Photovoltaic laser to electric converters are attractive for use with a space-based laser power station. This paper presents the results of modeling studies for a silicon vertical junction converter used with a Nd laser. A computer code was developed for the model and this code was used to conduct a parametric study for a Si vertical junction converter consisting of one p-n junction irradiated with a Nd laser. These calculations predict an efficiency over 50 percent for an optimized converter

Heinbockel, J. H.

Walker, G. H.

English

NASA Technical Reports Server

NASA-TM-89041 19860023404
NASA Technical Memorandum 89041'
PhotovoltaicConversion of Laser Power
to Electrical Power
Gilbert H. Walker and John H. Heinbockel
_OP_ D,_- _,_m__,$.,Ja. ,t., ._.L_.,;_. .,,.,.,,,_
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September 1986 __Iit_ _j_
] 'j _ ,_ ,
._._NGLEYEESEAlYCHC_,_TER
LI3RARY,NASA
a_OH/'_;,,,TOI_I,VIRGINIA
NationalAeronautics and
Space Administration
LangleyResearchCenter
Hampton,Virginia23665
https://ntrs.nasa.gov/search.jsp?R=19860023404 2020-03-20T13:16:33+00:00Z

Photovoltaic Conversion of Laser Power to Electrical Power
Gilbert H. Walker
NASALangley Research Center, Hampton, Virginia 23665-5225
and
John H. Heinbockel
Old Dominion University, Norfolk, Virginia 23508
Space-based laser power stations will require converters at the
receiving spacecraft to convert the laser radiation to electricity.
Photovoltaic converters are promising devices for this use (ref. I).
Special considerations must be given to the laser wavelength and to the
laser power density. Figure I shows some laser photon energies compared
to selected semiconductor bandgap energies. The semiconductor, for use as
the photovoltaic converter, must be chosen so that its bandgap energy is
slightly less than the energy of the laser photons to be converted into
electricity (ref. 2). Incident power densities may be as high as i x 103
watts cm-2. In a previous paper (ref. 2) vertical junction converters
were suggested as appropriate for use as laser photovoltaic converters. A
promising solar-pumped laser for use on a laser power station is a Nd
laser (ref. 3). From figure I, silicon is the appropriate semiconductor
for use with a Nd laser. The Si bandgap energy is I.II eV, slightly less
than the 1.17 eV energy of the photons from the Nd laser. The maximum
power density assumed in this study is 1 x 103 watts cm-2 at
1.06 _m or 3.47 x 1021 photonscm-2 sec"I. The photonsare absorbedat an
appreciabledepth into the semiconductorratherthan absorbed near the top
surface. This paper describesa model developedto study vertical
junctionlaser-photovoltaiconvertersand the applicationof this model
to the Nd laser-Sisingle verticaljunction photovoltaicconverter.
Model
The model (described in detail in Appendix A) for this vertical
junction converter uses the device geometry shown in figure 2 and assumes
a generation rate at a depth B given by
g(B) : €0(I - Re) a e-aB (I)
where @0 is the number of incidentphotons[cm-2 sec-1],_ is the
absorptioncoefficient[cm-1],and Re is the reflectioncoefficient.
The basic equationsfor a n/p device involvethe photocurrentfrom the n
and p materialsas well as the photocurrentfrom the depletionregions.
Current is assumedto flow in sheets parallelto the top surfaceof the
converter;thus the model contains no diffusionbetweensheets. These
currents,when summed, producethe total short circuitcurrent. At this
depth (B), we assume that a narrowstrip exists which behaves like a
conventionalphotoconverter. The short circuit currentand dark currents
are used in the equivalentcircuitdiagramof figure 3 togetherwith the
effects of the series resistance(Rs) and shunt resistance(Rsh) to
obtain a current-voltagerelationship.
The temperatureof the photoconverteris determinedby the balance
betweenthe rate of heat productiondue to the fractionof absorbed laser
power which is degradedto heat and the rate of heat loss by conduction.
The model includesa heat-transfercalculationfrom the converterto a
heat pipe at the back face of the device. The devicetemperaturemay be
controlledby varyingthe heat pipe temperatureand the heat-transfer
coefficient.
3Approach
Using the computer code developed for the model, a study of the Nd
" laser-Si vertical junction photovoltaic converter was conducted. (Table I
shows the baseline parameters used in this study.) In this study, these
baseline parameters were varied individually in order to determine the
optimum value for each parameter.
Results
Wavelen_th
Figure 4 shows the efficiency as a function of wavelength. The
efficiency varies from 8 percent at a wavelength of 0.6 _m to 54 percent
at a wavelength of 1.05 _m. At the wavelength of the Nd laser (1.06 um),
the converter efficiency is 53 percent at baseline conditions.
Converter Width
Figure 5 shows the effect of increasing the converter width with the
p-n junction located I0 um from one edge. The efficiency is highest for
the smaller widths. The efficiency is about 56 percent for a width of 20
_m, and it remains above 50 percent for widths as great as
55 um. Based on these data, for a small sacrifice of efficiency, wider
single crystal converters can be used. Thus, for a series-connected,
multijunction device, a range of currents and voltages can be achieved.
Although smaller width converters can produce slightly higher
efficiencies, for the purpose of this study, the optimum achievable width
is 20 _m.
4Junction Position
The efficiency for the baseline converter is a strong function of
the width of the p-region (here called junction position). Figure 6 shows
this efficiency as a function of junction position for the 20 um wide
baseline converter. As the junction position is changed from 2 um to 16
_m, the efficiency increases from approximately 38 percent to 57 percent.
As the junction position is moved to greater values, the width of the
p-region increases. The p-region has longer minority carrier diffusion
lengths thus accounting for an increased efficiency (ref. 4). For our
optimum cell, the junction position is chosen to be 16 _m..
Converter Thickness
Figure 7 shows the efficiency as a function of converter thickness
for the baseline converter. Thickness is the distance in the direction of
travel of the laser light within the converter. The efficiency
increases from less than 2 percent at a thickness of I x 10-3 cm to
greater than 53 percent at a thickness of 1.5 x 10-I cm. The photons from
the 1.06 _m laser are absorbed relatively deep in the semiconductor. From
this the thickness of our optimum cell is 1.5 x 10-1 cm.
Temperature and Heat-Transfer Coefficient
The interface between the heat pipe and the converter must be an
electrically insulating, thermally conducting surface. However, the major
emphasis of our investigations has been on the structure and performance
of the converter. The baseline heat-transfer coefficient was chosen to be
q
I00 cal sec-I cm-2 °C-1, corresponding to a layer of insulating material.
By varying the heat-transfer coefficient and the heat-pipe temperature,
the converter temperature can be varied. Figure 8 shows the efficiency as
a function of temperature. The efficiency at our baseline temperature of
293 K is 52 percent. This efficiency decreases to 28 percent at 500 K
5with a temperature coefficient of approximately -0.13 percent/K. Our
optimum cell uses a heat-transfer coefficient of 40 cal sec-I cm-2 °C-I to
maintain the operating temperature of 293 K.
Power Density
Lasers in space for power-transmission applications may provide power
densities up to I x 103 watt/cm 2 at the receiver. Figure 9 shows the
efficiency as a function of power density for baseline conditions. The
efficiency increases from about 41 percent at I watt/cm 2 to about 53
percent at i x 103 watts/cm 2. Not only the current, but also the voltage
increases with increasing absorbed power to produce this increased
efficiency. The incident power density for our optimum cell is chosen as
I x 103 watts/cm 2. For a 50 percent efficient converter a heat transfer
rate of 5 x 102 watts/cm 2 would be required.
Series Resistance
At high-power densities, the series resistance is one of the most
important photovoltaic converter parameters. The vertical junction
converter minimizes series resistance by minimizing the current path from
the junction to the contact. Figure I0 shows the efficiency as a function
of series resistance. As the series resistance increases from i x 10-3
ohm to I ohm, the efficiency decreases from 53 percent to less than
I0 percent. The series resistance chosen for our optimum converter is
I x 10-2 ohms, well above the bulk resistance of 9 x I0 -s _.
Carrier Concentration
Figure 11 shows the converter efficiency as a function of acceptor
concentration for four different donor concentrations. The peak
efficiency of 59 percent is reached for both a donor and acceptor
concentration of i x 1017 carriers cm-3. Therefore, for our optimum
6converter we have chosen both a donor and acceptor concentration of
-3
I x 1017 carriers cm .
Surface Recombination Velocity
The effect of surface recombination velocity on the converter
efficiency is shown in Figure 12. Increasing the surface recombination
velocity on the n-contact surface from I cm sec-z to I x I0 s cm sec-z
decreases the efficiency from 53 percent to 29 percent. Increasing the
surface recombination velocity on the p-contact surface from 1 cm sec-I to
I x 104 cm sec-I decreases the efficiency from 53 percent to 38 percent.
Recombination velocities of 5 x 102 cm sec-I are required to keep the
calculated efficiency above 50 percent. For our optimum converter we have
chosen a recombination velocity of I x 102 cm sec-I (ref. 4) on both the
n and p contact surfaces.
Conclusions
Table II shows the parameter values for our optimum single p-n
junction converter. The parameter values chosen for our optimum converter
are considered attainable. For example, a converter width of 20 um was
chosen as an attainable dimension, although narrower converters have a
higher theoretical efficiency. In reality, a practical device would be
composed of multiple p-n junctions connected in series. This has been
accomplished previously by mechanically stacking silicon wafers (each
containing a p-n junction) and providing a metal contact between each unit
(ref. 5); however, the silicon wafers were 240 _m wide. The narrower
width of fragile silicon p-n junctions in our proposed converter would
probably require a substantially different method of fabrication. It has
recently been demonstrated that an epitaxial single crystal composite of
7siliconand metallicCoSi2 can be fabricated(ref. 6). This opens the
possibilityof fabricatinga series-connectedmultiplep-n junctiondevice
where all the elementsof the device,even the metal contacts,are single
crystal. The shunt resistancefor our optimumconverterwas realistically
chosen as 1 x 106 ohm (ref. 4). A converterthicknessof 1.5 x 10-I cm
will allow for absorptionof the 1.06 _m Nd laser radiation. The junction
positionof 16 um providesthe maximumoutput for this width converter.
Carrier concentrationsof 1 x 1017 carriers cm-3 attainsthe highest
efficiency. The optimizedconverterhas a calculatedefficiencyof 55
percentfor the 1.06 _m Nd laser radiation.
8
APPENDIXA
Model
The model for this vertical junction converter uses the device
geometry shown in figure 2 and assumes a generation rate at a depth B
gi yen by
g(B) = €o(I - Re) _e-_B
where €o is the number of incidentphotons[cm-2 sec-1];_ is the
absorptioncoefficient[cm-1];and Re is the reflectioncoefficient.
The basic equationsfor a n/p device involvesthe photocurrentfrom the
n and p materialsas well as the photocurrentfrom the depletion
region. The currents,when summed,producethe total short circuit
current. Followingreference7, we assumethat there exists a narrow
strip at a depth B below the surfacewhich behaveslike a conventional
photoconverter. At this depth B, we have the hole excess in the n-region
giyen by
d2 (Pn - Pno) -g(B) Xj + Xn < X < B
Dp d-_ (Pn - Pno) - =p = ' -- --
which is subject to the boundary conditions
- Dp-_ (Pn - Pno) : Sp(Pn - Pno)JX : B
and
PnoJPn - X = Xj + Xn o
This produces the current density
d(Pn - Pno)
Jp : qDp dx IX = Xj + n = -qg(B)Lpf(Sp,Dp/Lp, (B-Xj-Xn)/Lp)
_ a - a cosh(c) - b sinh(c) 9
where f(a,b,c) b cosh(c) + a sinh (c)
Similarly, the electron excess in the p-region is given by
_ )(np npod2
- ) - : -g(B), o < X < Xj - XDn d-_ (np npo _n P
with boundaryconditions
- ) : Sn - ) Ix : oDn _ (np npo (np npo
- I Xp = onp npo X = Xj -
This produces the current density
Jn : -qDndx(np- nPo J X = Xj _ Xp= -qg(I3)Lnf(Sn, Dn/Ln, (Xj - Xp)/Ln)
where Xj is the junction depth and Xp,Xn define the space charge
region. The photocurrent from the depletion region is neglected, and we
have the total short circuit current density as a function of B
Jsc = Jsc (B) : Jn (B) + Jp(B)
The total current is obtained by integrating these current densities over
the depth of the photoconverter and
A
Isc = f Jsc(B)dB0
Following reference 4, the dark current is given by I = Ip* + In* where
we have assumed a photoconverter depth in the Z-direction of 1 cm to
obtain the dark currents:
B - Xj - Xn SD__p (eqV/kT_ 1Ip* : L_ F( kp ' ) • )a
I0
and
qDn X X SnLn
In. = _ n F( J - P' _ ) • [eqV/kT-z]APo Ln n
which gives the injection current
lin j = Ip. + In. = I o (eqV/kT-1) ,
where
B + tanh(A)F(A,B) - 1 + B tanh(A) "
Also, from reference 4, we use the recombination current density of
xqniW sinh(2V-q_kt)j :
rec /(T T ) q(Vb -V)/kT
pn i
where Vbi is the built in voltage, ni is the intrinsic carrier
density, W is the width of the depletion region, T is temperature, q is
electron charge, Tp and Tn are lifetimes, V is voltage, and k is
Boltzmann's constant. The short circuit currents and dark currents are
used in the equivalent circuit diagrams of figure 3, and we obtain the
current voltage relation
Rs - V/Rsh I rcq(V+IRs) -I] - II(I + _) = Isc - oL kT rec "
which includes the effects of the series resistance Rs and shunt
resistance Rsh.
11
Table I
Baseline Parameters
Series Resistance 0
Heat Pipe Temperature 20°C
Heat-TransferCoefficient 100 cal sec-1 cm-2 °C-I
SurfaceRecombinationVelocity on n-surface 0 cm sec-I
SurfaceRecombinationVelocity on p-surface 0 cm sec"I
Input Power 1 x 103 w/cm2
Laser Wavelength 1.06um
ConverterThickness 1.3 x 10-I cm
ConverterWidth 2.0 x 10-3 cm
ConverterLength 1 cm
Junction Position 1 x 10-3 cm
AcceptorCarrierConcentration 1.25 x 1017 cm-3
Donor CarrierConcentration 5.0 x 1019 cm-3
ReflectionCoefficient 0.05
Shunt Resistance 1 x 106 ohms
12
TableII
Parametersfor OptimizedConverter
Series Resistance 1 x 10-2 ohms
Heat Pipe Temperature 20°C
Heat-TransferCoefficient 40 cal sec-I cm-2 °C-i
RecombinationVelocity on n-Surface 100 cm/sec
RecombinationVelocity on p-Surface 100 cm/sec
Input Power 1 x 103 watts/cm2
Laser Wavelength 1.06um
ConverterThickness 1.5 x 10-1 cm
ConverterWidth 20 _m
ConverterLength 1 cm
Width of the p-region 16 _m
Acceptor CarrierConcentration 1 x 1017 carriers/cm3
Donor CarrierConcentration 1 x 1017 carriers/cm3
ReflectionCoefficient 0.05
Shunt Resistance 1 x 106 ohms
13
REFERENCES
1. DeYoung, R. J.; Tepper, W. D.; Conway, E. J.; and Humes, D. H.:
"Preliminary Comparison of Laser and Solar Space Power Systems."
- Proceedingsof the 18th IntersocietyEnergy ConversionEngineering
Conference. Orlando,FLorida;August, 1983; pp. 983-989.
2. Walker, G. H.: "Photovoltaic Conversion of Laser to Electrical
Power." Proceedings of the 18th Intersociety Energy Conversion
Engineering Conference. Orlando, Florida; August, 1983; pp.
1194-1199.
3. Williams, M. D.; Zapata, L.: "Solar-Pumped Solid State Lasers." NASA
TM87615, 1985.
4. Hovel, H. J.: Semiconductors and Semimetals, Volume II, Solar Cells,
Academic Press, 1975.
5. Sater, B. L.; Brandhorst, H. J., Jr.; Riley, T. J.; Hart, R. E., Jr.:
"The Multiple Junction Edge-llluminated Solar Cell," Conference
Record of the lOth Photovoltaic Specialist Conference, Nov., 1973,
Palo Alto, California, p. 181.
6. Hensel, J. C.; Levi, A. F. J.; Tung, R. T.; and Gibson, J. M.:
"Transistor Action in Si/CoSi2/Si Heterostructures," Appl. Phys.
Lett. 47, July 15, 1985, p. 151.
7. Grover, A.; Stella, P.: "Vertical Multijunction Solar Cell One
Dimensional Analysis," IEEE Transactions on Electron Devices, Vol.
ED-21, June, 1974, p. 351-356.
14
4.o.e
3.Oe I
Dye
.).5eV laser
GaP12.26eV) = energy
AlAs(2.16eV) = range
2.0eV IAISb(1.60eV)
InP (1.28eV) Laser
(1.18eV) Nd Depletion region
Si (1.11eV)1.0eV (0.95eV) C3F71 Y = A ,
1 o°
Oe (0.67eV) .).5 eV (0.45eV) IBr ' "
InAs (0.36eV) . (0.25eV) CO p-region J n-region I$
= (0.18eV) C02 !
y = O xj-Xp _jSemicondudor Energy Laser x = O xj+Xn x = B
Figure 1 - Semiconductor bandgap energy Figure 2 - Converter geometry
- laser photon energy relationship
60 Parameters: Baseline
RS Efficiency, %
"}lout 20Idark RSh RL I I I I I.6 0.7 0.8 0.9 1.0 1.1• Wavelength, IJm
Figure 3 - Equivalentcircuit Figure 4 - Converterefficiencyvs.
laser wavelength
15
Thickness = 1.3 x 10 "1cm
I_n = 1 x 103 W/crn 2 _ Parameters: Baseline
H= = lOOcal sec-lcm'2°C'l I 60
Tpipe = 20°C ! __
60 RS = 0
'°Lp = 21.9 pm
40 _ Ln =64.1=. pm Efficiency,%
Efficiency, % _ 20
2O
I llllllli ll[lilllll
0 _ 80 120 160 200 0 4 8 12 16 20
W_th, pm Junctlonposition, pm
Figure 5 - Converter efficiency vs. Figure 6 - Converter efficiency vs.
converter width junction position for a 20 _m-wide
converter
60 60
Parameters: Baseline
40 40Efficiency, % Efficiency, % Baselinewith variable heatpLoetemperature and heat
2C 20 transfer coefficient
I -I I 0 I I I I I
1 .4 10 10 "= 10 1 300 350 400 450 5000 o
Converter thickness,cm Temperature, K
Figure 7 - Converter efficiency vs. Figure 8 - Converter efficiency vs.
thickness temperature
16
Parameters: Basehf=e60 Parameters: Baseine with variable power in 6(_
40 40
Efficiency, % Efficiency. %
20 ', 20
0 I I I 0 I I I I
10 "= 10"1 lO't 100 10 "4 10-_ 10"= 10"1 10 °
Power in, kW cm"2 Series resistance, ohms
Figure 9 - Converterefficiencyvs. Figure 10 - Converterefficiencyvs.
input power density series resistance
Parameters: Baseline 60
6o ...............
40 Donor concentration 40 _- "-" -
I x lOtecm "=
1017__- "`Efficiency, % .... 1 x u,. Efficiency, %
...... 1 x 101=cm'=
-'--1 x 101*cm "=
20 20 _ S n
--- Sp
0_) I I i I I01Cie 1/'' 1_)'8 1_3" o 10' 10 = 10_ 10' 10s
Acceptor concentration, cm"= Surface recombinationvelocity, cm sec-t
Figure 11 - Converterefficiencyas a Figure 12 - Converterefficiencyvs.
function of acceptor concentration surfacerecombinationvelocityon the
for four differentdonor concentrations n- and p-contactsurfaces

1. Report No. 2. Government AccessionNo. 3. Recipient's Catalog No.
NASATM-89041
'4. Title and Subtitle 5. Report Date
Photovoltaic Conversion of Laser Power to September 1986
Electrical Power 6. PerformingOr anizationC de506-41-41-01
7. Author(s) 8. PerformingOrganization Report No.
Gilbert H. Walker and *John H. Heinbockel
10. Work Unit No.
9. PerformingOrganization Name and Address
NASALangley Research Center
Hampton, VA 23665-5225 11.Contractor Grant NO.
13. Ty_ of Report and Period Cover_
12. Sponsoring A_ncy Name and Addr_s
National Aeronautics and Space Administration Technical Memorandum
Washington, DC 20546 14. Sponsoring A_ncy Code
IS._pp_ementarvNotes*Old Dominion University, Norfolk, Virginia.
Presented at the Space Photovoltaic Research and Technology Conference,
Cleveland, Ohio, October 7-9, 1986.
16. Abstract
Photovoltaic laser to electric converters are attractive for use with a
space-based laser power station. This paper presents the results of
modeling studies for a silicon vertical junction converter used with a
Nd laser. A computer code was developed for the model and this code
was used to conduct a parametric study for a Si vertical junction
converter consisting of one p-n junction irradiated with a Nd laser.
These calculations predict an efficiency over 50 percent for an
optimized converter.
17. Key Words (Suggestedby Author(s)) 18. Distribution Statement
Energy conversion Unclassified - UnlimitedPhotovoltaic converters
Solid state devices Subject Category 44Laser-photovoltaic
19. Security Oassif. (of this report) 20. Security Cla.if. (of this _) 21. No. of Pages 22. Dice
Unclassified Unclassified 17 A02
N-30s ForsalebytheNationalTechnicalInformationService,Springfield,Virginia22161




Photovoltaic conversion of laser power to electrical power

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