given. The substitution of the N_{1} (aSi:H) layer by a N_{1} (μcSi:H) layer in the tandem structure (P_{1}I_{1}N_{1}/RL/P_{2}I_{2}N_{2}) leads to an improvement of the output cell parameters : J_{sc }increases from 11.607 to 12.00 mA cm^{2}, FF increases from 0.670 to 0.710, the V_{oc} increases from 1.347 V to 1.541 V and the efficiency increases from 10.460 to 13.127%. Moreover, the impact of the N_{1} layer and the profiling in the energy band gap realized by N_{1}P_{2} microcrystalline tunnel junction at the characteristics of tandem solar cells is also studied in this study.





Received: February 26, 2011;
Accepted: June 06, 2011;
Published: July 22, 2011


INTRODUCTION
Micromorph tandem solar cells consisting of an amorphous silicon top cell and
a microcrystalline bottom cell is one of the most promising new thinfilm silicon
solarcell concepts. Their promise lies in the hope of simultaneously achieving
high conversion efficiencies at relatively low manufacturing costs. The key
element of the micromorph cell is the hydrogenated microcrystalline silicon
bottom cell that opens new perspectives for lowtemperature thinfilm crystalline
silicon technology. So far, stabilized efficiencies of about 12% (10.7% independently
confirmed) could be obtained with micromorph solar cells (Keppner
et al., 1999; Khosroshahi et al., 2008).
Hydrogenated microcrystalline silicon (μcSi:H) was originally introduced
by Veprek and Marecek (1968), Veprek
and VeprekHeijman (1991) and Ahmed et al. (2008)
and is nowadays generally obtained by a Plasma Enhanced Chemical Vapour Deposition
(PECVD) process using a mixture of silane and hydrogen. Due to its efficient
doping properties, both for ntype as well as ptype material, μcSi:H
was form the beginning successfully used as ohmic contact layers in solar cells
and in thinfilm transistors (Keppner et al., 1999;
Khatib et al., 2009; Hamel
and Chibani, 2010). To use microcrystalline silicon alone as an active absorber
layer in solar cells was, due to the reasons mentioned above, for many years
not seriously taken into account for solar cell applications. The IMT Neuchâtel
also used a polymer substrate foil and obtained a stabilized solar energy conversion
efficiency of 7% for a single junction aSi:H solar cell and 8.3% for a smallarea
tandem junction aSi:H/μcSi:H solar cell (Van den
Donkera et al., 2007; AlHadidi and Ibrahim,
2008).
SIMULATION MODEL
AMPS can simulate an extremely general semiconductor device structure. In the
present version of AMPS1D there are two different approaches (1) Density of
States (DOS) picture and (2) carrier lifetime picture. The DOS picture is well
suited for materials like aSi:H and μcSi:H thin films due to the large
defect densities in Grain Boundaries (Gbs) (Tripathi and
Dusane, 2006).
In the electrical part of the model, three coupled differential equations: the Poisson’s equation and the two carrier continuity equation are solved simultaneously under nonequilibrium steady state conditions (i.e., under the effect of voltage or light bias, or both) by using the method of finite differences and NewtonRaphson technique, directly from the first principles. The equations used are: Poisson’s equation: Hole continuity equation: Electron continuity equation: where ρ (x) is the net charge density. and the electric field:
where, ε is the dielectric constant, E the electrostatic field, Ψ
(x) represents the position in energy of the local vacuum level, x the position
in the device, p and n the valenceband hole density and the conduction band
electron density, respectively, q the electronic charge, R the recombination
rate, p_{T} and n_{T} the trapped hole and electron population
density, respectively, N^{+}_{net} the net doping density, if
any, G the electronhole pair generation rate, J_{p} and J_{n}
the hole and electron current density respectively and E_{Fp} and E_{Fn}
the hole and electron quasiFermi levels. In our calculations, the three state
variables that completely define the state of a device have been taken to be
the local vacuum level, Ψ and the quasiFermi levels E_{Fp} and
E_{Fn}. Once these three dependent variables are known as a function
of x, all other information about the system can be determined as functions
of position. In thermodynamic equilibrium, the Fermi level is a constant as
a function of position and hence the three Eq. (13)
essentially reduce to only one equation viz., the Poisson’s equation. Therefore,
the local vacuum level Ψ (x) is the only unknown to be solved for in thermodynamic
equilibrium.
In the nonthermodynamic equilibrium steadystate, a system of three coupled nonlinear second order differential equations in the three unknowns (Ψ, E_{Fn}, E_{Fp}) are obtained. In order to solve these equations for our state variables (Ψ, E_{Fn}, E_{Fp}), we need six boundary conditions, two for each dependent variable. The first two boundary conditions are modified versions of the ones used for solving Poisson’s equation in thermodynamic equilibrium: and where, L is the length of the device, χ (0), χ (L) are the electron affinities at x = 0 and x = L, respectively and V is the applied voltage. It should also be mentioned here that the zero of Ψ = Ψ (x) is chosen to be the position in energy of the vacuum level at the boundary point x = L. The two boundary conditions for the Poisson’s equation in thermodynamic equilibrium are Eq. 6 with the applied voltage V term absent and Eq. 7. The four other boundary conditions are obtained from imposing constraints on the currents at the boundaries at x = 0 and x = L. These constraints force the mathematics to acknowledge the fact that the currents must cross at x = 0 and x = L (the contact positions) by either thermionic emission or interface recombination. Expressed mathematically, we obtain the following: where, S_{no}, S_{po} are surface recombination velocities for electrons and holes respectively at the x = 0 interface and the quantities S_{nL}, S_{pL} are the corresponding velocities at the x = L interface. The largest value they can have is ~ 10^{7} cm sec^{1} dictated by thermionic emission. Here, n (0) (p (0))are the electron (hole) density at x = 0, n (L) (p (L)) are the same at x = L.
n_{o} (0) (p_{0} (0)), n_{0} (L) (p_{0} (L))
are the electron (hole) density in the thermodynamic equilibrium at x = 0 and
x = L, respectively. With the help of the boundary conditions stated above,
the three Eq. 1 to 3 can be solved simultaneously for Ψ
= Ψ (x), E_{fn} = E_{fp} (x) and E_{Fp} = E_{Fp}
(x). For this, the different terms in the equations are to be calculated first.
The gap state model used in our calculations consists of the tail states and
two Gaussian distribution functions to simulate the deep dangling bond states.
The generation term in the continuity equations has been calculated using a
semiempirical model (Leblanc et al., 1994) that
has been integrated into the modelling program. Both specular interference effects
and diffused reflectances and transmittances due to interface roughness are
taken into account.
MICROMORPH SOLAR CELLS General aspects: The combination of an amorphous silicon top cell with a microcrystalline silicon bottom cell to form a stacked tandem cell is called the micromorph cell.
The different gap energies involved in the micromorph tandem cell of the top
and of the bottom cell make a striking difference to the wellknown doublejunction
aSi:H/aSi:H tandem cell. The concept of superposing two aSi:H cells is based
on the reduction in the StaeblerWronski (Staebler and Wronski,
1977) effect that can be obtained by keeping each individual ilayer as
thin as possible and not on a better utilization of the solar spectrum.
Whereas the doublejunction concept for aSi:H cells is useful for reducing
lightinduced degradation, that the micromorph tandem cells offers further the
possibility of a better utilisation of the sun spectrum. A possibility that
is also realized with aSi:H/aSiGe:H stacked cells, yet to a larger extent,
as it is so far not possible to obtain low enough band gaps with devicequality
amorphous silicongermanium alloys (Keppner et al.,
1999).
Stability: The stable μcSi:H bottom cell contributes to a better
stability of the entire micromorph tandem cell under lightsoaking. It could,
in fact, be shown that the lightinduced degradation of the micromorph cell
is due to the amorphous top cell alone (Shah et al.,
2000). In a First attempt to a further increase in stable efficiency, one
can use a thicker bottom cell that could deliver an enhanced photocurrent without
running itself into stability problems. The concept of a micromorph solar cell
brings progress via a new stable bottom cell into the thinfilms silicon scenario,
the stability of the amorphous silicon top cell remains still the crucial topic
(Keppner et al., 1999). For enhanced stability
of the aSi:H cell many approaches have been investigated in the past. The most
promising of them are the use of hydrogen dilution (Platz
et al., 1997; Mahan et al., 1991)
and the hot wire deposition technique (Ziegler et al.,
1997; Palit and Chatterjee, 1998).
RESULTS AND DISCUSSION
Hydrogenated amorphous silicon pin cell: The structure chosen for
the cell is paSiC:H/buffer iaSiC:H/iaSi:H/naSi:H. The main input parameters
used for this case are given in Table 1. The absorption profiles
were calculated for the standard global AM1.5 spectrum. For a 80 nm thickness
of iaSi:H the light JV characteristics of the cell yield a shortcircuit
current density of J_{sc} = 12.023 mA cm^{2}, an opencircuit
voltage V_{oc } = 0.841 volts, FillFactor FF = 0.690 and efficiency
η = 7.638 %. These results are in coincidence with those obtained by Palit
and Chatterjee (1999).
Microcrystalline silicon pin cell: Hydrogenated microcrystalline silicon
(μcSi :H) is of interest for large area electronics and photovoltaics.
This material exhibit a complex microstructure (crystallites, grain boundaries,
amorphous phase an voids/porosity) that depends not only on the deposition methodology
and parameters but also on the morphology and chemical nature of the substrate
(Losurdo et al., 2006; Johnson
et al., 2008).
We have simulated a microcrystalline pin solar cell having the structure:
pμcSi:H / (p/i) interface/ iμcSi:H/ naSi:H when the mobility
band gap varying according to the crystalline volume fraction. The mobility
band gap of pμcSi:H has been assumed to be 1.6 eV at F_{c} ~
18%, 1.4 eV at F_{c} ~ 52% and 1.2 eV at F_{c} ~ 70 % (Palit
and Chatterjee, 1999). The crystalline volume fraction (F_{c}) as
well as the large grain fraction in the sample were deduced from spectroscopic
ellipsometry.
The principal input parameters for the doped, interconnect and absorber layers
of the μcSi:H cell are given in Table 2. For a 1300
nm thickness of iμcSi:H, the light JV characteristics of the cell yields
a shortcircuit current density J_{sc }= 17.529 mA cm^{2},
an opencircuit voltage V_{oc }= 0.603 volts, a FillFactor FF = 0.676
and an efficiency η = 7.143 %. These results are in coincidence with experimental
results obtained by Johnson et al. (2008), Palit
and Chatterjee (1998) and Nath et al. (2010)
where the crystalline volume fraction ( F_{c }) of the intrinsic μcSi:H
layer the gap ( E_{F}=1.4 eV ) like that used in our simulation equal
to 79% .
Tandem solar cells modelling: In this study, we have simulated two types of double junction solar cells, the first type have the following structure: paSiC:H (10 nm)/buffer iaSiC:H(3 nm)/iaSi:H(80 nm) /naSi:H (10 nm)/RL/pμcSi:H(10 nm)/(p/i) interface(3 nm)/iμcSi:H (1300 nm)/naSi:H(10 nm) and the second type have the structure: paSiC:H(10 nm)/buffer iaSiC:H(3 nm)/iaSi:H(80 nm)/nμcSi:H(10 nm)/RL/pFcSi:H(10 nm)/(p/i) interface(3 nm)/ iμcSi:H(1300 nm)/naSi:H(10 nm). The input parameters that simulate the output characteristics of theses stacked structures are given in Table 1 and 2. Some parameters of the doped and intrinsic microcrystalline layers have been derived from our efforts to match the measured characteristics of single and double junction cells.
The absorption profiles in the tandem cells were calculated for the standard
global AM1.5 spectrum.
Table 1: 
Principal material parameters for the doped and absorber layers
used to simulate the output characteristics of the aSi: H single cell used
as top cell in micromorph tandem cell 

L: Layer thickness, χ: Electron affinity, Eμ: Mobility
band gap, E_{ac }: Activation energy, E_{D }/E_{A}:
Characteristic energy of the donor/acceptorlike tail states, G_{DO}
/G_{AO }: Exponential prefactors of the donor/acceptorlike tail
states, μ_{e}: Electron microscopic band mobility, μ_{h+}:
Hole microscopic band mobility, N_{D }: Dangling bond density of
states, σ_{n}: Neutral capture cross sections of the defect
states, σ_{c}: Charged capture cross sections of the defect
states (Palit and Chatterjee, 1999; Poissant
et al., 2003). 
Table 2: 
Principal material parameters for the doped, absorber and
interconnect (RL) layers used to simulate the output characteristics of
the μcSi: H single cell used as bottom cell in micromorph tandem cell 

L: Layer thickness, χ: Electron affinity, Eμ: Mobility
band gap, E_{ac}: Activation energy, E_{D }/E_{A}:
Characteristic energy of the donor/acceptorlike tail states, G_{DO}
/G_{AO}: Exponential prefactors of the donor/acceptorlike tail
states; μ_{e}: Electron microscopic band mobility, μ_{h+}:
Hole microscopic band mobility, N_{D }: Dangling bond density of
states, σ_{n}: Neutral capture cross sections of the defect
states, σ_{c}: Charged capture cross sections of the defect
states (Palit and Chatterjee, 1998; Palit
et al., 2000; Rubinelli et al., 2001). 
Band diagrams at thermodynamic equilibrium and under illumination at V = 0
volts of first micromorph structure: PIN(aSi: H)/RL/PI(μcSi: H)N(aSi:
H) and second micromorph structure: PI(aSi: H)N(μcSi: H)/RL/PI(μcSi:
H)N(aSi: H) are shown in Fig. 1 and 2,
respectively.
We have studied the effect of varying the mobility band gap (E_{μ})
of the interconnect layer (RL) on solar cell efficiency. Reducing the band gap
of this layer from 1.4 eV to 1.0 eV progressively increases the efficiency from
11.589 to 13.127% and V_{oc }from 1.443 to 1.541 volts, J_{sc}
and FF showing a smaller change. For E_{F}(RL) = 1.0 eV, the quasiFermi
levels in the n_{1 }and p_{2} regions on either side of the
recombination layer (RL) coincide and V_{oc} attains the maximum value
in the case of the second type structure (Fig. 2b2).
For both types of devices, the n_{1}/p_{2} junction has been
modelled by a highly defective RL (density of states: 10^{20} cm^{3})
with high capture cross sections and a reduced band gap 1.0 eV (Table
2). In our modeling both the nμcSi:H and pμcSi:H layers have
short tails and low activation energies (Table 2).
The substitution of the amorphous layer N_{1 }by another one microcrystalline
in micromorph tandem cell P_{1}I_{1}N_{1}/RL/P_{2}I_{2}N_{2}
leads to an improvement of all parameters of tandem cell as indicated in Fig.
3.

Fig. 1: 
Energy Band diagram of the first micromorph solar cell: paSiC:H(10
nm)/buffer iaSiC:H(3nm) /iaSi:H(80nm)/ naSi:H(10nm)/RL(3nm)/pμcSi:H(10nm)/(p/i)interface(3nm)/iμcSi:H(1300nm)/naSi:H(10nm)
The Conduction band edge (E_{c}), the valance band edge (E_{v}),
the electron quasiFermi level (E_{fn}), the hole quasiFermi level
(E_{fp}) and the Fermi level (E_{F}) are indicated. (a1),
(a2) Thermodynamic equilibrium (b1), (b2) Light on, V = 0 
The modeling results shows an opencircuit voltage, V_{oc} = 1.347
V when N_{1 }is amorphous and V_{oc} = 1.541 V when N_{1}
is microcrystalline. This gain in voltage is explained as follows: first, the
band discontinuity at the interface I_{1}/N_{1} (Fig.
2b2) leads to a strong electric field (Fig. 4) because
at this interface the density of state is about 10^{20 }cm^{3 }eV^{1}
(so the default concentration in the gap is 2 x 10^{15}cm^{3}).
Consequently, all the electrons diffusing from the microcrystalline layer N_{1}
towards the amorphous layer I_{1 }during the formation of the junction
are trapped in the conduction band tail on a thin thickness, on the other hand,
the thickness of the amorphous layer I_{1} (80 nm) promotes this strong
field to extend over the entire volume of the I layer as shown in Fig.
4. The presence of this strong field leads to a good collect of electronhole
pairs photogenerated from the first cell. The presence of the microcrystalline
layer N_{1 }with a gap 1.6 eV lower than 1.8 eV (the gap of the amorphous
layer N_{1}) followed by the reduced gap (1.0 eV) of the Recombination
Layer (RL) and then the microcrystalline layer P_{2 }gap (1.2 eV) favor
the good recombination taking place between electrons and holes photogenerated
in the first and second cell, respectively. This improvement in the efficiency
is supported by a best absorption in the red range and infrared spectrum by
the tandem cell as shown in Fig. 5.
In tandem solar cells we have to distinguish between “good” recombination
taking place between electrons and holes photogenerated in the first and second
cell, respectively and “bad” recombination occurring between electrons
and holes photogenerated in the same cell. Each electronhole pair annihilated
by good recombination contributes to the photocurrent.

Fig. 2: 
Energy Band diagram of the second micromorph solar cell: paSiC:H
(10 nm)/ buffer IaSiC:H( 3 nm) /IaSi:H (80 nm)/μcSi:H (10 nm)/RL
(3 nm)/pμcSi:H (10 nm)/(p/i) interface (3 nm)/iμcSi:H (1300
nm)/naSi:H (10 nm) The Conduction band edge (E_{c}), the valance
band edge (E_{v}), the electron quasiFermi level (E_{fn}),
the hole quasiFermi level (E_{fp}) and the Fermi level (E_{F})
are indicated. (a1), (a2) Thermodynamic equilibrium (b1), (b2) Light on,
V = 0 

Fig. 3: 
Modelled illuminated J(V) characteristics of tandem solar
cells: p_{1}i_{1} n_{1}(aSi:H) /RL/ p_{2}
n_{2} (μcSi:H) n_{2}(aSi:H) p_{1}i_{1}(aSi:H)n_{1}(μcSi:H)
/RL/ p_{2}i_{2}(μcSi:H)n_{2}(aSi:H) 

Fig. 4: 
Electric field profiles for tandem solar cells: p_{1}i_{1}
n_{1}(aSi:H) /RL/ p_{2} n_{2} (μcSi:H)
n_{2}(aSi:H) (dotted line) p_{1}i_{1}(aSi:H)n_{1}(μcSi:H)
/RL/ p_{2}i_{2}(μcSi:H)n_{2}(aSi:H) (solid
line) 

Fig. 5: 
Comparison of the spectral response curves of both types of
double junctions solar cells: p_{1}i_{1} n_{1}(aSi:H)
/RL/ p_{2} n_{2} (μcSi:H) n_{2}(aSi:H)
(dotted line) p_{1}i_{1}(aSi:H)n_{1}(μcSi:H)
/RL/ p_{2}i_{2}(μcSi:H)n_{2}(aSi:H) (solid
line) 
On the other hand, bad recombination occurring in p, i and n layers reduces
the total photocurrent leading to electrical losses. Back diffusion of electrons
and holes at the front and back contact, respectively, are not significant loss
mechanisms in tandem cells. If the tunnel or contact junction (RL) cannot provide
enough good recombination, more carriers will recombine through bad recombination
and the solar cell performance will deteriorate. Other undesired effects would
be the creation of a light induced dipole due to the accumulation of trapped
electrons and trapped holes what would weaken the electric field in the top
cell and in the bottom cell (Rubinelli et al., 2001)
In a TunnelRecombination Junction (TRJ) having the simple nμcSi:H/RL/pμcSi:H
structure the “good” recombination between electrons and holes photogenrated
in the first and second cells, respectively, takes place in a very narrow region
(~34 nm) located near the n/p interface and mainly inside the pμcSi:H
layer (Rubinelli et al., 2001).
CONCLUSION In this study, we have simulated a micromorph tandem cell aSi:H/μcSi:H using AMPS1D. The obtained results show clearly that the microcrystalline silicon (μcSi:H) is a very interesting material to be used in tandem TunnelRecombination Junction (TRJ) because of its low mobility gap that strongly favours good recombination and its low optical absorption minimizes optical losses. The substitution of the amorphous layer N_{1 }by a microcrystalline layer N_{1} in micromorph tandem cell P_{1}I_{1}N_{1}/RL/P_{2}I_{2}N_{2} leads to an improvement of the output cell parameters: J_{sc }increases from 11.607 mA cm^{2} (for N_{1} amorphous) to J_{sc}=12.00 mA cm^{2} for (N_{1} microcrystalline), FF from 0.670 to 0.710 .The V_{oc} increases from 1.347 to 1.541 V which leads to an increase of the efficiency from 10.460% for N_{1} amorphous; to 13.127% when N_{1 }is microcrystalline. This improvement is due to the band discontinuity at the interface I_{1}/N_{1 }which leads to a strong electric field and the profiling in the energy band gap realized by N_{1}P_{2} microcrystalline tunnel junction between the two pin subcells. Finally the results obtained by our simulation are in good agreement with experimental results reported in the literature.

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