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The Illuminated p-n Junction ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner The 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 bias ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Generation revisited Basic 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 other ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Optical 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 < EG then (ideally) no absorption – If E ≥ EG then absorption • • Energy above the band gap is lost as heat to the crystal lattice (phonons) Major fundamental losses for a solar cell excess holes ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Optical 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 absorption ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Absorption 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 generally have more rapid increase in the absorption – higher α • Absorption depth 1/α is often defined – intensity of light has dropped to 1/e of initial ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Absorption Coefficient • Absorption coefficient of direct materials has the form: (hν − EG ) 1 2 • 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 EG decreases and vice versa – Since band gap is shifted so is the absorption coefficient ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Generation Rate • • Need to know how many photons have been absorbed by a material at a particular depth x Given by the following: • NS is 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 number ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Generation 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 • • If x << 1/α then generation can be assumed to be constant Remember ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Illuminated 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? minority carriers majority carriers majority carriers minority carriers ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Illuminated 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. Bremner Illuminated 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. Bremner Meaning of I0 • We want to extract the light generated current with a forward bias meaning the diode current determined by I0 works 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 I0 to as low a value as possible in order to be able to extract as much light generated current as possible ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Short Circuit • Means no load attached but current can flow • Recombination is essentially what we expect for thermal equilibrium and can be ignored J SC = J 0 (e q .0 kT − 1) − J L = J 0 (1 − 1) − J L = − J L • 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 contacts without recombining • Can be measured as function of wavelength to give the quantum efficiency ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Open Circuit • Infinite load attached – no current flow J = J 0 (e VOC qVOC nkT − 1) − J L = 0 ⎛ JL ⎞ nkT ⎛ J L ⎞ = ln⎜⎜ − 1⎟⎟ ≈ ln⎜⎜ ⎟⎟ q ⎝ J0 ⎠ ⎝ J0 ⎠ • Tells us about the light generated current AND the “dark” current • Lower dark current means higher open circuit voltage but it scales logarithmically not linearly • Harder to “fix” than short circuit current ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner IV Curves • When illuminated the diodes ‘dark’ I-V characteristic is shifted • Note short circuit current and open circuit voltages for the illuminated case ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Reverse bias • Deliberately reverse bias the diode that is under illumination – diffusion current is switched off • Current seen is essentially equal to the light generated current – slight increase seen but if I0 is low we can neglect • Assuming that we get ~100% extraction of photons absorbed and absorption is good then the current is proportional to the number of photons with energy above the band gap • • Reverse bias This is how a photodetector works Note it doesn’t tell us what the photon energy is, just that it is above the band gap ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Reverse bias • Recall from the dark diode case that when we apply a reverse or negative bias the built-in field at the junction increases – this is an increase in the barrier to diffusion • Note that the drift current (light generated) is not increased but the diffusion current is made negligible • The slight increase in drift current is related to I0 and so we want this to be low • Obviously we will run at a voltage that ensures negligible diffusion current • Requirements for a photodetector - high absorption - high collection probability - low diffusion current are the same as for a solar cell ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Forward Bias • More than meets the eye to case of diode in the dark • If radiative recombination is efficient than we can get significant light emission when bias is applied • Direct band gap materials such as GaAs work best • Device designed to enhance recombination • This is the basis of light emitting diodes (LEDs) • Can even get a laser diode – This requires a bit more work ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Forward bias • What if we deliberately make the recombination of carriers very unlikely and shine light on it? • According to the IV characteristic we need a forward bias to raise the dark current to kill off the light generated current – this is VOC • This implies power is being generated by the diode - we have a current - we have a bias • We have a solar cell! ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner What is going on? • Light generates excess minority carriers • Carriers swept across junction by electric field – electrons and holes are separated • Do we get a voltage? Depends….. ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner What is going on? ….. on the load • We are sending carriers to opposite sides of the junction – if not extracted we have a build up of charge – get an electric field and potential difference between p and n regions – this corresponds to a forward bias across the p-n junction • So we can get both current and voltage extraction when illuminating the pn junction – can get power out! • We have a solar cell – i.e. it converts solar energy directly to electrical energy ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Conventions • • The light generated current being negative is simply a convention based upon it being in the direction opposite to the flow for a biased diode We are talking of power generation so we think of the light generated current as being positive and the diffusion current as being negative J = J L − J 0 (e • • • qV kT − 1) Burn this into your brain Think of the IV curve as what is shown here Power is simply I.V ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Circuit model • Simple circuit model can be used to understand the solar cell and how it operates • Need to add some more parts to make it ‘realistic’ ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Power Extracted • To find power simply multiply I by V • Get an increase as V is increased until a maximum and then get drop off until VOC when power is zero Pmax = Imp.Vmp ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Efficiency • We can easily find the power output and should be able to find the input power • Energy conversion efficiency is output divided by input power Pmax I mpVmp η= = Pin Pin • For unconcentrated sunlight the typical input power will be 1kW/m2 (what does this mean for units of ISC and VOC?) • How do the short circuit current and the open circuit voltage relate to the efficiency? ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Efficiency • Can also write the efficiency in the following way: η= • I mpVmp Pin I SCVOC = FF Pin FF = I mpVmp I SCVOC Fill factor is a measure of how ‘ideal’ the IV curve is – it is a measure of how much of area described by ISC and VOC is filled by the area described by Imp and Vmp ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner Fill Factor Glossary • ISC or JSC: Short circuit current – direct measure of light absorption and collection probability • VOC: Open circuit voltage – measure of ‘dark’ current as well as light current, scales logarithmically • FF: Fill factor – measure of how ‘ideal’ maximum power point is in filling power area defined by ISC and VOC • Dark current: diffusion current across pn junction due to bias – carriers recombine and are lost To make a good solar cell we must do the following: - Maximize JSC - Maximize VOC, this means minimize the dark current - Maximize FF, bit trickier as it involves non-idealities ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner