Chapter 7b

Effective Series Resistance

• Practical devices can deviate substantially from the ideal pn junction solar cell behavior.

• Consider an illuminated pn junction driving a load resistance RL and assume that photo-generation takes place in the depletion region.– Photo-generated electron has to transverse a surface

semiconductor region to reach the nearest finger electrode– All these electron paths in the n-layer surface region to

finger electrodes introduce an effective series resistance RSinto photovoltaic circuit as shown in Fig.9

Effective Series Resistance, cont

• If the finger electrodes are thin, then the resistance of the electrodes themselves will further increase RS

– This is also a series resistance due to the neutral p-region but this is generally small compared with the resistance of the electron paths to the finger electrodes.

Neutral

n-region

Neutral

p-region

Finger

electrode

Back

electrode

Depletion

region

RL

Rs

Rp

Series and shunt resistances and various fates of photegenerated EHPs.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Fig. 9

Equivalent circuit

• The photo-generation process is represented by a constant current generator Iph ( light intensity)

• The flow of photo-generated carrier across the junction gives rise to a photovoltaic voltage difference V across the junction– This voltage leads to the normal diode currentId = Io [exp(eV/nkBT) – 1] = 0

• Iph and Id are in opposite directions – So, in open circuit, the photovoltaic voltage is such that Iph

and Id have the same magnitude and cancel each other.

A

Iph Rp RLV

IIph

Id

Solar cell Load

B

Rs

The equivalent circuit of a solar cell


Fig. 10

• Fig. 10 shows the equivalent circuit of a more practical solar cell– The series resistance RS give rise to a voltage drop and

therefore prevents the full photovoltaic voltage from developing at the output between A and B.

• A fraction of the carriers flow through the crystal surface or grain boundaries in polycrystalline devices instead of external load RL

– These effects can be represented by an effective internal shunt or parallel resistance Rp

– Typically Rp less important than Rs unless the device is highly polycrystalline

Equivalent circuit

Series Resistance

• The series resistance Rs can significantly deteriorate the solar cell performance as Fig.11– Rs = 0 is the best solar cell case

• The available maximum output power decreases with the series resistance– Also reduces the cell efficiency– When Rs is sufficiently large, it limits the short circuit

current

• Low shunt resistance Rp due to material defects also reduces the efficiency– Low Rp leads to a reduced Voc

I (mA)

V

00

0.2 0.4 0.6

5

10

Vo c

Isc

Rs = 0

Rs = 20

Rs = 50

Iph

The series resistance broadens the I-V curve and reduces the maximumavailable power and hence the overall efficiency of the solar cell. The exampleis a Si solar cell with n 1.5 and Io 310-6 mA. Illumination is such thatthe photocurrent Iph = 10 mA.


Fig. 11

Example

• Consider two identical solar cells with the properties Io= 2510–6mA, n= 1.5, Rs=20 subjected to the same illumination so that Iph =10mA.

• Explain the characteristics of two solar cells connected in parallel.

• Find the maximum power that can be delivered by one cell and two cells in series and also find the corresponding voltage and current at the maximum power point (assume Rp=)

Solution

• Consider one individual solar cell as shown in Fig.10. The voltage Vd across the diode is V – RsI so that the external current I is,

I = –Iph + Io [exp(eV/nkBT) – 1]

= –Iph + Ioexp[e(V – IRs)/nkBT] – Io (1)

• Eqn (1) gives the I-V characteristic of 1 cell and is plotted in Fig.12.

• The output P=IV is also plotted in Fig.12– The maximum power=2.2mW when I=8mA V=0.27V and

load = 34

0.60.40.20246

5

15

Voltage (V)Power (mW)

Current (mA)

20

10

1 cell

2 cells in parallel

Current vs. Voltage and Power vs. Current characteristics of one cell and twocells in parallel. The two parallel devices have Rs/2 and 2Iph.


Fig. 12

Solution, cont

• Fig 13 shows the equivalent circuit of the two solar cells in parallel running a load RL.

• I and V now refer to the whole system of two devices in parallel

• Each device is now delivering a current I/2. The diode voltage for one cell is V – RsI/2 . Thus,

½I = –Iph+Ioexp[(eV – ½IRs)/nkBT] – Io

I = –2Iph+2Ioexp[(eV – ½IRs)/nkBT] – 2Io(2)

Solution, cont

• Comparing Eqs.(2) & (1), we see that the parallel combination has halved the series resistance, doubled the photocurrent and doubled the diode reverse saturation current Io.

• All these in line with intuitive expectation as the device are has now been effectively doubled

• Fig.12 shows the I-V & I-P characteristics of the combined device– The maximum power 4.4 mW, I16mA, V0.27V and load = 17

– The parallel connection increases the available current and allows a lower resistance load to be driven

A

Iph

V

Iph

Id

B

Rs

RL

I/2

Id

Iph

I

RsI/2

Two identical solar cells in parallel under the same illumination anddriving a load RL.


Fig. 13

Solution, cont

• If we were to use the two solar cells in series, then Voc= 1V, Isc=Iph=10mA and maximum power = 4.4mW at I=8mA, V= 0.55V & load= 34.

• These simple ideas however do not work when the cells are not identical.– The connections of such mismatched cells can lead to

much poorer performance than idealized predictions based on parallel and series connections of matched devices.

Temperature Effect

• The output voltage and the efficiency of a solar cell increases with decreasing temperature; solar cells operate best at lower temperature.

• Consider the open circuit voltage Voc of the device in Fig. 8(b)– As the total cell current is zero, Iph generated by light must

be balanced by Id generated by Voc

• If ni is the intrinsic concentration, Io ni2

– Which means Io decreases rapidly with decreasing temperature

Temperature Effect, cont

• A greater voltage is developed to generate the necessary Id that balances Iph

• The output voltage Voc when Voc »nkBT/e is given by Voc = nkBT/e ln(Iph/Io)

• In Eq (1), Io is the reverse saturation current– Io is strongly temperature dependent because it depends

on ni2

• Since Iph=KI, we can write Eq (1) as

Voc = nkBT/e ln(KI/Io) or eVoc/nkBT = ln(KI/Io)


• Assuming n=1, at two different temperature T1 and T2but at the same illumination level

eVoc2/kBT2 – eVoc1/kBT1= ln(KI/Io2) – ln(KI/Io1)

= ln(Io1/Io2) ln(ni12/ni2

2)

• Where the subscripts 1 and 2 refer to the temperature T1 or T2 respectively


• We can substitute ni2 = NcNvexp(–Eg/kBT) and

neglect the temperature dependences of Nc

and Nv compared with the exponential part to obtain,

eVoc2/kBT2 – eVoc1/kBT1= Eg/kB(1/T2–1/T1)

• Rearranging for Voc2 in terms of other parameters we find,

Voc2 = Voc1(T2/T1) + Eg/e(1– T2/T1)


• For example, a Si solar cell that has Voc1 = 0.55V at 20C (T1=293K) will have Voc2 at 60C (T2=333K) given by

Voc2= (0.55V)(333/293)+(1.1V)(1 – 333/293) = 0.475 V

• If we assume to first order that the absorption characteristics are unaltered (Eg, diffusion length etc remaining roughly the same), so that Iph remains the same, the efficiency decreases at least by this factor.

Solar cells efficiency

• The efficiency of a solar cell is one of its most important characteristics – Because it allows the device to be assessed economically in

comparison to other energy conversion devices

• The solar cell efficiency refers to the fraction of incident light energy converted to electrical energy

• For a given spectrum, the conversion efficiency depends on – the semiconductor material properties & the device structure.

– the effect of ambient conditions i.e. the temperature & high radiation damage by energy particle (for space application)

Solar cells efficiency

• Solar cells efficiency is affected by

– Significant changes in the sun’s spectrum from one location to another

– In location with a substantial diffuse component in the spectrum, a device using a higher band-gap semiconductor is more efficient

– Using solar concentrators to focus the light onto a solar cell can substantially increase the overall efficiency.

Solar cells materials

• Most solar cells are silicon based

– Because Si fabrication is now a mature technology that enables cost effective devices to be manufactured

• Typical Si based solar cell efficiencies

– about 18% for polycrystalline

– 22-24% for high efficiency single crystal device

• Fig. 14 illustrates how various factors typically reduce the efficiency of a Si solar cell

100% Incident radiation

Insufficient photon energy

h < Eg

Excessive photon energy

Near surface EHP recombination

h > Eg

Collection efficiency of photons

Voc (0.6Eg)/(ekB)

21%

FF0.85

Overall efficiency

Accounting for various losses of energy in a high efficiency Sisolar cell. Adapted from C. Hu and R. M. White, Solar Cells(McGraw-Hill Inc, New York, 1983, Figure 3.17, p. 61).


Fig. 14

Solar cells materials, cont

• Some 25% of solar energy is wasted because of photon not having sufficient energy to generate EHPs.

• At the end of the spectrum, high energy photons are absorbed near the crystal surface & these EHPs disappear by recombination

• The cell has to absorb as many of the useful photon as possible– The photon collection efficiency factor depends on the

particular device structure

Passivated Emitter Rear Locally-diffused

• Solar cells fabricated by a pn junction in the same crystal are called homo-junctions– Best homo-junction solar cell efficiencies are about

24% for single crystal PERL cells

• PERL or Passivated Emitter Rear Locally-diffused have a texture surface as in Fig.15– an array of “inverted pyramid” etched into the surface

to capture the incoming light– Reflection inside the pyramid allow a second or third

chance for absorption– After reflection, photon would be entering the

semiconductor at oblique angles or absorbed within Leof the depletion layer.

LightOxide

np

Inverted pyramid textured surface substantially reduces reflectionlosses and increases absorption probability in the device

Le


Fig. 15

Hetero-junctions

• There are a number of III-V semiconductor alloys – that can be prepared with different bandgaps but with the

same lattice constant.

• Fig.16 shows a thin AlGaAs layer on GaAs passivates the surface defect in a homogenous GaAs cell– AlGaAs has a wider bandgap than GaAs and would allow

most of solar photon to pass through

– AlGaAs window layer overcomes the surface recombination limitation and improves the cell efficiency (~24%)

p-AlGaAs window (< 0.02 m)

p-GaAs

n-GaAs

Passivated GaAs surface

AlGaAs window layer on GaAs passivates the surface statesand thereby increases the low wavelength photogenerationefficiency


Fig. 16

• Hetero-junctions between different bandgap III-V semiconductors that are lattice matched offer the potential of developing high efficiency solar cells

• The simplest single hetero-junction example is shown in Fig.17– It consists of a pn-junction using a wider bandgap n-AlGaAs with p-GaAs

– Energetic photons (h>2eV) are absorbed in AlGaAs

– Less energetic photons (1.4<h<2eV) are absorbed in the GaAs

• In more sophisticated cell, the bandgap of AlGaAs is graded slowly from the surface by varying the composition of AlGaAs layer

Fig. 17

Tandem or cascaded cells

• Tandem (cascaded) cells use two or more cells in tandem or in cascade to increase the absorbed photon from the incident light as Fig. 18.– The first cell is made from a wider bandgap material and

only absorbs photons with h > Eg1.

– The second cell absorbs photons that pass the first cell and have h > Eg2.

• The whole structure can be grown within a single crystal by using lattice matched crystalline layers leading to a monolithic tandem cell.

Tandem cells

• Light concentrators are used to further increase the efficiency of tandem cell.

• A GaAs-GaSb tandem cell operating under a 100-sun condition have exhibited an efficiency of about 34%– 100 times of ordinary sunlight

• Tandem cells have been used in thin film a-Si:H (amorphous hydrogenated amorphous Si) pin solar cells to obtain efficiencies up to 12%– Tandem cells have a-Si:H & a-Si:Ge:H cells are easily

fabricated in large areas.

np

Cell 1 (Eg1

) Cell 2 (Eg2

< Eg1

)

n p

Connecting region.

A tandem cell. Cell 1 has a wider bandgap and absorbs energeticphotons with h> Eg1. Cell 2 absorbs photons that pass cell 1 andhave h> Eg2.


Fig. 18

Technology

Chapter 7b