ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerThe Illuminated p-n JunctionELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerThe Illuminated pn Junction• Generation re-visited– Basic requirements– Optical Generation– Absorption Coefficient– Optical Generation Rate• The Illuminated pn Junction – IV equation – Physical Meaning of I0– What is going on?• Different Operating Conditions– Short circuit condition– Open circuit condition– Forward bias– Reverse biasELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerGeneration revisitedBasic requirements:• Need to move carriers from one band to the other, so require: – Energy increase greater than the band gap– Must be a carrier available for excitation– Must be a vacant state available for carrier to move to• Energy can be provided by any means, however: – Thermal energy only gives nett increase with thermal gradients across device. – Optical absorption does not have such a restriction – will consider ONLY optical absorption• Important to remember that each absorption process has its own inverse process (we may not be able to observe them easily but they are there)– In thermal equilibrium they balance exactly– Steady state they are both present though one will be much stronger than the otherELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerOptical Generation• Absorption of photons where the energy of each photon is given by:• Energy of photon is primary determinant of what happens when it hits the semiconductor– If E < EGthen (ideally) no absorption– If E ≥ EG then absorption• Energy above the band gapis lost as heat to the crystallattice (phonons)• Major fundamental lossesfor a solar cellexcess holesELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerOptical Generation• Recall that the bands are actually more complex and vary with crystal momentum – Direct and indirect band gaps arise– Absorption for indirect band gap requires phonons, a three particle process meaning lower absorptionELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerAbsorption Coefficient• Absorption coefficient, α, is a measure of the probability that a photon is absorbed– Varies with wavelength– Material specific• Absorption depends on likelihood of transition – lower around the band edge increasing further away• Direct band gap materials generallyhave more rapid increase in the absorption – higher α• Absorption depth 1/α is oftendefined – intensity of light has dropped to 1/e of initialELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerAbsorption Coefficient• Absorption coefficient of direct materials has the form:• Not so straight-forward for indirect band gap materials, like Si, also get absorption below EG• Temperature of the material shifts the band gap.–As T increase EGdecreases and vice versa– Since band gap is shifted so is the absorption coefficient21)(GEh −νELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerGeneration Rate• Need to know how many photons have been absorbed by a material at a particular depth x• Given by the following:• NSis number of photons at surface (x = 0), α is absorption coefficient• Generation rate can then be found:• Important to distinguish between two – remember which is a rate and which is a total numberELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerGeneration Rate• Generation rate depends on the wavelength of light and the depth in the material• Larger absorption coefficient means generation is predominantly near the surface• Small absorption coefficient means generation is more uniform•Ifx << 1/α then generation can be assumed to be constantRememberELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerIlluminated pn junction• pn junction has optical generation of carriers that may be swept across the junction by the drift field• Optical generated carriers are swept from being minority carriers on one side to being majority carriers on the other• How is the IV equation affected by the optical generation? majoritycarriersminoritycarriers majoritycarriersminoritycarriersELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerIlluminated IV equation• We can solve for the IV equation in exactly the same manner as previously but this time don’t assume G = 0• This means the differential equation to be solved for the carrier concentration increase is given by:• We simplify by assuming that the generation is constant (solving it otherwise is a nightmare)• Means we get the following simple solution to the differential equation:ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerIlluminated IV equation• We can proceed in an identical manner as for the un-illuminated case i.e. differentiate the carrier concentration increase to find the current and then equating the currents on the p and n sides of the junction, we then end up with:• This means the light generated current is simply a superposition on top of what we get for the un-illumined case!• We bundle this information up in the following expression:ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerMeaning of I0• We want to extract the light generated current with a forward bias meaning the diode current determined by I0works AGAINST the light generated current• The first term is a recombination current found by considering the diode without illumination – often referred to as the dark current• We therefore want to reduce I0to as low a value as possible in order to be able to extract as much light generated current as possibleELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. BremnerShort Circuit• Means no load attached but current can flow• Recombination is essentially what we expect for thermal equilibrium and can be ignored• Short circuit current is therefore the light generated current• This makes the short circuit current VERY important because it tells us how much light generated current there is• Gives us good idea about absorption of the light but carriers still have to get to