Solar Cell Efficiency

The Solar Cell

4.7 Solar Cell Efficiency

We obtain a current magnitude due to the electron flux flowing to the left of xG, using Equation 4.18, of

J1n(xp=xG) =qαDn

L_n

exp xG

L_n

+exp −xG

L_n

and current magnitude due to electron flux flowing to the right of xG, using Equation 4.20, of

J2n(xp=xG) =qαD_n L_n

exp

x_G L_n

−exp −xG

L_n

The total generated current density at xbis the sum of these two current magnitudes, or

|Jtotal(xb)| =2qαDn

Ln

exp xG

Ln

(4.22) The fraction η of this total current that reaches the depletion region is obtained by dividing Equation 4.21 by Equation 4.22 to yield

η=exp

−xG

Ln

This means that the contribution to the usable current flow decreases exponentially as a function of the distance between the depletion region and the position of electron-hole pair (EHP) generation in the p-type region. For optimum performance in solar cells of semi-infinite thickness (x_b L_n) we therefore require that the absorption depth of photons is smaller than the diffusion length L_n.

In silicon, photons are absorbed over a depth of approximately 100μm and diffusion lengths in the range of 1 mm are achievable. This implies that the thickness of the solar cell should be more than 1 mm. Since silicon wafers under 0.2 mm in thickness may be cut and processed into solar cells in large volumes it is clear that a low effective surface recombination velocity at the rear contact is required. This may be achieved by forming a p⁺ doped region near the back contact. Figure 4.14 shows the resulting solar cell band diagram. A potential step near the back contact is formed that helps to prevent minority electrons from reaching the back silicon-metal interface due to the back surface electric field that is created at the step. Much lower effective rear surface recombination velocities result from this and the rear p⁺-region is therefore part of the standard solar cell design.

n⁺ p p⁺

Front

Solar cell junction

Back Energy step in conduction Ef band

Figure 4.14 Back surface field formed by a p⁺doped region near the back of the solar cell. A potential energy step that generates a built-in electric field decreases the likelihood of electrons reaching the back surface of the silicon

0 0 10 20 30 40 50

Ge Si

GaAs

AM 1 300 K

C = 1000

CdS C = 1

Efficiency (%)

E_g (eV)

1 2 3

Figure 4.15 Efficiency limit of solar cells based on a number of well-known semiconductors.

Note the increase in efficiency potentially available if the sunlight intensity is increased to 1000 times the normal sun intensity. This increase can be understood since from (4-8) ISC is proportional to G, and in addition from (4-7) and (4-9)VOCalso increases gradually with G.

Hence ISCVOCincreases more quickly than the solar radiation intensity and the cell efficiency will increase. Reprinted from Sze, S.M., Semiconductor Devices: Physics and Technology, 9780471837046. Copyright (1985) with permission from John Wiley & Sons, New York

which clearly shows the sensitivity of I0on ni. From Equation 1.37, nidecreases exponen- tially as energy gap Egincreases and as T decreases:

ni=NcNvexp −Eg

2kT

(4.24) The other quantity that must be as large as possible is the short circuit current ISC, which depends linearly on the optical generation rate G from Equation 4.8. G will decrease once Eg exceeds the photon energy of incoming photons. This means that there is an optimal energy gap, as shown in Figure 4.15, for a number of semiconductors.

There are two major contributions to efficiency loss in p-n junction solar cells. The first arises from photons having energies higher than E_g. The extra photon energy becomes carrier kinetic energy, which quickly gets converted to heat as the carriers relax or thermalize to their lower energy states. This happens before the carriers can be collected and utilized.

This would not be an issue if the solar spectrum was monochromatic, but the broad blackbody solar spectrum immediately limits efficiency values to under 50% for a single- junction solar cell.

The second is the discrepancy between the optimum operating voltage VMP and the bandgap Egof the semiconductor used. A minimum photon energy corresponding to Egis needed to create electron-hole pairs; however, VMPis less than Eg. For example, in silicon,

VMP

E_g ∼= ^0.6_1.1, or about 55%. This means that the overall efficiency of a single-junction solar cell will be under 30%. Silicon solar cells have reached approximately 25% efficiency in the lab, and 24% in production. See Problem 4.14. GaAs-based solar cells having an optimal direct gap have reached only slightly higher values of 26%.

Figure 4.16 shows the trend towards higher efficiencies in solar cell technology as time progresses. Note that the higher efficiency solar cell types are multi-junction solar cells, which will be covered in Section 4.13. Production single-crystal silicon solar cells are in the range of 16–24% efficient.

Solar cell efficiency also depends on the operating temperature of the solar cell p-n junction. In general there will be a decrease in efficiency at higher temperatures due to the increase in I0. This means that it may be advantageous to generate solar power at higher latitudes where ambient temperatures are lower. The disadvantage, however, is the lower angle of the sun relative to locations near the Equator. See Example 4.2.

Example 4.2

For the solar cell of Example 4.1,

(a) Find the saturation currents at−50^◦C and at+100^◦C relative to the saturation current at room temperature (300 K).

(b) Find the predicted maximum output power at−50^◦C and at+100^◦C and compare to the maximum output power at room temperature (300 K).

Make and state any necessary assumptions Solution

(a) In order to obtain saturation current I₀at various temperatures we will assume that N_c, N_v, E_g, D_n,D_p, L_nand L_pare temperature independent. This is not

44 40 36 32 28 24 20 16 12 8 4 0 19751980

RCARCA RCA

University of Maine

Matsushita Monosolar Boeing

Boeing

Westing- house BoeingKodak

KodakSolarexARCO

ARCO No. Carolina State Univ.

Varian

Spire

SpireKopin

NREL

Best Research-Cell EfficienciesMultijunction Concentration Three-junction (2-terminal, monolithic) Two-junction (2-terminal, monolithic) Single-junction GaAs Single crystal Single crystal Multicrystalline Thick Si film Thin-Film Technologies Cu(In.Ga)Se2 CdTe Amorphous Si: H (stabilized) Nano-, micro-, ploy-Si Multijunction ploycrystalline Emerging PV Dye-sensitized cells Organic cells (various technologies)Thin film Crystalline Si Cells

Concentrator NRELNREL/ Spectrolab

Spectrolab

Boeing- Spectrolab

Boeing- Spectrolab (metamorphic) NREL (inverted, semi-mismatched) Japan Energy Stanford

Stanford (140x conc.)

Efficiency (%)

Varian (216x conc.)SunPower (96x conc.) AMETEkPhoton Energy

Boeing

University So. Florida Boeing RCARCARCA

RCA

Solarex EPFL

EPFL Groningen

Sharp

NRELNREL

NREL

NREL Cu(In, Ga)Se2 (14x conc.)

FhG-ISE

Amonix (92x conc.) FhG-ISE NREL Euro-CIS

AstroPower (small-area)

Univ. Stuttgart (45 μm thin-film transfer)

UNSW SharpUNSW Georgia Tech

Georgia TechUNSW

UNSWUNSWUNSWUNSW NREL NRELNRELNREL

NREL Sharp

(large-area)

NREL Siemens University LinzUniversity Linz

Plextronics

NREL Konarka Univ. Linz

NREL (CdTe/CIS) United Solar

United Solar United Solar Kaneka (2 μm on glass) 198519901995200020052010

5.4%11.1%12.1%

16.5%

19.9%20.3%

24.7%

27.6%

33.8%

40.7% NREL (inverted, semi- mismatched, 1-sun) Figure4.16Bestresearchsolarcellefficienciesachievedinagivenyear.CourtesyofUnitedStatesDepartmentofEnergy,PropertyoftheU.S FederalGovernment.DatacompiledbyLawrenceKazmerski,NationalRenewableEnergyLaboratory(NREL)