ADVANCED APPROACHES

257

CHAPTER VII: ADVANCED APPROACHES

Introduction In Chapters IV through VI we considered the performance of solar cells both in the abstract and utilizing concrete examples wherein the semiconductor, optical orientation, and construction technology were specified. These examinations of performance took place under AMO and AMI conditions. We may consider a solar cell system operating under simple AMO or AMI conditions to be a stage one solar cell system. Let us define a stage two solar cell system as one which concentrates sunlight and allows this concentrated light to impact the solar cells. There exist several powerful reasons for using concentrated sunlight as the energy source. The principal reason is cost. Note that the single crystal semiconductor solar cells which we have been considering are expensive (both in terms of "dollars" and in terms of time) to fabricate and that they exhibit a number of loss mechanisms (hole-electron pair recombination, series resistance, etc.). It is, generally, less expensive to fabricate mirrors and/or lenses which can then be used to collect sunlight over a large area and to focus this light on a relatively small area of semiconducting solar cells. Not only do we replace large amounts of expensive solar cells with inexpensive lenses (or mirrors), but the intense, focused sunlight which illuminates the solar cells tends to saturate a number of solar cell loss mechanisms and so improve overall solar cell efficiency. It should be noted that when we concentrate sunlight we need to have some tracking mechanism so that the solar power system is aligned with the sun. However, even with the additional cost and complication of a tracking mechanism, the overall system cost per provided KWH of a concentrating solar energy system can be significantly lower than for a non-concentrating, non-tracking system [1-4]. Another reason for the use of concentrated sunlight arisesft-omthe availability of thermal as well electrical energy fi"om the solar power system. The solar cells are exposed to a high concentration of photons.

258

CHAPTER VH: ADVANCED APPROACHES

Though the efficiency of the solar cells increases, a significant fraction of the solar energy is still converted to heat in the semiconductor. This is undesirable since, as we shall see in this chapter, increased solar cell temperature results in reduced efficiency in converting solar energy to electrical energy. Thus, this heat must be removed from the solar cells and if the energy density is sufficient, then the thermal energy removed from the solar cells while cooling them can be used to heat water, or living spaces, or for some industrial purpose We will spend most of this chapter on these stage two solar cell systems. There is a stage three type of solar power system. From our earlier discussions it is evident that no semiconductor is an ideal match for the solar spectrum (either AMO or AMI). There are too many high energy photons in sunlight, which, when absorbed, yield the standard Eg of electrical energy with the rest of the photon energy ending up as heat. There are also too many low energy photons in the solar spectrumphotons that pass completely through the semiconductor. Third stage solar energy systems initially alter the spectral distribution of sunlight to a form which is a closer match to the ideal spectrum for a particular semiconductor. These third stage systems also furnish the energy consumer with both electrical and thermal energy. We will consider the theoretical aspects of these systems in the following chapter. If we consider the effects of optical concentration on solar cells, the observed phenomena are of three kinds. First, with increased photon flux density the hole-electron pair generation increases. From the discussions in Chapter HI, the greater density of holes and electrons will increase the recombination rate, however, the recombination mechanisms will begin to saturate as the carrier density increases. Thus a smaller percentage of the hole-electron pairs will be lost via recombination, and title photocurrent and device output power density will increase, yielding a higher operating efficiency. Second, the increased number of electronhole pairs in the relatively lightly doped substrate layer of the solar cells tends to reduce the resistance of the substrate (an effect improving device efficiency) while depressing the collecting electric field. This results, unfortunately, in an increased surface recombination rate. Finally, the principal effects of the use of concentrated sunlight are thermal. The incoming light energy is converted to both electrical and thermal forms of energy. The thermal energy will act to raise the junction temperature of title solar cells, in tum decreasing the efficiency with which they convert optical to electrical energy.

CHAPTER Vn: ADVANCED APPROACHES

259

As in our earlier studies, our examination of the effects of optical concentration on solar cells will be based on studying the example semiconductors and design philosophies addressed for the first stage systems in Chapter VI. We begin with an examination of temperature.

Temperature Effects From Chapter V, the saturation current densities for the various types of junctions under consideration are: (a) for pn junctions qDpnHi' J3=

qD^pn^' -h

-Lpn-No

,

(VEl)

LjjpN^

where the first term on the right hand side refers to the n-type region of the junction and the second term to the p-type region. Recall fi'om the discussions in Chapter VI, that pn junction solar cells are constructed fi*om a moderately doped substrate and a heavily doped, "fi*ont layer". F r o m the typical impurity concentration levels of the examples in Chapter V I it is clear that the contribution of the "fi-ont layer" to the saturation current density is minimal, reducing Equation V n . l to but a single term, that due to the substrate:

(b) for heterojunction devices Js = JsH = (qDsn,^/LsNs)XT ,

(VIL2)

where the narrow energy gap substrate is primarily responsible for the saturation current density and the only effect fi-om the wide energy gap "fi*ont layer" is the X^ which accounts for carrier transport effects across the junction. This factor is characteristically less than iinity [5]. In this analysis, we will make the conservative estimate that X^ is unity and, fiirthermore, is not a function of the temperature [6]: (c) for a Schottky barrier the saturation current is

260

CHAPTER VH: ADVANCED APPROACHES

Js = Jss = A*T^exp{-q(l)3,/kT} ,

(Vn3)

and (d) for mos type Schottky barriers Js = Jss = A**T2exp{.q(t)B,/kT} ,

(VIL4)

where A* is the Richardson constant and A** is the modified Richardson constant. As indicated in Chapters V and VI, the mos-Schottky device is imperfectly understood at present and sufficient data for a fiill engineering analysis is not available. We will not consider mos-Schottky barriers further. Beginning with the pn junction let us consider the saturation current densities for pn, heterojunction and Schottky barriers in detail. From Chapters IE and VI we have, for the diffusion constant and diffusion length of the lightly doped substrate region: Ds = {kT/qj^is and Ls = /{Dsis} .

(VIL5)

From Chapter in it is clear that the mobility and lifetime in the substrate are temperature dependent. Assuming that the carrier capture cross section and trap density are temperature independent, then lifetime for trap recombination will vary roughly inversely with the square root of the temperature. Thus, the principal variation with temperature of the saturation current in pn junctions is due to the temperature variation of the intrinsic carrier concentration which has a dependence of the form: n/ oc T'exp{Eg(T)/kT} .

(VIL6)

To first order, we may write for pn junctions: Js(T)/Js(300) = (T/300)'exp{Eg(300)/k300 - Eg(T)/kT} .

(VET)

The variations in energy gap with temperature for the example semiconductors used in this work are provided in Appendix B. Specific values of the intrinsic carrier concentration squared are furnished in Table m.2 and the ratio of Js(T) to Js(300) for Si, InP, GaAs, CdTe and AlSb are displayed in Figure VII.l. Note that the range in temperature is ft'om 300°K to 500°K. Study of Figure VII.l combined with observation of Figures V.8 through V.15 indicates that the output power density of pn

261

CHAPTER VH: ADVANCED APPROACHES

junction solar cells at SOO^K lies between 10 and 40% of the value at 300°K. Even at 400°K the performance is much degraded. 10'^ -

CdSe AlSb

I0'2 -

/ /

10'°

o

O

CdTe GaAs y/y^^ InP

Silicon

fl

ro 10® ^t/>

•^ \

S>'°'

/ /

J^/

•-D

10^

/ / ^

^

10^

-

1

300

400

500

Figure Vn.l. PN and heterqjunction saturation current densities as a function of the temperature, normalized to the saturation current density at 300°K with the substrate semiconductor as a parameter. Examination of Equation Vn.2, which provides the saturation current density for heterojunctions as a function of temperature,

262

CHAPTER VH: ADVANCED APPROACHES

indicates that the temperature dependence of the saturation current for these devices exhibits the same characteristics as the pn junctions of Figure VII. 1. The curve in this figure for cadmium selenide is seen to be that for a heterojunction on n-type CdSe. Note that we can maintain a low junction temperature in a solar cell by cooling it. If we do this, we can use a portion of this thermal energy to provide space and/or material (e.g., water) heating. In such a situation, overall system energy requirements may actually encourage some decrease in electric output from the solar cells while the resulting increase in junction temperature yields a more efficient extraction of thermal energy (see Equation 1.4). At this juncture, without full system and economic details, we can do no more than to remark that operation for solar cell junction temperatures in excess of approximately 400°K is inefficient. Consider the changes in Schottky barrier saturation current induced by shifts in temperature. Assuming that the effective mass is temperature independent, then, from Equation VII.3: Js(T)/Js(300) = (T/300)^exp{q(l)3,(300)/k300 - q(|)Bo(T)/kT} .

(Vtt8)

In Table VI.4, a number of Schottky barrier energy values (at 300°K) for the six example semiconductors are presented. As the temperature increases, we expect the barrier energy to vary as [8]: 4>Bo(T) = (t)Bo(300) -h A^T) .

(VIL9)

In covalent semiconductors, the presence of surface states pins the Fermi level, at the surface, relative to the conduction band edge. In such instances, it has been found that the barrier energy varies in temperature as does the energy gap [9]. This is the situation for silicon. The other five example semiconductors are ionic, or nearly ionic. In an ionic semiconductor, the Fermi level, at the semiconductor surface, can move freely between the conduction and valence band edges. This variation of surface barrier energy with temperature is expected to be proportional to that fraction of the energy gap occupied by the Schottky barrier. Therefore: A, = d<\>JdT = ((J)B,/E^(aE^aT) .

(VBLIO)

CHAPTER Vn: ADVANCED APPROACHES

263

The temperature dependence of the saturation current density for selected Schottky barriers is presented in Figure VII.2. Because of the I0«

Pt on GaAs Pt on Si

n-TYPE

o "0^

Pt on CdTe

o

Pt on InP Pt on AlSb Auon CdSe

^

h-

w

,^

^^ .^^^^


*r>

"" -

10^

-

1

300

400

500

T^K) 10*

Hf on Si

p-TYPE O >0

Au on InP Pt on CdTe

h-

o

Au on AlSb

^ 10^

Au on GaAs

Y ^

10'h

Y . 300

400

500

Figure Vn.2. Saturation current density for selected Schottky barriers versus temperature, normalized to the saturation current density at 300°K.

264

CHAPTER VU: ADVANCED APPROACHES

smaller barrier heights, the increase in current with temperature is less for Schottky barriers than for pn or heterojunctions. However, our studies in the preceding chapters have indicated that, with present day technology, we start with a higher level of saturation current density, and hence, with a lower solar cell efficiency. Study of Figures Vn.l and Vn.2 makes it all-too-plain that the allowable degree of temperature rise is limited. The exact degree of permissible temperature rise is the result of trading off photovoltaic efficiency and produced electric power with increasing utilization of the heat rejected by the solar cells to some cooling medium [10].

Heat Flow within a Solar Cell Figure VII.3 displays thermal diagrams for standard and vertical configuration solar cells, assuming heat flow into the sink located on the down or non-illuminated surface only. Note that heat is generated in two ways in these solar cells. First, there are ohmic losses (l\) as a result of the current flowing through the resistance, r^, of the solar cell. Second, there is the thermal energy which represents the difference between the energy of the absorbed solar photons and the realized electrical energy of the generated electron-hole pairs. For air-mass-one conditions these two components of heat energy will range in size from 107N mW/cm^ (a solar cell with zero percent efficiency for conversion to electrical energy where N is the degree of optical concentration) to approximately SON mW/cm'2 for a solar cell of 25% electrical conversion efficiency. This heat energy is distributed over the entire volume of tiie solar cell. However, as can be seen from study of the absorption curves of Chapter IV and the series resistance discussion of Chapter VI, the bulk of the heat is generated near the illuminated surface*. The conservative approach to thermal analysis that we will follow here, is to assume that

* Figure VII.3 depicts standard and vertical configuration solar cells. An inverted configuration resembles an upside down standard configuration cell. For such a device the thermal energy derived from the excess photon energy is generated near the illuminated surface. However, the bulk of the heat energy derived from the flow of current is generated close to the heat sink.

CHAPTER VII: ADVANCED APPROACHES

265

LIGHT

i

T

"FRONT LAYER"

150 urn

SUBSTRATE

1

MOUNTING SOLDER

25ftm

7777777Z

T

HEAT SINK

V

LIGHT

i

T

SOLAR CELL

150/xm

1 T

MOUNTING SOLDER

y///////////////A

Figure Vn.3. Thermal configurations for standard (the upper figure) and vertical (the lower figure) configuration solar cells. the thermal energy is generated at the illuminated surface and then flows through the semiconductor to reach the heat sink. Let Tg be the temperature of the heat sink, and Rj be the thermal resistance of the solar cell and other material between the heat sink and the solar cell junction. Then, for a heat energy flow, 0^, between the junction and the heat sink, the temperature of the junction, Tj, is: Tj = Ts + RT0T

where R^ is given by:

(VDLll)

266

CHAPTER VH: ADVANCED APPROACHES

R T = /{pT(z)/A(z)}dz ,

(yiL12)

where the integral is from the heat sink to the solar cell junction (in the direction z); A(z) is the cross sectional area through which the heat is flowing; and p^Cz) is the thermal resistivity of the semiconductor, the mounting solder and any other materials between the heat sink and the junction. The thermal resistivity of mounting solder is difficult to accurately determine. From sales literature, a value of 4°C-cm per watt is obtainable, if the solar cell is correctly mounted on the heat sink. If it is not, the solder thermal resistivity may be one to ten orders of magnitude higher. The thermal resistivity of the example semiconductors is presented in Table VH.l. Table VH.l The thermal resistivity (°C-cm/watt) at SOO^K Semiconductor PT

Reference

Si

InP

GaAs

CdTe

AlSb

CdSe

1 [11]

1.43 [12]

1.13 [13]

14.29 [14]

1.11 [15]

15.87 [16]

It should be noted that the thermal resistivity is a function of temperature for most materials and certainly is so for semiconductors [17]. However, it is clear, from our earlier study of saturation current density, that large excursions in temperature are undesirable. Therefore, for this first order study of thermal effects, we will assume a constant value of thermal resistivity for our semiconductors. The junction temperature of a standard, vertical or inverted configuration solar cell can now be determined if we know the degree of optical concentration, N; the thermal resistance or the solder and semiconductor; and the operating temperature of the heat sink. The heat flow power density under the conditions of maximum electrical power output power density is: 0T = NI^{1 -Ti/lOO} ,

(WB)

CHAPTER Vn: ADVANCED APPROACHES

267

where I^ = 135.3 mW/cm^ for AMO conditions and equals 107 mW/cm^ for AMI conditions, and: Tls = Pn^lAoNI^} ,

(VIL14)

where P^ax/Ao is determined using Equation VI. 18 subject to the conditions that the photocurrent density, Jp^, is N times its unconcentrated value and that the operating voltage for maximum power output, V^', and the diode loss factor, K', must mutually satisfy Equations VI. 16 and VI.17. For vertical configuration solar cells the situation is somewhat more complicated than for the standard and inverted configuration devices. The saturation current depends upon the temperature of the junction andfi*omFigure Vn.3 it is clear that the junction temperature for vertical configuration cells varies across the device. Returning to Equation V n . l l , we can write for vertical configuration solar cells: T. = Ts + AT, (z),

(VKIS)

where AT^ (z) is the temperature rise across the semiconductor and mounting solder, assuming z = 0 to be the heat sink location. This comphcation makes it necessary to integrate fi"om the heat sink to the illuminated surface in order to determine the saturation current density for a vertical configuration solar cell. As discussed in Chapter VI, the vertical configuration solar cell has a tendency to exhibit a higher photovoltage at the illuminated surface-due to the nature of the absorption coefficient. The combination of temperature and photovoltage variations makes it difficult to analyze the efficiency of these devices in detail, unless the exact structure of the cell is known. Rough calculations suggest a saturation current density of fi-om 20 to 60 percent of the value calculated assiuning that the entire junction is at a temperature equivalent to the illuminated surface. The inverted solar cell has its junction close to the heat sink which means that its operating junction temperature is somewhat lower than the other devices; again depending on construction details. It is clear, at this point, that further pursuit of the thermal analysis of solar cell systems would involve much detailed analysis of materials, fabrication techniques, thermal energy exchange between solar cell and heat sink, and of the general ambient conditions. Still, it is

268

CHAPTER VH: ADVANCED APPROACHES

important that we consider the effects of temperature on the perforaiance of solar cells. Either deliberately (owing to the desire for extra thermal energy) or accidentally (because of faulty construction techniques) it is possible to encounter high operating temperatures. Study of Figures Vn.l and Vn.2 and the general performance data of Chapter V indicates that it is unwise to consider solar cell operation at junction temperatures much in excess of 400°K. For the purposes of our initial study of the effects of junction temperature, let us assume that the junction temperature is either 300, 350 or 400°K. Earlier, in Chapter VI, we considered the 300°K case under single sun (N=l) illumination. We now commence our broader study by determining the saturation current density for our example semiconductors as a function of temperature using Figures Vn.l and

vn.2. Table Vn.2 M(T) = Js(T)/Js(300°K) as a function of barrier type, temperature, substrate and semiconductor Semiconductor

Si

InP

GaAs

CdTe

AlSb

CdSe

350°K PN & Heterojunction l.lxlOM.2xlO'7.8x10'9.3x10' 2.5x10' 5.0x10' Schottky on n-type 290 053 430 130 48 25 * Schottky on p-type 381 140 026 120 48 400°K PN & Heterojunction 1.8x10^ 2.4x10'7.5xlOM.0x10^ 5.6x10^ 1.3x10^ Schottky on n-type 3.0x10' 1000 5.6x10' 5620 1000 237 Schottky on p-type 3.2x10'4730 237 1540 0750 ™* *p-type CdSe is not commercially available

We will be examining the temperature variations by using specific examples. In tum, this will indicate that some designs of solar cells are more temperature sensitive than others and some semiconductors are more sensitive than others. In this work, it will merely be noted that the design of solar cells for high junction temperature operation may be beneficial in that it allows more efficient use of the heat rejected to the cooling

CHAPTER Vn: ADVANCED APPROACHES

269

system. The scientific literature has been relatively silent on such designs, but some work is being done [18-21]. As we treat optical concentration in this chapter, the reader will be able to draw conclusions as to the amount of effort which may prudently be expended on heat sinking and thermal matters in general.

Optical Concentration - Photocurrent The hole-electron pairs generated by incoming photons serve to reduce the series resistance in the substrate as well as to provide the photocurrent. In Chapter VI an estimate was made of the photocurrent generated under single sun conditions for the various device configurations and junctions. For convenience, these values are reproduced in Table Vn.3. Note that these values are not the ideal current densities, but have been reduced to account for reflection and transmission losses of incoming photons, bulk and surface recombination effects and surface metallization effects. In particular note that the metallization required to form Schottky barrier standard configiu*ation cells drastically reduces the available photocurrent. Also note that the expected photociurent for inverted configuration solar cells is quite high. This is a direct result of the construction employed for these cells—a construction which effectively results in a light collecting area which is double the junction area. This, in turn, results in an effective optical concentration of ^1.95 for an inverted configuration solar cell. The photocurrent densities listed in Table Vn.3 are conservative estimates based upon the discussions in Chapters III through VI and upon work elsewhere upon various collection models [19, 22]. The distribution of the hole-electron pairs which gives rise to this current, is not uniform over the entire thickness of the solar cell, but is skewed towards the illuminated side. The exact nature of the generated carrier distribution may be inferred from Figures rV.6 and rv.7. Let us currently assume that the distribution of generated carriers is roughly even over the entire solar cell. (Note-a photocurrent density of 32 mA/cm^ such as that predicted for GaAs standard configuration heterojunctions under AMO conditions in Table VII.3 implies an electron-hole pair generation rate of 2 x lO'Vcm^-sec.) From the discussion on solar cell design in Chapter VI, the optimum solar cell design has its lowest substrate impurity

270

CHAPTER Vn: ADVANCED APPROACHES

Table Vn.3 The photocurrent density (mA/cm^) for standard, inverted and vertical configuration solar cells vinder AMO and AMI illumination for pn, heterojunction and Schottky barrier solar cells Semiconductor

Si

InP

GaAs

CdTe

AlSb

Inverted configuration (all junctions) 69.81 54.34 87.07 81.31 72.54 53.04 42.71 70.40 62.01 55.97 Vertical configuration (all junctions) AMO 33.90 27.10 42.70 39.50 35.30 AMI 25.70 20.80 34.20 30.10 27.20 Standard configuration (Schottky barrier) AMO 07.53 06.15 10.59 02.34 06.96 AMI 08.34 01.89 05.25 05.70 04.68 (pn junctions) AMO 22.54 18.45 31.77 07.02 20.88 14.04 AMI 25.02 05.67 15.75 17.10 (heterojunctions) AMO 30.43 24.31 37.97 35.44 31.62 AMI 23.12 18.62 30.68 27.03 24.40 •Recall that p- type CdSe is not commercially available

AMO AMI

CdSe

50.70* 39.98* 24.70* 19.50*

03.75* 03.06* * *

22.10* 17.42*

concentration close to the junction. Here, Ng is on the order of 10^Vcm^ In the "front layer" the impurity concentration is close to lO^Vcm^ in both pn and heterojunction solar cells. Near the substrate contact, when the substrate is graded to facilitate carrier collection, the impurity concentration approaches 10^7cm^ Thus, solely near the junction in the substrate region of the solar cell, is the addition of hole-electron pairs liable to make a major contribution to the reduction of the device series resistance. In a well designed solar cell it is just this region that is subject to the greatest density of optically generated charge carriers. The actual contribution to the conductivity of these optically generated charge carriers is the result of specific device parameters. The expected resistance times area product of the substrate for solar cells made from our six

CHAPTER Vn: ADVANCED APPROACHES

271

example semiconductors was presented in Chapter VI. Call this value (ADIDX^. In keeping with the first order approximations made elsewhere in this chapter, and utilizing a non-uniform generated carrier concentration, peaking near the junction, we have, from Figures IV.6 and IV.7, the following useful approximation for the effects of optical concentration on the series resistance of the substrate: (ADrD)s=(ADao/{l + . 1 N } .

(VIL16)

Consider the effect on recombination and the reflecting back contact of the increasing electron-hole pair density as the optical concentration increases. In standard configuration solar cells the generation for optically driven hole-electron pairs is primarily near the "fi-ont layer" surface, and does not affect the reflecting nature of the substrate contact. In vertical configuration solar cells this is not necessarily so, particularly in the direct gap semiconductors where the bulk of carrier generation is close to the illuminated surface. In inverted configuration solar cells the optical generation of hole-electron pairs is, in direct semiconductors, close to the reflecting surface and can have major effects. Once again, exact analysis, for all three configurations, depends on the surface recombination velocity of the substrate contact, on the precise nature of the impurity concentration in the substrate, and upon the absorption coefficient of the semiconductor. For our purposes, in this first order analysis, let us assume that the substrate contact remains reflecting. From Chapter HI, the recombination rate, U, for hole-electron pairs increases in proportion to: U oc {pn - ni'}/{p + n} .

(VIL17)

As p and n increase above n^^ the recombination rate becomes proportional to the electron (or hole) concentration. Thus, recombination, for high optical concentration levels, is dependent on the generated carrier density. At the same time, the lifetime, which is a measure of the time available to collect these optically generated carriers, increases to a maximum, x^^, equal to [23]:

272

CHAPTER VH: ADVANCED APPROACHES

The mechanism responsible for recombination becomes saturated at high carrier concentrations and the result is an increase in the photocurrent. In our first order analysis of solar cells this effect will be neglected and the photocurrent will be taken to be the unconcentrated photocurrent (see Table Vn.3) times the optical concentration, N.

Performance Under Concentration We are now in a position to make estimates of solar cell performance as a function of the level of optical concentration using Equations VI. 16 through VI. 18 and VTI.14 to compute output power density, efficiency, operating voltage and loss factor with temperature as a parameter. In the following figures, we examine solar cell performance for optical concentrations, N, varying from unity to 1000. At each concentration level we will assume junction temperatures of 300°K, 350°K and 400°K. The saturation current density is obtained from Tables Vn.2 and VI. 13 for pn, heterojunction and Schottky barrier solar cells. The photociirrent is obtained from Table Vn.3 using the appropriate value of N. The resistance times area product is that determined in Chapter VI*. Figures Vn.4 through Vn.9 present computed output power density and efficiency for standard configuration solar cells exposed to an AMO type of spectrum (N = 1 corresponds to AMO light, while N = 10 corresponds to light of the same AMO spectral distribution, but contains 10 times as many photons). Data are presented for solar cells made from silicon, indium phosphide, gallium arsenide, cadmium telluride, aluminum antimonide and cadmiimi selenide with n-type substrates. Results for solar cells with p-type substrates are similar to these values, with variations primarily due to Schottky barrier height variations and minor resistance and lifetime changes. Study of Figures Vn.4 through Vn.9 reveals that the output power density increases with increasing optical concentration level for all of

* Recall that this product depends upon both the substrate and "front layers" as demonstrated in Tables VI. 14 through VI. 16 and, for standard configuration solar cells, the "front layer" area times resistance product is a function of the geometry.

273

CHAPTER Vn: ADVANCED APPROACHES 40

pn junction 1 3

10 4 Power 1 Density .4 in .1 W/cm' .04

1 3 1 3

1 3

1 3 1 3

1 .001 2 3 .004 1 10

Schottky

heterojunction

1 3

1 3 1 3

1 2 3

4 1 10 100 10' 1 10 100 10' Solar Concentration Key: 1--:> T = 300°K, 2-> T = 350°K, 3 - > T = 400''K Efficiency (%) Temperatur e 5olar Concentration Level CK) 1000 316 1 10 31.6 100 3.16 pn junctions 10.3 300 13.6 11.4 12.0 12.6 13.2 13.5 08.4 10.8 350 09.3 08.6 10.1 10.7 11.1 06.8 08.8 400 06.0 07.7 08.4 09.0 06.9 heterojunctions 11.4 15.4 300 13.7 15.2 15.9 16.2 14.5 09.2 12.7 10.4 350 12.1 12.9 13.3 11.3 07.3 10.3 07.4 400 08.4 09.3 10.2 10.8 Schottky barriers 2.88 300 3.03 2.34 2.13 2.56 2.76 2.94 2.33 2.23 1.28 350 1.52 1.76 1.99 2.20 1.58 1.54 400 0.94 1.18 1.42 0.70 0.48 Figure Vn.4. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for standard configuration silicon solar cells with n-type substrates and under AMO-like spectral distribution. 100

10^

{

274

40

CHAPTER VH: ADVANCED APPROACHES heterojunction

pn junction

1 Schottky 3

10 4 Power 1 Density .4 in .1 W/cm^ .04

1 3

1 3

1 3 1 3 1 3

.01 .004 4 1 10

1 2 3

1 3 1 2

-a—

1 10 100 10^ 1 10 100 10' Solar Concentration Key: 1-:> T = 300°K, 2-> T = 350°K, 3-.>T = 400°K Efficiency (%) ( Temperature Solar Concentration Level 1000 CK) 1 316 3.16 10 31.6 100 pn junctions 4.44 3.81 4.37 300 3.67 3.96 4.11 4.25 3.94 3.85 350 3.02 3.36 3.54 3.70 3.19 3.44 3.32 400 2.41 2.77 2.96 3.15 2.57 heterojunctions 21.0 22.4 300 19.6 20.3 21.0 21.7 22.3 18.7 19.9 350 16.5 18.2 19.0 19.7 17.3 15.3 16.2 17.0 16.4 17.4 400 13.4 14.4 Schottky barriers .319 .281 300 .078 .114 .154 .196 .239 .197 .156 350 .007 .002 .042 .073 .113 .097 .002 .061 400 .001 .005 .014 .032 Figure Vn.5. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for standard configuration indium phosphide solar cells with n-type substrates and under AMO-like spectral distribution. 100

10^

CHAPTER Vn: ADVANCED APPROACHES 40

heterojunction

pn junction

275

1 Schottky

13 10 4 Power 1 Density] .4 in .1 W/cm^ .04

1 3

1 3

1 2

1 3

1 3

1 3

.01 .004 1 10

1 10 100 10' 1 10 100 10' Solar Concentration Key: 1- > T = 300°K, 1~> T = 350% 3 -->T = 400°K Efficiency (%)
10^

276 40

CHAPTER VII: ADVANCED APPROACHES pn junction

heterojunction 1-3

Schottky 1-3

10 4 Power 1

1 2,3

1 2 3.

1 2,3

Lyensiiy

.4 in .1 W/cm' .04

1 2,3

1 2

1,2 3

3 1 2,3

1-3

1-2

.01 .004

3— 1 10 100 10' 1 10 100 10' Solar Concentration Key: 1-:> T = 300''K, 2-> T = 350°K, 3 -->T = 400''K Efficiency (%) Temperature Solar Concentration Level CK) 1 1000 316 3.16 10 31.6 100 pn junctions 300 16.1 16.6 17.0 17.4 17.6 17.2 14.7 350 14.3 15.8 13.5 15.4 15.9 16.1 14.9 400 12.2 14.4 12.5 13.7 14.3 14.6 13.1 heterojunctions 300 21.9 23.1 23.6 23.7 22.7 18.1 22.5 350 20.9 16.5 19.5 21.0 21.6 21.8 20.3 400 19.0 14.8 17.1 18.7 19.4 19.8 17.9 Schottky barriers 300 1.31 1.46 1.61 1.76 1.88 1.94 1.80 350 1.54 1.43 0.81 0.97 1.14 1.30 1.45 400 0.12 0.76 0.73 0.22 0.36 0.51 0.66 1 10

100

10^

Figure V1I.7. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for standard configuration cadmium telluride solar cells with n-type substrates and under AMO-like spectral distribution.

277

CHAPTER Vn: ADVANCED APPROACHES 40

pn junction

Schottky

heterojunction

10 1 2,3

4 Power 1 Density! .4 in .1 W/cm' .04

1-3

1-3

1-3 1 2-3

1-3

1-2 1 2

1 2-3

1-3

3

.01 1

3

.004 1

10

100

10'

1 10 100 10' 1 10 100 10' Solar Concentration Key: l - > T = 300°K, 2-> T = 350°K, 3-> T = 400°K Efficiency (%) Temperature Solar Concentration Level CK) 1 316 1000 10 31.6 100 3.16 pn junctions 300 03.8 09.9 13.9 14.3 14.5 14.5 13.6 03.4 350 12.2 08.6 12.9 13.0 12.1 12.6 02.9 07.4 10.4 400 10.9 11.3 11.4 10.6 heterojunctions 03.9 300 10.9 18.4 19.2 19.0 17.2 18.9 03.4 09.4 350 16.2 16.7 17.1 17.0 15.3 02.9 400 08.0 13.9 15.0 14.9 13.4 14.5 Schottky barriers 300 .173 .341 .370 .245 .438 .516 .522 .098 350 .175 .033 .141 .212 .243 .076 400 .043 .062 .002 •016 .037 .060 .006 Figure VII.8. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for standard configuration aluminum antimonide solar cells with n-type substrates and under AMO-like spectral distribution.

278

CHAPTER VII: ADVANCED APPROACHES

40

Ipn junction

Schottky

heterojxinction 1-3

10 4 Power 1 Density! Not available .4 in .1 W/cm^ .04

1 2,3

1 2,3

1 2

1-3

1

3

.01 .004

-3T3

1

1 10 100 10^ 1 10 100 10' Solar Concentration Key: 1~> T = 300°K, 2~> T = 350°K, 3~> T = 400°K Efficiency < Temperature Solar Concentration Level 1000 CK) 316 1 10 31.6 100 3.16 pn junctions

300 350 400

10

100

10^

Not available, owing to lack of p-type CdSe

heterojunctions 13.8 17.8 18.9 18.7 18.8 300 12.1 15.9 350 16.3 16.7 16.8 14.2 10.6 14.3 14.8 15.0 400 Schottky barriers .158 .151 .043 .081 .124 .007 .019 300 .050 .040 .000 .003 .009 .022 .001 350 .010 .005 .000 .000 .001 .002 400 .000 Figure VII.9. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for standard configuration cadmium selenide solar cells with n-type substrates and under AMO-like spectral distribution. 17.5 15.2 13.1

18.0 15.8 13.7

CHAPTER Vn: ADVANCED APPROACHES

279

the example semiconductors irrespective of the junction type, while an increase in junction temperature reduces the output power density. Note, however, that as the optical concentration level increases the operating efficiency of the solar cells increases rapidly, slows and eventually begins to decrease with increasing optical concentration levels. Also note that the heterojunction devices perform at a higher level with greater output power densities and higher efficiencies than do the pn junction devices. This is a consequence of a superior collection efficiency with a smaller effective "dead layer". Also, the standard configuration Schottky barrier devices are seen to perform very poorly—owing to smaller effective photocurrent and higher saturation current density. Figures VH.IO through Vn.l5 present computed output power density and solar cell efficiency for vertical configuration solar cells exposed to an AMO-like spectrum as the concentration level and junction temperature are varied. Data are presented for silicon, indium phosphide, gallium arsenide, cadmium telluride, aluminum antimonide and cadmium selenide solar cells constructed on n-type substrates. Results for solar cells constructed on p-type substrates are similar to these values, with variations primarily due to changes in Schottky barrier height, and minor resistance and lifetime changes. Study of Figures Vn.lO through Vn.l5 reveals that as the optical concentration level increases, the output power density for vertical configuration solar cells increases, while an increase in operating junction temperature results in a decrease in output power density. Note that the Schottky barrier solar cells have a significantly lower performance than either the pn or heterojunctions~a result of their higher saturation current density. Also, note that the vertical configuration solar cells have an improved performance (output power density and efficiency) over the standard configuration solar cells of Figures Vn.4 through Vn.9. Figures Vn.l6 through Vn.21 complete our study of the performance of the various solar cell optical configiu^ations by presenting the theoretical output power density and efficiency for inverted configuration solar cells exposed to AMO-like spectral inputs of varying concentration levels, while the junction temperatures are varied. Data are presented for silicon, indium phosphide, gallium arsenide, cadmium telluride, aluminum antimonide and cadmium selenide solar cells constructed on n-type substrates. Results for solar cells constructed on ptype substrates are essentially similar with variations due to changes in Schottky barrier height and minor changes in resistance and lifetime.

280

CHAPTER VH: ADVANCED APPROACHES Schottky barrier

pn & heterojunction 39.8 25.1 15.8 10.00

1,2 3

1 2 3

01.58 01.00

03.98 Power 01.58 01.00 Density 00.40

1 2,3

00.398 00.158 00.100

1 2,3

in 00.16 00.10 W/cm^ 00.04 00.02 00.01

1 2,3

10.00 06.51 03.98

1 2 3

00.04

00.016 00.010

1 2

La1

00.004 00.003

1 10 100 10' Solar Concentration Key: l - > T = 300% 2-> T = 350°K, 3--> T = 400''K 10

100

10'

Efficiency (%) Temperature Solar Concentration Level 1000 316 1 CK) 10 31.6 100 3.16 pn junctions and heterojunctions 12.8 300 17.2 18.0 18.2 17.3 15.5 16.4 14.4 10.3 350 11.8 12.8 13.8 14.6 15.1 08.2 11.7 08.4 400 10.6 11.6 12.2 09.5 Schottky barriers 07.5 11.5 300 09.6 11.3 12.0 12.3 10.5 05.7 08.9 06.3 08.2 09.1 09.5 350 07.3 03.9 06.1 03.0 400 04.0 0.50 0.59 06.5 Figure VH.IO. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for vertical configuration silicon solar cells with n-type substrates and under AMO-like spectral distributions.

CHAPTER Vn: ADVANCED APPROACHES pn & lieterojunction 1 2,3

39.8 25.1 15.8 10.00 03.98 Power 01.58 01.00 Density 00.40 in 00.16 00.10 W/cm^ 00.04 00.02 00.01

1 2,3

Schottky barrier 10.00 06.31 03.98

1 2 3

01.58 01.00 1 2 3

00.398

1 2,3

281

00.158 00.100 1 00.04 2 00.016 00.010

3

1,2 3

00.004 1 - 00.003 1 10 100 10' 1 10 100 10' Solar Concentration Key: l - > T = 300°K, 2-> T = 350°K, 3--> T = 400''K

Efficiency (%) Solar Concentration Level CK) 1 316 1000 3.16 10 31.6 100 pn junctions and heterojunctions 300 23.5 21.9 22.7 23.5 24.3 24.9 25.0 350 18.4 19.4 22.2 20.9 20.4 21.3 22.0 400 15.0 16.1 19.5 18.3 17.2 18.2 19.1 Schottky barriers 300 2.91 4.72 3.64 5.78 4.37 5.06 5.64 350 3.22 0.93 3.91 1.53 2.22 2.96 3.62 400 0.13 2.00 0.34 2.31 0.74 1.30 1.91 Figure VII.l 1. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for vertical configuration indium phosphide solar cells with n-type substrates and under AMO-like spectral distributions.

Temperature

282

CHAPTER VD: ADVANCED APPROACHES pn &1leterojunction 1,2 3

39.8 25.1 15.8 10.00 03.98 Power 01.58 01.00 Density 00.40 in 00.16 00.10 W/cm^ 00.04 00.02 00.01

1 2 3

Schottky barrier 10.00 06.31 03.98

1 2

01.58 01.00 1

3

00.398 2 00.158 00.100

1 2,3

1 00.04 3 00.016 00.010

1 2 3

1

2

00.004 1 - 00.003

1 10 100 10' 10^ Solar Concentration Key: 1- > T = 300°K, 2--> T = 350% 3-> T = 400°K 10

Temperature

CK)

1

300 350 400

22.9 19.9 16.8

300 350 400

2.58 0.20 0.00

100

Efficiency (%) Solar Concentration Level 316 10 31.6 100 3.16 pn junctions and heterojunctions 24.4 25.1 25.8 27.3 23.6 23.8 21.6 22.4 23.2 20.7 21.3 18.8 19.7 20.6 17.8 Schottky barriers 5.59 3.88 4.54 5.15 3.22 2.51 0.89 1.43 2.01 0.47 0.32 0.02 0.06 0.15 0.01

1000 26.0 23.8 21.4 5.48 2.61 0.47

Figure VII. 12. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for vertical configuration gallium arsenide solar cells with n-type substrates and under AMO-like spectral distributions.

283

CHAPTER VH: ADVANCED APPROACHES Schottky barrier

pn &he iterojunction 39.8 25.1 15.8 10.00 03.98 Power 01.58 01.00 Density 00.40 in 00.16 00.10 W/cm^ 00.04 00.02 00 01

1,2 3

1,2 3

10.00 06.31 03.98

1,2 3 1 2 3

01.58 01.00 00.398

1 2,3

00.158 00.100

1 2 3

00.04 00.016 00.010 1 2 00.004 00.003 1 10 100 10' 1 10 100 10' Solar Concentration Key: l--> T = 300°K, 2--> T = 350°K, 3--> T = 400°K

1 2,3

Efficiency (%) Temperature Solar Concentration Level 1000 1 CK) 316 10 31.6 100 3.16 pn junctions and heterojunctions 20.1 300 25.8 26.4 26.5 25.3 25.2 24.5 18.3 350 23.3 21.8 23.4 24.1 24.3 22.6 16.5 21.2 400 19.2 21.0 21.7 22.1 20.1 Schottky barriers 4.40 7.74 300 6.80 8.10 8.62 8.77 7.47 3.49 350 6.18 4.62 5.37 6.09 6.72 6.98 2.64 4.64 400 2.56 3.34 4.12 4.83 5.21 Figure V1I.13. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for vertical configuration cadmium telluride solar cells with n-type substrates and under AMO-like spectral distributions.

284

CHAPTER Vn: ADVANCED APPROACHES Schottky barrier

pn & heteroj\mction 39.8 25.1 15.8 10.00

10.00 06.31 03.98 1 2,3

03.98 Power 01.58 01.00 Density 00.40 in 00.16 00.10 W/cm^ 00.04 00.02 00.01

1-3

01.58 01.00 1 2

00.398 1 2

00.158 00.100

1-3 00.04

00.016 00.010 1-3 1

1 2

00.004 00.003

10

100

10' 1 10 100 10' Solar Concentration Key: 1~> T = 300°K, 2~> T = 350°K, 3~> T = 400°K

Efficiency (%) Temperature Solar Concentration Level 1000 1 CK) 316 10 31.6 100 3.16 pn junctions and heterojunctions 04.3 300 20.6 21.4 21.2 19.2 12.1 21.1 03.8 10.5 18.1 350 19.1 19.0 17.1 18.7 03.3 08.9 15.5 16.2 400 16.7 16.7 14.9 Schottky barriers 0.26 300 0.65 1.63 2.36 2.27 1.46 2.05 0.17 0.41 0.38 350 }m 1.09 0.76 0.72 0.09 0.17 0.03 400 0.09 0.20 0.30 0.27 Figure VII. 14. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for vertical configuration aluminum antimonide solar cells with n-type substrates and under AMO-like spectral distributions.

CHAPTER Vn: ADVANCED APPROACHES Schottky barrier

pn & heterojunction 39.8 25.1 15.8 10.00

1-3

10.00 06.31 03.98 01.58 01.00

03.98 Power 01.58 01.00 Density 00.40

1-3 00.398 00.158 00.100

in

1-3

00.16 00.10 W/cm' 00.04 00.02 0001

285

00.04

00.016 00.010

1,2 3 1

00.0041 00.0031

100 10' 10' 1 10 Solar Concentration Key: 1~> T = 300°K, 2-> T = 350°K, 3~> T = 400°K 10

100

Efficiency (%) Temperature Solar Concentration Level CK) 1000 316 1 10 31.6 100 3.16 heterojunctions 15.4 19.9 20.6 21.0 21.0 19.6 20.1 300 13.5 17.8 17.1 18.3 18.7 18.8 350 17.7 11.8 15.9 15.4 14.7 16.1 16.6 16.8 400 Schottky barriers 0.40 0.82 0.72 0.99 1.10 0.22 0.44 300 0.20 0.32 0.04 0.01 0.11 0.23 0.34 350 0.08 0.08 400 0.00 0.00 0.01 0.03 0.06 Figure VII.IS. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for vertical configuration cadmium selenide solar cells with n-type substrates and under AMO-like spectral distributions. i

286

CHAPTER VH: ADVANCED APPROACHES

Study of Figures Vn.l6 through VII.21 indicates that inverted configuration Schottky barrier solar cells are less efficient than inverted configuration pn and heterojunction solar cells. As was the case for standard and vertical configuration solar cells, inverted configuration solar cell performance increases with increasing optical concentration level and decreases with increasing junction temperature. Note that the pn and heterojunction solar cells of all three optical configurations are more efficient and provide higher output power density than the Schottky barrier solar cells. It is, of course, possible that, at sometime in the future a Schottky junction will be discovered tiiat possesses a sufficiently high junction barrier height, or a mos barrier will be devised that allows for improved solar cell performance. Before discussing these optical configurations under AMI spectral illumination, let us spend a few moments discussing the operating voltage and loss factors for some of the example solar cells discussed in Figures Vn.4 through VII.21. Study of Table Vn.4 reveals that the operating voltage for maximum delivered output power density increases slowly as the optical concentration level is increased. Note also that the operating voltage decreases with increasing junction temperature. The operating voltage for vertical configuration devices lies between that for the standard configuration design and the inverted optical configuration devices. Recall that the higher the operating voltage, the fewer devices which must be electrically stacked to provide a given system voltage. The reader will observe that solar cells made fi*om indium phosphide, aluminum antimonide and cadmium selenide have been ignored in Table V1I.4. This is because the data contained in this chapter, in Chapter VI and the following chapters indicate that the semiconductors listed in Table Vn.4 are the most likely to be useful in future semiconductors. The operating voltages for pn junctions are essentially the same as those given for heterojunctions, while the operating voltages for Schottky solar cells are somewhat less. The overall performance of the Schottky solar cells fi^om Figures Vn.4 through Vn.21 are so poor, compared to the heterojunction and pn junction devices that we will not comment on them further. The loss factors considered in Chapters V and VI were quite small, normally less than unity. The theoretical loss factors for heterojunction devices of Table Vn.4 are presented in Table Vn.5. From Equation VII. 15 the loss factor depends on the series resistance times area product of the solar cell. Owing to the high carrier mobility of GaAs this

287

CHAPTER Vn: ADVANCED APPROACHES Schottky barrier

pn & heterojunction 100.0 063.1 039.8 025.1 015.8 10.00 Power 3.98 Density 1.58 1.00 in .40 W/cm^ .16 .10 .04 .03

15.80 10.00 1 2 3 1,2 3

1 2 3

03.98 01.58 01.00 .398 .158 .100

1,2 3

1,2 3

1 2 3

.04 1 .016 2 .010 3

1,2

L^— 1

100 10' 10^ 10 1 Solar Concentration Key: 1 -> T = 300°K, 2-> T = 350°K, 3-> T = 400°K 10

100

Efficiency (%) Solar Concentration Level 1 1000 3.16 10 31.6 100 316 pn junctions and heterojunctions 15.7 08.1 300 16.4 17.2 18.0 18.6 18.3 12.9 06.6 350 12.6 13.7 14.6 15.3 15.2 10.4 05.3 400 09.3 10.4 11.5 12.3 12.4 Schottky barriers 09.9 04.7 300 10.4 11.2 12.0 12.6 12.4 03.6 07.6 350 07.1 08.0 08.9 09.6 09.6 05.2 02.5 400 03.7 04.7 05.7 06.5 06.7 Figure VII. 16. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for inverted configuration silicon solar cells with n-type substrates and under AMO-like spectral distributions.

Temperature CK)

288

CHAPTER Vn: ADVANCED APPROACHES Schottky barrier

pn & heterojunction 100.0 063.1 039.8 025.1 015.8 10.00 Power 3.98 Density 1.58 1.00

15.80 10.00

1 2,3

03.98

1 2 3

01.58 01.00

1,2 3

.398 .158 .100

1,2 3

in .40

1 2

W/cm'

.04

.16 .10 .04 .03

1 2 3

3 .016 .010 1

1,2 3

.004 -X. 1 10 100 10' 1 10 100 10^ Solar Concentration Key: 1- > T = 300''K, 2-> T = 350°K, 3-> T = 400°K -

Efficiency (%) Temperature Solar Concentration Level 1000 CK) 316 1 10 31.6 100 3.16 pn junctions and heterojunctions 21.5 300 24.7 25.5 25.9 25.2 23.1 23.9 19.0 22.5 19.6 21.6 22.4 23.0 350 20.6 19.8 16.5 16.2 18.4 19.4 20.0 400 17.3 Schottky barriers 5.60 3.49 300 3.47 4.96 5.62 6.02 4.22 3.84 2.43 1.33 2.77 3.50 4.02 350 2.03 1.58 2.31 0.25 1.11 1.75 2.30 400 0.58 Figiire Vn.17. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for inverted configuration indium phosphide solar cells with n-type substrates and under AMO-like spectral distributions.

CHAPTER VH: ADVANCED APPROACHES Schottky barrier

pn & heterojunction 100.0 063.1 039.8 025.1 015.8 10.00 Power 3.98 Density 1.58 1.00 in .40 W/cm' .16 .10 .04 03 m\JJ

1-3

289

1

15.80 10.00

2 03.98

1-3

1

01.58 01.00

3

2 .398

1-3

.158 .100

1

.04

2

.016 .010

1,2 3

1

3

004 ,V\/*T'

1

10 ]Key:

100

1-• > T

=

100 10^ 10^ 1 10 Solar Concentration :iOO°K, 2~> T = 350°K, 3 --> T = 400''K

Efficiency (%) Temperature Solar Concentration Level (°K:) 1000 3.16 31.6 100 "316 10 ~i pn junctions and heterojunctions 25.9 27.0 26.2 26.8 300 24.8 24.0 25.5 350 23.6 24.6 21.0 23.6 24.3 21.8 22.7 21.3 22.1 400 17.9 18.9 20.8 21.7 19.9 Schottky barriers 5.02 5.83 5.07 5.62 4.41 300 3.73 3.06 2.39 350 2.76 0.36 0.73 1.85 2.43 1.40 400 0.51 0.46 0.00 0.04 0.11 0.26 0.01 Figure Vn.l8. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for inverted configuration gallium arsenide solar cells with n-type substrates and under AMO-like spectral distributions.

290

CHAPTER VH: ADVANCED APPROACHES

Schottky barrier

pn & heterojunction 100.0 063.1 039.8 025.1 015.8 10.00 Power 3.98

15.80 10.00

1,2 3

1,2 3

03.98 1

1-3

2,3

01.58 01.00 .398

jjcnsiiy

1.58 1.00

.158 .100

1-2;

in .40

1 2 3

.04

W/cm^

.16 .10

.016 1,2 .010

1-3 .04

3

01

1

100 10^ 10' 1 10 Solar Concentration Key: 1~> T = 300''K, 2~> T = 350°K, 3~> T = 400°K 10

100

Efficiency (% Solar Concentration Level CK) 1000 1 316 10 31.6 100 3.16 pn junctions and heterojunctions 23.7 13.6 27.0 27.4 26.9 26.4 25.6 300 21.7 12.3 350 23.0 24.6 25.1 24.6 23.8 11.0 19.7 20.3 22.1 22.7 22.5 400 21.2 Schottky barriers 8.11 8.71 9.07 8.66 6.18 2.60 7.43 300 2.11 5.24 4.88 350 6.70 7.18 6.93 6.00 1.64 3.14 3.66 4.72 5.30 5.23 400 3.95 Figure Vn.l9. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for inverted configuration cadmium telluride solar cells with n-type substrates and under AMO-like spectral distributions.

Temperature

CHAPTER Vn: ADVANCED APPROACHES pn &hejterojunction 100.0 063.1 039.8 025.1 015.8 10.00 Power 3.98 Density 1.58 1.00 in .40 W/cm^ .16 .10 .04 .03

291

Schottky barrier 15.80 10.00 03.98

1-3

01.58 01.00

1,2 3

.398 1 2

.158 .100

1 2,3

1

1 2 3

3

.04 2 .016 .010

1 2,3

1 -

3

.004

10' 1 100 10^ 1 10 100 10 Solar Concentration Key: l-> T = 300°K, 2--> T = 350°K, 3--> T = 400°K Temperature

CK)

1

300 350 400

21.0 18.2 16.0

300 350 400

1.90 0.60 0.07

Efficiency (%) Solar Concentration Level 316 10 31.6 100 3.16 pn junctions and heterojunctions 21.4 21.5 20.5 16.3 07.1 06.2 19.2 18.4 14.3 19.0 05.3 16.9 16.2 12.4 16.6 Schottky barriers 0.40 2.42 1.93 0.97 2.28 0.25 1.14 0.97 0.55 0.93 0.13 0.28 0.32 0.23 0.16

1000 02.4 02.1 01.8 0.15 0.10 0.06

Figure VIL20. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for inverted configuration aluminum antimonide solar cells with n-type substrates and under AMO-like spectral distributions.

CHAPTER Vn: ADVANCED APPROACHES

292

Schottky barrier

heterojunction 15.80 10.00

100.0 063.1 039.8 025.1 015.8 10.00 Power 3.98 Density 1.58 1.00

1,2

1 2,3

01.58 01.00

1 2

.398

1

in .40

3

.158 .100

1 2,3

2

W/cm'

.04

.16 .10 .04

03.98

3

1 1 2,3

004

03

.V/J

1

3

.016 .010 T

10^ 100 1 10 10^ Solar Concentration Key: 1--> T = 300°K, 2-> T == 350°K, 3--> T = 400°K 10

100

Efficiency ' (%) Solar Concentrjttion Level Temperature 1000 316 CK;) 100 10 31.6i 3.16 ~i heterojunc:tions 10.1 21.1 18.4 21.4 21.(3 20.5 21.0 300 08.7 16.4 19.0 17.9 19.1 19.^i 350 18.5 07.6 14.5 17.0 15.6 400 16.9 17.:J 16.2 Schottky barriers 1.02 0.59 0.27 0.92 l.i:i 0.62 0.35 300 0.14 0.27 0.36 0.03 350 0.18 0.3:I 0.08 0.07 0.09 0.08 0.00 400 0.02 o.o:5 0.01 Figure Vn.21. Output electrical power density and efficiency as functions of solar concentration with junction temperature as a parameter for inverted configuration cadmium selenide solar cells with n-type substrates and under AMO-like spectral distributions.

CHAPTER Vn: ADVANCED APPROACHES

293

Table Vn.4 The solar cell operating voltage for maximum electrical output power density for heterojunction solar cells on n-type substrates as a function of optical configuration, solar concentration level and junction temperature Semiconductor

Si

GaAs

CdTe

Si

GaAs

CdTe

Temperature CK) 300 350 400 300 350 400 300 350 400 300 350 400 300 350 400 300 350 400

Solar Concentration 1000 100 1 10 Standard Configuration 0.714 0.629 0.570 0.513 0.633 0.532 0.464 0.399 0.554 0.444 0.367 0.294 1.076 1.015 0.957 0.899 0.992 0.922 0.854 0.787 0.904 0.824 0.748 0.672 1.195 1.117 1.057 0.999 1.127 1.034 0.965 0.897 1.055 0.949 0.870 0.793 Inverted ConfiguratiorI 0.766 0.652 0.590 0.533 0.687 0.559 0.488 0.422 0.614 0.474 0.394 0.320 1.100 1.037 0.978 0.920 1.019 0.946 0.878 0.811 0.936 0.852 0.775 0.699 1.255 1.140 1.079 1.020 1.193 1.061 0.990 0.922 1.128 0.979 0.898 0.821

parameter is lower for GaAs than for the other semiconductors under consideration. Note that the loss factor for all of these semiconductors increases with increasing optical concentration and junction temperature. Similar computations for pn and Schottky barrier solar cells on both nand p-type substrates yield similar results for Si, GaAs and CdTe as well as for InP, AlSb and CdSe. Figures Vn.4 through Vn.21 employ concentrated light of an AMO-like spectrum. We could derive similar results for AMI-like spectral illumination. Because there is less energy in AMI spectral

CHAPTER Vn: ADVANCED APPROACHES

294 Table Vn.5

The loss factors for standard and inverted configuration heterojunction solar cells on n-type substrates when exposed to AMO-like illumination of varying concentratiion as a function of junction temperatures Semiconductor

CK) Si GaAs

CdTe

Si GaAs

CdTe

Solar Concentration

Temperature

1

300 350 400 300 350 400 300 350 400

.001 .001 .002 .000 .000 .000 .001 .001 .001

300 350 400 300 350 400 300 350 400

.002 .003 .003 .000 .000 .000 .001 .002 .002

10

100

1000

Standard ConfigurationI 2.53 .096 .010 3.17 .113 .011 3.85 .135 .015 0.115 .011 .001 0.125 .012 .001 0.137 .013 .002 1.41 .069 .007 1.57 .074 .007 1.78 .081 .008 Inverted Configuration 16.5 .202 .019 16.6 .239 .023 16.5 .285 .028 0.238 .021 .002 0.259 .023 .002 0.285 .025 .003 12.4 .145 .014 12.4 .156 .015 12.6 .170 .016

light, the ouput power density of solar cells under AMI-like illumination is less than that for AMO-like light. Rather than detail the performance of our example semiconductors as was done in Figures Vn.4 through Vn.21 and in Tables Vn.4 and Vn.5 for AMO, let us extract but a single set of values for each junction-configuration-semiconductor combination under concentrated AMI-like illumination. We will assume that the substrates are all n-type~the results for p-type substrates are similar. The values in Table Vn.6 are those for the highest operating efficiencies while delivering the most power to an external load.

CHAPTER Vn: ADVANCED APPROACHES

295

Table Vn.6 The maximum delivered power operating conditions (VD', K', f^A^ and TiJ under AMI-like concentrated sunlight as a function of optical concentration, junction type, junction temperature and semiconductor for standard configuration solar cells with n-type substrates SemiconJunction ConcenVD tration TCK) Type* ductor (V) 0.62 100 HET 300 Si HET 350 0.53 100 0.44 HET 400 100 300 InP HET 0.88 316 HET 400 0.73 316 HET GaAs 300 1.07 1000 HET 350 0.98 1000 HET 400 0.90 1000 HET CdTe 300 1.11 100 HET 350 1.03 100 HET 400 0.94 100 HET 300 AlSb 1.10 10 0.92 HET 400 31.6 CdSe 300 HET 1.21 100 HET 400 0.98 100 Si 0.62 PN 300 100 PN 0.47 400 316 PN 300 InP 0.90 1000 GaAs 300 PN 1.06 1000 0.88 PN 400 1000 CdTe 300 1.10 PN 100 0.93 PN 400 100 AlSb PN 300 1.13 31.6 Si 0.43 316 SH 300 0.21 SH 300 InP 1000 GaAs 300 0.24 SH 1000 CdTe 300 SH 0.39 316 SH 300 AlSb 0.18 100 SH CdSe 300 0.13 1000 *HET denotes heterojunction; PN, pn junction;

K'

Pmaj/Ao

W/cm^ 01.76 .077 01.45 .091 01.17 .109 07.32 .068 05.67 .085 24.40 .087 22.20 .095 20.00 .104 02.44 .052 02.24 .056 02.03 .061 00.20 .028 00.49 .112 02.00 .058 01.60 .071 01.44 .062 03.01 .304 04.85 .045 15.80 .055 12.90 .066 01.81 .038 01.50 .045 00.47 .067 01.02 .095 00.34 .059 01.07 .077 00.63 .115 00.05 .555 00.17 1.609 and SH, Schottky ~

Tls %

16.5 13.6 10.9 21.6 16.8 22.8 20.8 18.6 22.8 20.9 19.0 18.5 14.5 18.7 14.9 13.4 08.9 04.5 14.8 12.0 16.9 14.0 14.0 03.0 00.3 01.0 01.8 00.5 00.2

296

CHAPTER VH: ADVANCED APPROACHES

Note that the performance of standard configuration Schottky barrier solar cells under AMI conditions is very poor and that the heterojunction devices are superior to the types using other junctions. Table Vn.7 provides similar data for vertical configuration solar cells and Table Vn.8 does the same for inverted configuration solar cells. Table Vn.7 The maximum delivered power operating conditions (VQ', K', P^ax/Ao and TiJ under AMI-like concentrated sunlight as a fiinction of optical concentration, junction type, junction temperature and semiconductor for vertical configuration solar cells with n-type substrates SemiconK' ConcenJunction VD' Pmaj/Ao ~ W/cm^ tration T(°K) Type* ductor (V) 01.98 .078 0.63 100 PNH 300 Si 01.63 .092 350 0.53 PNH 100 01.31 .110 400 0.44 100 PNH 08.17 .069 300 InP 0.91 316 PNH 06.35 .086 400 0.73 316 PNH 27.30 .086 GaAs 300 1.07 PNH 1000 24.90 .093 350 0.99 1000 PNH 22.40 .102 400 0.90 PNH 1000 02.72 .052 CdTe 300 1.11 100 PNH 02.50 .056 350 1.03 100 PNH 02.26 .061 0.94 400 100 PNH 00.22 .028 300 AlSb 1.11 10 PNH 00.55 .114 0.92 400 31.6 HET 02.25 .059 1.21 CdSe 300 100 HET 01.80 .072 400 0.99 HET 100 01.34 .112 Si 0.44 300 SH 100 01.90 .272 InP SH 300 0.25 316 05.83 .380 GaAs 300 SH 0.28 1000 00.90 .150 SH CdTe 300 0.40 100 00.08 .743 SH 300 AlSb 0.18 31.6 00.12 CdSe 300 .791 SH 0.11 100 *PNH denotes pn junction and heterojun<;tion, HET is heterojunction, and SH is Schottky barrier

Tls %

18.5 15.2 12.3 24.2 18.8 25.5 23.3 20.9 25.4 23.3 21.2 20.8 16.3 21.0 16.8 12.5 05.6 05.4 08.4 02.3 01.1 solely

CHAPTER Vn: ADVANCED APPROACHES

297

Table Vn.8 The maximum delivered power operating conditions (VD', K', ^^nJAj^ and TiJ under AMI-like concentrated sunlight as a fimction of optical concentration, junction type, junction temperature and semiconductor for inverted configuration solar cells with n-type substrates SemiconK' Junction ConcenPmaj/Ao VD' ductor W/cm^ ~ T(°K) Type* tration (V) 01.28 . Si 300 .048 PNH 0.61 31.6 03.36 350 .188 PNH 0.55 100 02.73 .224 400 PNH 0.47 100 InP 05.33 .042 PNH 300 0.90 100 13.00 PNH 400 .173 0.76 316 17.80 GaAs 300 .051 PNH 1.06 316 16.20 350 .056 PNH 0.97 316 14.60 .061 PNH 400 0.88 316 01.77 .032 CdTe 300 PNH 1.10 31.6 01.62 350 .035 1.02 PNH 31.6 04.66 PNH 400 .126 0.97 100 00.46 .054 AlSb PNH 300 1.13 10 00.36 .067 PNH 400 0.90 10 01.46 CdSe HET 300 .036 1.20 31.6 01.16 .044 400 HET 0.97 31.6 02.73 Si .234 SH 300 0.46 100 01.23 InP .160 SH 300 0.24 100 03.86 GaAs 300 .216 SH 0.26 316 00.59 CdTe 300 .092 SH 0.39 31.6 00.05 AlSb .402 SH 300 0.17 10 00.08 SH 300 CdSe .466 0.10 31.6 *PNH denotes pn junction and heterojtinction, HET is heterojunction, and SH is Schottky barrier

Tl. %

18.9 15.7 12.8 24.9 19.3 26.4 23.9 21.5 26.2 24.0 21.8 21.4 16.8 21.6 17.2 12.8 05.8 05.7 08.7 02.4 01.1 solely

Note that the performance improves from standard, through vertical to inverted configuration solar cells, and that the performance of Schottky barriers is significantly the lowest. Solar cells with p-type substrates have roughly the same behavior under AMI-like illumination as tiie n-type solar cells surveyed in Tables Vn.6 through Vn.8.

29 8

CHAPTER VH: ADVANCED APPROACHES

Study of Tables Vn.6 through VII.8 indicates that Si, GaAs and CdTe based heterojunction solar cells have better performance under AMI-like illumination than the other semiconductor and junction solar cells—a characteristic also seen under AMO-like illumination. The performance of these devices appears to be similar to, but, in general, not as "good" as under AMO conditions. Let us conclude this chapter by presenting the maximum efficiency operating characteristics for n-type substrate solar cells under AMO-like conditions in the same form as was done for AMI-like illumination, and drawing conclusions from them. Table VII.9 The maximum delivered power operating conditions (VQ', K', ?^AJ^ and T],) under AMO-like concentrated sunlight as a function of optical concentration, junction type, junction temperature, optical orientation and semiconductor for solar cells with n-type substrates SemiconJunction ductor T(°K) Type* Si

GaAs

CdTe

Si

GaAs

CdTe

Concentration

300 350 400 300 350 400 300 350 400

HET HET HET HET HET HET HET HET HET

100 100 100 316 316 1000 100 100 100

300 350 400 300 350 400 300 350 400

PNH PNH PNH PNH PNH PNH PNH PNH PNH

100 100 100 316 316 1000 100 100 100

K' Tls Vo' ^mJ^D % W/cm^ ~ (V) Standard Configuration 16.2 02.18 .096 0.63 13.3 01.80 .113 0.53 10.8 01.45 .136 0.44 23.4 10.00 .035 1.04 21.2 09.09 .037 0.96 19.0 25.80 .137 0.90 23.7 03.21 .069 1.12 21.8 02.95 .074 1.03 19.8 02.67 .081 0.95 Vertical Configuration 18.2 02.47 .098 .063 02.04 15.1 .115 .054 12.2 01.65 .138 .045 27.3 11.70 .036 1.05 23.8 10.20 .037 0.96 21.4 28.90 .135 0.90 26.5 03.58 .070 1.12 24.3 03.29 .075 1.04 22.1 02.99 .081 0.95

CHAPTER Vn: ADVANCED APPROACHES

299

Table Vn.9, continued SemiconJunction ductor TfK) Type*

Concentration

31.6 PNH 300 PNH 350 31.6 PNH 400 100 PNH GaAs 300 316 PNH 350 316 PNH 400 316 CdTe 300 PNH 31.6 PNH 350 31.6 PNH 400 31.6 *PNH denotes pn junction and heterojunction Si

VD

K"

^miJ-^D

Tls

% W/cm^ (V) Inverted Configuration 18.6 01.59 .059 0.62 15.3 01.31 .070 0.52 12.4 08.87 0.53 1.440 27.0 23.10 .067 1.07 24.6 21.00 .073 0.98 22.1 18.90 .079 0.89 27.3 02.34 .043 1.11 25.1 02.14 .046 1.02 22.7 01.94 .051 0.94 heterojunction, HET is solely —

The second generation solar cells investigated in this chapter have exhibited improved theoretical performance over the first generation solar cells of Chapters V and VI. Considering the efficiency of optical energy to electrical energy conversion, it would seem that pn and heterojunctions are to be preferred to Schottky solar cells and that inverted configuration solar cells are slightly better than vertical configuration and much better than standard configuration solar cells. We shall use the theoretical data derived in this chapter in the next chapter, as we consider additional important aspects of second generation solar systems; aspects dealing with thermal energy as well as electrical energy outputfi*omthese second generation solar cell systems. References 1 2 3 4

Electronics Review, 22 July 1976, p. 41. Popular Science, March 1977, p. 14. Electronics, 11 Nov. 1976, p. 86. See numerous articles in the Proceedings of the Annual Meetings of the American and International Solar Energy Societies for the years 1976 through 1993.

300

CHAPTER VD: ADVANCED APPROACHES

5 H. J. Hovel, Semiconductors and Semimetals, Vol. n. Academic Press, New York, 1977, p. 133. 6 It is probable that X^ is caused by mechanisms similar to tfiose responsible for tunnel current in Schottky barriers. If so, the temperature dependence will be small [7]. 7 G. H. Parker, "Tunneling in Schottky Barriers", Thesis, Califomia Institute of Technology, 1969, p. 8 and 19. 8 R. C. Neville and C. A. Mead, in Journal of Applied Physics, Vol. 41, 1970, p. 3795. 9 H. K. Henisch, Rectifying Semiconductor Contacts, Clarendon Press, Oxford, 1957. 10 R. C. Neville, "Study of Combined (Photovoltaic-Thermal) Solar Energy Systems", Proceedings of the 2nd Miami International Conference on Altemative Energy Sources, Miami Beach, FL, Dec. 1979, p. 1267. 11 T. Runyan, Silicon Semiconductor Technology, McGraw-Hill, New York, 1965. 12 T. Kadman and E. F. Steigmeer, in Physics Review, Vol. 133, 1964, p. A1665. 13 R. Keys, in Physics Review, Vol. 115, 1959, p. 564. 14 G. A. Slack and G. Galginatais, in Physics Review, Vol. 133, 1964, p. A253. 15 Unpublished data by author. 16 A. V. loffe and A. F. loffe, in Sov. Physics Solid State, Vol. 2, 1960, p. 719. 17 R. A. Smith, Semiconductors, Cambridge University Press, 1959, Chap. 6. 18 B. L. Slater, in Proceedings of the 11th Annual IEEE Photovoltaic Specialists Conference, 1975, IEEE Press, New York. 19 P. F. Ordung et al.. Photovoltaic Solar Energy Conference, Luxembourg, Sept. 1977. 20 R. C. Neville, Intemational Solar Energy Society Meeting, Brighton, UK, 1981. 21 R. C. Neville, Intemational Solar Energy Society Meeting, Montreal, Canada, 1985. 22 H. C. Card, in Journal of Apphed Physics, Vol. 47, 1976, p. 4964. 23 W. Schockley and G. T. Reed, Jr., in Physics Review, Vol. 87, 1952. p. 835.