Variable band-gap semiconductors as the basis of new solar cells

Variable band-gap semiconductors as the basis of new solar cells
Arturo Morales-Acevedo *
Centro de Investigacio
´n y de Estudios Avanzados del IPN,Electrical Engineering Department,Avenida IPN No.2508,07360Me ´xico,DF,Mexico Received 4October 2008;accepted 3April 2009
Available online 8May 2009Communicated by:Associate Editor Nicola Romeo
Abstract
Some basic concepts related to variable band-gap absorbing semiconductors in solar cell structures,such as the associated quasi-electric field,will be discussed.The effects of this quasi-electric field upon the minority carrier drift-diffusion length and the back surface recombina-tion velocity may induce a larger generated carrier collection at the junction with the corresponding increase of the illumination current den-sity.It will also be shown that an additional improvement of the open-circuit voltage is possible when the band-gap is reduced within the space charge region so that the dark saturation current density is reduced there.Our estimation is that in the case of a solar cell where the band-gap is changed about 0.5eV within the space charge region,an increase of the open-circuit voltage around 115mV will be observed with respect to the single minimum band-gap absorbing material case.A similar band-gap variation in the bulk of the material will cause an increase of the minority carrier drift-diffusion length by a factor of 10with respect to the single band-gap material.Therefore,based on these physical con-cepts,two possible structures with variable band-gap layers are proposed in order to have higher efficiencies than for cells without any band-gap grading.It will be shown that these concepts can be applied to II–VI,III–V chalcopyrite and even amorphous semiconductor solar cells.Ó2009Elsevier Ltd.All rights reserved.
Keywords:Solar cells;Band-gap grading;Thin films
1.Introduction
Introducing a spatial variation of the band-gap within the absorbing layer of a solar cell,the photon absorption and the carrier collection probability can be optimized in order to achieve a higher short circuit current density (Jsc).In addition,the band-gap profile can be optimized so that the open-circuit voltage (Voc)is also improved.Increasing the open-circuit voltage to improve the efficiency of CIGS,II–VI,III–V and even amorphous semiconductor solar cells is highly desirable since Voc is usually the remaining parameter to be improved for most of the present solar cell technologies.Thus,band-gap engineering in the absorber layer can lead to enhancing the overall performance of solar cells.However,an understand-ing of the fundamental device physics is necessary in order to exploit the benefits of a design strategy for its ing the physical concepts developed here an optimal struc-ture can be analyzed,and then a refined numerical model can be used to have a more exact prediction of the cell behavior for a particular material or technology.
Therefore,in this paper,first some basic concepts relevant for designing highly efficient thin film solar cells,where the band-gap energy of the absorber layer is not uniform,are dis-cussed.Then,based on these concepts,band-gap profiles are proposed in order to have thin film solar cells with high effi-ciencies.The best band-gap profile will depend upon the par-ticular material to be used (II–VI,I–III–VI 2or amorphous semiconductor)for the solar cell structure.
2.Basic concepts for solar cells with varying band-gap absorber layers
2.1.Absorption in variable band-gap materials
We shall assume that materials to be used as the absor-ber layers (base)of the solar cells have direct band-gap
0038-092X/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.solener.2009.04.004
*
Tel.:+525557473781.
E-mail address:amorales@solar.cinvestav.mx
/locate/solener
Available online at
Solar Energy 83(2009)
1466–1471
absorption,characterized by an absorption coefficient of the form:a ¼0
h m <E g a ¼A Ãðh m ÀE g Þ1
2
E g <h m
ð1Þ
where E g is the single band-gap of the material,h m is the photon energy of the incident radiation and A *is a con-stant which depends upon the effective masses of electrons and holes in the conduction and valence bands,respectively.
In a recent study,the author Morales-Acevedo (2009)has shown that absorption in a direct band semiconductor where the band-gap varies as a function of position (see Fig.1),between E g max and E g min ,the photon absorption rate can be calculated in a similar manner than for single band-gap materials with an effective absorption coefficient a effof the form:a eff ¼00<h m <E g min
a eff ¼23a g min h m ÀE g min
E g max ÀE g min
E g min <h m <32
ðE g max ÀE g min ÞþE g min
a eff ¼a g min
3
ðE g max ÀE g min ÞþE g min <h m
ð2Þ
where a g min is the absorption coefficient given by Eq.(1)for E g =E g min .The maximum and minimum band-gaps E g max and E g min are described in Fig.1for a material with linear band-gap variation between these two values.
In the above mentioned previous work (Morales-Aceve-do,2009),it was also shown that the expected reduction of photocurrent for a material with a given total band-gap variation D E g =E g max ÀE g min is much less than the photo-current loss due to a material with the corresponding aver-age band-gap,when compared with the expected photocurrent for a material with the minimum band-gap E g min .In other words,grading the band-gap does not cause much variation of the photon absorption,but it
causes an internal quasi-electric field which can help improving the collection of photo-generated carriers.Fur-thermore,the open-circuit voltage can also be improved by grading the band-gap as will be shown in the following sections.
Therefore,instead of looking for an optimum single band-gap material we can now look for an optimal band-gap grading profile so that the expected efficiency could be even greater than for an absorber material with opti-mum single band-gap.However,the graded regions within the structure of a solar cell have to be placed in the appro-priate position in order to achieve the proposed improve-ment,as discussed below.
2.2.Internal electric field associated to band-gap grading For simplicity,in this paper,the band-gap variation will be assumed to be due mainly to a variation of the electron affinity.In addition,the absorbing layer will be assumed to be p-type as occurs in CIGS/CdS and CdTe/CdS solar cells.In other words,the minority carriers in the active layer will be electrons moving in a variable conduction band.Notice,however,that most of the concepts devel-oped here can be applied to more general cases where the band-gap variation is in part due to the conduction band variation and in part due to the valence band variation.In Fig.1,it can be seen that due to the conduction band-gap variation with position,electrons will feel a force sim-ilar to the drift force due to an electric field.The electron current density,taking into account the electric potential variation,the electron affinity variation and the carrier dif-fusion will be:
J n ¼Àq l n n
d V þ1
q v e
dx þqD n dn dx ð3Þwhere n (x )is the electron concentration at any position x in
the conduction band,l n is the electron mobility,D n is the electron diffusion coefficient,V is the electric potential,v e is the electron affinity and q is the magnitude of the elec-tron’s charge.V +v e /q is the total electrochemical poten-tial in the semiconductor.Then,electrons are drifted by means of the total quasi-electric field:
n e ¼À
d V þ1
v e
dx ¼ÀdV dx À1q d v e dx ¼ÀdV dx þ1q dE C
dx ð4Þwhere E C (x )is the conduction band energy at position x .A
similar expression can be written for holes in the valence band,but for simplicity we shall discuss only the case of electrons in the conduction band since we are assuming that electrons are the minority carriers in the absorbing semiconductor,as explained before.
According to Eq.(4),electrons will be drifted by the electric field due to the potential variation and by the addi-tional quasi-electric field associated to the affinity (conduc-tion band)variation with position.This field,in the appropriate direction,can reduce both the back
surface
Fig.1.Band diagram for a material with linear band-gap variation as a function of position (total thickness d ).For simplicity,we have assumed that the band-gap change is mainly due to the conduction band (affinity)variation.
A.Morales-Acevedo /Solar Energy 83(2009)1466–14711467
recombination(at the ohmic contact)and the bulk recom-bination,typically characterized by the diffusion length.In the case of a graded band-gap material it is more appropri-ate to define a drift-diffusion length.If the electron drift and diffusion current components are in the same direction, the drift-diffusion length will be(Hovel et al.,1975):
L n¼
l n
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þn e l n
2V T
2
r
Àn e l n
2V T
ð5Þ
l n is the electron diffusion length,V T is the thermal poten-tial(kT/q)and n e is the quasi-electricfield in the respective region.
As an example,let us consider a2l m linearly graded layer,which is a typical thickness in current thinfilm solar cells,with an electron diffusion length of the order of1l m, and in which the total band-gap(conduction band)change is D E g=0.5eV.In this case,the quasi-electricfield will be around2.5Â103V/cm and the drift-diffusion length will become about10times the diffusion length,i.e.around 10l m.Of course,this higher drift-diffusion length will increase the probability of electron collection at the het-ero-junction,if the quasi-electricfield is such that carriers are drifted towards it.Another effect due to this quasi-elec-tricfield would be the reduction of the carrier recombina-tion at the back contact.If the surface recombination velocity there was1Â105cm/s,and the electron mobility was only50cm2/Vs,the above quasi-electricfield (2.5Â103V/cm)should be enough to compensate for the recombination at the back rger recombination velocities would require larger back surfacefields.
In summary,the quasi-electricfield associated to a vary-ing band-gap material in a solar cell structure should cause both reduced bulk and surface recombination,if thefield is in the appropriate direction.In the case of a p-type mate-rial,the needed quasi-electricfield should be directed towards the back contact so that electrons are drifted in the opposite direction.In other words,in this case,the band-gap must increase towards the back contact.
2.3.Effect of the band-gap variation upon the dark current in
a solar cell
Current transport in hetero-junction solar cells under dark conditions occurs as a consequence of different mech-anisms.Ideally,the dominant current transport mechanism is carrier injection at the junction and diffusion due to the carrier gradient caused by recombination at the bulk and surface of the respective material at each side of the junc-tion.However,in real non-ideal junctions other mechanism are present,such as recombination caused by traps at the junction interface enhanced by tunneling,or due to Shock-ley–Read–Hall recombination at deep levels within the space charge region of the junction.In the case of thinfilm solar cells it has been observed that the latter mechanism is typically the dominant one,limiting the open-circuit volt-age.Therefore,our discussion below will be based on this observation,but the concept can also be applied for a het-ero-junction solar cell closer to the ideal case,where the dominant current mechanism is due to diffusion in the base of the solar cell.
Let us remember that for a(hetero)junction,dominated by deep level recombination at the space charge region (within the base),the dark current density(for V>2V T) can be approximated by
JffiJ0exp
V
2V T
ð6Þ
where V is the external potential.In this case,the dark sat-uration current is
J0%qn i V Rð7Þn i is the intrinsic carrier density and V R is an effective recombination velocity which depends upon the space charge width and the effective carrier recombination life-time(related to the trap density and the capture cross sec-tions for carriers)within the space charge region at the base of the solar cell.The important issue here is the dependence of J0on the intrinsic carrier concentration n i.This depen-dence is mainly due to the fact that the more effective cen-ters for recombination are those closer to the mid-gap of the semiconductor.
From Eq.(7),the reduction of the dark saturation cur-rent density,when a variable gap material is inserted within the space charge region,can be estimated.For doing this, let us consider an average of the intrinsic carrier concentra-tion which will vary along this region since the band-gap will not be constant.Therefore,in this case,it can be shown that the expected dark saturation current density can be estimated by
J0ffiJ0min
2V T
D V g
1ÀexpÀ
D V g
2V T
ð8Þ
with D V g=D E g/q,the total band potential change,and J0min being the dark saturation current density for a mate-rial with the minimum band-gap E g min.As an example,let us consider again a graded band-gap material in which D V g=0.5V.In this case,at room temperature,the dark saturation current density would be reduced by an order of magnitude(factor of10)approximately.
Then,if a variable band-gap material is produced close to the hetero-junction in such a way that the gap is changed from E g max to E g min within the space charge region,the open-circuit voltage might increase about115mV,when the total D E g=E g maxÀE g min=0.5eV,neglecting the short circuit current loss due to the larger average band-gap within this very thin region.
In order to have the improvement discussed above, without causing photo-current losses,two conditions are required.Thefirst one is that the quasi-electricfield pro-duced by the band-gap variation in the space charge region must be smaller than the electricfield caused by the ionized acceptors there,otherwise there would be no collection of
1468 A.Morales-Acevedo/Solar Energy83(2009)1466–1471
photo-generated carriers at the junction since these two fields would be in opposite directions for a material with decreasing band-gap from the junction interface towards the quasi-neutral region.The space charge width for this kind of cell could be of the order of 0.2l m.Therefore,it is advisable to have D E g to be at most 1eV in this region.The quasi-electric field caused by this band-gap variation would be around 5Â104V/cm directed towards the junc-tion interface.We must remember,on the other hand,that electric fields due to ionized acceptors within the space charge region are typically around 2–5Â105V/cm in con-ventional semiconductor hetero-junctions (directed from the junction interface to the bulk of the semiconductor).In addition,a second condition is that the region for the band-gap variation should not extend beyond the space charge region since this quasi-electric field would oppose the motion of the photo-generated carriers from the bulk of the semiconductor towards the collecting junction.3.Proposed profiles for improved solar cells with graded band-gap layers
The basic structure for a thin film solar cell is depicted in Fig.2.The absorber layer has the usual band-gap profile described in Fig.3(a).In other words,the band-gap is uni-form along the whole thickness of this layer.
Two possible device structures can be proposed in order to have improved solar cells.The absorber layer band-gap profiles are shown in Fig.3(b)and (c).In the first one,a decreasing band-gap region within the space charge is inserted in such a way that the open-circuit voltage can be increased,as explained above.Then,a second layer is graded with an increasing band-gap towards the contact,so that the electron collection at the junction is improved due to the reduced bulk and surface recombination,as explained in Section 2.Notice,that the band-gap grading will cause slight reduced photon absorption,as calculated by the author in a preceding paper (Morales-Acevedo,
2009).Therefore,D E g for this region should be optimized for a given absorber film thickness and diffusion length so that there is a real increase of the photo-current with respect to the one obtained with the non-graded material.This kind of absorber profile has already been studied experimentally for CIGS solar cells (Dullweber et al.,2001)and some of the effects described above have been observed,but the band-gap grading in each region have not been optimized.
Another band-gap profile for the absorber layer in a solar cell structure is proposed in Fig.3(c).In this struc-ture,in the region close to the junction,the band-gap E g will have a total reduction D E g within the space charge region,causing the increase on the open-circuit voltage.Then,a second layer will have a constant band-gap which will be the optimum for single gap solar cells.For example,1.15eV for CIGS or 1.5eV for CdTe solar cells.Then,close to the contact,a third region with increasing band-gap in a small distance will cause a quasi-electric back sur-face field that will reduce the surface recombination at the contact.In this case,notice that even for small D E g of the order of 0.2eV,back surface recombination velocities as high as 1Â106cm/s can be compensated by the back sur-face quasi-electric field,if the above grading occurs in only 0.1l m and the electron mobility was around 50cm 2
/Vs.
Fig.2.Schematics of a typical thin film solar cell structure.Thickness of the layers may vary according to the technology used for deposition.The proposal here is to modify the active layer to have non-constant band-gap profile instead of the usual single band-gap semiconductor commonly
used.
Fig.3.Different absorber layer band-gap profiles in a thin film solar cell.(a)Uniform band-gap.(b)One of the two possible non-uniform profiles that will allow better performance than for the case shown in (a)due to the quasi-electric field in the material bulk.The maximum band-gap at the back contact will have to be optimized in order to obtain a maximum short circuit current density.(c)Another structure that will allow better performance than in case (a).The band-gap variation at the junction interface will cause an increased open-circuit voltage,and the band-gap variation at the back interface will cause reduced bulk and back minority carrier recombination.In all cases,we assume that the junction interface is at the left side and the back contact interface is at the right side.
A.Morales-Acevedo /Solar Energy 83(2009)1466–14711469
Numerical work will have to be done in order to opti-mize both of the structures shown in Fig.3(b)and(c) and determine which one of them can attain the highest efficiency for a particular material.However,using the above analysis,it can be expected that any of these struc-tures will have an improved efficiency with respect to solar cells without any intentional band-gap grading.
4.Possible application of the developed concepts to thinfilm solar cells of current interest
The concepts discussed before explain some of the observed results for amorphous silicon alloys and for CIGS solar cells.For example,a-SiGe:H and a-SiC:H have been used(Nakata et al.,1993)to control the band-gap with a profile similar to the one proposed in Fig.3(b),but in this case there was a variation of both the hole and the electron bands.For a-SiGe:H pin solar cells,the position of the minimum band-gap was changed within the intrinsic a-SiGe alloy(total thickness of250nm)to be at40,125 and210nm from the p-type front semiconductor.The best results were obtained for a position of the minimum band-gap closer to the p-type material.This result can be explained in part due to the larger drift-diffusion length for holes and to the photon absorption distribution within the intrinsic layer as compared to the other two cases.
For CIGS solar cells the experiments made by Dullweber et al.(2001)show agreement with the concepts presented above.Again,a band-gap profile similar to that of Fig.3(b)was used for the CuInGaSe2layer by varying the Ga content.Their results showed that higher efficiency solar cells could be achieved as D E g was higher for the front band-gap grading.Their cells gave the best open-circuit voltage for D E g=0.135V in the space charge region as compared with cells with smaller D E g.Our previous discussion indicates that even higher D E g values could have been attempted for increasing the open-circuit voltage still more.On the other hand,the short circuit current density was almost the same for all the cells since the minimum band-gap E g min was about the same in all cases and the back gradings(towards the back contact)had also similar slopes.Our prediction is that for this kind of CIGS solar cells,the band-gap profile shown in Fig.3(c)with an optimum minimum band-gap(1.15–
1.2eV)would have been better,or either using an optimized
E g max for the back grading in order to avoid the absorption losses due to the higher average band-gap at this region, which extended for a large distance(about2l m)within the absorber layer(total thickness of2.5l m).In other words,their results could have been improved if E g max at the back had been optimized.
The above results encourage us to suggest a new kind of CdTe solar cell.CdS/CdTe solar cells have not advanced much regarding their record efficiency for more that15years. In a previous paper(Morales-Acevedo,2006),the author has shown that with the current technology it is very likely that the record efficiency for this kind of solar cells will not increase above17–18%.Therefore,a new device structure is needed in order to have better CdTe solar cells.Our pro-posal based on the above concepts is to use the band-gap pro-file shown in Fig.3(c),where the central constant band-gap material would be CdTe and the graded layers at the junction and the back contact would be made with CdZnTe by vary-ing the Zn content.In this way the band-gap can be changed from2.25eV for ZnTe down to1.5eV for CdTe at the junc-tion interface,and from1.5to2.25eV for the graded layer at the back contact.If the dark current were dominated by recombination at the space charge region,according to the previous calculations,the open-circuit voltage could increase by about138mV,which would represent an increase of the present record open-circuit voltage (845mV)by about14.3%.In other words,the record effi-ciency might increase up to18.8%,assuming that the other parameters of the solar cell(Jsc and FF)remain constant. CdZnTe layers can be made with variable Zn content by a special CCS technology recently developed by researchers at Texas University at El Paso(Zubia and McClure,Private communication)and soon this kind of solar cell structures will be prepared.
5.Conclusions
In this paper,some basic concepts related to the applica-tion of variable band-gap absorbing semiconductors in solar cells have been discussed.For example,the effects due to the associated quasi-electricfield on the drift-diffu-sion length and the back surface recombination velocity will cause a larger carrier collection with a likely increase of the illumination current density.It was also shown that for an additional improvement of the open-circuit voltage, a band-gap reduction is needed within the space charge region so that the dark saturation current density reduces. Assuming that deep level recombination dominates the dark current,our estimation is that in the case of a solar cell where the band-gap reduces0.5eV,at the space charge region(of the order of0.2l m),an increase of the open-cir-cuit voltage by around115mV will be observed with respect to the single(minimum)band-gap absorbing mate-rial case.Two possible absorber band-gap profiles have been proposed in order to have higher efficiencies than for cells without any band-gap grading.Better efficiencies have already been observed for a-SiGe solar cells and for CuInGaSe2solar cells when using one of the band-gap pro-files proposed here confirming the validity of the concepts, so that we can think of applying them for other solar cells.
A new structure based on CdZnTe has been proposed in order to have better efficiencies than present CdS/CdTe solar cells.Record efficiencies close to19%are predicted in this case.
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