ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerThe p-n JunctionELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerThe pn Junction• The pn Junction in Equilibrium– Built in voltage– Carrier concentrations– Depletion Region• The pn Junction Under Bias– Carrier Injection• IV equation for pn junction – Minority carrier current in quasi-neutral regions– Current flow in depletion region– Physical Meaning of I0– Reverse breakdown• Quasi-Fermi Levels• Non-idealities– Series resistance– High Injection– Depletion Region RecombinationELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremnerpn Junction in Equilibrium• Bring p type and n type material together physically• Thermal equilibrium means no extra heat, no applied voltages, nolight• The electrons from the n type material will diffuse into the p type material (and vice versa for holes) • After crossing the junction the electrons in the p type (holes in n type) material are minority carriers with a recombination lifetime• Keep in mind the dopant atoms don’t move – they are part of the crystalELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremnerpn Junction in Equilibrium• Movement of carriers across junction leaves ionized dopant atoms behind• Material is now charged since the balancing charge carrier is gone• Electric field is now present around the junction• Region around the junction is called the space charge region or more commonly the depletion region (since the region surroundingthe junction is depleted of carriers)Note: remember Electric field direction is defined for a positive chargeELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremnerpn Junction in Equilibrium• This is a drift current – the E field sweeps holes in n type material to the p type material (minority to majority carriers) and vice versa• Unless the minority carrier concentration is increased somehow (heat, optical generation, carrier injection) the drift current will remain low (more on this later)• Under Equilibrium the nett current is zero i.e. the drift current equals the diffusion currentNote: remember Electric field direction is defined for a positive chargeELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremnerpn Junction in Equilibrium• For a system in equilibrium the average energy must be constant (obvious). This also means the Fermi level must be constant• Away from the junction the original bulk conditions dominate and so the band diagram is unaffected• Close to the junction the bends bend due to the constant Fermi level, with the bending indicating the strength of the electric fieldSeparateJunctionELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerBuilt-in Voltage• The electric field across the pnjunction means a built-in voltage Ψ0is present• Don’t bother trying to measure it with voltmeter, you can’t• Built-in voltage is given by the difference between the Fermi levels of the p and n type material• Use previously given expressions for carrier concentrations to find expression in terms of doping levelsELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerCarrier Conc. Under ≡rm• Away from the depletion region the carrier concentrations are unaffected• Energy difference between Fermi level and conduction (valence) band edge gives electron (hole) concentration – can sketch carrier concentration from band diagram• Recall the built-in voltage depends on the doping – so we can relate carrier concentrations to the built-in voltage and each otherELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerThe Depletion Region• Depletion region surround pn junction where carriers have diffused out leaving the ionized dopant atoms• Tails off exponentially away from the junction – assuming that it vanishes at some distance from the junction, the deplation region approximation, helps simplify things greatly• For constant doping, depletion region approximation means charge density in depletion region is constant (though different on each side of the junction) and zero outside of depletion region• The total amount of charge on either side of the junction in the depletion region must be equalELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerDepletion Region Width• We can find the depletion region width by integrating the charge density over the region to get the electric field• The electric field can then be integrated across the region to obtain the built-in voltage• We already know the built-in voltage in terms of Fermi levels and so we can get the maximum electric field:ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerDepletion Region Width• Depletion region width is found to be:With the two lengths either side of the junctiongiven by:Maximum electric field increases with doping and is determined primarily by the lower level of dopingThe lower level of doping has the largest effect on the depletion region widthELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremnerpn Junction Under Bias• Forward bias is a voltage applied to the pn junction that REDUCES the electric field at the barrier, Reverse bias INCREASES the electric field at the junction• When bias is applied the balance between drift and diffusion current is destroyed – nett current flow• In forward bias, drift current decreases very slightly (can assume it stays the same) but diffusion current increases –Nett current flow• In reverse bias opposite occurs with diffusion current decreasing anddrift remaining same –Nett current flow (this one isvery small)ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremnerpn Junction Under Bias• Band diagram summary of the three types of bias possibleEquilibriumForward BiasReverse BiasNett current0+ve-veELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerDepletion Region Under Bias• Since the applied bias changes the electric field at the junction we can expect the depletion region width to also be changed• Assume that the voltage drop is only across the depletion region then for applied bias Vawe have• This will also affect