2.626 Fundamentals of Photovoltaics

Transcription

1 MIT OpenCourseWare Fundamentals of Photovoltaics Fall 2008 For information about citing these materials or our Terms of Use, visit:

2 Charge Separation: How Voltage and Current Are Formed Lecture Tonio Buonassisi

3 Discussion Concept Quiz Results

4 General Announcements Books Print Outs of Lecture Notes

5 Homework Assignment Read: Martin Green, Chapter 4 Read: PVCDROM: Chapters 3 and 4

6 Books: Sticker shock, anyone? If not, we ll call in the order! Images removed due to copyright restrictions. Please see the covers of: Green, Martin A. Solar Cells: Operating Principles, Technology, and System Applications. Englewood Cliffs, NJ: Prentice-Hall, Green, Martin A. Silicon Solar Cells: Advanced Principles and Practice. Sydney, Australia: Centre for Photovoltaic Devices and Systems, Wenham, Stuart A., et al. Applied Photovoltaics. Sterling, VA: Earthscan, 2007.

7 Outline Review: pn junctions Minority carrier current Ideal diode equation

8 Review: Diffusion Courtesy Christiana Honsberg and Stuart Bowden. Used with permission. From PVCDROM

9 Review: Drift Current From PVCDROM Courtesy Christiana Honsberg and Stuart Bowden. Used with permission.

10 Review: pn junction Courtesy Christiana Honsberg and Stuart Bowden. Used with permission. Eventually, the accumulation of like charges [(h + + P + ) or (e + B )] balances out the diffusion, and steady state condition is reached.

11 Nicer figure at Wikipedia! Image removed due to copyright restrictions. Please see n_junction

12 Pn junction under bias Image removed due to copyright restrictions. Please see Emitting Diodes dotorg/chap04/chap04.htm

13 Bias Across a pn Junction Image removed due to copyright restrictions. Please see Built in pn junction potential a function of dopant concentrations.

14 Bias Across a pn Junction Image removed due to copyright restrictions. Please see Built in pn junction potential a function of dopant concentrations.

15 Bias Across a pn Junction The potential across a biased pn junction device is

16 Carrier Concentrations Across a pn Junction Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n = n p0 n i2 /N A p = p n0 n i2 /N D Distance, x Approximation 1: Device can be split into two types of region: quasineutral regions (space charge density is assumed zero) and the depletion region (where carrier concentrations are small, and ionized dopants contribute to fixed charge).

17 Width of space charge region Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n = n p0 n i2 /N A p = p n0 n i2 /N D Distance, x

18 Width of space charge region Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n = n p0 n i2 /N A Width of the space charge region NB: Actually ε * ε p = p n0 n i2 /N o, where ε o, D the vacuum permittivity, is 8.85x10 12 F/m or Distance, 5.53x10x 7 e/(v*m)

19 Capacitance Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n = n p0 n i2 /N A p = p n0 n i2 /N D Device capacitance Distance, x pn junction area

20 Capacitance Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n = n p0 n i2 /N A p = p n0 n i2 /N D Distance, x When one side of the pn junction is heavily doped, the capacitance reduces to this expression

21 Pn junction under zero bias Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n = n p0 n i2 /N A p = p n0 n i2 /N D Distance, x

22 Pn junction under forward bias Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n pa n p0 p nb p n0 a b Distance, x

23 Pn junction under forward bias Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n pa n p0 p nb p n0 a b Distance, x At zero bias:

24 Current flow through the depletion region Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n pa n p0 p nb Drift current p n0 a b Distance, x Diffusion current For holes:

25 Current flow through the depletion region Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n pa n p0 p nb p n0 a b Distance, x Approximation 2: Assume J h is small! For holes:

26 Current flow through the depletion region Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n pa n p0 p nb p n0 a b Distance, x Integrating

27 Current flow through the depletion region Transition region n = n n0 N D p = p p0 N A Ln (n), Ln (p) n pa n p0 p nb p n0 a b Distance, x Approximation 3: Only cases where minority carriers have a much lower concentration than majority carriers will be considered, i.e., p pa >> n pa, n na >> p na

28 Current densities Calculate (diffusive) currents in quasi neutral region: J J e J h x a b x

29 Current densities Magnitude of the change in current across the depletion region: Key assumption: W is small compared to L e and L h. Therefore, integral is negligible. It follows that the current J e and J h are essentially constant across the depletion region, as shown below. J total J h J e J J e J h x a b x

30 Ideal Diode Equation Since J e and J h are known at all points in the depletion region, we can calculate the total current: This leads to the ideal diode law:

31 Next Class Ideal diode equation discussion Contacts Review Part 1