Semina Pinmattroi

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9.5/the effect of grain boundaries in polycrystalline solar cells because of the large densities of defects and segregated impurities at grain boundaries, and because of the local minority carrier collecting fields, the boundaries are regions of strong recombination. the reduction of the photovoltaic parameter,j,v, and ff by this recombination is strongly dependent on the grain size in the px layers. the importance of these effects is highlighted by the beam- induced current image of fig.9.37 , which show grain boundaries that are electrically active as dark contrast ảnh hưởng của ranh giới pin năng lượng mặt trời đa tinh thể. vì Mật độ lớn của khuyết tật và tách biệt tại ranh giới hạt tạp chất, và Do hạt tải thiểu số địa phương thu thập các trường, ranh giới là khu vực tái tổ hợp mạnh mẽ. giảm các thông số quang điện, j, v, và ff bằng tái tổ hợp này là 'phụ thuộc rất nhiều vào kích thước hạt trong lớp px. các, tầm quan trọng của hiệu ứng tổng hợp được đánh dấu bởi hình ảnh hiện tại chùm gây ra của fig.9.37, nào cho thấy ranh giới đã được kích hoạt bằng điện như tương phản tối to gain an overall perspective, we consider a simple p/n junction in a px material with columnar grains oriented normal to the junction plane as shown in figs 9.38 and 9.39. for the moment we assume zero bias voltage. under illumination the photogenerated carrier density np is highest along the central axis of each columnar grain and decreases toward the grain boundry where the carriers recombine more rapidly. in the direction perpendicular to the junction plane there are the usual carrier density variations produced by the boundary conditions and the spatial variation of photogeneration fig.9.38b. thus the calculation of minority carrier density within the grains requires the solution of a three-dimensional transport equation để đạt được một cái nhìn tổng thể, chúng tôi xem xét một nối p / n đơn giản trong một vật liệu px với hạt hình trụ theo định hướng bình thường với mặt phẳng nối như trong sung 9.38 và 9.39. cho thời điểm này chúng tôi giả định điện áp bằng không thiên vị. dưới ánh sáng các photogenerated mật độ hat tai np là cao nhất dọc theo trục trung tâm

Transcript of Semina Pinmattroi

Page 1: Semina Pinmattroi

9.5/the effect of grain boundaries in polycrystalline solar cells

because of the large densities of defects and segregated impurities at grain boundaries, and because of the local minority carrier collecting fields, the boundaries are regions of strong recombination. the reduction of the photovoltaic parameter,j,v, and ff by this recombination is strongly dependent on the grain size in the px layers. the importance of these effects is highlighted by the beam-induced current image of fig.9.37 , which show grain boundaries that are electrically active as dark contrast

ảnh hưởng của ranh giới pin năng lượng mặt trời đa tinh thể.

vì Mật độ lớn của khuyết tật và tách biệt tại ranh giới hạt tạp chất, và Do hạt tải thiểu số địa phương thu thập các trường, ranh giới là khu vực tái tổ hợp mạnh mẽ. giảm các thông số quang điện, j, v, và ff bằng tái tổ hợp này là 'phụ thuộc rất nhiều vào kích thước hạt trong lớp px. các, tầm quan trọng của hiệu ứng tổng hợp được đánh dấu bởi hình ảnh hiện tại chùm gây ra của fig.9.37, nào cho thấy ranh giới đã được kích hoạt bằng điện như tương phản tối

to gain an overall perspective, we consider a simple p/n junction in a px material with columnar grains oriented normal to the junction plane as shown in figs 9.38 and 9.39. for the moment we assume zero bias voltage. under illumination the photogenerated carrier density np is highest along the central axis of each columnar grain and decreases toward the grain boundry where the carriers recombine more rapidly. in the direction perpendicular to the junction plane there are the usual carrier density variations produced by the boundary conditions and the spatial variation of photogeneration fig.9.38b. thus the calculation of minority carrier density within the grains requires the solution of a three-dimensional transport equation

để đạt được một cái nhìn tổng thể, chúng tôi xem xét một nối p / n đơn giản trong một vật liệu px với hạt hình trụ theo định hướng bình thường với mặt phẳng nối như trong sung 9.38 và 9.39. cho thời điểm này chúng tôi giả định điện áp bằng không thiên vị. dưới ánh sáng các photogenerated mật độ hat tai np là cao nhất dọc theo trục trung tâm của mỗi hạt hình trụ và giảm đối với các ranh giới hạt nơi hat tai kết hợp lại nhanh hơn. theo hướng vuông góc với mặt phẳng nối có các biến thể mật độ hat tai thông thường được sản xuất bởi các điều kiện biên và sự thay đổi không gian của photogeneration fig.9.38b. do đó việc tính toán mật độ hat tai dân tộc thiểu số trong hạt đòi hỏi các giải pháp của một phương trình vận chuyển ba chiều

what is the boundary condition at the grain boundary? since the potential barrier height (phi), the effective recombination velocity (S), and the excess carrier density np(x,y) are interdependent, the loss there cannot ve expressed by a simple constant lifetime formalism. (chu thap) instead we have

điều kiện biên tại ranh giới hạt là gì? từ chiều cao thế năng rào cản (phi), vận tốc tái tổ hợp có hiệu quả (S), và np mật độ hat tai vượt quá (x, y) là phụ thuộc lẫn nhau, sự mất mát đó không thể đã thể hiện bằng thời gian sống(chu kỳ bán rã) hình thức liên tục đơn giản. (chu thap) thay vì chúng ta có

@@công thức

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where the symbols have their usual meanings and (Tg) is the lifetime of the grain's interior material. the region of recombinative influence of the grain boundary is roughly equal to the larger of either the grain interior

(chu thap) the spatial coordinates used here are x = ( distance away from the junction) and y=(distance away from the grain boundary).

nơi ký hiệu có ý nghĩa thông thường của họ và (Tg) là tuổi thọ của bên trong vật liệu của hạt. khu vực ảnh hưởng tái tổ hợp ranh giới hạt là gần bằng lớn hơn của một trong hai bên trong hạt

(chu thap) tọa độ không gian sử dụng ở đây là x = (khoảng cách đi lớp chuyển tiếp) và y = (xa ra khỏi ranh giới hạt).

scanning EBJC response of an area of an ito/si solar cell fabricated with Monsato zone- refined px si. the surface shown is almost featureless under an optical microscope. subsequent etching revealed etch pits corresponding to the small dark spots in area B. the dark spots are cause by active dislocations in the intergrain regions. the portion of the sample imaged is about 1.1mm in its longest dimension.

phản ứng quét EBJC của một khu vực của một pin ito / si năng lượng mặt trời được chế tạo với Monsato khu tinh chế px si. bề mặt hiển thị là gần như không đ c bi t dưới kính hiển vi quang học. khắc tiếp theoă ê tiết lộ hố khắc bằng axit tương ứng với các đốm đen n

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hỏ trong khu vực B. đốm đen là nguyên nhân của những biến động trong khu vực intergrain. phần của mẫu chụp ảnh là khoảng 1.1mm trong chiều dài của nó.

diffusion length Lg or the grain boundary depletion layer width Wdgb. thus the problem has not only three spatial dimensions but a position dependent, nonlinear boundary condition (Lindholm and Fossum 1981). given the recombination parameters, the solution could presimably be obtained by a machine calculation. because of the three-dimensional nature of the problem, it is, strictly speaking, not possible to assign a unique theoretical average lifetime or diffusion length to the x aggregate, since it is crucial how and where that average is taken. we examine that consideration further in the next section.

chiều dài khuếch tán LG hoặc lớp suy giảm ranh giới hạt rộng Wdgb. do đó vấn đề không chỉ có ba chiều không gian nhưng một vị trí phụ thuộc, điều kiện biên phi tuyến (Lindholm và Fossum 1981). được các thông số tái tổ hợp, các giải pháp có thể presimably thu được bằng cách tính toán máy. vì bản chất ba chiều của vấn đề, đó là, nói đúng, không thể chỉ định chu kỳ bán rã trung bình lý thuyết duy nhất hoặc chiều dài khuếch tán đến x tổng hợp, vì nó là rất quan trọng như thế nào và nơi trung bình được thực hiện. chúng tôi kiểm tra xem xét hơn nữa trong phần tiếp theo.

the situation is even more complex at forward bias. for the sake of argument, assume that Sgb is very large and consider the value of np(x,0) along the grain boundary, represented by line y=y0 in fig 9.38c. the large value of Sgb implies that np(x,0) approaches np0 along the grain boundary, but this conflicts with the commonly assmued boudary condition at the junction depletion layer edge Xp, namely that np(Xp,y)=np0exp(qV/kT). forward-bias-injected carriers are funneled into the grain boundary regions by the depletion layers intersecting at the grain boundary and at the junction. the carrier density in these regions, denoted by the shaded area in fig.9.38c. is difficult to model satisfactorily. thus both lateral carrier transport within the grain and transport along the grain boundary deplention layer by diffusion( and possibly conduction) must be considered for a complete solution. shockley (1949 sections 4.6 4.7 and appendix 5 therein), apparently discussed this problem first, but did not offer a complete solution.

tình hình thậm chí còn phức tạp hơn ở chuyển tiếp xu hướng. vì lợi ích của chứng minh, cho rằng SGB là rất lớn và xem xét giá trị của np (x, 0) dọc theo ranh giới hạt, đại diện bởi dòng y = y0 trong hình 9.38c. giá trị lớn SGB ngụ ý rằng np (x, 0) phương pháp tiếp cận np0 dọc theo ranh giới hạt, nhưng xung đột với các điều kiện biên thường giả định ở rìa lớp suy giảm ngã ba Xp, cụ thể là np đó (Xp, y) = np0exp (QV / KT). hạt tải chuyển tiếp thiên vị tiêm được đổ vào các khu vực ranh giới hạt của các lớp suy giảm giao nhau tại ranh giới hạt và ở ngã ba. mật độ vận chuyển trong các khu vực này, biểu hiện bằng các khu vực bóng mờ trong fig.9.38c. rất khó để mô hình một cách thỏa đáng. do đó cả hai hạt tải vận chuyển bên trong hạt(lớp) và vận chuyển dọc theo ranh giới hạt deplention lớp bằng cách khuếch tán (và có thể dẫn) phải được xem xét một giải pháp hoàn chỉnh. Shockley (1949 phần 4.6 4.7 và phụ lục 5 trong đó), dường như đã thảo luận vấn đề này đầu tiên, nhưng không đưa ra một giải pháp hoàn chỉnh.

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fig.9.38 intersection of a grain boundary with a p/n homojunction

(a)/ plan view: junction is at x=0, with junction depletion layer edges at xp and xn.

b/ carrier density np(x,y) under illumination for zero applied bias. values of np(x,y) are shown on two lines within the grain, y1 and y2, and on the grain boudary,y0, assuming Sgb->vô cực.

c/ carrier density np(x,y) under illumination with forward bias injection, shaded portion represents uncertainly in the description of np(x,y) near Xp.

d/ sections of the band diagram parallel to the junction plane at x1 and x2 under illumination, now assuming that Sgb < Vth/4.

giao fig.9.38 của ranh giới thớ với ap / n homojunction

(a) / xem mặt phẳng: đường giao nhau là tại x = 0, với ngã ba suy giảm cạnh lớp tại xp và xn.

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b / hạt tải mật độ np (x, y) dưới ánh sáng cho không áp dụng sai lệch. giá trị của np (x, y) được hiển thị trên hai dòng trong grain, y1 và y2, và trên boudary hạt(lớp), y0, giả sử SGB-> Vô Cực.

c / hạt tải mật độ np (x, y) dưới ánh sáng với hệ thống phun xu hướng về phía trước, phần tô đậm biểu không chắc chắn trong các mô tả của np (x, y) gần Xp.

d / phần của ban nhạc sơ đồ song song với mặt phẳng giao nhau tại x1 và x2 dưới chiếu sáng, bây giờ giả định rằng SGB <Theo TTXVN / 4.

Fig9.39 band diagram with two spatial dimensions a heterojunction solar cell with a grain boundary traversing the junction depletion layer. the grain boundary region is depleted in both n- and p-type components

several workers have simplifies the problem by finding an average lifetime T or diffusion length L characteristic of the PX aggregate, but this concept must be used with caution. considering fig.9.2 for a moment, it can be seen, at least qualitatively, that the probability of recombination is larger for photogeneration that the probability of the absorber and/or close to the grain boundaries. also because the grain boundary recombination rate depends on np in a nonlinear way, the value of L depends on the injection level as determined by forward bias and the intensity of the illumination at each point in the absorber. thus L(CONG THUC) an the carrier loss form an elemental volume dx dy dz depends on the excitation level as well as its position within the grain

một số nhân viên đã đơn giản hóa vấn đề bằng cách tìm một thời gian bán rã trung bình T hoặc khuếch tán chiều dài L đặc trưng của tổng PX, nhưng khái niệm này phải được sử dụng cẩn thận. xem xét fig.9.2 cho một thời điểm, nó có thể được nhìn thấy, ít nhất là về chất lượng, mà xác suất của sự tái tổ hợp là lớn hơn cho photogeneration rằng xác suất của sự hấp thụ và / hoặc gần biên giới hạt. cũng bởi vì tỷ lệ tái tổ hợp ranh giới hạt phụ thuộc vào np một cách phi tuyến, giá trị của L phụ thuộc vào mức độ tiêm được xác định bởi thiên vị về phía trước và cường độ của ánh sáng tại mỗi điểm trong hấp thụ. do đó L (CONG THUC) một sự mất mát hạt tải tạo thành một khối lượng nguyên tố dx dy dz phụ thuộc vào mức độ kích thích cũng như vị trí của nó trong ngũ cốc

we begin the first part of this section by focusing on studies of recombination at boundaries in single crystals and bicrystals. int he next part theories relating the photovoltaic parameters to grain size in

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px materials are explored. the following part examines some of the more esoteric considerations such as the possible effect of reduction of the band gap at the disordered grain boundary. finally we cite some attempts at passivation of grain boundary recombination.

chúng ta bắt đầu phần đầu tiên của phần này tập trung vào các nghiên cứu về sự tái tổ hợp ở ranh giới trong các đơn tinh thể và lưỡng tinh thể. int ông tiếp theo lý thuyết một phần liên quan các thông số quang điện kích thước hạt trong vật liệu px được khám phá. phần sau đây xem xét một số trong những cân nhắc sâu xa hơn như hiệu quả có thể giảm khoảng cách ban nhạc tại ranh giới hạt rối loạn. cuối cùng chúng tôi trích dẫn một số nỗ lực thụ động của ranh giới hạt tái tổ hợp.

9.5.1 recombination at grain boundaries-bicrystal and large-grain polycrystal investigations

9.5.1 tái tổ hợp ở hạt ranh giới-lưỡng tinh thể và điều tra đa tinh thể lớn ngũ cốc

under illumination photogenerated excess minority carriers are draw to the grain boundaries by the depletion layer fields surrounding them. since the supply of majority carries at the maxima of the grain boundary potential barriers is intially small, minority carriers are trapped at the grain boundary states, reducing the charge there and lowering the potential barriers. stead state is reached when the majority carrier density at the grain boundary barrier maximun is high enough so that Np there (for a p-type material, where Sn and Sg are the grain boundary recombination velocities for electrons and holes, respectively). the number of charged grain boundary interface states Ng and hence phi** is changed radically by illumination of solar intensity

dưới ánh sáng photogenerated hạt tải vượt quá thiểu số được rút ra để các ranh giới hạt của các trường lớp cạn kiệt xung quanh chúng. từ việc cung cấp phần lớn mang ở cực đại của ranh giới hạt rào cản tiềm năng là intially nhỏ, các tàu sân bay thiểu số đang bị mắc kẹt tại các tiểu bang biên giới hạt, giảm phí đó và hạ thấp các rào cản tiềm năng. nhà nước thay vì đạt được khi mật độ tàu sân bay lớn ở hàng rào ranh giới hạt maximun là đủ cao để có Np (đối với vật liệu loại p, nơi Sn và Vn là vận tốc tái tổ hợp ranh giới hạt cho electron và lỗ trống, tương ứng). số lượng tính phí giao diện ranh giới hạt nói Ng và do đó phi ** được thay đổi hoàn toàn bởi ánh sáng cường độ năng lượng mặt trời

this section begins with a treatment of recombination at the boundaries of filamentary grains in which recombination is quantified as a grain boundary recombination velocity Sg wich does not vary with carrier density. this is followed by a description of experimental measurements of Sg in bicrytals and large-grain polycrystals. the section ends with a description of several theories which relate grain boundary barrier height, recombination rate, and illumination intensity

Phần này bắt đầu với trị liệu tái tổ hợp ở ranh giới của các loại ngũ cốc dạng sợi trong đó tái tổ hợp được xác định như là một ranh giới hạt tốc độ tái tổ hợp Vn Mà không thay đổi với mật độ tàu sân bay. điều này được theo sau là một mô tả của các phép đo thực nghiệm của Vn trong bicrytals và polycrystals lớn ngũ cốc. phần kết thúc với một mô tả của một số giả thuyết đó liên quan hạt ranh giới chiều cao hàng rào, tỷ lệ tái tổ hợp, và cường độ chiếu sang

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recombination at grain boundaries has been under fundamental investigation for many years, without regard to solar cell applications. Shockley developed a theory for the time decay of excess carrier density by recombination in isolated semiconductor filaments with recombination velocity Sg, for the time intervals following uniform excitation. he assumed a rectangular filament with dimensions of Y= and Z= and a length x that was effctively infinite. solution constant is d and T is the grain-interior lifetime . solution of the transport equation in two dimensions yields an eigenfunction series with each succeeding term having a smaller characteristic lifetime. after excittation ceases, the higher-order terms decay rapidly and only the term with the longest life time remains, giving an approximate " filament lifetime" corresponding to the lowest-order eigenvalues n and et.

Phuong trinh

Where n0 tan n0=?? And e0 tan e0=??. If g is effectively infinite, then the filament life time reduces to

Phuong trinh

For small Sg the tangent can be approximated by its argument and

Phuongt

From these equations it can be seen that the smallest dimension of the filament dominates thelifetime. Since the analysis pertains essentially to the later part of a transient reponse after the cessation of uniform excitation, it may not always be appropriate to deduce a value of T or L for steady state, nonuniform excitation from it.

Shockley also applied these ideas to flow across a biased p/n junction into such a filament (injection in the x direction into one end of the filament) and found that the use of T from eq.9.24 in the standard diode equation eq.5.13 is a reasonable approximation, providing that Sg is small enough so that tan N0 and N0 . for PX solar cell systems this condition is generally not satisfied. For larger Sg values a complex series solution is required since the terms do not converge rapidly. The depletion layer surrounding the grain boundary was not considered in either of these situations.

Other investigators concentrated on finding the experimental electronic properties of grain boundaries in bicrystals. Vogel et al. set up a grain boundary model that regarded the closely spaced dislocation cores at low-angle grain boundaries as a sheet of recombination centers characterzed by a recombination velocity Sgb. In their experments with lineage boundaries (i.e., boundaries with such low angle that the dislocations may be on the order of micrometers apert) in n-ge they found Sgb=1200-2600 cm sec-1 by using optical probe( essentially dark conditions).

Sosnowski 1959 reviewed early work on si and ge bicrystals, finding that large-angle grain boundries had considerably larger values of phi** and much greater photoelectronic activity, but, curiously, smaller recombination velocities. He also reported considerably greater conductivity along the grain boundaries in ge and concluded that they were so highly charged as to be degenerate p-type. Mckelvey developed a model for recombination at lineage and twin boundaries in ge to obtain experimental values of Sgb, but neglected any effects of the potential barrier fielfs. Matare 1971 has made a comprehensive theoretical

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study of all types of grain boundaries, from both a structuaral and electronic point of view. His experimental evidence, particularly with regard to electronic properties, is largely confined to ge.

Daud et al 1978 studied grain boundary recombination in p/n junctions made on p-si bicrystals, using EBIC techniques beveled geometry. They measured an effective diffusion length L=2mm at the grain boundary that increased almost linearly with distance away from the grain boundary until it staturated at the single-crystal value L=12. The region of deraded L extendedapproximately Lg on either side of the grain boundary, a distance much greater than the grain boundary depetion layer with(W<1mm in this case).

Several workers have studied the recombination at grain boundaries in large-grain polycrystalline material by scanning light spot or electron beam method. For example. Ermtrong et al.1980 related the crystallographic orientation pf the grain boundaries with their recombination behavior for Si.

The work discussed thus far in this section is confined essentially to the dark case (sometimes with small-area probe illumination) and the recombination properties are usually quantified by a constant value of Sg which does not depend on carrier density. The illuminated case has been studied by Card and Yang(1977), who considered the effect of illumination on the grain boundary potential barrier and the recombination there using the shochley-read-hall model. For an n-type material under illumination, photogenerated holes neutralize the negatively charged grain boundary states to reduce the barrierheight untul the recombination currents fo electrons and holes are equal. Card and yang assumed that Ef and Efp were constant across the grain boundary depeletion layer. Then, assuming equal recombination cross sections for electrons and holes,congthuc, astable condition is reached when the nonequilibrium carrier densities np(x,0) and pp(x,0) at the grain boundary are equal. This maximizes the recombination rate. Only the states between Ef and Efp. Contribute significantly to the recombination crrent, which is given by.

Cong thuc

Where Vth is the thermal velocity and congthuc is the interface state density distribution. The resulting relation between the illuminated grain boundary barrier diffusion voltage Vdg,Np, and dNgb/dE under AM1 illumination is shown in Fig9.27. the density of holes at the grain boundary is enhanced by the presence of the remaining grai boundary barrier so that the recombination velocity at the grain boundary depletion layer edge Sg *Wdg) is given by.

Cong thuc

The resulting grain boundary recombination rate

Congthuc

Is not linear in congthuc. The congthuc term is a minor source of nonlinearity in the range of interest. However, the exponential dependence on illuminated barrier height can result in a much greater nonlinearity since Vdg also depends on Efn and Efp. Thus the regions of the cell that are highly excited [congthuc, small Vdgb] have propertionatedly weaker recombination than do portions where low

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excitation [small congthuc, large Vdg] prevails. chuthap because of the relation of the Vdg to doping density Nd (fig.9.22 9.27a) there is also a fairly strong dependence of Sgb on Nd for larger values of dNgb/dE.

Card and Yang calculated an average lifetime T for square columnar grain ( y by y), assuming uniform photoexcitation throughout the area and length of the grain. To do this they treated the grain boundary recombination centers as if they were spread uniformly throughout the volume of PX material, eith their effectiveness enhanced proportionately by the grain boundary depletion layer fild. This gives.

Congthuc

And the relation of T to y, congthuc, and Nd is shown in fig.9.40 for an n-type material.

The analysis by fossum and lindholm(1980a) adds considerable depth to the theoretical treatment of px solar cells. Several important observations were made concerning the dependence of Sgb on illumination. For the case of lower values of Sgb, when Efn and Efp are constant across the grain boundary depletion layer, they found that the recombination rate there could be written

Congthuc

Where congthuc, and phin,phip are the recombination criss sections for electrons and holes at empty recombination sites. This result is true only when sufficient excitation exists such that (Efn-Efp)>4kt so that certain approximations in the Shockley-read-hall model can be made. The result is similar to that of card and yang (eq.9.25) except that it is written in terms of Efn and Efp rather than Vdgb.2chuthap

Chuthap for example, using the parameters assumed by card and yang shows that for congthuc,congthuc, swereas for congthuc,congthuc.

2chuthap for sufficient illumination the results are the same since congthuc.

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Fig.9.40. a/ calculated dependence of average minority carrier lifetime T inpx si on grain size (called d here) and grain boundary stae density N(equals dNgb/dE) for Nd=10^16cm. rapid initial decrease of T is due to increase in Vd (illuminated) with Nis.b/ dependence of average minority carrier lifetome on Np and grain size, for Nis=10^12cmev.

Equation 9.29 makes the striking assertion that the value of the potential varrier height phi** at the grain boundary has little or no effect on the recombination there, provided sufficient illumination exists.

For low-level injection in a p-type absorber,congthuc in the grain’s interior so that congthuc there and an effective Sgb can be written

Congthuc

Where congthuc is the carrier density at the grain boundary depletion layer edge under illumination. Note that this treatment, like that of card and yang, predicts that congthuc decreases with increasing excitation level and increases with increasing soping level.

With regard to solution of the transport equation. Eq.9.30 is a nonlinear boundary condition, dependent on injection level. However. For high injection levels congthuc. Also when congthuc is so high that congthuc in the grain boundary depletion layer, the barrier height becomes fixed at its dark value and congthuc. For these two cases the boundary condition is linear. The expressions of Eqs.9.26 and 9.30 do much to lessen the uncertainly of description transport at the intersection of the grain boundary and the junction depletion layer edge(f.g9.38c). provided that conduction along the grain boundary core can be neglected.

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Seager 1981 proposed a theory for recombination at single grain boundaries in n-si (e.g, bicrystals) for a wide range of illumination intensities. Using detailed balance arguments similar to those of hall 1952 and of Shockley and read in their treatment of surface recombination, seager coupled these results with his earlier model for the conductivity and capacitance of grain boundaries in si to formulate his model seager assumed that:

1/ the carrier densities and currents are controlled by thermal emission over the grain boundary barriers( section 9.4.2 and 9.4.3)

2/the same states that are involved in recombination are also involved in the trapping of charge that controls Vdgb.

3/ all the grain-boundary states are at a single energy level;

4/ uniform excitation and low injection conditions prevail congthuc, and

5/the capture and emission processes are unaffected by illumination.

One of the main differences between seager’s theory and those mentioned previously is that the quasi-fermi levels are permitted to vary with distance across the grain-boundary depletion layer. With some only moderately restrictive assumptions, seager was able to for mulate a relation between the illuminated barrier height Vdbg, the illumination intensity R. the donor density Np, the recombination cross section for holes Phi**, and the dark barrier height Vdgbd. Although the resulting transcendental equations had to be solved numerically, several conclusions were drawn.

1/ whereas large grain-boundary barriers are sensitive to even very low illumination levels, barriers with small Vdgbd remain essentially unchanged.

2/ for large Vdgbd( e.g, 0,4ev), illumination produces a substrantial readjustment of barrier height that is, to first order, independent of the recombination cross section for holes phi**, for phi**<10^-18cm2.

3/for smaller values of Vdgbd( 0.25ev), the effective grainboundary recombination velocity is given by.

Congthuc

Thus implying that congthuc decreases rapidly as Vdgb becomes smaller. For example, seager assumed the values congthuc,congthuc, and R=0,3 suns and his calculations showed that conthuc for congthuc, whereas congthuc for congthuc.

4/ the value of congthuc is insensitive to illumination level for small Vdgb(0,25ev). However for larger Vdgb(0.25ev) the value of congthuc begins to decrease when the illumination level increases above =0,3sun.

5/ for small Vdgb and/or high illumination level (>3suns) the hole quasi-fermi level becomes nearly constant within the depletion layer, as was assumed by card and yang and by fossum and lindholm.

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Seager’s calculation agree well with his measurements on neutrontransmutation doped n-Si over the range of intensities studied (dark to 0,3 suns).

9.5.2 polycrystalline solar cell theories

Because f the complexity of the three-dimensional transport problem in px material, various simplifying assumptions have been made to obtain estimates for the relation of solar efficiency to px grain size and other material parameters. Several of these estimates are compared with experimental values in fig.9.41. all the theories discussed here assume that most of the grain-boundary volume is undepleted (conthuc)

Fig9.41 solar efficiency versus grain size for si solar cells. The curves are theoretical results. The date points are experimental values obtaind by(0) Feldman et al.1978. the theoretical data of card and yang were estimated assuming ff=0,70

Soclof and iles 1975 assumed s->vocuc and that any photogenerated carries entering the grain-boundary depletion layer (of width Wdgb) were lost. Thus they subtracted the depletion layer widths from the grain size to obtain an effective grain size congthuc. An average diffusion length L=?? was then calculated from an equation such as eq.9.24 and used in the conventional expressions (such as eq.4.19) to obtain Jsc. Their values of Voc and ff were estimated from single-crystal cell data and the resulting relation of Ns to y is shown in fig.9.41.

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Fig.9.42 a/ grain model used for the calculations of lanza and hovel. b/ excess carrier density as a function of position in a 10mm thick grain of GaAs. The density goes to zero at the junction depletion layer edge.

Value of Sgb, although Jl was altered somewhat by the change in junction depletion layer width with bias voltage. The values of Voc and ff for these schottky barrier cells were calculated assuming that the junction properties were not affected by the presence of the grain boundaries. One of the si results is shown in fig9.41.chuthap

Koliwad and daud used the empirical spatial variation of Leff described in their earlier paper to integrate the contributions to the photogenerated current over each rectangular grain. The integration war performed over the solar spectrum as well, using euqations such as eqs.4.19 and 4.26. this conceptual model enabled them to estimate the variation of Jsc with grain size. Subsequent measurements of Jsc with grain size. Subsequent measurements of Jsc for PX solar cells fabricated from Si with Y>100mm gave good agreement with the theory. No attempt was made to model the dependence of Voc and ff on Leff. Other than that introduced by changes in Jsc. From their experimental results koliwad and daud found the following percentage increases in the photovoltaic parameter in going from 100 to 1000 mm average grain size:

Congthuc

These relative changes among the photovoltaic parameters are fairly typical for px si cells. Inparticular the relative losses in Jsc and Voc are similar in magnitude. These authors noted that the A=2 portion of the diode current increased strongly as frain size was dezreased, but that this had a negligible effect on Voc under AM1 conditions.

Card and yang1977 added several important refinements to the theory of px solar cells. They allowed Sgb to ve finite and considered the effect of illumination on the grain boundary potential barriers and the recombination there to calculate an average lifetime T for the px Si absorber ( as described in the previous section). Card and yang’s estimates for Jsc and Voc are made by straightforward insertion of

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this T from Eq.9.28 into the standard expression: cpng thuc with G, the generation rate, independent of position, and eqs5.12 and 6.2a. perhaps the most serious shortcoming of the card and yang theory is theassumption of uniform injection throughout the length of the grain. For this reason the theory gives good results for small grains ( where activity is confined to thin layer, ie, small x), but considerably underestimates Ns for larger grain fig.9.41.

Ghosh et al.1980 advanced a model that follows card and yang in averaging the grain boundary recombination centers as though they were spread throughout the volume of the semiconductor. However, these authors do not consider the depletion layers at the grain boundaries or the effect of illumination on recombination there. For cubic grains of dimension Y on a side, they obtain

Congthuc

The corresponding empirical relationship congthuc, where Y is in cm appears to fit a variety of Si experimental data for congthuc. Shosh et al.1980 use this value of T with a semiempirical carrier mobility dependence on Y to obtain the Jl for the quasi-neutral absorber. The standard transport equation solutions (eq.4.22 with infinite backsurface recombination ) are used. The contribution to Jl from the junction depletion layer (congthuc) is given by

Congthuc

Where M=1 for congthuc and congthuc, and where T is the transit time for carries crossing the depletion layer (congthuc). The total Jsc is shown in fig9.43a. to account for differences in Jsc versus Y from the preceding theory and experimental data at small Y, these author assume a substantial shrinkage of the junction depletion layer under illumination congthuc because of trapping in defect states there (fig9.43b). the values of Voc are calculated using the standard diode equations (e.g.eqs 5.12 and 5.27) with the derived values of jsc and Jo. For small grain sizes recombination/generation dominates the J-v characteristics, whereas for larger Y, injection/diffusion controls and the appropriate Jo values are calculated from T. the results are shown in fig 9,44.

In their treatments of the px solar cell fossum and lindholm included the effects of grain boundaries within the junction depketion region. If Efn and Efp are nearly flat across the junction depletion layer, including the part occupied by the grain boundary, then eq.9.30 can be used directly to calculate the recombination current there. The situation involves a three-dimensional flow of carriers within Wd. But because of the high fields and diffusion currents present, the quasi-fermi levels can be considered flat and then congthuc. The recombination rate eq9.29 chuthap must be multiplied by the “exposed” grain boundary area Agb present in the depletion layer, i.e., for square columnar Y by Y grain congthuc. The cuurent density for each grain traversing the depletion layer is given by

Congthuc

Chuthap since we are interested in recombination from only one side of the grain boundary here, Ugb is divide by 2.

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Fig9.43 a/ Jsc versus grain size for varius px Si film thicknesses. b/ effect of barrier shrinkage and mobility assumptions on Jsc. Experimental point symbols are the same as for fig.9.41 except for (??) from the work cited here. All date are normalized to AM1, with some corrections for reflection and grid coverage losses where necessary. A decrease in Wd some corrections for reflection and grid coverage losses where necessary. A decrease in Wd form 0.75 to 0.05 mm inder illumination was assumed for Y<10mm.

Bulk recombination is neglected here. Fossum and lindholm emphasized that the a factor of exactly 2 results from the assumptions of quasiequilibrium and the steady-state conditions for maximum Ugb at the grain boundary. Henry et al 1977,1978 chuthap using different but equivalent reasoning, obtained the exp(qV/2lT). dependencefor surface recombination at the periphery of congthuc heterojunctions (single crystal). Henry et al. used an “interaction length” rather than Wd in evaluating the exposed grain boundary area.

Chuthap the 1978 paper is highly recommended.

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Fig9.44 effect of grain size on Si solar efficiency.(a) for different px Si layer thicknesses. b/ with(I) and without(II) junction varrier shrinkage effect. Point symbols are the same as in fig.9.43

Comparison of the experimental date of Feldman et al.1978 for px p/n si solar cells with eq.9.33 (using a value of congthuc and congthuc) gives excellent agreement with the Jo values of the A=2 branches for the dark J-V curves of cells having 0.2<Y<6mm.

Although these results are presented in terms of average grain size, it is evident that the important parameter is grain-boundary area. Thus in materials with a distribution of grain sizes, the smaller grains, with their greater surface-to-volume ratio, can considerably increase the value indicated by “average” grain size.

Makram-ebeid did a computer calculation for the two-dimentsional transport problem in a px si solar cell composed of planes of material separated by grain boundaries. They used a simplified form of the Shockley-read-hall expression to model the grainboundary recombination velocity. Both n and p-type layers were included with recombination at the front and back surfaces of the cell, in addition to the grain-boundary recombination. Temperature variation was accounted for and the calculation was further embellished by allowing the angle between the grain-boundary planes and the junction plane to vary. The effect of the poisson distribution of distances between the grain boundary planes was also tested. The predicted spectral response congthuc was in good agreement with date for px Si cells. Chuthap in addition, the computer simulation predicted a variation of congthuc with illumination intensity, in excellent qualitative agreement with experiment results that showrd an 18% increase in Nq at 0.875mm when the cell was flooded with approximately 1 sun of AM1 illumination.

Other theoretical treatments of interest follow:

1/ card and hwang 1980 and e.s.yang et al.1981 focused on the recombinative effects of grain boundaries that are parallel to the junction plane, under dark and illuminated conditions . such barriers also impede majority carrier flow.

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2/kazmerski 1978,1980a expanded on the card and yang 1977 theory for direct band-gap materials , in particular CuInSe. Kazmerski 1980b also presented a comprehensive overview of the status of PX solar cell research and development.

3/ green 1978 used a novel three-demensional equivalent circuit approach and focused on the role of grain boundaries in the junction depletion layer.

4/rothwarf 1976 used the assumption that all carriers generated closer to the cylindrical grain boundaries than to the junction are lost(i.e. the recombination cone concept of fig.9.2) to estimatethe Jsc for the congthuc cell. Although admittedly an approximation, thus theory does take account of the nonuniform generation rate congthuc in a real cell, which many of the other theories do not.

The three-dimensional transport problem in ox material is so complex as to practically defy complete solution. Chuthap thus the transport models presented here are necessarily approximations and must be accompanied by some important qualifications

1/ by their nature, averaging methods for T and L omit important aspects of the transport problem.

Chuthap made by the ribbon-ageinst-drop process, in which molten si is coated onto a pyrocarbon coating on a moving carbon ribbon

Chuthap a good overview of the problem is given by lindholm and fossum 1981.

2/ for most of the conditions encountered in solar cells the use of the filament lifetimes of eq.9.23 is quentionable.

3/the treatment of forward-bias injection into the QNRs and, in particular, the consideration of Sgb at the junction depletion layer edge under forward bias have been ignored in many of the midels.

4/ the treatment of the paremeters Voc and ff( includingthe possible bias dependence of photogenerated current collection) has been generally superficial.

The effective grain-boundary recombination velocity congthuc has been considered for extreme cases: for the dark case and for the illuminated case where grain-boundary barriers are considerably reduced. For the illuminated case, congthuc is either taken as infinite or calculated for the situation in which there is sufficient excitation so that the charging effects of the grain boundary states are effectively overwhelmed. A more rigorous treatment of the intermediate cases would be helpful, particularly for diagnostics of px material.

There is reasonably good agreement between theory and experiment for px silicon based cells, particularly with larger grain sizes. However, for cells based on direct band-gap materials, the Voc and ff values are generally considerably smaller than predicted and more precise modeling appears to be necessary.

In spite of such criticisms, these theories have substantially increased our understanding of px solar cells. For example, the dependence congthuc from eq.9.30, suggests that considerable gains in solar

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efficiency might be obtained with solar concentration (using ratios of, say, 3 to 20). The combination of px solar cells and low ratio concentrator systems has been largely ignored up to this time but might prove cost effective. Similarly the dependence congthuc suggests the use of lower doping densities in the absorber layer to improve Jsc, although a compromise with the variation of Voc with Na is required.

9.5.3 other considerations for px solar cells

In this section we consider grain boundary core conduction and the effects of different doping level configurations and depositions sequences in heterojunctions

Grain boundary sheet conduction and dislocation banding fraas 1978,1980 and fraas and zonio 1980 have pointed out that, at least in some materials, the banding of the dense arrays of dislocation and dilatation states at the core of a grain boundary can lead to a significant decrease in the band gap there as well as parallel sheet conduction along the grain boundary. The effects of decreased band gap have been observed in ge and cds by optical absorption and electroluminescence. If such decreased core band gaps are present in solar cell, they should lead to the transport pathways shown in fig.9.45, and the activation energies in the diode Jo term arising from grain boundary recombination should be significantly lowered.

Sheet conduction along grain boundaries has been observed in ge with values of 2000-10000 and in insb. Such a conductive grain boundary can be throught of qualitatively as another junction device in parallel with the junction comprising the bulk (interiors) of the grains, that shares the same (ohmic) contacts. Consider, for example, the case for which the Fermi level within the boundary material os pinned near the conduction band in the n-type side of the junction and near thevalence band in the p-type side (fig.9.45). in this casea potential barrier of nearly Egb still exists along the grain boundary to inhibit conduction. Grain-boundary conduction might be negligible in such a diviece. On the other hand, if the Fermi level were pinned close to the valence band on both sides of the junction (as could be the case for Ge, for which P grain-boundary pinning is observed in both n- and p-type matrices), then no such barrier is at one of the cell contacts, which is more likely to be leaky tha the bulk cell junction. Chuthap thus conduction might

Chuthap the ohmic contac to the n-type side of the bulk junction acts as a tunneling contact to the grain boundary material in this case.

Table 9.III : possible grain boundary doping configurations

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QNR is the grain interior quasi-neutral region; GB is the grain boundary.

Occur along the grain boundary material between ohmic contacts on either side of the divice giving a prohibitively low shunting resistance. Unfortunately, it is difficult to separate shunt resistance Rp from diode factor A=2 effects for forward J-V characteristics, event in single-crystal cells, and grain boundary sheet resistance data for Si and orther solarcell materials are difficult to obtain from existing date. Chuthap effects have also been considered in a more general way by Shockley.

Doping configurations for heterohunction cell. Fraas 1978 also considered the effects of intentionally controlled grain boundary doping ( with respect to grain interior values) as a means of optimizing photovoltaic parameters. Assuming that the alternatives of fig.9.21 are available, there are nine possibilities as shown in table 9.III. a depleted or inverted grain boundary region (p- or n) in a p-type absorber attracts minority carrier and increases congthuc. In contract, the presence of a p+ grain boundary barrier could act much like a back-surface field in a conventional Si solar cell to decrease congthuc and increase Jsc. Configurations 7,8,9 are thus eliminated because of potentially high recombination losses. Configurations 1,3,6 are eliminated because of potentially high Jo( and thus low Voc) because of tunneling or low barrier height at the junction. This leaves configuration 2,4,5 as promising candidates. Configuration 2, the closest to the optimum, is shown in fig 9.46. since grain boundary diffusion of dopant is generally many orders of magnitude faster (and with lower activation energies) than bulk diffusion, the possibility of preferential doping of the grain boundaries is certainly feasible. There are still little experimental data on the effect of preferential doping in Sgb, however.

Chuthap to our knowledge such grain boundary sheet conductance has not been observed unambiguously in Si or GaAs. However the work of Ghandi et al. suggests that grain boundaries in n-GaAs can be diffusion-doped to detrimental levels during CVD deposition on n-GaAs substrates.

Deposition configurations at the inset of deposition of a layer, especially on an amorphous substrate, the material tends to ve more disordered, becoming increasingly like a single crystal as the film thickness increases, as shown in fig .9.13 and discussed in section 9.2.2. since we wish most of the photogeneration to take place in the most well-ordered region we are left with two possibilities shown in fig.9.47 the relative independence of the photovoltaic parameters on the properties of the window layer shown in some heterojunctions (e.g., large lattice mismatch in the ZnO/CdTe and ITO/Si cells) also reinforces this conclusion. Other factors aside, ease of cleaning and hermetic sealing argue for

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configuration b, whereas problems with current collection at the glass/window layer interface in b might favor configuration a.

Measurements in px material layer measurement of the electronic properties of px semiconductor layer is comples because of the presence the grain boundary potential barriers, with height depending on doping density and the possibility of total depletion of the the grains. Some measurements can be made by conventional techniques such as fourpoint resistance probing, hall effect, thermoelectricpower, and capacitance. But to be meaningful for solar cell applications, the measurements must be made under illumination of intensity comparable, to actual use in a solar cell. For example, grain-boundary-dominated series resistance values that are prohibitive in the dark can change to quite acceptable values under AM1 conditions. Scanning EBIC is a powerfull toll for assessing the effects of grain boundary strucuture, but again it must be interpreted with care unless done under illuminated conditions. A large number of measurement techniques for PX materials are discussed in a 1979 seri workshop.chuthap.

Chuthap photovoltaic matetial and device measurements workshop, focus on polycrystalline thin film cells, seri/tp-49-185, Arlington,Virginia 1979. Most of the articles have been reprinted in solar cells,1,nos,2 and 3 1980.

Fig.9.46 optimal grain boundary doping configuration.

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Fig.9.47tow possible configuarations fpr heterojunction px solar cells. Dot-shraded area is the principal photogeneration region of thickness alpha.

9.5.4/ passivation of grain boundary recombination

There appear to be three maun ways in which grain boundaries may be modified to reduce the losses there:1/ neutralization of the electrical activity of the grain boundary states by the addition of selected impurities, 2/ preferentially “capping” the intersection of the grain boundary and the junction with an insulator, and 3/ making te grain boundary into part of the junction by preferential diffusion doping of the grain boundary to the opposite type (e.g an n-type boundary in a p-type absorber), thus producing an analog to the vertical multijunction cell (fig.7.24).

Neutralization of grain boundary states has been accomplished by a number of workers. Seager and ginley used anneals in atomic H to increase the conductivity across grain boundaries in Si bicrystals, effectively removing all measurable boundary potential varies (measured at 300k), to a depth of 0.2-0.5mm. modest improvements in Jsc, Voc, and ff in px Si cells were indicated by conventional diffusion processing and annealed in atomic H after contacting. Other passivation experiments have been done using atomic H and using Li.

Daud and koliwad found that the addition of Cu apparently partially reduced grain boundary losses to increase Ns in px si solar cells. The Cu was introduced by diffusion from the surface in wacker-cast p-Si and during crytal growth of cz material, before junction formation by diffusion of P. although the Cu substantially increased the Ns of smallgrain material congthuc, the opposite effect was noted for large-grain material congthuc. The greatest effect of the addition of Cu was on the values of ff and Voc. In particular, the low-voltage, A=2 branch of the dark ln J versus V curve was most affected, as would be expected from the theory of fossum and lundholm.

Less than a monolayer of Ru on n-GaAs has been shown by nelson tp decrease surface recombination velocity by at least an order of magnitude. This might be expected to have similar effects at grain boundaries in this material.

The approach of electrically isolating the grain boundaries at the junction with an insulator war followed by ghandi et al 1979 for the congthuc schottky cell. A thick oxide was then judiciously etched with HCl to provide a thin oxide layer over the centers of the grains (0-20amtrong), but to leave a thick layer (<100amtrong) over the grain boundaries (:ghandi caps”). The au schottky barrier was then deposited over all. Withoit the oxide caps the grain boundaries behave as n+ material (possibly by diffusion from n+-GaAs layer during CVD), effectively shorting the cell. Leakage currents are reduced by factors of 10^5-10^6 by the oxide passivation treatment.

The third approach to overcoming the effects of polycrystallinity in a solar cell is to utilize the boundaries of columnar grains as pasrt of the junction, in effect producing a vertical multijunction cell. In the approach by distefano and coumo, P dopant is preferentially introduced into the grain boundaries of p-type silicon by a low-temperature diffusion process. A subsequent high-temperature diffusion forms a highly n-doped, convoluted skin covering a portion of each grain. The resulting junction around each

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grain collects carriers that might otherwise recombine at the grain boundaries. The grain boundary still intercepts the junction, although the intersection is no longer in a strongly illuminated region. The process must be used judiciously, f course, to avoid shorting to the back contact. The px thin film congthuc has this geometry.

9.6 epilogue

Polycrystalline thin-film solar cells have great potential large-scale use provided that adequate solar efficiency and stability can be achieved. Cells based on large-grain PX si have demonstrated that high Ns and the presence of grain boundaries are not mutually exclusive, as was compresence of grain boundaries are not mutually exclusive, as was commonly believed earlier. However, since this material must ve sliced, it does not offer significant cost advantages. The real advantage of px material lies in utilization of high throughput, thin-film deposition technology and the reduction in thichness of the active volumes of the cell by transferring the role of mechanical spport to a cheap substrate material.

For large-grained px si cells, there is a small loss in Jsc,ff, and Voc with respect to single-crystal cells, based on direct band-gap px materials have been show to maintain their Jsc despite small grain size. However, for all small-grained materials there is a considerable loss in Voc and ff, and therein lies the major challenge in increasing Ns for these devise.

The success of px thin-film solar cells depends largely on reducing losses at the grain boundaries. This can be done by (1) reducing their desity by modification during and/or after deposition to increase grain size; (2) passivation of their effect by removing or deactivating the recombination pathways there; and(3) use of materials in which the grain boundaries appear to be inherently inactive

The high quantum efficiencies observed in films of CuxS and cuinse2 with small grain size and/or thicknesses suggests that grain boundaries in these materials are inherently inactive, at least with respect to generation of Jsc. However, their interfaces with heterojunction parners are still lossy, reducing the obtainable Voc and ff. these materials may offer important clues as to the mechanisms involved in grain boundary passivation in orther semiconductors and at heterojunction interfaces.