Ideal Diode Equation II + Intro to Solar Cells
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1 ECE-35: Spring 15 Ideal Diode Equation II + Intro to Solar Cells Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA lundstro@purdue.edu Pierret, Semiconductor Device Fundamentals (SDF) pp /7/15 outline 1) Review ) Ideal diode equation (long base) 3) Ideal diode equation (short base) 4) Discussion 5) A Primer Solar Cells
2 e-band diagram under bias E V = E C F n q( V bi ) > q F n F p = q F p E V W n p 3 recombination and current minority carriers injected across junction F n q F P + 4 Every time a minority electron recombines on the p-side, one electron flows in the eternal current.
3 ecess electrons on the p-side of junction n N N D n P >> n P q( V bi ) What is Δn() on the p-side? F n F p Answer: Solve the MCDE. p P 5 outline 1) Review ) Ideal diode equation (long base) 3) Ideal diode equation (short base) 4) Discussion 5) A Primer on Solar Cells 6
4 solving the MCDE Δn = n i e q k BT 1 Δn( ) = q( V bi ) >> F n F p p P d Δn Δn d L = L D n nτ n n 7 Δn() on p-side (long p region) Δn( ) Δn = n i e q k BT 1 Δn( ) = Δn( )e / What is Δn() on the p-side? Answer: Solve the MCDE. W p >> W p Δn 8
5 total recombination on p-side of junction Δn( ) D n dδn d Δn( ) = Δn( )e / How many electrons recombine per second? Answer: dδn R TOT = A D n d = A D n Δn 9 current (long region) Δn( ) Δn = n i e q k BT 1 Δn( ) = Δn( )e / = qr TOT = qa D n Δn( ) = qa D n e q k ( BT 1) W p >> Δn 1
6 diode current (long) I n = qaδn( )D n = qa D n eq /k T B 1 V = > I p = qaδp( )D p L p = qa D p L p N D eq /k T B 1 ( ) = I p ( ) + I n ( ) A 11 diode current ideal diode equation Shockley diode equation = I e q /k 1) 1 I = qa D n + D p L p N D
7 outline 1) Review ) Ideal diode equation (long case) 3) Ideal diode equation (short case) 4) Discussion 5) A Primer on Solar Cells 13 short p-side We have assumed that >> (long diode). What happens if << (short diode)? 14
8 solving the MCDE Δn = n i e q k BT 1 Δn( = ) = q( V bi ) F n << F p p P d Δn d = D n τ n >> 15 short p-side Δn( ) Δn = n i e q k BT 1 Δn( ) = Δn( ) 1 dδn( ) I n = qad n d = I n = qa D n Δn( ) W p << 16
9 diode current (short) I n = qa D n eq /k T B 1 V = > I p = qa D p W N N D eq /k T B 1 L p W N 17 outline 1) Review ) Ideal diode equation (long base) 3) Ideal diode equation (short base) 4) Discussion 5) A Primer on Solar Cells 18
10 Ideal diode equation = I e q /k 1) 19 I = qa D n long + D p L p N D I = qa D n short + D p W N N D diode current ( pa) ( ma) = I e q /k 1).6.7 V
11 How large of a voltage can we apply? = I e q /k 1) Reverse bias: breakdown Forward bias:? 1 e-band diagram under bias E < V bi E C q( V bi ) V = F n > q F p E V W n p
12 eample n+ p-si D I = qa n or + D p L p or W N N D W N 3 N D = 1 cm -3 = 1 17 cm -3 W N =.1 µm τ p = 1 µs = I e q /k 1) = 5 µm I =? τ n = 1 µs Question: one-sided? n+ p-si I n D I = qa n or I p + D p L p or W N N D W N Is this a one-sided diode? Yes: N D >> 4 We only need to consider the electrons injected into the P-region.
13 question (long or short) n+ p-si W N I = qa D n I = qa D n or 5 eample = 1 17 cm -3 = 5 µm µ n = 8 cm V-s D n = k T B µ n q D n = 1 cm τ n = 1 µs = D n τ n = 144 µm s > W p I = qa D n I = qa D n 6
14 eample I = qa D n What is the diode current for a forward bias of.6 V? A = 1 cm 1 I = = A = I e q /k 1) = ( e.6/.6 1) = 7 ma 7 outline 1) Review ) Ideal diode equation (long base) 3) Ideal diode equation (short base) 4) Discussion 5) A Primer Solar Cells 8
15 Solar cells modern Si solar cell Chapin, Pearson, Fuller, solar cells today 3 SunPower
16 recombination and dark current minority carriers injected across junction F n q F P + 31 Every time a minority electron recombines on the p- side, one electron flows Lundstrom in the ECE 35 eternal S15 current. generation and current minority carriers collected by junction hf > E G F n q F P I L < 3 Every time a minority electros generated and collected by the PN junction, one electron flows in the eternal current.
17 light and dark current J ( ma) J D = J e q /k 1) dark current.7 V photocurrent J L < 33 solar cell operation 1) Light generates e-h pairs E F 34
18 solar cell operation ) PN junction collects e-h pairs 3) Current flows through load I L < E F > R L V L + 35 forward bias across PN junction develops solar cell operation 4) Forward bias reduces current 5) IV characteristic is a superposition I TOT = I e qv D k 1) I SC F n qv D F p diode (dark) current light-generated current 36
19 IV characteristic = I e qv D k 1) I TOT = I e qv D k 1) I SC V OC η = P out P in = I SCV OC FF P in V D P out = I TOT V OC = I SC 37 P out = I SC V D = P out = I mp V mp = I SC V OC FF P D = I TOT V D < solar cell efficiency η = P out P in = I SC V OC FF P in 1) Short circuit current ) Open-circuit voltage 3) Fill factor 38
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