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Produced by the NASA Center for Aerospace Information (CASI)
March 1, 1985

Distribution Category UC

63  ..

(NISI-C8-175b43) MEN SIG6-EFFICIENCY W85-23244

SILICON SCL18 CAIIS Final Feport, 11 lug.

1983 - 28 Pete 1915 (Jet Prciulsion Lab.)

42 p 8C 103/BF A01 CSCL 10l Onclas

G3/44 14805

New High-Efficiency

Silicon Solar Cells Final Report

August 11, 1983 - February 28, 1985

Taher Daud

Gerald T. Crotty

Prepared for

The Solar Energy Rasearch Institute

Through an Agreement with

National Aeronautics and Space Administration

by

Jet Propulsion Laboratory

California Institute of Technology

Pasadena, California
New High-Efficiency

Silicon Solar Cells

Final Report

August 11, 1983 - February 28, 1985

Taher Daud

Gerald T. Crotty

March 1. 1985

Prepared for

The Solar Energy Research Institute

Through an Agreement with

National Aeronautics and Space Administration

by

Jet Propulsion Laboratory

California Institute of Technology

Pasadena. Califnrnia
Prepared by the let Propulsion Laboratory, California Institute of Technology,

for the U.S. Department of Energy through an agreement with the National

Aeronautics and Space Administration.

This report was prepared as an account of work sponsored by an agency of the

United States Government. Neither the United States Government nor any

agency thereof, nor any of their employees, makes any warranty, express or

implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process

disclosed, or represents that its use would not infringe privately owned rights.

Reference herein to any specific commercial product, process, or service by trade

name, trademark, manufacturer, or otherwise, does not necessarily constitute or

imply its endorsement, recommendation, or favoring by the United States

Government or any agency thereof. The views and opinions of authors

expressed herein do not necessarily state or reflect those of the United States

Government or any agency thereof.
ABSTRACT

A new design for silicon solar cells was investigated as an approach to

increasing the cell open-circuit voltage and efficiency for flat-plate terrestrial photovoltaic applications. This deviates from past designs for such

applications, where either the entire front surface of the cell is covered by

a planar junction or the surface is textured before junction formation, which

results in an even greater (up to 70%) junction area. The heavily doped front

region and the junction space charge region are potential areas of high recombination for generated and injected minority carriers.

The new design reduces junction area by spreading equidiameter dot junctions across the surface of the cell, spaced about a diffusion length or less

from each other. Various dot diameters and spacings allowed var'_ations 'n

total junction area.

A simplified analysis was done to obtain a first-order design optimization.

Efficiencies cf up to 19% can be obtained.

Cell fabrication involved extra masking steps for selective junction diffusion, and made surface passivation a key element in obtaining good collection.

it also involved photolithography, with line widths down to 5 fcm.

A method is demonstrated for achieving potentially high open-circuit

voltages and solar-cell efficiencies.

iii
t The objective of this program was to investigate a new design for silicon

solar cells for flat-plate photovoltaic application^ that features reduced

junction area on the surface of the cell to reduce minority-carrier recombination and increase cell efficiency.

4. The innovative design consists of equidiameter dot junctions uniformly

distributed over the cell surface, spaced about one diffusion length or less

apart. In this design, therefore, the junctions cover only a small fraction

of the total cell area. Studies of this design are motivated by prospects of

• reduction of reverse saturation current and increase of short-wavelength radiation absorption within the lightly-doped p-type base silicon rather than within

the more heavily dope3 n + region at the device surface.

The reduced saturation current helps to improve the open circuit voltage;

effective surface passivation between the junction dots and proper design of

junction configuration allows good collection efficiency. To understand the

effects of reduced junction areas and to improve future solar-cell designs,

the program was divided into the following tasks:

(1) Design of junction dot patterns

(2) Cell fabrication

(3) Cell characterization

(4) Modeling and correlation of results

PRECEDING PAGE BI:AN1K NOT F NI FID

v
ACKNOWLEDGMENTS

The authors acknowledge helpful discussions with 0. von Roos. Assistance in spectral response measurements by B. Anspaugh is also acknowledged.

The authors also thank K.M. Koliwad and A.D. Morrison for helpful suggestions

and encouragement, and are grateful to J. Milstein of SERI for his advice.

Secretarial help by M.J. Koop is also appreciated.

This document reports on work done under Solar Energy Research Institute

Subcontract No. DB-3-03038-1, Contract NAS7-918, Task Order RE152, Amendment

383, and sponsored by the U.S. Department of Energy under interagency agreement with the National Aeronautics and Space Administration.

PAGE

vii
11Y-T VlCk.NX Nl_ T ''r t"'

ix

A.

CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

II. THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

A. OPEN-CIRCUIT VOLTAGE . . . . . . . . . . . . . . . . . . . . . . 2-1

B. SHORT-CIRCUIT CURRENT . . . . . . . . . . . . . . . . . . . . . 2-2

III. DESIGN OF MASKS . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

A. CONCENTRIC RINGS . . . . . . . . . . . . . . . . . . . . . . . . 3-1

B. PARALLEL-JUNCTION PATTERN . . . . . . . . . . . . . . . . . . . 3-1

C. DOT COLLECTORS . . . . . . . . . . . . . . . . . . . . . . . . 3-1

IV. MODELING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

V. EXPERIMENTS AND TESTING . . . . . . . . . . . . . . . . . . . . . . 5-1

VI. DISCUSSION AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . 6-1

REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R-1

APPENDIXA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Figures

2-1. Open-Circuit Voltage vs Percentage Area Ratio . . . . . . . . 2-2

3-1. Concentric Ring Pattern . . . . . . . . . . . . . . . . . . . 3-2

3-2. Parallel-Junction Pattern . . . . . . . . . . . . . . . . . . 3-3

3-3. Dot-Collector Pattern . . . . . . . . . . . . . . . . . . . . 3-3

4-1a. Unit Subcells With Square Junctions . . . . . . . . . . . . . 4-2

4-lb. One Unit Subcell With a Dot-Collector Junction . . . . . . . 4-2

Wr 4-1c. Two Volumes, I and II, of the Unit Subcell With

Carrier Collection Distances and Calculations

for the Truncated Rings . . . . . . . . . . . . . . . . . . . 4-3
Tables

4-2. Calculated Short-Circuit Current Density for Different

Dot-Collector Designs and Bulk D'.ffusion Lengths . . . . . . . 4-5

5-1. Schematic of Solar-Cell Fabrication . . . . . . . . . . . . . 5-2

5-2. Dark I-V Characteristics of 100 pm-Dia Dot Junction . . . . . 5-4

5-3. Photomicrographs of Two Dot-Collector Cells . . . . . . . . . 5-5

5-4. Dark I-V Curves for Dot-Collector and Control (C-1)

Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7

5-5. Spectral Response of Cell 100-75 With and Without Bias

Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8

5-6. Capacitance-Voltage Measurement for Passivating Oxide . . . . 5-10

6-1. Dark I-V Characteristics of Dot-Collector Solar Cells . . . . 6-2

3-1. Dot-Collector and Metal-Grid Mask Designs . . . . . . . . . . 3-4

4-1. Calculated Solar-Cell Parameters for Different

Dot-Collector Designs . . . . . . . . . . . . . . . . . . . . 4-6

5-1. Mesa-Etched Solar Cells . . . . . . . . . . . . . . . . . . . 5-3

5-2. Summary of Dot-Collector Cell Results . . . . . . . . . . . . 5-6

5-3. Summary of Solar-Cell Results . . . . . . . . . . . . . . . . 5-9

1

X
SECTION I

INTRODUCTION

Since the advent of solar cells in 1954 (Reference 1), efforts to increase

the efficicncy of p-n junction silicon solar cells have continued. Research

in materials and device technology (References 2, 3 and 4) has been responsible

for better understanding of device physics ard imp:ovement in the performance

of silicon solar cells.

Development in silicon growth technology has resulted in wafers with

reduced dislocation densities and chemical impurities, and thus increased

minority-carrier diffusion lengths (References 5 and 6). Research in p-n

junction formation, surface preparation with multilayer anzireflective (AR)

coatings and back-surface reflection has helped in attaining more efficient

light absorption. These have contributed to better short-circuit current.

Incorporation of a back-surface field (References 3 and 7) was one very

successful design feature that effectively decreased dark current and thereby

improved the open-circuit voltage, in addition to increasing the short-circuit

curren^.

In parallel with this, metal-insulator semiconductor (MIS) solar cells

(References 8 and 9) have been optimized for improved V oc t

 but current colle,:-

tion has suffered consiL'erabl,-. In addition, long-term srability problems

related to metallization, uxide charges and semiconductor surfaces have not

been solved. Other approaches such as tandem cell-, (References 10, 11 and 12),

etc., suffer from larger dark currents because of increased junction areas for

the same cell area.

This program was directed toward reduction of junction area to reduce dark

current and improve open-circuit voltage. It was divided into the foilowing

four tasks for understanding of the effects of junction-area reduction and for

evaluation of more optimal cell design:

(1) design of junction dot patterns

(2) modeling

(3) cell fabrication

(4) cell characterization

These tasks are described following a brief description of theory. Discussions

and conclusions are presented. A computer program written in BASIC, which was

used in the modeling, is provided in Appendix A.

A similar effort with devices called point-contact solar cells has been

made with thermal-photovoltaic cells (Reference 13) and concentrator cells

(Reference 14).

- ­>;-, - - 
SECTION II

THEORY

A. OPEN-CIRCUIT VOLTAGE

A p-n junction silicon solar cell can be represented by a constant current

generator in parallel with a diode. Ideally, a diode with only diffusion

current, Id , can be represented by the diode equation

I d - I,[exp(gV/nkT) - 11 (1)

or

Id - Jo - Aj [exp(gV/nkT - 1)]

where I d- reverse saturation current

Jo

= reverse saturation current density

Aj

- area of the p-n junction

q = electronic charge

V = applied voltage

n - diode ideality

k = Boltzmann constant

T = diode temperature, K

This ignores any series and shunt resistances and the space charge carrier

recombination. The photogenerated current, I sc , can be added algebraically to

the diode current (Equation 1) to obtain the solar-cell output current as

I - I sc - Jo - Ad

[exp(gV/nkT) - 1] (2)

If the total area of incident radiat:'.on on the solar cell is AT , i.e., Isc

J sc ' AT , then Equation 2 becomes

I - J sc - AT - Jo - Aj (exp(gV/nkT) - I] (3)

Under open-circuit conditions, I - 0 and V - V oc and hence, from Equation 3,

the open-circuit v oltage is given by

2-1 
Voc - ( nkT /q ) ln [ ( J sc - Af/Jo - AP + 11 ^^)

or

Voc - ( nkT / q )l n [Jsc /Jo (Aj

/AT )] + 1

Thus, the ratio Aj /AT can be changed to alter Voc . A plot of Voc vs Aj /AT is

shown in Figure 2-1 for n - 1, where J sc and Jo are used as parameters with

J sc of 30 and 40 mA/cm 2 and Jo of 10 -10 , 10 -11 , and 10 -12 A/cm2 . It is seen

that an order-of-magnitude reduction in the area ratio A j /AT results in a

theoretical increase of about 60 mV in V oc . This may translate into an 8% to

10% increase in efficiency.

^^^♦ Jo (A/Cm2)

10-12

JSC (mA/Cm2)

10-11

40

30

10-10

40

30

40

30

1 10 100

JUNCTION AREA (Aj/At), % x 100

Figtire 2-1. Open-Circuit Voltage vs Percentage Area Ratio

2-2

750

E

0 700

Z

CLU7

650 J

O

600

V

C;

v

z 550 W

CL

O

500
In a conventional p-n jurattion solar cell, most of the charge carriers

generated in the bulk are shielded from front-surface effects by the shallow

junction spread across the area of the cell. Also, the charge carriers generated within the heavily doped front region can be prevented from combining at

the front surface if the surface is passivated. A recent study (Reference 15)

shows that the blue response can be improved considerably by thermally grown

thin oxide at the front surface.

In the design presented here, the junction covers only part of the front

surface; the lets junction area covered (as a fraction of the total area), the

less separation of the bulk from the surface by the junction. Thus, most of

the photogenerated carriers may not be prevented from reaching the surface.

In this case, the surface must be Well passivated to enable all the generated

carriers to reach the junction. Similarly, the small area junctions must be

judiciously spread to within at least a diffusion length of the minority

carriers in the base.

Small-area junctions afford another advantage in terms of the current-flow

pattern. In conventional cells, the current flow in the diffused region is

lateral within the depth of the junction, which is only a fraction of a m,

whereas in dot junctions the flow is nearly perpendicular to junction surface;

this is likely to result in lower series resistance.

The value of the short-circuit current will depend on minority-carrier

diffusion length, junction spacing, cell thickness, and design of junctions on

the cell surface. A variety of junction designs were considered, and are

described in Section III.
SECTION III

DESIGN OF MASKS

Fur thermal diffusion on selective areas of the cell, au etched-out pattern

on oxide was troughs to be the easiest and moAt conventional way. For this, a

photolithography step was necessary. Three patterns were considered.

A. CONCENTRIC RINGS

This pattern consists of concentric rings spreading out from the center

of the cell with increasing radii, such that the radial distance between two

consecutive ring edges is of the order of two diffusion lengths or less. The

metal grid and annular diffusion patterns ar ,_ vhown in Figure 3-1. It was clear

from this design that the metal grid must run along both the base and the

diffused areas of the cell and another misk with an intricate pattern will be

needed to open up windows in the oxide fir metal cootdct in areas where the

grid pattern crosses the rings. With increasing ring diameter, a slight misalignment in the mask would result in either no contact with the diffused

region or a shorting of a p-n junction. Further, for larger-diameter rings, a

short at one place would short out a fairly large area of the junction. Because

of these complications, this design was discarded.

B. PARALLEL-JUNCTION PATTERN

Figure 3-2 shows a design in which a junction is formed with all grid

lines and the bus bar on the diffused area, and most of the uncovered area of

the cell having no junction. The distance between two consecutive gride would

be 200 to 300 Y.m, which is of the order cf two diffusion lengths. In general,

the junction area Ai would be about 3% to 8%. No metal would run over s nondiffused area, thus avoiding any chance of junction shorting. This approach

has been tried (Reference 16) using aluminum as a dopant for a p }n device. The

results were not encouraging. In this design, the junction-area distribution

is not uniform; hence, fo ► the sam area, the rollec:ion of current is less

efficient. However, grid pattern alignment is easier, with less chance of

junction shorting in case of a processing error.

C. LOT COLLECTORS

A very efficient scheme is to form equidiameter current-collecting dot

junctions spaced 100 to 200 m apart on the cell surface, staggered in alternate columns with grid lines connecting the dots along each column. Different

dot diameters give different ratios of Junction area to total area Aj/AT

(Figure 3-3). As an example, 25-"-dia (d) junctions spaced such that the

vertical and horizontal spacings S 100 μm will give an area coverage in

percentage: (Aj /AT ) - (7f/8) • (d/S) 2 - 2.5%.

As in the ring design, the metal grid will run on areas both with and

without diffusion. However, because of their symmetrical nature, similar dot

3-1
INCTION AREAS

GRID METAL

Fir-r- 3-1. Concentric Ring Pattern

3-2
JUNCTION AREAS

GRID METAL

Jnc U on

a —

Metal Grlos

Junction Area _ 2Pl(d) 2/4

Total Area 4S2

CJ

Figure 3-2. Parallel Junction Pattern

Figure 3-3. Dot-Collector Pattern

3-3
patterns with smaller dot sizes can be used to open windows in oxide for metalgrid contacts on the diffused region only. The remaining oxide acts as a 

barrier between the silicon surface and the metal grid.

This pattern has the advantage of easily enabling variation in area coverage

and offers very efficient current collection for a given area coverage.

This pattern was selected for experimentation.

A set of junction mask designs were worked out for S = 200 μm and 100,4m

with d varying from 15Eun to 100 μm, to obtain area coverage varying from 1% to

20%. A suitable set of designs for metal grids was also chosen. Parameters of

these sets are shown in Table 3-1, with the percentages of area coverage.

The metal grid mask design along with percentage of area shadowing is

given, with W as the width of each grid finger. A line width of 5 μin was

considered difficult to obtain at the time; it was thought that it , s ight be

necessary to accept higher shadowing losses until the photolithography for

finer line widths was in place.

Table 3-1. Dot-Collector and Metal-Gri,i Mask Designs

Set No. S, k.m d, μ.m Aj/AT,

(Dot Collector)

1 100 15 0.88

2 100 25 2.45

3 100 50 9.82

4 100 75 22.09

5 200 25 0.61

6 200 50 2.45

7 200 75 5.52

8 200 100 9.82

Set No. S, N.m W, μm Shadow,

(Metal Grid)

1 100 5 6.1

2 100 10 8.5

3 200 20 6.1

4 200 20 8.5

3-4
SECT ION IV

MODELING

The solar-cell design calls for a three-dimensional code to solve for the

cell parameters. This is a time-intensive and costly process. Therefore, it

was decided to seek a simpler, two-dimensional solution.

As an initial attempt, the cell was divided into a number of unit subcells

(see Figure 4-1a), each with a square collecting junction at its center. It

was then modeled as a semi-infinite surface with surface recombination velocity

of either infinity or zero. After analysis it was concluded that this was not

workable, because of the divergence of the dark current when assuming abruptly

changing boundary conditions at the edges of the square collecting junctions.

This led to an independent investigation of the origin of this divergence

(Reference 17). However, this approach was abandoned for solar-cell modeling.

Another approach was to assume a zero surface recombination velocity and

an exponential bulk recombination decrease. This model is described below:

Consider a square unit

center of its surface, with

Z t , is the thickness of the

into two volumes, I and II;

at the front surface, and I

(Figure 4-1c).

subcell with a dot junction of diameter d in the

each side of the subcell equal to S. The height,

cell (Figure 4-1b). This unit subcell is divided

I is the cylinder of diameter d with the junction

I is the remaining volume of the unit subcell

The number of photons, Nph , incident on the surface will generate electronhole pairs, in accordance with Lambert's law, throughout the volume of the unit

subcell. The number of electron-hole pairs collected by the junction will

depend exponentially on the distance of the generation point from the junction.

For volume I, this distance equals the depth of the generation point;

for volume II, the distance is the square root of the sum of squares of the

horizontal (r) and vertical (z) distances. For volume II, up to a c'_ameter S,

the differential surface area consists of a ring of width dr with r varying

from d/2 to S/2. For r from S/2 to S/V, the differential surface area consists

of a truncated annular ring of width dr and circular arc of length 2 r - 8r

arc cos (S/2r).

For bulk diffusion length of L b , the current collection in volume I will

be proportional to exp(-z/L b ) and in volume II it will be proportional to

exp(-SQRT(r + z )/Lb ). The short-circuit current density is therefore written

as:

4-1

r ^ N
1

5^

-lb. One Unit Subcell With a Dot Collector Junction

4-2

Figure 4-1a. Unit Subcells With Square Junctions
2

+ z

2 Yv

dr

S

r

B

f- S

2

B = arc cos (SI

2r

dr

Figure 4-1c. Two Volumes, I and II, of the Unit Subcell

With Carrier Collection Distances and

Calculations for the Trun:ated Rings

4-3

A.
z s/2 1/z 

1 t -az 7rd2 -z/I +^ - 1(r-d/2) 2 + Lb

z 21 /

Jsc 2 g ^N h e dz d e 2 dre J

P 

S

^ o 

S/`^ _ l r 2 +z 2 ) (5)

+ [27rr - 8rcos -1 (S/2r), a 1/\ / dr

S/2 

where cz = optical absorption coefficient in silicon

Nph = number of photons incident per cm 2 -sec μm

z t = thickness of the cell

The I-V curve is obtained from the equation

J = Jsc - Jo ( eqV/kT - 1) (6)

where V = output voltage

Jo = reverse saturation current density

= ( gn i 2 / NA ) • (Dn /L b ) • (7rd2/4S2)

and J = output current density.

A plot of J sc vs junction diameter d for S = 50, 100, 150 and 200μm and

for Lb = 100 and 300 m is given in Figure 4-2.

Cell parameters of V Qc , J sc , F^ and efficiency at 100 m2/ cm2 for Lb = 100,

200, and 300 fcm and with NA = 1x10 per cm and D = 15 cm /sec are shown in

Table 4-1. It is interesting to note tLat for 100 μm and 200 μm diffusion

.lengths, a d/S of 25/50 offers highest efficiency; for 300 μm diffusion-length

material, a d/S of 25/100 is best. Thus for good material, lesser junctionarea coverage is beneficial.

4-4

7

-- ---
35

30

25

20

N

EU

Q

E

U

N

7

15

S. μm

50

X100

50

150

200

100

150

200

Lb 300 μm

—a--^— Lb 100 μm

10

5

0

25 50 75 100 125 150 175 20

d, μm

Figure 4-2. Calculated Short-Circuit Current Density for Different

Dot Collector Designs and Bulk Diffusion Lengths

F`

r^

4-5
4-6

s Idol 

Table 4-1. CalculateA Solar-Cell Parameters for Different Dot-Collector Designs

Lb , μm S, μm d, )am Voc, mV Jsc, mA/cm2 FF Eff. ,%

100 50 25 682 28.6 0.843 16.45

50 648 30.0 0.836 16.28

100 25 714 24.6 0.835 14.65

50 681 27.1 0.843 15.53

75 662 29.0 0.823 15.82

100 648 30.1 0.837 16.33

150 25 730 20.8 0.852 12.94

50 697 23.2 0.847 13.69

75 679 25.5 0.843 14.57

100 666 27.5 0.832 15.23

125 656 29.1 0.839 15.99

150 648 30.0 0.836 16.27

200 25 741 17.6 0.853 11.15

50 708 19.7 0.848 11.85

75 690 21.9 0.845 12.75

100 677 24.0 0.843 13.69

125 668 26.0 0.834 14.46

150 660 27.7 0.840 15.33

175 654 29.0 0.837 15.88

200 647 29.9 0.838 16.19

200 50 25 702 30.8 0.846 18.28

50 667 31.5 0.832 17.50

100 25 736 28.7 0.852 17.97

50 701 30.1 0.847 17.84

75 681 31.1 0.843 17.88

i0c 667 31.7 0.833 17.61

150 25 755 26.4 0.854 17.00

50 720 27.8 0.844 16.89

75 701 29.2 0.843 17.28

100 687 30.3 0.844 17.56

125 676 31.2 0.841 17.72

150 667 31.7 0.832 17.58

200 25 767 24.2 0.846 15.68

50 733 25.6 0.851 15.96

75 713 26.9 0.834 16.02

100 700 28.2 0.846 16.72

125 689 29.4 0.845 17.11

150 681 30.4 0.843 17.44

175 673 31.1 0.840 17.59

200 667 31.6 0.832 17.54
Table 4-1. Calculated Solar-Cell Parameters for Different Dot-Collector Designs

(Cont'd)

Lb , fun S, '4m d, fum Voc, mV Jac, mA/cm 2

FF Eff.,%

300 50 25 713 31.7 0.833 18.82

50 678 32.2 0.842 18.36

100 25 748 30.3 0.853 19.33

50 713 31.3 0.832 18.55

75 693 32.0 0.844 18.72

100 678 32.4 0.842 18.49

150 25 767 28.6 0.846 18.58

50 732 29.7 0.852 18.51

75 712 30.6 0.849 18.51

100 698 31.4 0.846 18.57

125 687 32.0 0.844 18.58

150 018 32.4 0.942 18.48

200 25 781 27.0 0.857 18.10

50 746 28.1 0.853 17.86

75 726 29.1 0.848 17.89

100 712 30.0 0.848 18.10

125 701 30.8 0.846 18.28

150 692 31.5 0.845 18.42

175 685 32.1 0.843 18.49

200 678 32...j 0.842 18.46

4-7
SECTION V

EXPERIMENTS AND TESTING

Solar-cell fabrication was done on 3-in.-dia, (100) orientation, 1 to

2 a-cm, 0.3 to 0.4 mm (17 to 16 mils)-thick Czochralski (Cz) or float-zone (FZ)

wafers using masks to obtain four 2 x 2-cm cells per wafer. The general processing steps needed (see Figure 5-1) were:

(a) Oxidation of front and back surface, 3000 to 4000 A thick, to act as

a diffusion mask.

(b) Etching windows on front surface with photolithography, followed by

phosphorus diffusion at 850°C for 20 min. with PH3.

(c) Etching of oxide and phosphosilicate glass using 10% to 20% HF

solution.

(d) Thermal oxidation, 100 to 150 A thick, on the front surface to passivate the cell surface and form an insulation layer on the p substrate

to avoid shorting by metallization, and yet etch windows for contact

with the diffused regions.

(e) Back metallization by evaporation of A1-Ti-Pd-Ag (600-600-400-25K A)

and sintering at 600°C in H 2 ; front metallization and lift-oft ;y

evaporation of Ti-Pd-Ag (600-400-40K A).

(f) Single or multilayer AR ccating for good photon absorption. Single

layer is 725 A SiO x and multilayer consists of T10 2 and Al 203 sputtered and sintered at 400°C for 20 min.

A number of runs of cells were made with minor changes in the processing

steps as described.

Before receipt of the masks, a preliminary run with a larger-area dot mask

was done. A batch of p-type Cz wafers were thermally diffused and mesa-etched

to form a dot pattern. A 50% reduction in area reduced the cell Efficiency

(with no AR coating) from 8.9% to 3.6% (100 mW /cm 2 ). A slight improvement was

noticed after growth of a thin oxide at 200°C (Table 5-1). Junction area after

etching was reduced from 4 cm2 to 2.14 cm2.

After receipt of the masks, the first two runs could not be completed

because of problems with photo-resists and mask aligner. Proper delineation of

dot junctions and grid metal could not be achieved, resulting in aborted cells.

The next run was made to study the fabrication and testing of 100-}Lm-dia

and 50-pm-dia junctions only. Wet oxidation for diffusion masking was done at

1100°C for 1 h.

Dark I-V measurements were made on representative junctions over an area

of 4 x 4 cm. It was found that, in general, the diode factor degraded with

smi ller junctions: about 1:35 to 1:40 for 100-}am-dia junctions and about 1:38

to 1 : 44 for 50 μm-dia junctions. A typical dark I-V curve is shown in Figure 5-2

5-1

I I 'F ^^^^ 'r 
METAL AR COATING 

na

Si02

n+ DIFFUSION

Si SUBSTRATE (P) 71

(a) (b)

n + DIFFUSION'

Si02

(C) (d) 

(e ) (f)

Figure 5-1. Schematic of Solar-Cell Fabrication

5-2
Table 5-1. Mesa-Etched Solar Cells

Before Etch After Etch After Oxidation

Voc 564 mV 527 mV 557 mV

Isc 86.2 mA 38 mA 40 mA

FF 73% 71% 73%

71 (No AR Coat) 8.9% 3.6% 4.1%

Junction area after etch: 2.14 cm2

Junction area before etch: 4 cm2

Oxide: =20 A S10 2 at 200°C

for a 100 arm-dia junction. This fabrication run involved a high-temperature

(1100°C, 1 h) oxidation step, which may have not only caused degradation of

bulk lifetime but also a depletion of boron at the front-surface p region. A

discussion of this effect is presented in Section VI.

To avoid high-temperature oxidation and yet provide a diffusion mask,

experiments with different evaporated films of oxides (SiO x , InO, Ta 2 0 5 ) were

tried. Indium oxide and tantalum pentoxide films were strongly adherent and

did not etch out properly after the photolithography step. Silicon oxide

evaporation with substrate heated at about 200°C in the presence of oxygen

resulted in the formation of (probably) Si 2 0 3 , which was found to be conducive

to subsequent etching and thermal diffusion.

A run with evaporated silicon oxide was made on 1 to 2C2^-cm, (100),

0.375 mm (15 mils)-thick, 76 mm (3 in.)-dia FZ wafers, using masks with 2001Lm

dot spacings (S) and dot diameter of 100 μm (referred to hereinafter as

200-100) and with spacing of 100 μm and dot diameters of 75 and 50 μm (100-75

and 100-50), respectively.

After cleaning of the wa:ers, evaporation of silicon oxide and opening of

windows through the oxide, thermal diffusion of phosphorus was done at 850°C

to obtain a sheet resistivity of 100 SVO. A psssivating oxide (40 to 46 A)

was grown at 800°C for 30 min. followed by 15 min. annealing in nitrogen.

Alignment for the front metallization on thin oxide, as well as after Ta20c

AR coating, did not succeed. A third try to align, by indexing on two side

edges, was finally successful. Ten 2 x 2-cm cells with dot collectors were

fabricated. Figure 5-3 shows photomicrographs of two cells. The cell in

Figure 5-3a is 200-50 configuration with 20-,Lm-wide metal grids, and the cell

in Figure 5-3b is a 100-75 configuration with 10-pm-wide grids. Following this

experience, a revision of the mask design for smaller -cell geometry with better

registration marks and finer grid-line geometry. In addition, four 2 x 2-cm

control cells were fabricated with conventional junctions and with th: . finer

grid pattern used for dot -collector cells.

These cells were tested for light and dark I-V characteristics. It was

found that the reverse saturation current density was very high ( zl to 2 x 10-8

5-3
1

10-1

10-4

n = 1.38

Jp - 4 x 10 - 8 A/cm2

r

10-2

NE

7U

l

Y

r

2

W

H

Z

W

Q

cc

D

U 

10-3

10-5

0 100 200 300 400 500 600

VOLTAGE, mV

Figure 5-2. Dark I-V Characteristics of 100-. ,=-Dia Dot Junction

S-4 
200-50-20 N.m 100-75-10 μm

Figure 5-3. Photomicrographs of Two Dot Collector Cells

A/cm 2 ) and the light-generated current collection was very low (Table 5-2)

The last column shows a calculated Voc for cell-current collection of the order

of 120 mA. Part of the current-collection degradation can be accounted for by

greater grid widths due to undercutting during the etching of the oxide. It

is estimated that the metal coverag aas of the order of 12.5% on these cells.

Figure 5-4 shows dark I-V characteristics of typical cells from each set. Spectral response measurement (Figure 5-5) with and without bias show the presence

of trap levels. Surface photovolLage (SFV) measurement showed a degradation

minority carrier diffusion length from 150 to 200 m in untreated wafers to less

than 40 μ.m in the cells. This degradation is attributed traced to the SiOx

evaporation step and, therefore, to the SiO x purity. High-temperature diffusion

following the SiO x evaporation may have incorporated those impurities within

the Si.

The next run was done on L SZ cm FZ wafers with a deposited oxide (using a

Low-temperature CVD system, by courtesy of Applied Solar Energy Corp.) as a

diffusion barrier. Similar prucess steps were followed with a passivating

oxide of 150 A thickness, 10 and 15μm-wide metal fin-ers (Ti-Pd-Ag), and a

double AR coating. Light and dark I-V tests were performed. Table 5-3 gives

the solar-cell parameters. The best efficiercy obtained was 14.3% for a

75-^Lm-dia dot collector and 100-k4,1 junction spacing configuration. It was

interesting to note that the 200-100 cells gave approximately the same current

collection as did the 100-75 cells. A retest after two days of storage showed

considerable degradation in cell parameters, as shown in Table 5-3 by figures

in pirenrhesis. Spectral response measurement showed light bias effect similar

to that shown in Figure 5-5. Higher quantum efficiency at longer wavelengths

with bias cannot be explained by oxide traps alone. Capacitance-voltage (C-V)

measurements of oxide showed a flat-band shift of -1.45 volts (see Fig,ire 5-6)

5-5
Table 5-2. Summary of Dot-Collector Cell Results

Set No. Cell No. Voc , mV Isc , mA FF 7, % Io, A Voc, mV, for

I sc = 120 mA

1 C-1 570 100 0.79 11.3

2 C-2 576 105 0.79 11.9 2.6 x 10-8 578

3 C-3 570 102 0.79 11.4

4 C-4 571 102 0.79 11.4

5 200-100/1 522 20.1 0.62 1.6 3.2 x 10-8 572

6 200-100/2 522 19.3 0.63 1.6

7 100-75/1 516 38.6 0.65 3.2

8 100-75/2 507 29.2 0.66 2.4 8.0 x 10-8 550

9 100-75/3 515 35.4 0.68 3.1

10 100-75/4 510 30.5 0.67 2.6

11 100-50/1 522 28.3 0.59 2.2

12 100-50/2 516 25.8 0.58 1.9 4.6 x 10 -8 564

13 100-50/3 521 28.2 0.58 2.1

14 100-50/4 518 26.2 0.58 2.0

with an oxide interface state density of 10 12 /cm2 , as against values of -1.1

volts and z,.1011/cm2, respectively, for good oxide.

The degradation in the cell performance is presumed to be due to changes

in the oxide properties. Further work in understanding of thin oxides for

surface passivation must be done to explore the full potential of this cell

design.

5-6
L t

IE-3

Q

z

w

cc

cc

U

IE-4

IE-5

f

/

/

/

/

/ C-1

/ ---- 100.75

700-100

/ ----^— 100-50

^t

^I

^t

rl

IE-6

0.1 0.2 0.3 0.4 0.5 U.6 0.7

VOLTAGE, V

Figure 5-4. Dark I-V Curves for Dot Collector and Control (C-1) Cells

5-7
I^

O

it

rl

r

W

..a

as

0

t

u

3

.ti

C

u

,a

3

Ln

E I

a p

3 O

z

w r-+

w J

Q

3 0

v

C

O

a

v

DC

ro

v

a

a

I

CJ

N

00

w

c

a

c

O

(D

0

z

0

x

Lc)

O

N

cc

Q

V

O

o ^ P o n

O

O

O p

Mu'/Vu' '3SNOdS3U IVH103dS 31f11OS6V

5-8

O O

O
Table 5-3. Summary of Solar-Cell Results

(1.5 R-cm FZ Substrates)

Set Cell No. Cell Voc , mV Isc , mV FF Eff., % Area Shadow, %

No. Config. Ratio, %

n t 1 036-1-1 200-50 585 123.4 0.568 10.24

(583) (117.7) (0.546) (9.38)

2 036-1-2 594 126.1 0.554 10.37

(592) (120.5) (0.546) (9.74) 2.5

3 036-1-3 590 123.7 0.580 10.57

(589) (118.4) (0.572) (9.97)

4 036-1-4 597 125.4 0.588 11.02

(593) (118.7) (0.544) (9.58)

5 036-4-1 100-25 584 119.7 0.635 11.10

(588) (115.3) (0.658 (11.15)

6 036-4-2 590 118.7 0.687 12.03

(589) (112.8) (0.676) (11.24) 2.5

7 036-4-3 --- ----- ----- -----

(582) (109.4) (0.577) (8.86)

8 036-4-4 590 120.7 0.670 11.92

(584) (111.8) (0.644) (10.51)

9 036-2-1 100-50 585 115.7 0.689 11.66

(583) (111.2) (0.673) (10.90)

10 036-2-2 548 116.0 0.565 8.97

(547) (111.9) (0.550) (8.41) 10.0

11 036-2-3 531 119.1 0.561 8.87

(530) (113.5) (0.556) (8.36)

12 036-2-4 577 117.7 0.679 11.53

(576) (110.8) (0.674) (10.76)

8.5

13 036-3-1 100-75 598 124.3 0.751 13.96

(597) (117.8) (0.758) (13.32)

14 036-3-2 596 122.1 0.764 13.89

(596) (117.2) (0.756) (13.21) 22.0

15 036-3-3 596 125.2 0.754 14.06

(594) (119.0) (0.754) (13.32)

16 036-3-4 597 124.5 0.771 14.32

(596) (119.7) (0.768) (13.69)

5-9
No. 346.036

900

800

jL 700

a

v 600

z

500

U

400 CL

a

U 300

0

dox = 150 A

VFB = -1.45 V

NSS = 1.06 x 1012J=2

200 

100

-10-8 -6 -4 -2 0 2 4 6 8 10

APPLIED DC BIAS, V

Figure 5-6. Capacitance-Voltage Measurements for Passivating Oxide

5-10
SECTION VI

DISCUSSION AND CONCLUSIONS

The modeling calculations show that smaller spacing with proper dot-junction

areas give improved cell performance. Thus, a potential has been demonstrated

for achieving high efficiency with these cells.

Fabrication experiments during the later part of this program were fruitful

in demonstrating the feasibility of this approach and also in pointing out some

of the design and fabrication pitfalls.

One of the problems faced during fabrication was that the registration

marks on the masks were too far apart, leading to difficulties in alignment.

High-temperature wet-oxide growth on p-type substrates introduces an extra

high-temperature step that reduces the diffusion length. In addition, with the

p-type silicon/Si02 interface, it is known that due to redistribution, boron

tends to escape into S10 2 at high temperature (References 18 and 19), leading

to a depleted region along the surface surrounding the junction. This tends

to increase surface leakage along the p-type surface and to space-charge

recombination in the depleted subsurface regions surrounding the dot junctions.

Low-temperature-CVD-deposited oxide has solved this problem.

Dark I-V data (Figure 5-4) shows that a conventional junction gives a

much better diode ideality factor than is obtained by the dot collectors. A

comparison of dark I-V data from the last run is shown in Figure 6-1. The

improvement in the characteristics with reduction in junction area is clear.

However, the diode ideality factor was found to be 1.2 to 1.25, which is high.

In addition, the cell results show considerable shorting, probably due to

metal grids running over p regions with a thin (150 A) oxide. A high series

resistance was also noted. These problems led to the degradation of cell

performance shown in Table 5-3. A closer look at the metal grid design or

suitable alteration in the fabrication procedure may be needed.

More work is needed in theoretical analysis to further optimize the design

and determine limits to cell performance. Passivation of front surfaces is

important; more research in thin-oxide growth and characterization is needed to

arrive at optimum thickness and fabrication procedure. More cell fabrication

runs with design variations are also needed to improve performance and to

understand the limiting loss mechanisms.

In summary, this work has shown that the dot-junction design has good

potential for improving cell efficiency and also that work in key areas of

theoretical analysis, oxide passivation and cell fabrication is required.

6-1
1E-1

1 E-2

Q 1 E-3

zW

v 1E-4

1E-5

S d (μm) ^

200-50 ,I•^•'^

............. 100-25

---- 100-50

---100-75

p

r:.

.y

1 E-6

0.1 0.2 0.3 0.4 0.5 0.6 0.7

VOLTAGE, V

Figure 6-1. Dark I-V Characteristics of Dot Collector Solar Cells

6-2 
REFERENCES

1. Chapin, D.M., Fuller, C.S., and Pearson, G.L., "A New Silicon P-N Junction

Photocell for Converting Solar Radiation into Electrical_ 'rower," J. Appl.

Phys., Vol. 25, pp. 676-677, May 1954.

2. Lindmayer, J., and Allison, J.F., Comsat Technical Review, Vol. 3, No. 1,

1973.

3. Mandelkorn, J., and Lamneck, J.H., Jr., "Simplified Fabrication of Back

Surface Electric Field Silicon Cells and Novel Characteristics of Such

Cells," Proceedings of the 9th IEEE Photovoltaic Specialists Conference,

Silver Springs, Florida, May 2-3, 1972, p. 66.

4. Van Overstraeten, R.J., "Advances in Silicon Solar Cell Processing," Proceedings of the 15th IEEE Photovoltaic Specialists Conference, Kissimmee,

Florida, May 12-15, 1981, p. 372.

5. Hovel, H.J., "Semiconductors and Semimetals," Solar Cells, Vol. 11, Ed.

R.K. Willardson and A.C. Beer, Academic Press, New York, 1975.

6. Wolf, M., "High Efficiency Silicon Solar Cells," Proceedings of the 14th

IEEE Photovoltaic Specialists Conference, San Diego, California, January

7-10, 1980, p. 674.

7. Godlewski, M.P., Baraona, C.R., and Brandhorst, H.W., Jr., "Low-High

Junction Theory Applied to Solar Cells," Proceedings of the 10th IEEE

Photovoltaic Specialists Conference, Palo Alto, California, November

3-15, 1973, p. 40.

8. Green, M.A., et al, "The MINP Solar Cell--A New High Voltage, High Efficiency Silicon Solar Cell," Proceedings of the 15th IEEE Photovoltaic

Specialists Conference, Kissimmee, Florida, May 12-15, 1981, p. 1405.

9. Anderson, W.A., Delahoy, A.E., and Milano, R.A., J. Appl. Phys. 45, 3913,

1974.

10. Lindholm, F.A., and Fossum, J.G., "Review of Physics Underlying Recent

Improvements in Silicon Solar-Cell Performance," Proceedings of the 14th

IEEE Photovoltaic Specialists Conference, San Diego, California, January

7-10, 1980, p. 680.

11. Scott-Monck, J.A., Gay, C.F., Stella, P.M., and Uno, F.M., High Efficiency

Solar Panel (HESP), Final Report, AFAPL-TR-77-36, Spectrolab, Inc., Sylmar,

California, July 1977.

12- Hall, R.N., and Soltys, T.J., "Polka Dot Solar Cell," Proceedings of

the 14th Photovoltaic Specialists Conference, San Diego, California,

January 7-10, 1980, p. 550.

13. Swanson, R.M., "Point-Contact Silicon Solar Cells," EPRI Report AP-2859,

Electric Power Research Institute, May 1983.

R-1
14. Swanson, R.M., Beckwith, S.K., Crane, R.A., Eades, W.D., Kwark, Y.H.,

Sinton, R.A., and Swirhun, S.E., "Point-Contact Silicon Solar Cells,"

IEEE Transactions on Electron Devices, Vol. ED-31, p. 661, 1984.

15. Spitzer, M.B., Keavney, C.J., Tobin, S.P., Lindholm, F.A., and Neugroschel,

A., "Mechanisms Limiting Open Circuit Voltage in Silicon Solar Cells,"

Proceedings of the 17th IEEE Photovoltaic Specialists Conference, Kissimmee,

Florida, May 1-4, 1984, p. 1218.

16. Loferski, J.J., et al, "Theoretical and Experimental Investigation of

'Grating' Type Photovoltaic Cells," Proceedings of the 10th IEEE Photovoltaic Specialists Conference, Palo Alto, California, November 13-15,

1973, p. 58.

17. Von Roos, 0., and Lindholm, F.A., "Steady-State Currents in p-n Junction

Filaments or Grains in Case of Large Surface Recombination Velocities at

Lateral Surfaces," J. Appl. Phys. (in press).

18. Kato, T., and Hishi, Y., "Redistribution of Diffused Boron in Silicon by

Thermal Oxidation," Japan J. Appl. Phys., 3, 377, 1964.

19. Gandhi, S.K., VLSI Fabrication Principles, p. 172, John Wiley, New York,

1983.

R-2
APPENDIX A

COMPUTER PROGRAM FOR SOLAR-CELL MODELING

100 REM ############*#######*###################

110 REM # #

120 REM # DOT COLLECTOR SOLAR CELL MODELING #

130 REM # #

14e REM * DATE 12-26-84 #

iSJ REM # #

60 REM *############*########**#############*##

170 PRINT 037,26:0

180 PAGE

190 INIT

200 N=124

210 Y=150

,20 DIM Wi(N),Eph(N),Ai(N),A(2),C(2),EO(3),E1(3),F9(N),Mi(N),P(2)

230 DIM Nph(N),W2(N),Vo(Y),Io(Y),Po(Y)

240 T-300

250 Zt=0.03

260 READ Q,Qi,Hi,CO,Vt

270 REM -----------------------------------

280 REM READ AM i.S GLOBAL DATA FROM FILE i

290 REM ##########*#######*###*#***###**##

300 FIND i

310 FOR I = 1 TO N

320 INPUT 033:W1(I),Eph(I)

330 NEXT I

340 REM ---------------------------------------

350 REM CALCULATE ABSORPTION COEFFICIENT, OIPHA

360 REM ######*####**#########*################

370 READ B2,Gi,C(i),C(2),A(i),A(2),A4,KO,EO(i),EO(2),EO(;3)

380 REAL r(i),P(2),H2

390 FOR I = 1 TO 3

400 Ei(I)=EO(I)-B2*T"2/(T+Gi)

410 NEXT I

420 FOR K = 1 TO N

430 F9(K)=1.239644/Wi(K)

440 Ai(K)=0

450 FOR I=1 TO 2

460 FOR J= i TO 2

470 Ml(K)-0

480 IF F9(K)(Ei(J)-P(I) THEN S30

490 Mi(K)=C(I)*A(J)*(F^(K)-Ei(J)+P(I))"2/(EXP(P(I)/(KO*T))--1)

500 IF F9(K)(=Ei(J)+P..:) THEN S30

S10 Zi-C(I)*A(J)*(F9(K)-Ei(J)-P(I))"2/(i-EXP(-P(I)/(KO*1)))

S20 Mi(K)=Mi(K)+Zi

530 Ai(K)=Ai(K)+Mi(K)

540 NEXT J

550 NEXT I

S60 IF F9(K))Ei(3) THEN S80

A-1
S70 GO TO 600

580 Mi(K)-A4#(F9(K)-Ei(3))"O.S

S90 Ai(K)=Ai(K)+Ml(K)

600 NEXT K

610 DATA 32,i.601864E-iy,6.623773E-34,2.9979022E+10,0.02586

620 DATA 7..-2iE-4,1108,5.5,4,323.1,7237,1OS2000,8.616E-5,1.1557,2.5

630 DATA 3.2,0.01827,0.05773,6.582E-16

640 REM --------------------------------------

6SO REM CALCULATIONS FOR SHORT CIRCUIT CURRENT

660 REM ##*###############################**##

670 IF Q=32 THEN 690

680 PRINT 637,26-1

690 Dr-2.SE-4

700 N1-100

710 N2-60

720 N3=74

730 Lb-O.Oi

740 PRINT L9Q: " Lb 5 D Voc Jsc FF EffJ_"

750 FOR N4=i TO 3

;'60 S=0.005

770 FOR Li-i TO 4

780 Si-5#10000 

790 PRINT QQ: USING 2260:Lb#i0000,Si

800 Ri-0.00125

810 FOR M2-i TO 8

820 D-2*Ri#10000

830 C6-0

840 C:3=0

850 FOR I = 1 TO N3

860 Z2=0

870 U-0

880 IF Ai(I))1000000 THEN 980

890 IF Ai(I))400000 THEN 1000

900 IF Al(I))i00000 THEN 1020

910 IF Ai(I))40000 THEN 1040

920 IF Ai(I))10000 THEN 1060

930 IF Ai(I))4000 THEN 1080

940 IF Ai (I) )i 000 THEN 1100

950 IF Ai(I))100 THEN 1120

960 Dz=0.005

970 GO TO 1130 

980 Dz-S.OE-8

990 GO TO 1130

1000 Dz= i.OE-7

1010 GO TO 1130

1020 Dz=S.OE-7

1030 GO TO 1130

1040 Dz=i.OE-6

1050 GO TO 1130

1060 Dz-5.0E-6

107C GO TO 1130 

1080 Dz-i.0E-5

1090 GO TO 1130

iiOG Dz="'.OE-5

A-2
1110 GO TO 1130

1120 Dz-i.0E-4

1130 IF I)i THEN 1160

1140 W2(I)-0.0032

1150 GO TO 1170

1160 W2(I)-Wi(I)-W1(I-i)

1170 Nph(I)-Wi(I)*i. OE-8*A1(I) *Eph(I)*W2(I)/(Hi*CO)

1180 FOR J u l TO Ni

1190 R-Ri

1200 Az=Ai(I)*(Z2+Dz/2)

1210 C8-0

1220 IF Az)100 THEN 1680

1230 FOR K-1 TO N2

1240 IF R(S/2 THEN 1270

1250 C2=8*(R+Dr/2)*ACS(S/(2*(R+Dr/2)))

1260 GO TO 1280

1270 C2-0

1280 C9-(2*PI*(R+Dr/2)-C2)*Dr*EXP(-SQR((R+Dr/2-Ri)"2+(

Z2+Dz/2)"2)/Lb)

1290 C8-C8+C9

i700 K-R+Dr

1710 IF R=)S/2^0.S THEN 1330

:320 NEXT K

1330 Di-PI*Ri 42*EXP(- (Z2+Dz/2)/Lb)

1340 Ex-EXP( -Az)

1350 C7=Nph ( I) *Ex *Dz

1360 C6=C6+C7*(DT+CB)

1370 IF U-)1 THEN 1410

1380 IF Az(-0.S THEN 16SO

1390 U=1

1400 Dz-Dz*2

1410 IF U-)2 THEN 1450

1420 IF Az(-i THEN 1650

1430 U-2

1440 Dz- 2 *Dz

14SO IF U-)3 THEN 1490

1460 IF Az(=2 THEN 1650

1470 U-3

1480 Dz-2*Dz

1490 IF U-)4 THEN 1530

1500 IF Az( =4 THEN 1650

1510 U-4

1520 Dz-4*Dz

1530 IF U=)S THEN 1570

iS40 IF' Az(=10 THEN 1650

1550 U=S

1560 Dz-4*Dz

1570 IF U-)6 THEN 1610

1580 IF Az(=20 THEN 1650

1590 U=6

1600 Dz-10*Dz

1610 IF U-7 THEN 1650

1620 IF Az(40 THEN 1650

163P, U-7

A-3
1640 Dz=10#Dz

1650 Z2 n Z2+Da

1660 IF Z2=)Zt THEN 1680

1670 NEXT J

1680 NEXT

1690 Ci=Qi#C6*i000/S 42

1700 GOSUB 1810

1710 Ri=R1+0.00125

1720 IF S<2#Ri THEN 1740

1730 NEXT M2

1 ­ 40 S-S+0. 005

,750 NEXT Li

1760 Lb=Lb+0.01

1770 NEXT N4

1780 PRINT 037,26:0

1790 PRINT "JJJJJJJJJJ ALL DONEGGGGG"

1800 END

1810 REM ----------------------------------------

1820 REM CALCULATIONS FOR Voc, FF, AND EFFICIENCY

1830 REM #####*################################*#

1840 Z-0

i850 Isc=Ci/1000

1860 Nun=PI*1.6E-i9*1.45E+1042#15

1870 Den=4#1.SE+i6#Lb

1880 Ravi=Nun/Den#(D/Si)"2

1690 FOR IO s i TO 20

1900 Vo(IO)=I0#0.05

1910 Io(IO)=Isc-Revi*(EXP(Vo(IL)/Vt)-1)

1920 IF Z=1 THEN 2080

1930 Po(IO)-Vo(IO)*Io(IO)

1940 IF 10=i THEN 2080

1950 IF Po(IO))Po(IO-1) THEN 2080

1960 FOR L=1 TO 12

1970 M=IO+L-i

1980 Vo(M)=Vo(M-1)+0.005

1990 Io(M)=Isc-Revi*(EXP(Vo(M)/Vt)-i)

2000 Po(M)=Vo(M)*Io(M)

2010 IF Po(M))Po(M-i) THEN 2060

2020 Pm=Po(M-1)

2030 Z=1

2040 REM

2050 GO TO 2080

2060 REM

2070 NEXT L

2080 IF Io(IO)(0 THEN 2120

2090 REM

2100 NEX1 10

2110 END

2120 FUZZ S,9.OE-4

2130 FOR K=1 TO 100

2140 J-IO+K -2

2150 Vo(J)-Vo(I0-i)+(K-i) #i.QE-3

2160 Io(J)=Isc -Ravi*(EXP(Vo(l)/Vt)-i)

2170 IF Io(J)(=0 THEN 2210

A-4
2160 NEXT K

2190 PRINT "JJ Voc NOT FOUNDGGG"

2200 RETURN

2210 Voc=t'o (J )

2220 Ff=PAN/(Voc*Isc)

2230 Eff =Pf-*i000

2240 Jsc=Isc*i000

2250 PRINT RQ: USING 2270:D,Voc,Jsc,Ff,Eff

2260 RETURN

2270 IMAGE 12X,3D,2X,D.3D,2X,3D.D,2X,D.3D,2X,2D.2D

2280 IMAGE 2X,3D,2X,3D

A-5