Research Article Analysis of the High Conversion Efficiencies ...Research Article Analysis of the...
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Research ArticleAnalysis of the High Conversion Efficiencies π½-FeSi
2and BaSi
2
n-i-p Thin Film Solar Cells
Jung-Sheng Huang, Kuan-Wei Lee, and Yu-Hsiang Tseng
Department of Electronic Engineering, I-Shou University, Kaohsiung 840, Taiwan
Correspondence should be addressed to Jung-Sheng Huang; [email protected]
Received 20 June 2014; Revised 20 September 2014; Accepted 22 September 2014; Published 29 December 2014
Academic Editor: Chien-Jung Huang
Copyright Β© 2014 Jung-Sheng Huang et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
Both π½-FeSi2and BaSi
2are silicides and have large absorption coefficients; thus they are very promising Si-based new materials
for solar cell applications. In this paper, the dc πΌ-π characteristics of n-Si/i-π½FeSi2/p-Si and n-Si/i-BaSi
2/p-Si thin film solar cells
are investigated by solving the charge transport equations with optical generations. The diffusion current densities of free electronand hole are calculated first. Then the drift current density in the depletion regions is obtained. The total current density is thesum of diffusion and drift current densities. The conversion efficiencies are obtained from the calculated πΌ-π curves. The optimumconversion efficiency of n-Si/i-π½FeSi
2/p-Si thin film solar cell is 27.8% and that of n-Si/i-BaSi
2/p-Si thin film solar cell is 30.4%, both
are larger than that of Si n-i-p solar cell (π is 20.6%). These results are consistent with their absorption spectrum. The calculatedconversion efficiency of Si n-i-p solar cell is consistent with the reported researches. Therefore, these calculation results are valid inthis work.
1. Introduction
A silicide is a compound that has silicon with more elec-tropositive elements. The metal silicides have been widelyinvestigated for several years because of their potentialapplications in electronics [1]. Semiconducting beta-phaseiron disilicide (π½-FeSi
2) and orthorhombic barium silicide
(BaSi2) are two transition metal silicides and they are very
promising Si-based new materials for solar cell applications.It is desirable for solar cellmaterials to have a large absorptioncoefficient to yield high conversion efficiencies. π½-FeSi
2has
a large optical absorption coefficient (>105 cmβ1 at 1.5 eV)and a direct band gap of βΌ0.87 eV [2β4]. Lin et al. [5]reported a conversion efficiency of 3.7% for p- (or n-)type π½-FeSi
2/n- (or p-) type Si solar cell. Gao et al. [6]
simulated a p-Si/i-π½FeSi2/n-Si solar cell structure by using
the AMPS-1D software. The conversion efficiency is 24.7%.The orthorhombic barium silicide (BaSi
2) also has a large
absorption coefficient of over 105 cmβ1 at 1.5 eV [7]. Recentreports on the photoresponse properties of BaSi
2have shown
that BaSi2is a new silicide material suitable for solar cell
applications [8, 9].
Therefore, in this paper the conversion efficiencies of n-Si/i-π½FeSi
2/p-Si and n-Si/i-BaSi
2/p-Si thin film solar cells are
investigated by using self-developed analytical methods. Forsemiconductor solar cells, the n-i-p structure usually hassuperior πΌ-π characteristics than the n-p structure. Since thebuilt-in electric field exists in the intrinsic layer, the generatedelectron-hole pairs in the intrinsic layer are drifted by theelectric field and produce larger short-circuit current andopen-circuit voltage. In addition, the intrinsic silicide layerdoes not need doping and its manufacturing is compatiblewith the well-established Si solar cells. The distributions ofminority carrier concentrations in the neutral n-Si and p-Siregions are calculated first. Then the total current density isthe sum of diffusion current densities of free electron andhole and the drift current density in the depletion regions.The conversion efficiencies are calculated from the πΌ-π curvesof the solar cells with illumination of light. The calculatedoptimum conversion efficiency of π½-FeSi
2n-i-p solar cell is
27.8% and that of BaSi2p-i-n solar cell is 30.4% and that of Si
n-i-p solar cell is 20.6%.Therefore, the conversion efficienciesof π½-FeSi
2and BaSi
2n-i-p solar cells are significantly larger
than that of the conventional Si n-i-p solar cells.The reported
Hindawi Publishing CorporationJournal of NanomaterialsVolume 2014, Article ID 238291, 5 pageshttp://dx.doi.org/10.1155/2014/238291
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2 Journal of Nanomaterials
or
or
BaSi2
Beta-FeSi2
Wn Wp
xpxn W
x = 0 x = Wn β xn x = Wn x = Wn + W x = Wn + W+ xp x = Wn + W+Wp
i-Sin-Si p-Si
hοΏ½
Figure 1: A one-dimensional analysis model of n-i-p thin film solar cells.
conversion efficiency of Si n-i-p solar cell is consistent withthis calculation work [10]. Therefore, the calculation resultsare valid in this work.
2. Analysis Methods
Then-i-p structure of solar cells under investigation is shownin Figure 1. The calculations are under global AM1.5 solarspectrum (Wmβ2) at 25βC. At the surface of the solar cell (i.e.,at π₯ = 0), the generation rate of electron-hole pairs, πΊ
0(π)
(sβ1mβ3), is [11]
πΊ0(π) = π
π [1 β π (π)]
πΌopt
βππΌ (π) , (1)
where π = the wavelength of the incident light (m), ππ=
the intrinsic quantum efficiency to account for the averagenumber (100% maximum) of electron-hole pairs generatedper incident photon, π (π) = the optical reflectivity betweenthe air and the semiconductor, πΌopt = the incident opticalpower intensity (Wmβ2), βπ = the energy of the incidentphoton (Joul), and πΌ(π) = the absorption spectrum (mβ1).
The generation rate of electron-hole pairs in the solar celldevice (π₯ > 0) is
πΊ (π₯, π) = πΊ0(π) πβπΌ(π)π₯
. (2)
In the neutral n-Si region, the charge transport equation forthe excess hole concentration, πΏπ
π, is
π2
ππ₯2πΏππ(π₯, π) β
1
πΏ2
π
πΏππ(π₯, π) = β
1
π·π
πΊ (π₯, π) , (3)
where πΏπ= the average diffusion length of holes in π-type
region (m) and π·π= the diffusion coefficient of minority
holes (m2sβ1).The two boundary conditions to solve (3) are as follows.
(a) At the edge of n-Si depletion region (π₯ = ππβ ππ):
πΏππ= πππ
[ππV/ππ‘
β 1] . (4)
(b) At the surface of n-Si (π₯ = 0):
π·π
π
ππ₯πΏππ= πππΏππ, (5)
where ππis the surface recombination velocity of holes
(msβ1).Then the hole diffusion current density is calculated at the
edge of the n-Si depletion region as
π½π,diff = βππ·π
π
ππ₯πΏππ
π₯=π€πβπ₯π
. (6)
Similarly, the distribution of free electron density, πΏππ(π₯, π),
in the neutral region of the p-Si can be obtained by solving thecharge transport equation for πΏπ
π. And the electron diffusion
current density is calculated at the edge of the p-Si depletionregion as
π½π,diff = ππ·π
π
ππ₯πΏππ
π₯=π€π+π€+π₯
π
. (7)
The drift current density due to optical generation in thedepletion regions is calculated as
π½drift = πβ«n-Si
πΊ0(Si) πβπ(Si)π₯ππ₯
+ πβ«
i-regionπΊ0(π½ β FeSi
2) πβπ(π½βFeSi2)π₯
ππ₯
+ πβ«
p-SiπΊ0(Si) πβπ(Si)π₯ππ₯,
(8)
where the first term accounts for the drift current densityobtained from the depletion region in n-Si. The second termis the drift current density from the intrinsic layer and thethird term is the drift current density from the depletionregion in p-Si.
The total current density for an incident photon flux at agiven wavelength is
π½ (π) = π½π,diff (π) + π½π,diff (π) + π½drift (π) . (9)
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Journal of Nanomaterials 3
Table 1: The optimum parameters used in the calculations of n-i-psolar cells with different intrinsic layer materials.
Parameters Si π½-FeSi2 BaSi2Energy gap (eV) 1.12 0.85 1.086Relative permittivity 11.9 22.5 11.17Diffusion coefficient (cm2/s), π·
π35
Diffusion coefficient (cm2/s), π·π
12.4Diffusion length (πm), πΏ
π13.2
Diffusion length (πm), πΏπ
4.9Surface recombination velocity (cm/s), π
π104
Surface recombination velocity (cm/s), ππ
104
Intrinsic quantum efficiency, ππ
0.6Optical reflectivity, π 0.1
Then the total photo current is obtained by integrating allwavelengths from 300 nm to (βπ/πΈ
π) (πΈπ= the energy gap
of the semiconductor material).The fill-factor (FF) is definedas
FF =πππΌπ
πocπΌsc, (10)
where πππΌπ= the maximum power output which occurs at a
point on the πΌ-π curve, πoc = the open-circuit voltage whichoccurs at the point with πΌ = 0 on the πΌ-π curve, and πΌsc = theshort-circuit current which occurs at the point with π = 0.
Finally, the conversion efficiency, π, is obtained as
π =πocπΌscπopt
FF, (11)
where πopt = the incident optical power on the solar cellsurface (W).
The optimum parameters used in this calculation aregiven in Table 1. The absorption spectrums of π½-FeSi
2and
BaSi2are obtained by using the experiment results reported in
[2], and the absorption spectrum of Si is obtained from [12].
3. Results and Discussion
The calculated p-Si/i-π½FeSi2/n-Si double heterojunction
energy band diagram in thermal equilibrium is shown inFigure 2. The doping concentrations for both p-Si and n-Silayers are 1018 cmβ3. The thicknesses for both p-Si and n-Silayers are 1 πm and for intrinsic π½-FeSi
2(or BaSi
2) layer is
0.3 πm. The p-Si and n-Si layers have larger bandgap energythan π½-FeSi
2and BaSi
2. The wavelengths of solar radiation
absorbed by the semiconductor materials are from 300 nmto (βπ/πΈ
π). Therefore, the π½-FeSi
2and BaSi
2have wider
wavelength absorption ranges than Si. The generation rateof electron-hole pairs in π½-FeSi
2n-i-p solar cell is shown
in Figure 3 by calculating (1) and (2). At the surface of thesolar cell (i.e., at π₯ = 0), the generation rate of electron-hole pairs, πΊ
0(π) (sβ1mβ3), is proportional to the absorption
spectrum, πΌ(π) (mβ1). The thickness of intrinsic layer is0.3 πm.The generation rate of electron-hole pairs, πΊ(π₯, π), isa function of position, π₯, and the incident wavelength, π. The
0
β0.2
β0.4
β0.6
β0.8
β1
β1.2
β1.4
β1.6
β1.8
β2β1 β0.5 0 0.5 1
Thickness (cm)
E (e
V)
p-Si n-Si
EF = β1.06 eV
EV = β1.12 eV
ΞEC = 0.11 eVπ½-FeSi2
EC = β0.73 eV
ΞEV = 0.14 eV EV = β1.85 eV
Γ10β4
EC = 0 eV
Figure 2:The equilibriumenergy banddiagram for p-Si/i-π½FeSi2/n-
Si solar cell.
(a)
(a)(a)
(b)(b)
(c)
(d)1030
1020
100
10β10
10β20
10β30
Γ10β41 20
Wp + W+Wn
G(X
) (1
/cm3 β
s)1010
Figure 3: The generation rate as a function of position π₯ withdifferent wavelengths, π, for π½-FeSi
2n-i-p solar cell. (a) π =
0.405 πm, (b) π = 1.101 πm, (c) π = 0.305 πm, and (d) π = 1.193 πm.
generation rate is exponentially decreased with the positionπ₯ increased. There are four curves in Figure 3 correspondingto four different incident wavelengths. Note that, at incidentoptical wavelength π = 1.193 πm (curve (d)), the generationrate is zero in Si regions, but in π½-FeSi
2region, the generation
rate reaches maximum. Figure 4 shows the generation rateof electron-hole pairs in BaSi
2n-i-p solar cell. Similarly, at
incident optical wavelength π = 1.086 πm (curve (d)), thegeneration rate is zero in Si regions, but in BaSi
2region, the
generation rate is maximum.The minority carrier density distributions of π½-FeSi
2n-i-
p solar cell with applied voltage ππ= 0 are shown in Figure 5
by solving (3) to (5). The doping concentrations in n-Si andp-Si regions are both equal to 1018 cmβ3. The intrinsic layerthickness is 0.4 πm. The slopes of these minority carrierdensity distributions at the depletion region edges determinethe magnitudes of the diffusion currents (as shown in (6)and (7)). As shown in Figure 5, the maximum reverse holediffusion current density is at wavelength π = 0.55 πm(because the slope is maximum at this wavelength). Thesolar radiation is incident from n-Si to p-Si. Thus, thegeneration rates of electron-hole pairs in n-Si region are
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4 Journal of Nanomaterials
(a)
(a)(a)
(b)(b)
(c)
(d)1030
1020
100
10β10
10β20
10β30
Γ10β41 20
Wp + W+Wn
G(X
) (1
/cm3β
s)
1010
Figure 4: The generation rate as a function of position π₯ withdifferent wavelengths for BaSi
2n-i-p solar cell. (a) π = 0.405 πm, (b)
π = 1.101 πm, (c) π = 0.305 πm, and (d) π = 1.086 πm.
0 1 2Γ10β4
0
0.5
1
1.5
2
2.5
Γ1011
Thickness (cm)
Min
ority
carr
ies d
ensit
y (1
/cm3)
Depletionregion(a)
(a)
(b)
(b)(c) (c)
Figure 5: The minority carrier density distributions at ππ= 0V for
π½-FeSi2solar cell with different wavelengths. (a) π = 0.455 πm, (b) π
= 0.665 πm, and (c) π = 1.101 πm.
larger than that in p-Si region.Therefore, theminority carrierdensity in n-Si region is larger than that in p-Si region atall wavelengths (as shown in Figure 5). And the diffusioncurrent density is mainly determined by the hole diffusioncurrent density. When the applied voltage reaches the open-circuit voltage (πoc = 0.591V, now the total current iszero), the minority carrier density distributions of π½-FeSi
2
solar cell are shown in Figure 6. Compared with Figure 5,the minority carrier densities are increased exponentiallywith applied forward-biased voltage at the edges of depletionregion. And the hole diffusion current density is negativeat π = 0.455 πm but is positive at π = 1.101 πm. Thecalculated minority carrier diffusion current densities as afunction of wavelengths for π½-FeSi
2solar cell are shown
in Figure 7 by calculating (6) and (7). When the appliedvoltage is zero (curve (a)), all of theminority carrier diffusioncurrent densities are negative, and the maximum negativediffusion current density is at wavelength π = 0.55 πm.Whenthe applied voltage reaches the open-circuit voltage, πoc =0.591 V (curve(b)), the minority carrier diffusion currentdensities are still negative at wavelengths 0.5 πm to 0.7πm,but the magnitudes are decreased. However, at wavelengthsbetween 0.3 πm to 0.5 πm and 0.7 πm to 1.1 πm, the minoritycarrier diffusion current densities become positive, and themaximum values are at 0.3 πm and 1.1 πm. The calculated
0 1 2Γ10β4
1.9
1.85
1.8
1.75
1.7
1.65
1.6
Γ1012
Thickness (cm)
Min
ority
carr
ies d
ensit
y (1
/cm3)
Depletionregion
(a)
(a)
(b)
(b)
(c)
(c)
Figure 6: The minority carrier density distributions at ππ= πoc
= 0.591 V for π½-FeSi2solar cell with different wavelengths. (a) π =
0.455 πm, (b) π = 0.665 πm, and (c) π = 1.101 πm.
0 0.2 0.4 0.6 0.8 1 1.2Γ10β4
β0.015
β0.01
β0.005
0
0.005
0.01
Wavelength (cm)
Diff
usio
n cu
rren
t den
sity
(A/c
m2)
(a)
(b)
Figure 7:The calculatedminority carrier diffusion current densitiesas a function of wavelengths for π½-FeSi
2solar cell. (a) π
π= 0V, (b)
ππ= πoc = 0.591 V.
drift current densities as a function ofwavelengths forπ½-FeSi2
solar cell are shown in Figure 8 by calculating (8). The driftcurrent densities are calculated in the depletion regions.Theyare almost the same betweenπ
π= 0V (curve (a)) andπ
π=πoc
= 0.591 V (curve (b)). The drift current densities are alwaysnegative and are almost a constant for different wavelengths.
The calculated πΌ-π curves with different intrinsic layermaterials (the intrinsic layer thickness is 0.5πm now) areshown in Figure 9. The reverse current density of BaSi
2n-i-
p solar cell is larger than that of π½-FeSi2and Si n-i-p solar
cells. The calculated results of Figure 9 are listed in Table 2.Note that BaSi
2has the maximum open-circuit current
density (|π½sc| = 22.93mA/cm2), the maximum fill factor
(FF = 82.63%), and the maximum conversion efficiency (π= 30.4%). The calculated optimum conversion efficiency ofπ½-FeSi
2n-i-p solar cells is 27.8% and that of Si n-i-p solar
cell is 20.6%. BaSi2has the maximum absorption spectrum
and Si has the minimum absorption spectrum. Therefore,the calculation results of conversion efficiency for differentmaterials are consistent with their absorption spectrum. Thereported [10] efficiency of amorphous Si : H (pin) solar cell is10.1%, and that of polycrystalline Si solar cell is 20.4% whichis consistent with this calculation work.Thus, the calculationresults are valid in this work.
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Journal of Nanomaterials 5
2 4 6 8 10 12 14 16
Γ10β5Wavelength (cm)
Drift
curr
ent d
ensit
y (A
/cm2)
(a)(b)
β10β25
β10β20
β10β15
β10β10
β10β5
β100
Figure 8: The calculated drift current densities as a function ofwavelengths for π½-FeSi
2solar cell. (a)π
π= 0V, (b)π
π=πoc = 0.591 V.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7β0.025
β0.02
β0.015
β0.01
β0.005
0
Tota
l cur
rent
den
sity
(A/c
m2)
(a)
(b)(c)
Va (V)
Figure 9:The calculated πΌ-π curves of n-i-p solar cells with differentintrinsic layer materials: (a) Si, (b) π½-FeSi
2, and (c) BaSi
2.
Table 2: The calculated results for n-i-p solar cells with differentintrinsic layer materials.
Intrinsic layermaterials πoc (V) π½sc (mA/cm
2) FF (%) π (%)
Si 0.584 15.83 82.33 20.6π½-FeSi2 0.591 21.02 82.59 27.8BaSi2 0.594 22.93 82.63 30.4
4. Conclusion
The dc πΌ-π characteristics of π½-FeSi2and BaSi
2n-i-p solar
cells are investigated by using the analytical calculations.The distributions of minority carrier densities, the diffusioncurrent densities of free electron and hole, and the driftcurrent density in the depletion regions are calculated. Theconversion efficiencies are obtained from the calculated πΌ-π curves. The calculated results show that the conversionefficiency of π½-FeSi
2solar cell is 27.8% and that of BaSi
2solar
cell is 30.4%, both are larger than that of the Si n-i-p solarcell (π is 20.6% which is consistent with the reported results).These results are consistent with their absorption spectrum.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
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