1. Photovoltaic Devices

3. Outlines Solar energy spectrum Photovoltaic device principles
I-V Characteristics

4. Solar Energy Spectrum
Photovoltaic devices (solar cells) convert the incident solar radiation energy into electrical energy.
Absorbed photons  photogeneration  current (photocurrent) in external cicuit.
Power range: from < mW (calculator) to few MW (photovoltaic power generation)

5. Solar Energy Spectrum Spectral intensity Iλ: Intensity per wavelength.
Iλδλ: intensity in a small interval δλ.
Total intensity I: integration of Iλ over the whole spectrum.
Solar constant or air-mass zero (AM0): the total intensity above earth’s atmosphere, approximately constant at kW m-2.

6. Solar Energy Spectrum
On sunny day, light intensity on earth’s surface is about 70% of the intensity above the atmosphere.
Absorption and scattering effects increase with the sun beam’s path through the atmosphere.
The shortest path through the atmosphere is when the sun is directly above that location and the received spectrum is called air mass one (AM1).
Air mass m (AMm): the ratio of the actual radiation path h to the shortest path h0, m = h/h0.
Since h = h0secθ, AMm is AMsecθ.

7. Solar Energy Spectrum
The spectral distribution AM1.5 has several sharp absorption peaks at certain wavelengths which are due to those wavelength being absorbed by various molecule in the atmosphere, such as ozone, air, and water vapor molecules.
Dust particles scatter the sun light  reduces the intensity and gives rise to the sun’s rays arriving at random angle.

8. Solar Energy Spectrum
Thus, the terrestrial light has a diffuse component in addition to direct component.
Cloud and sun position  increase diffuse component  spectrum shifted toward the blue light.
Scattering also increase with decreasing wavelength.
On a clear day, diffusion component can be about 20% of the total radiation.
The amount of incident radiation depends on the position of the sun.  Photovoltaic device flat will receive less solar energy by factor cosθ  However it can be tilted to directly face the sun to maximize the collection efficiency.

9. Florida Solar Energy Center9

10. PV Cells have efficiencies approaching 21.5%
Florida Solar Energy Center 10

11. Silicon Solar Cell

12. PV Modules have efficiencies approaching 17%
Florida Solar Energy Center 12

13. Florida Solar Energy Center13

14. Solar Panel Solar panel by BP Solar at a German autobahn bridge
Solar panels are devices for capturing the energy in sunlight. The term solar panel can be applied to either solar hot water panels (usually used for providing domestic hot water) or solar photovoltaic panels (providing electricity).
Solar panel by BP solar at a German autobahn bridge. pic taken 4/04 by Thomas Springer.
Solar panel by BP Solar at a German autobahn bridge 14

15. Florida Solar Energy Center15

18. Spacecraft International Space Station Hubble Telescope Mars Rover 18
Probably the most successful use of solar panels is on spacecraft, including most spacecraft that orbit the Earth and Mars, and spacecraft going to other destinations in the inner solar system. In the outer solar system, the sunlight is too weak to produce sufficient power and radioisotope thermal generators are used.
Research is underway to develop solar power satellites: space-based solar plants — satellites with large arrays of photovoltaic cells that would beam the energy to Earth using microwaves or lasers. Japanese and European space agencies have announced plans to develop such power plants in the first quarter of the 21st century.
As opposed to chemical rockets, which are powered by a chemical reaction of the propellant, and uses the exhaust gases as reaction mass, some spacecraft propulsion methods have a method of expelling reaction mass powered by electricity. Either solar energy or nuclear energy is used. These methods typically have a higher specific impulse. The amount of reaction mass needed always grows exponentially with the delta-v to be produced, but more mildly if the specific impulse is high (but it should not be too high because for large specific impulse the power needed is proportional to it). With solar power the acceleration that can be produced is very low (much too low for a launch), but enduring. Typical burn times are months instead of minutes. The power the solar panel produces per kg, as an upper limit of the power the spacecraft has at its disposal per kg spacecraft (including solar panels) is an important factor. See also energy needed for propulsion methods.
Solar panels need to have a lot of surface area that can be pointed towards the Sun as the spacecraft moves. More exposed surface area means more electricity can be converted from light energy from the Sun. Sometimes, satellite scientists purposefully orient the solar panels to "off point," or out of direct alignment from the Sun. This happens if the batteries are completely charged and the amount of electricity needed is lower than the amount of electricity made. The extra power will just be vented by a shunt into space as heat.
Spacecraft are built so that the solar panels can be pivoted as the spacecraft moves. Thus, they can always stay in the direct path of the light rays no matter how the spacecraft is pointed. Spacecraft are usually designed with solar panels that can always be pointed at the Sun, even as the rest of the body of the spacecraft moves around, much as a tank turret can be aimed independently of where the tank is going. A tracking mechanism is often incorporated into the solar arrays to keep the array pointed towards the sun.
Mars Rover 18

19. Cross Section of PV Cell
When a photon of light hits a piece of silicon, one of three things can happen. The first is that the photon can pass straight through the silicon. This (generally) happens when the energy of the photon is lower than the bandgap energy of the silicon semiconductor. The second thing that can happen is that the photon is reflected off the surface. The third thing is that it can be absorbed by the silicon. This (generally) happens if the photon energy is greater than the bandgap energy of silicon. When a photon is absorbed, its energy is given to an electron in the crystal lattice. Usually this electron is in the valence band, and is tightly bound in covalent bonds between neighboring atoms, and hence unable to move far. The energy given to it by the photon "excites" it into the conduction band, where it is free to move around within the semiconductor. The covalent bond that the electron was previously a part of now has one less electron - this is known as a hole. The presence of a missing covalent bond allows the bonded electrons of neighboring atoms to move into the "hole," leaving another hole behind, and in this way a hole can move through the lattice. Thus, it can be said that photons absorbed in the semiconductor create mobile electron-hole pairs.
A photon need only have greater energy than that of the band gap in order to excite an electron from the valence band into the conduction band. However, the solar frequency spectrum approximates a black body spectrum at ~6000 K, and as such, much of the solar radiation reaching the Earth is composed of photons with energies greater than the band gap of silicon. These higher energy photons will be absorbed by the solar cell, but the difference in energy between these photons and the silicon band gap is converted into heat (via lattice vibrations - called phonons) rather than into usable electrical energy. 19

20. Photovoltaic Device Principles
Consider pn+ junction with very narrow n-region.
The illumination is through then thin n-side.
The SCL extend mainly in p-region with built-in field E0.
Electrode at n-side must allow illumination to enter the device and at the same time result in a small series resistance.
This electrode is formed from array of finger electrodes.

21. Photovoltaic Device Principles
Photons are absorbed in SCL within the neutral p-side (lp)  photogenerated EHP in this region.
The electron drifts and reaches the neutral n+ side whereupon it makes this region negative by an amount of charge –e.
Similarly, hole drifts and reaches the neutral p-side and thereby makes this side positive  open circuit voltage between terminals of the device.
If there is external load, electron will travel through it and recombine with the excess holes in p- side.

22. Photovoltaic Device Principles
Therefore the existence of built-in field E0 is important to create accumulated electrons in the n-side and holes in the p-side.
For long wavelength photons  absorbed in the neutral p-side  no E field  diffusion.
Minority carrier diffusion length Le.
τe: recombination lifetime of electron.
De: diffusion coefficient in the p-side.

23. Role of Diffusion Length
Only those EHPs photogenerated within the Le to the depletion layer can contribute to the photovoltaic effect.
Those photogenerated EHPs further away from SCL than Le are lost by recombination.
Thus, it is important to have the minority carrier diffusion length Le as long as possible.  By choosing Si pn junction to be p-type which makes electrons to be minority carriers; the electron diffuse length in Si > the hole diffusion length.

24. absorption coefficient
Role of hole diffusion length and short circuit current
For EHPs photogenerated by short-wavelength photons absorbed in the n-side, within diffusion length Lh, can reach SCL and swept across to the p-side.
The photogenerated of EHPs that contribute to the photovoltaic effect occurs in a volume of
absorption coefficient
Lh + W + Le.
If the terminals are shorted then the excess electrons in the n-side can flow through the external circuit to neutralize the excess holes in the p-side  this current is called photocurrent.

25. Photovoltaic Device Principles
Under steady state operation  no net current through an open circuit solar cell  Photocurrent inside the device due to photo generated carriers must be balanced by a flow of carriers in the opposite direction.
Those are minority carriers that become injected by the appearance of the photovoltaic voltage across the pn junction as in normal diode.

26. absorption coefficient
Device optimization and carrier losses
For long wavelengths, 1 – 1.2 μm, α is small  absorption depth 1/α is typically greater than 100 μm.  Need a thick p-side and long minority carrier diffusion length Le.
Thus, p-side is 200 – 500 μm and Le is shorter than that.
Si has Eg = 1.1 eV  correspond to a threshold wavelength of 1.1 μm  The incident energy with wavelength > 1.1μm is then wasted (~ 25%).
Photons are absorbed and recombined near the crystal surface  losses.
absorption coefficient

27. Sources of carrier losses
Photons are absorbed and recombined near the crystal surface  losses  severely reduce efficiency.
Crystal surface and interface contain high concentration of recombination-center.
Those facilitate the recombination of photogenerated EHP near the surface.
The losses due to this event as high as ~ 40%.
These combined effect bring the efficiency down to about 45%.
Antireflection coating is also contributing the reduction of photons collection due to imprefection with factor of 0.8 – 0.9.
And including the limitation of photovoltaic action the upper limit to a photovoltaic device that uses single crystal of Si is about 24 – 26% at room temperature.

28. pn Junction Photovoltaic I-V Characteristics
Consider an ideal pn junction photovoltaic device connected to a resistive load R.
I and V define the convention for the direction of positive current and positive voltage.
If the load is short circuit  the only current in the circuit is due to photogenerated (photocurrent),Iph.

29. pn Junction Photovoltaic I-V Characteristics
If I is the light intensity, then the short circuit current is
The photocurrent does not depend on the voltage across the pn jucntion, because it always some internal field to drift the photogenerated EHP.
If R is not short circuit  the positive voltage V appears across the pn junction as a result of the current passing through.
K is constant that depends on particular device

30. pn Junction Photovoltaic I-V Characteristics
The voltage across the load R (with opposite polarity) reduces the built in potential V0 of the pn junction and hence leads to minority carrier injection and diffusion.
Thus, in addition to Iph there is also a forward diode current Id in the circuit which arises from the voltage developed across R.
Since Id is due to the normal pn junction behavior  diode characteristics,
where I0 is the reverse saturation current, n is the ideality factor which depends on semiconductor material and fabrication chaeacteristics (n = 1 – 2).

31. pn Junction Photovoltaic I-V Characteristics
Thus, the total current (solar cell current),
The I-V characteristics of a typical Si solar cell (Fig.).
Normal dark characteristics being shifted down by photocurrent Iph (short circuit), which depend on light intensity, I.
The open circuit voltage, Voc, is given by the point where the I-V curve cuts the V-axis (I = 0).

32. pn Junction Photovoltaic I-V Characteristics
The I-V curves for positive current requires an external bias voltage.
Although Voc depends on the light intensity, it value lies between 0.4 – 0.6 V.
Photovoltaic operation is always in the negative current region.
Thus the load line,

33. pn Junction Photovoltaic I-V Characteristics
When a solar cell drives a load R, R has the same voltage as the solar cell but the current through it is in the opposite direction to the convention that current flows from high to low potential.
The current I’ and voltage V’ can be found by solving two previous equations simultaneously  not trivial analytical procedure.

34. Photovoltaic I-V Characteristics (load line analysis)
Or they can be found easily from load line construction.
The load line cuts the solar cell characteristics at P. Point P satisfies both equations  represent the operating point of the circuit.

35. Maximum power and fill factor
The power delivered to the load is Pout = I’V’ the area bound by I- and V-axes and the dashed lines.
Maximum power delivered  by changing R  max area when I’ = Im and V’ = Vm.
The fill factor FF,
FF range is 70 – 80%
FF is a measure of the closeness of the
solar cell I-V curve to the rectangular shape

37. Series Resistance and Equivalent Circuit
Practical devices ≠ ideal pn junction device.
Photogenerated electron has to transverse a surface semiconductor region to reach the nearest finger electrode create an effective series resistance Rs.

38. Series Resistance and Equivalent Circuit
Equivalent circuit of an ideal pn junction solar is represented by a constant current generator Iph.
The flow of photogenerated carriers across the junction gives rise to a photovoltaic voltage V. This voltage leads to a normal diode current Id = I0[exp(eV/nkBT)-1]  Id is represented by and ideal pn junction diode.
Iph and Id are in opposite directions  open circuit the photovoltaic voltage is such that Iph and Id have the same magnitude and cancel each other.

39. Series Resistance and Equivalent Circuit
Equivalent circuit for practical solar cell include series resistance Rs  gives rise to a voltage drop.
Photogenerated carriers can also flow through the crystal surfaces or grain boundaries in polycrystalline devices, instead of flowing through the external load RL  represented by an effective internal shunt or parallel resistance Rp.
Typically Rp is less important than Rs unless the device is highly polycrystalline.

40. Series Resistance and Equivalent Circuit
Series resistance Rs can significantly deteriorate the cell performance. The max power decrease  reduce cell efficiency.

41. Temperature Effects
Temperature decreases  Output voltage and efficiency increase.
Solar cell operate best at lower temperature.
The output voltage Voc, when Voc >> nkBT/e,
I0 is reverse saturation current and strongly depend on temperature, because it depends on square of ni.
If I is light intensity,

42. Temperature Effects
Assuming n = 1, at two different temperatures T1 and T2 but the same illumination level, by subtraction,
Substitute,
Thus,
Rearrange for Voc2,

43. Temperature Effects
Example, Si solar cell has Voc1 = 0.55 V at 20 oC (T1 = 293 K), at 60 oC (T2 = 333 K),

44. Solar Cells Materials, Devices and Efficiencies
For a given solar spectrum, conversion efficiency depends on the semiconductor material properties and the device structure.
Si based solar cell efficiencies 18% for polycrystalline and 22 – 24% for single crystal devices.
About 25% solar energy is wasted  not enough energy  unable to generate EHPs.
Considering all losses, the maximum electrical output power is ~20% for a high efficiency Si solar cell.

46. Solar Cells Materials, Devices and Efficiencies
Si homojunction solar cell efficiencies ~24%. Single crystal PERL (Passivated Emitter Rear Locally-diffused) cells.

47. Solar Cells Materials, Devices and Efficiencies
Semiconductor alloy III-V  different bandgap with the same lattice constant  Heterojunction.

48. Solar Cells Materials, Devices and Efficiencies
Example n-AlGaAs with p-GaAs.

49. Solar Cells Materials, Devices and Efficiencies
To further increase the absorbed photons  tandem or cascade cells (use two or more cells in tandem), such as GaAs – GaSb.