This document provides an introduction to the physics of photovoltaic devices. It discusses key concepts such as the pn junction, band diagrams, carrier transport mechanisms, and the operation of solar cells under illumination and bias. The document also describes factors that influence solar cell performance such as thickness, resistances, temperature, and illumination intensity.

1. Introduction to Photovoltaic Device Physics Joseph Y. Lee June 23, 2010 [email_address]

2. Diamond Lattice of Si Cu vs. Si n-type and p-type Semiconductor Band Diagram Construction for pn Junction at 0V Bias Concept of Potential Energy and Contact Junction pn Junction Diode - Forward and Reverse Bias Thermal Equilibrium and Non- Equilibrium Conditions Basic Structure of PV Solar Cell pn Junction PV Process Work-function Requirement for Ohmic and Solar Cell Contact Thickness Factors in pn Junction SC Basic Physics for PV See the difference between both diagrams I-V Curves Short Circuit Current Open Circuit Voltage Efficiency Characteristic Resistance Effect of Characteristic Resistances Impact of Series and Shunt Resistances Effect of Temperature Effect of Intensity Fill Factor (FF)

3. Diamond Lattice of Si http://sol.sci.uop.edu/~jfalward/semiconductordevices/semiconductordevices.html

4. Cu vs. Si Atomic Cu: 1 s 2 2 s 2 2 p 6 3 s 1 3 p 6 3 d 10 4s 1 4p 0 Atomic Si: 1 s 2 2 s 2 2 p 6 3 s 2 3 p 2 Crystal Si: 1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 Crystal Cu: 1 s 2 2 s 2 2 p 6 3 s 1 3 p 6 3 d 10 4s 1 4p 0 Most electrons are unpaired and free to move around. Conductor The electrons are fully paired, so they are difficult to move around. Semiconductor Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si

5. n-type and p-type Semiconductor n-Type p-Type In n-type semiconductor, the conduction occurs by the movement of electrons. In p-type semiconductor, the conduction occurs by the movement of holes. Charge carriers are negatively charged. Charge carriers are positively charged. Si Si Si Si Si Si Si Si Si B Si Si Si Si Si Si  h Si Si Si Si Si Si Si Si Si P Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si P Si Si Si Si Si Si electron Si Si Si Si Si Si Si Si Si B Si Si Si Si Si Si hole

6. Band Diagram Construction for pn Junction at 0V Bias Conventionally, the Fermi energy level is represented by a horizontal line in energy band diagrams. (Barrett, Nix, Tetelman, p.433) This makes the bands bend-down on the p-side and bend-up on the n-side. Before Contact Thermal Equilibrium Low E F side (p-type) gains electrons and so negatively charged. High E F side (n-type) loses electrons and so positively charged. Electrons deplete on the n-side interface and accumulate on the p-side interface, until the built-in potential tends to reverse the charge flow, or an equilibrium is reached. e - Upon contact, electrons flow from high to low E F or from n-type to p-type until an equilibrium is reached. Junction n-type p-type Missing electrons (holes) Gained electrons depletion zone space charge E o : built-in field Junction n-type p-type n-type E c E F E V E F p-type e -

7. Concept of Potential Energy and Contact Junction In non-equilibrium, water flows from the high potential energy position to the lower potential energy position until the level of both water containers equilibrates. The Fermi energy level (E F ) is tantamount to the level of chemical potential energy. It means that electrons flow from high to low Fermi energy upon contact. The equilibrium condition is reached by raising the water level of the container ‘B’ to the level of ‘A’ resulting in band bending . Metal/metal or metal/p-type contact analogy: If the two containers makes a contact, at the interface, ‘A’ sees the bend-down vacuum level and raised Fermi E-level (water level) on the ‘B’ side (electron gain on B-side, negatively charged space charge layer, SCL ), and ‘B’ sees a bend-up vacuum level on ‘A’ side (electron depletion on A-side or positive charges) . Non-equilibrium A High Potential B Low Potential Equilibrium A B Vacuum level E F E V

8. pn Junction Diode - Forward and Reverse Bias Forward diode current The depletion layer does not shrink to zero for the forward bias. It is common mistake when many believe the depletion layer shrinks to zero for the forward bias. Depletion is always present for both reverse and forward bias even though the depletion layer for the forward bias is smaller than the depletion layer for the reverse bias. The difference between forward and reverse bias is the absence of the diffusion current in reverse bias while the diffusion current for the forward bias overwhelms built voltage from the depletion layer. As a result, you have a forward bias current flowing due to the diffusion current. The red line is the diffusion current while the blue line is the drift current from the built-in voltage. The diffusion current overwhelms the drift and the current is flowing in the forward bias. Since the diffusion current is not greater than drift current from the built-in voltage, there is little current for the reverse bias. I I V Forward biased Reverse biased Forward Biased Reverse Biased

9. Thermal Equilibrium and Non-Equilibrium Conditions Equilibrium: under thermal condition The potential difference ( φ o ) from the electric field across the pn-junction cannot be measured at the terminals of the cells. It is strictly cancelled by the diffusion voltage current. electrons: minority carrier in p-type holes: minority carrier in n-type SCR: Space Charge Region Non-Equilibrium: under sunlight Photons generate e-h pairs and result in large excess minority carriers are generated – minority electrons in p-type bulk and minority holes in the n-type bulk region. Majority carriers can move in response to an electric field (Coulomb force). Minority carriers, on the other hand, tend to move in response to concentration gradients (diffusive force) across the built-in potential. Once they cross the junction, they become majority carrier. These excess charges tend to move toward the external contacts by repulsive Coulomb force – source of solar current This lowers the field strength allowing the majority carriers flood across the junction in opposition to the illumination current. This the forward-biased dark diode current as if a battery were being applied across it. Much effort devotes to minimizing the dark diode current to improve solar efficiency. Thermal Equilibrium http://people.seas.harvard.edu/~jones/ap216/images/pn_junction/Homo_biased.gif Thermal Non-Equilibrium Quasi-Fermi Levels

10. Basic Structure of PV Solar Cell In a photovoltaic (PV) cell, the absorbed photon energy generates electron-hole pairs that become a source of electricity. Electrons flow to the positive side of the load and holes flow to the negative side of the load. In pn junction solar cell, a built-in potential is the major driving force. The difference in work-functions of two contacts could be another driving force in charge separation .  m1 (Al, 4.08 eV) <  p  and  n <  m2 (ITO, 4.7 eV) Electrons flow from low to high work-function material (from high to low chemical potential) . (e.g., Al  p-type  n-type  ITO) Conductive Grid or Transparent Conductive Film (eg., ITO) ARC (e.g., SiO 2 - not blocking the electrodes) n-Type Semiconductor p-Type Semiconductor Conductive Contact (e.g., Al) Photons e - electrons holes e - h +

11. p-n Junction PV Process In the pn junction solar cell, the built-in electrostatic potential is the major driver for the separation of photo-generated electron-hole pairs. Note: Fermi level in the diagram is not exactly correct. It is a schematic diagram. With some loss of generality, Fermi level is shown at equilibrium. When there is light absorption, Fermi level will be in a quasi, non-equilibrium or non-steady state. You can think of two batteries in series. Metal A and p-type acts and np junction while the n-type and metal B acts another np junction. light absorption charge separation charge accumulation charge transport Fermi level hv Metal A Metal B p-type n-type e - h + 3 2 1 4 4 2 3  ITO : 4.7 eV  Al : 4.08 eV  Si : 4.2 eV

12. Work-function Requirement for Ohmic and Solar Cell Contact At metal/semiconductor contact interface, electrons flow from low work-function to high work-function, or from high Fermi energy to low Fermi energy. Ex: Ni (4.90 eV), As (5.2 eV) Ex: Ba (2.39eV), Mg (3.46eV) Ohmic Contact (non-rectifying) requirement  m1 >  Si(p) >  Si(n)  m1 electrons Contact-1 Contact-2  m1  m2 p-type n-type  Si = 4.2 eV (intrinsic) Ex: ITO (4.7 eV) Ex: Al (4.08 eV) electrons Anode Cathode  m1  m2 p-type n-type p-n Junction Solar Cell contact requirement  m1 <  Si(p)  Si(n)  <  m1  Si = 4.2 eV (intrinsic) LOAD

13. Thickness Factors in p-n Junction SC Photovoltaic effect occurs in a volume covering L h + W + L e . EHP (electron-hole pair) generated near the surface of the n-side disappear by recombination due to short lifetime, so the n-layer is made very thin, typically less than 0.2  m or less. At long  , around 1 – 1.2  m, the absorption coefficient  of Si is small and the absorption depth (1/  ) is typically greater than 100  m. It is thus needed to make the p-side thick to capture the long wavelength, typically 200 – 500  m (The thick silicon makes the sc-Si based solar cell expensive) . S. O Kasap, MacGraw-Hill, 2 nd ed. (2002) p.490. electrons Anode Cathode p-type n-type depletion region W l p V OC l n neutral n-region diffusion Long  Short  Medium  L e Mean diffusion distance for e Drift L h Mean diffusion distance for hole neutral p-region E o Back electrode Internal field p-n junction

14. See the difference between both diagrams Positive forward bias current shown as the red line flows from the p to n-type on the left figure. Holes in the pn junction on the right figure flows n to p-type in the opposite direction to the diffusion current on the left figure. This is very important to see this. The forward bias positive diffusion current will act as a parasitic dark current for the solar cell. If you do not understand this, then you will not understand the next slide. This is why you want the V ext (V oc ) to be zero. This will reduce the parasitic diffusion dark current. Forward Biased hv Metal A Metal B p-type n-type e - h + 3 2 1 4 4 2 3  ITO : 4.7 eV  Al : 4.08 eV  Si : 4.2 eV

15. I-V Curves Example: I o =1e-10 A I L = 0.5 A T= 300K V= 0.5V I= 0.453 A Ideality factor n= 1 If recombination occurs via band-to-band only Total solar cell current I V I V V I I V I L Light Current I V I V I L Light Current I V I V I L Light Current Without illumination, a solar cell has the same electrical characteristics as a large diode. When light shines on the cell, the I-V curve shifts as the cell begins to generate power. The greater the light intensity, the greater the amount of shift. Since the cell is generating power, the convention is to invert the current axis.

16. Short Circuit Current Short-circuit current depends on: the area of the solar cell - to remove the dependence of the solar cell area, it is more common to list the short-circuit current density (J sc in mA/cm 2 ) rather than the short-circuit current. the number of photons (i.e., the power of the incident light source) - I sc from a solar cell is directly dependant on the light intensity. the spectrum of the incident light - For most solar cell measurement, the spectrum is standardized to the AM1.5 spectrum . the optical properties - absorption and reflection of the solar cell the collection probability of the solar cell - depends chiefly on the surface passivation and the minority carrier lifetime in the base. When comparing solar cells of the same material type, the most critical material parameter is the diffusion length and surface passivation. In a cell with perfectly passivated surface and uniform generation, the equation for the short-circuit current density can be approximated as: where G is the generation rate, and L n and L p are the electron and hole diffusion lengths respectively. Voltage Current V OC I-V Curve of solar cell The short circuit current, I SC , is the maximum current from a solar cell and occurs when the voltage across the voltmeter or ammeter is zero. Power from the solar cell I SC

17. Open Circuit Voltage Laboratory silicon solar cells have open-circuit voltages of up to 720 mV under one sun and AM1.5 conditions, while commercial devices typically have open-circuit voltages of less than 600 mV. n: ideality factor Voltage Current V OC I-V Curve of solar cell The open circuit voltage, V OC , is the maximum voltage from a solar cell and occurs when the net current through the device is zero. Power from the solar cell I SC   1) ln( O L OC I I q nkT V

18. Efficiency Example: V oc =0.611 V I SC = 2.75 A FF=0.7 P in = 7.8 W P max = 1.18 W Efficiency = 15.1 % Practical PV cells: FF= 0.70 – 0.85 Single crystal Si: FF= 0.8, V oc = 0.588 V, J sc = 35 mA/cm 2 , 100 cm 2 cell -> 1.6 watts I sc and V oc varies in opposite direction. Thus with increasing E g , V oc increases and I sc decreases. Theoretical: η=29 % (max) near E g =1.2eV, Practical : η <20 % P FF I V P P in SC OC in   max 

19. Characteristic Resistance Characteristic resistance is a useful parameter in solar cell analysis, particularly in examining the impact of parasitic loss mechanisms. Inverse of slope I V R or I V R SC OC CH mp mp CH   Voltage Current V OC V mp , I mp I SC CH OC SC R V I slope 1  

20. Effect of Characteristic Resistances Since the value of resistance depends on the area of the solar cell, when comparing the series resistance of solar cells which may have different areas, a common unit for resistance is in  cm 2 . V I L R S Series resistance Current Shunt resistance R SH

21. Impact of Series and Shunt Resistances Series resistance sources: (1) the movement of current through the emitter and base of the solar cell (2) the contact resistance between the metal contact and the silicon (3) the resistance of the top and rear metal contacts Main impact: (1) reduce the fill factor (2) reduce short-circuit current if shunt resistance is excessively high Low shunt resistance sources: (1) typically manufacturing defects, rather than poor solar cell design Main impact: (1) power losses by providing an alternate current path, which is particularly severe at low light levels Both the magnitude and impact of series and shunt resistance depend on the geometry of the solar cell. The major huddle is the improvement of efficiency by design, process control, and materials choice.

22. Increasing the temperature reduces the band gap resulting in reduced V OC and increased I SC . Effect of Temperature Voltage Current V OC decreases I SC increases High T cell Low T cell

23. Effect of Intensity Changing the light intensity incident on a solar cell changes all solar cell parameters, including the short-circuit current, the open-circuit voltage, the FF, the efficiency and the impact of series and shunt resistances. Flat Plate Module (1 Sun) 1 Sun = 1 kW/m 2 at AM1.5 Concentrators (>1 sun) 10 Sun = 10 kW/m 2 at AM1.5 Voltage (V) Current Density (A/cm 2 ) decreasing # of Suns

24. Fill Factor (FF) Graphically, the FF is a measure of the &quot;squareness&quot; of IV curve, the area of the largest rectangle (A) which will fit in the IV curve. B Area A Area V I V I FF OC SC mp mp   Voltage Current , Power V OC V mp , I mp I SC V mp , P max A B FF I V I V P SC OC mp mp   max

25. MOSFET Models for SPICE Simulation, Including BSIM3 and BSIM4 (2001) PSPICE and Matlab for Electronics – An Integrated Approach (2002) Electronic Properties of Semiconductor Interfaces with 146 Figures and 17 Tables (2004) Metal-Semiconductor Contacts 2nd Edition by E. H. Rhoderick & R. H. Williams (1988) Metal-Semiconductor Interfaces by Akio Hiraki (1995) Semiconductor Contacts: An approach to ideas and models by Heinz K. Henisch (1984) Modelling Photovoltaic Systems Using PSPICE (2002) References

26. PSPICE Simulations 1000 W/m 2 800 W/m 2 400 W/m 2 200 W/m 2 600 W/m 2 I(V) plots of a solar cell under several irradiance values.

27. PSPICE Simulations Isc = 4.3869A Voc = 0.446V I(V) plot of a solar cell under a temperature at 80 °C.

28. PSPICE Simulations This is a case of two solar cells in series at 700W/m 2 and 1000W/m 2 irradiances. Notice there is a reduction in current while there is an increase of Voc voltage. Isc = 3A Voc = 1.125V

29. Acknowledgements Eal H. Lee, Ph.D. TaeEui Kim, Ph.D. Sung Yi, Ph.D.

30. 감사합니다 .