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A δ-Doped Substructure in Solar Cells: Carriers Confinement and Photocurrent
F. Pélanchon, Y. Moreau, P. Mialhe
To cite this version:
F. Pélanchon, Y. Moreau, P. Mialhe. Aδ-Doped Substructure in Solar Cells: Carriers Confinement and Photocurrent. Journal de Physique III, EDP Sciences, 1997, 7 (1), pp.117-131. �10.1051/jp3:1997114�.
�jpa-00249563�
A b-Doped Substructure in Solar Cells: Carriers Confinement and Photocurrent
F. PAlanchon (~), Y. Moreau (~>*) and P. Mialhe (~)
(~) C-E M., Umversit6 Montpellier II, 34095 Montpellier Cedex 05, France
(~) C E-F-, Universit6 de Perpignan, avenue de Villeneuve, 66860 Perpignan Cedex, France
(Receii~ed 25 March 1996, accepted I October 1996)
PACS.73.00 Electronic structure and electrical properties of surfaces, interfaces and thin films
Abstract. This paper presents a modelhng of the Low-High interfaces effects due to the
implantation, in the emitter of a silicon solar cell, of a complex structure consisting of a b-doping profile coincident with a defect layer. It leads to analytical expressions of the potential barriers
and the drift electric fields due to these interfaces. The confinement of the holes generated by
the infrared absorption is studied. In parallel, we propose a numerical approach for the electric
phenomena occurring in the cell emitter with a complex interface: it confirms our theoretical results. The electron photocurrent due to the normal absorption is shown not to be altered by the
complex structure The hole confinement, near the front surface, can improve the performances
of the cell. Both our theoretical expressions and our numerical results predict this photocurrent
increase.
R4sum4. Ce travail prdsente une mod6Iisation des effets d'interfaces cr66s par I'implanta- tion, dans l'6metteur d'une cellule solaire au silicium, d'une structure complexe consistant en
un 6-dopage comcidant avec une couche de d6fauts. Les expressions analytiques des barriAres de potentiel et des champs d'entrainement montrent l'int6rAt de ce 6-dopage additionnel : le
confinement des trous g6n6r6s par l'absorption infra-rouge
,
le photocourant dfi h l'absorption normale n'est cependant pas alt6r6 par cette structure additionnelle. Une approche num4rique parallAle, fondle
sur les 6quations de transports complAtes, confirme les r6sultats thAoriques, tant
au mveau du confinement des trous, que de l'am6boration des performances de la cellule sous
6dairement AMI.5 : courant de court-circuit, tension de circuit ouvert et puissance maximale dispomble.
1. Introduction
Higher efficiency and lower cost are required in new solar cells. The most important property of the material for solar cell design is its optical absorption coefficient that dictates, in par-
ticular, the thickness of three hundred microns for usual silicon solar cells 11,2]. It has been shown possible [3] to reduce the cost of silicon material by developing optimized thin cells with thickness of the order of 50 ~m. The incorporation of light trapping to offset the weak
absorption of near-band-gap-energy photons offers the opportunity of higher performances [4].
(*) Author for correspondence (e-mail. moreau©cem2.univ-montp2 fr)
© Les #ditions de Physique 1997
Some theoretical and experimental works have been published [5,6] concerning an improve-
ment of the Back Surface Field (BSF) solar cells. The efficiency could be improved by the insertion of an absorbing substructure inside the thin emitter. This buried substructure within the silicon monocrystal can be formed by P ion implantation at m 180 kev and a subsequent thermal treatment [6]: an amorphous 70 nm thick layer is placed below a single-crystal layer of 97.5 nm. This implanted structure allows optical absorption of the long wavelength pho-
tons [7-9], with an absorption coefficient greater than a few hundreds cm~l for both near infrared and infrared photons. To avoid the reduction of the effective carrier lifetime in the
substructure due to the presence of recombination centers [10], a d-doping profile is inserted on the substructure [11] it yields two Low-High (L-H) interfaces of the b-doping kind and creates two built-in electric fields drifting the carriers away from the substructure.
This complex interface (defect substructure + two L-H interfaces due to the b-doping) con-
fines minority carriers in the front part of the emitter [12]. In this paper, we propose a modelling of the L-H interfaces in order to express:
. the built-in potential barrier and the built-in electric fields provided by the L-H interfaces,
. the range of influence of the electric drift fields (= space charge regions widths) in the emitter.
These expressions allow us to estimate the influences of these L-H interfaces on the electron flow in the emitter and also to calculate the maximal additional hole flux in the emitter due to the infrared absorption. The hole confinement near the front surface of the cell yields a reduction of the potential barrier due to the L-H interface and creates an internal electric field that in turn drifts electrons towards the front contact which could increase the cell performance.
This analytical study has required some assumptions concerning the carriers mobilities, diffusions and lifetimes through the whole device. These assumptions have been justified by a parallel numerical approach.
An extra electron photocurrent due to the infrared generation confirms experimental results
[9]. The electron photocurrent due to the normal absorption is shown not to be altered by the
complex structure. The hole confinement, near the front surface, can improve the performances of the cell. Both theoretical expressions and numerical results evaluate this photocurrent
increase.
2. Modelling of the Emitter
In order to model the emitter structure, some assumptions are made:
Ii) The emitter front surface effects do not affect complex interface effects:
I.e. the distance from the front surface to the complex interface is large enough.
(ii) The two L-H interfaces are abrupt.
The complex interface inserted in the emitter yields two L-H (Low-High) interfaces, i, e. two
potential barriers and two electric fields. Referring to Figure I, the physical process may be described as follows. The right electric field drifts the carriers in an useful direction for the
photocurrent: for instance, when considering a n+ n++ n+ cell, this electric field drifts electrons towards the cell front surface and the holes backwards. On the contrary, the left electric field drifts the carriers in a non efficient direction: in a n+ n++ n+ cell, the holes
are confined, by the left potential barrier, in the cell Front Emitter bulk, as it is detailed in the appendix.
These two potential barriers are due to the ratio b-dopinglemitter doping. The two inter- faces are actually not symmetrical since, all along the emitter bulk, the doping is a decreasing
n+ n++ n+
~
~Q
towards emitter
fl
g_ junction-$ 4
-
Jphot ~
Fig, I. Carriers drift near the substructure: the electrons from the junction are drifted towards the front surface because of the right "Low-High transition", while a part of generated holes are drifted to the front surface because of the left "Low-High transition".
'
n~ ~~~ ~~ ~
~....
l
l I I
~ ~
Wtot
Fig. 2 Detalls and notations of the emitter regions in the improved solar cell.
function according to the depth in the cell lit is usually admitted that this function is an
erf-type function). Thus, the two space-charge created by the L-H interfaces are of different width: that induces different influence ranges of the two electric fields.
Emitter dimding ttp: The emitter (Wtot-width) is divided up in different parts presented in
Figure 2:
The front emitter bulk, WFE width, corresponds to the emitter region out of range from the left electric field (but, probably influenced by the front surface effects).
The left space-charge region: the electric field drifts the holes to the left. This region
consists of a negative space-charge part of width WLL ILL for Left-Low interface), and of a positive space-charge part of width WLH (LH for Left-High interface).
The right space-charge region: the electric field drifts the holes to the right. This region
consists of a positive space-charge part of width WRH (RH for Right-High interface), and
of a negative space-charge part of width WRL (RL for Right-Low interface).
The region, of width WH, situated within the complex interface, and not subject to the drift electric fields influence. In some cases (see below), this part can be made as
vanishing to zero which increases the majority carriers collection.
(The total complex interface width is WLH + IVH + WRH).
The back emitter bulk, the remaining of the emitter situated between the right space- charge region and the n-p junction, of width WBE.
~
,
emitter w
,
substructure -f
,
front
~ VLH VRH
junction
,
WFE WLL
~ WRH WRL
Fig. 3. Potential barriers due to the L-H interfaces. The decrease of the emitter doping along
-~-axis builds asymmetric Low-High transitions. This improves the electron drift towards the collecting electrode.
2.I. COMPARISON oF THE INFLUENCE RANGES oF THE DRIFT ELECTRIC FIELDS. Let
us consider the front emitter bulk, the complex interface and the back emitter bulk, with their respective doping level: NLD, N6, NRD. Then, the space-charge region widths are expressed (Appendix, Eqs. (A.16), (A.17)) by:
j~~2
~'~i~6/~iLDj
~~ INLD + N6)1lN6/NLD] j~~
j~~2 ~~~i~6/~iLDj
~~ (NLD + N6)1INLD/N6] j~~
~~~ (NR~~~~~~/N6j ~~~
~~~ (NR~~~~~~~~/RDj ~~~
with C
= 2ekT/q~ (e is the dielectric constant, k the Boltzmann's constant, T the temperature and q the electron charge)
Moreover, the potential barriers (Fig. 3) ~iH (front emitter bulk -complex interface) and VRH
(complex interface-back emitter bulk) may be estimated with common doping levels (Appendix, Eq. (A.15)). We obtained:
v~~ = ~)injN~/N~~j j5)
v~~ =
~~ injN~/N~~j j6)
2.I.I. Numerical Application. We consider silicon material
N6 "10~° cm~~; NLD "10~~ cm~~; NRD "10~~ cm~~;
l§'LL " 11.8 nm; WRL " 45.8 nm;
WLH and WRH are negligible (0.l18 nm and 0.0458 nm, respectively).
Potential barriers: VLH " l19 mV; VRH
" 179 mV.
Remark: In each space-charge region, the subdivision corresponding to the less doped part, is much wider than the other. That can lead to a b-doped layer less wide than the defect structure
layer [13]: in this case, it has been shown [13] that the electric fields act more efficiently on the carriers and allow to avoid a part of the extra recombination due to the defects.
The highest intensities of the drift electric fields are given by (Appendix, Eq. (A.18)):
EL " (~/£)N6WLH
ER " (qle)N6WRH
)
=
~~H= NRDIn[N5/NR~j
~ ~~~ ~/LDlnlN6/NLD] ~~~/6/NLD » 1.
With the previous numerical values, we obtained:
EL = 1.8 x 10~ V cm~~;ER
= 0.7 x 10~ V cm~~; EL/ER " 2.6.
2,1.2. Electron Flow. The defect zone allows an extra electron generation, but the efficiency
is really improved only if the total electron collection is increased. The substructure introduces
a potential barrier which might reduce the electron flow towards the front contact.
Let us consider an electron situated in the back emitter bulk, without any initial speed (this assumption leads to ignore the junction electric field effect for electrons coming from the junction, and takes into account the electrons created in the emitter). This electron achieves, (see Fig. 3), thanks to the right electric field ER, a speed ~ equal to ~ = ~tER (p is the electron
mobility). ER can be expressed as VRH/(WRL+WRH) i,e. ER * VRH/IVRL When this electron reaches the left potential barrier, if a possible slowing down due to the defects is ignored (see below), its energy equals 1/2 m~~. It crosses the potential barrier if its energy is greater than qVLH. It is easy to numerically verify that:
(For instance, with the numerical values obtained above, ~~~~~~~~~~~
= 570.26 » 1).
2 qVLH
Thus, the complex interface does not prevent the electron displacement and does not affect the photocurrent generated by the normal absorption.
Moreover, when the cell is illuminated, the infrared generation creates holes that are confined in the front emitter bulk: these holes lower the potential barrier due to the L-H interface, which
eases the electron drift and increases their collection in proportion.
3. Carrier Densities and Currents
In this section, we calculate the hole densities due to the normal absorption and to the infrared absorption.
The front surface is situated at x = 0, the front emitter bulk width is WFE, the width of the defect layer region that generates holes drifted towards the cell front surface is Wdef (Wdef " WLL + l§'LH). The total emitter width is Wtot.
One could think that the defect layer implantation degrades both the lifetimes and the mobilities of the carriers. From a static point of view of the transport phenomenon (static continuity equations), these degradations imply an increase of the recombination but localized to this defect layer. Our numerical computations (see Sect. 4) have shown that dividing mobil- ities and lifetimes, in the substructure, by a factor greater than 50, implies a minor decrease
50
45
4o
35
u)
E?
j
)~
I3
~° unchangedmobilities : ~
raded
15
Conventional cell(without
io 5
o
0
3.I. HOLE DENSITY DUE To THE NORMAL LIGHT ABSORPTION. The generation rate of the carriers created by the AMI.5 incident light on the front surface of the cell can be
expressed [14,15] by:
3
G(x) =
~ja~ exp(-b~x)) (7)
1=1
where a~ and b~ are empirical coefficients.
The continuity equation for the excess hole density p(x) in the emitter reads:
~d~plx) 1
~ _~~~~ ~~~
dx2 T
(D, T are respectively the diffusion coefficient and the lifetime of the holes in the emitter).
3. I. I. Boundary Conditions. Considering a cell front surface recombination velocity equal to S and the cell operating under open-circuit condition, two boundary conditions can be written:
3.1.2. Mathematical Results
jci): j1°~
=
ljj
pjo)x
(C2): ~'~j~~°~~
= 0
The solution p(x) of equation (8) with (Cl-C2) is:
Fix) = Ni COSh ~~
~/~°~~ + N2 Sinh 1~ N3 COSh Ill
~D
~
(l /L2 b)) ~~~~ ~~~~ ~~~
with L, the hole diffusion length, and N~ ii = 1, 2, 3, 4) defined by:
~~ j~N4
II
(lli~~~ b)) ~~~~~ (
(l/L~~-
))~
~~~~
~~ ~N4 [ (llii~~
b)) ~~~~ ~~~°~~ ~~~~
3
' LDN4 [ (1ll~
b)) ~~~~ ~~~°~~ ~~~~
N4 = cosh l~~) ~) sinh (~°~) (13)
L L L
Then, the hole current density J(x)
= -qDdp(x)/dx, at each point x in the emitter, may be expressed in the form:
Jixi
= -~D (l~ Sinh ~~ /~°~~j + (l~ C°Sh Ill (l~ Sinh Ill
ii/ii~~ ~i~ exPib>x)1 i14)
and, at the cell front surface:
J10)
- ~D lll~l Sinh11°~l l~ +
Ill (
ii/ii~~
i~j
its)
3.2. INFRARED ABSORPTION. It is assumed that the traps are situated in the middle of
the silicon band gap [15], and that there exists a sufficiently efficient light trapping (more
than a hundred of reflecting paths) to ensure an optimal absorption of the 2 x N incident infrared photons (per second and per cm~). This is naturally an ideal case where all photons
are efficient, i.e., each pair of infrared photons generates an electron-hole pair, through the two steps process, in the complex substructure [15] of W~~b width (W~~b " WLH + WH + WRH).
Thus, if this infrared absorption is assumed to be homogeneous throughout the defect structure, only N x Wdef/lI~[~ holes are generated by this infrared absorption in the active part of the
defect layer of width equal to Wdef = WLL + WLH, and are drifted towards the cell front surface. Since the hole diffusion length L m WFE, these holes spread all along in the front emitter bulk where they are confined. All the holes generated in the other part of the defect layer are drifted backwards the n-p junction and do not participate to the hole current in the
front emitter bulk.
Therefore, the hole generation rate Po (cm~~ s~~) in the front emitter bulk, due to the infrared absorption in the defect layer may be:
Po " IN Wdeilwj~~)/WFE, if we consider that the confined holes are homogeneously dis-
tributed. The continuity equation in the front emitter bulk for the holes generated by the infrared absorption is written:
D~ ~(~ ~~~~
= -Po. (16)
x
t
3.2.I. Boundary Conditions. The front surface boundary condition has been written (Cl).
The left electric field (due to the left L-H interface, see above) is so great that the holes situated at the frontier of the front emitter bulk (Fig. 2) are the only ones drifted from the L-H interface:
(C3): p(WFE) " ~~j~~~~
~ub
3.2.2. Mathematical Results. The general solution of (16) reads:
PIT) = TAO + >e~/~ + /1e~~/~. (ii)
The two boundary conditions (Cl)-(C3) give- p(X) = TAO +
~~ ~~~~ ~~
~
~ ~ ~~~ ~°~~ ~~~ ~~~~
(18)
13
with ( ii
= 1, 2, 3) defined by:
13 = ()) cosh (~~~L D~ sinh (~~~L (19)
fi " +~/° (20)
12 " -rPo +
~~~'~~~
(21)
W~~b
Then, the infrared generated hole current density J(x)
= -qDdp(x)/dx at each point x in the emitter expresses:
J(x) =
$ fi
cosh l~~~) ~j j sinh ())
+ (~)) cosh ())j (22)
and, at the cell front surface:
J(0) =
~ [fi cosh(WFE) + (I2S/D)] (23)
3.2.3. Remark. All the holes generated by the infrared absorption and confined in the front emitter bulk yield a small Dember-type field [16]. This field contributes to the electron displacement towards the front surface and increases the electron current density (see below, Sect. 4).
This field E
= (-kT/q)(I /p(x)dp(x)/dx), due to the hole movement in the front emitter bulk may be computed in first order (S
= 0):
~ l rPo~~~~~~)~/L)]
~~~~
4. Numerical Approach
The complete numerical device simulation through the use of commercial codes like PISCES, MEDICI, ATLAS etc. is accurate, and widens the domain of investigation to a large variety of geometries, physical phenomena etc. However its efficiency is diminished by its difficult
reading. One needs many exploratory runs to detect the influence of a given parameter (this
is direct in a mathematical model) Important computational resources are also needed.
Our numerical approach uses a home developed software: the ambipolar transport equations
are solved numerically, thus avoiding some of the necessary assumptions used in analytical
models. However only one dimension is taken into account. It avoids large computational
resources and is implemented in a desktop environment on a micro-computer. The user does
not need to invest time in learning, and furthermore, the results can be directly transferred into a conventional spreadsheet for analyzing or plotting.
The total photocurrent created by solar light is derived from the three basic differential transport equations, with the conventional notations:
div lE gradi~l))
= in P + NA ND) 125)
div jJ~) = Rjx) G(x) (26)
divjJ~)
= -Rjx)+Gjx). j27)
The basic quantities the electrostatic potential ~l, the carrier densities i1 and p are globally
Avaluated as a three component vector defined at each node of an x-mesh. The three differential equations are transformed into a reasonable number of finite difference vector equations. The derived coefficient matrix has only three diagonals whose elements are not scalar but 3 x 3
matrices. The system is then easily solved through adapted factorization. The linearization
uses a damped Newton-Raphson algorithm.
The electron and hole currents, Jn and J~, are derived through Gummel's discretization which assumes a correct dependence between the basic quantities. The direct discretization
