1. Slide 1EE40 Fall 2007Prof. Chang-Hasnain EE40 Lecture 32 Prof. Chang-Hasnain 11/21/07 Reading: Supplementary Reader

2. Slide 2EE40 Fall 2007Prof. Chang-Hasnain Electron and Hole Densities in Doped Si Instrinsic (undoped) Si N-doped Si –Assume each dopant contribute to one electron p-doped Si –Assume each dopant contribute to one hole

3. Slide 3EE40 Fall 2007Prof. Chang-Hasnain Summary of n- and p-type silicon Pure silicon is an insulator. At high temperatures it conducts weakly. If we add an impurity with extra electrons (e.g. arsenic, phosphorus) these extra electrons are set free and we have a pretty good conductor (n-type silicon). If we add an impurity with a deficit of electrons (e.g. boron) then bonding electrons are missing (holes), and the resulting holes can move around … again a pretty good conductor (p-type silicon) Now what is really interesting is when we join n-type and p-type silicon, that is make a pn junction. It has interesting electrical properties.

4. Slide 4EE40 Fall 2007Prof. Chang-Hasnain Junctions of n- and p-type Regions A silicon chip may have 10 8 to 10 9 p-n junctions today. p-n junctions form the essential basis of all semiconductor devices. How do they behave*? What happens to the electrons and holes? What is the electrical circuit model for such junctions? n and p regions are brought into contact : *Note that the textbook has a very good explanation.

5. Slide 5EE40 Fall 2007Prof. Chang-Hasnain The pn Junction Diode Schematic diagram p-type n-type IDID + V D – Circuit symbol Physical structure: (an example) p-type Si n-type Si SiO 2 metal IDID +VD–+VD– net donor concentration N D net acceptor concentration N A For simplicity, assume that the doping profile changes abruptly at the junction. cross-sectional area A D

6. Slide 6EE40 Fall 2007Prof. Chang-Hasnain When the junction is first formed, mobile carriers diffuse across the junction (due to the concentration gradients) –Holes diffuse from the p side to the n side, leaving behind negatively charged immobile acceptor ions –Electrons diffuse from the n side to the p side, leaving behind positively charged immobile donor ions  A region depleted of mobile carriers is formed at the junction. The space charge due to immobile ions in the depletion region establishes an electric field that opposes carrier diffusion. Depletion Region Approximation + + + + + – – – – – p n acceptor ions donor ions

7. Slide 7EE40 Fall 2007Prof. Chang-Hasnain Summary: pn-Junction Diode I-V Under forward bias, the potential barrier is reduced, so that carriers flow (by diffusion) across the junction –Current increases exponentially with increasing forward bias –The carriers become minority carriers once they cross the junction; as they diffuse in the quasi-neutral regions, they recombine with majority carriers (supplied by the metal contacts) “injection” of minority carriers Under reverse bias, the potential barrier is increased, so that negligible carriers flow across the junction –If a minority carrier enters the depletion region (by thermal generation or diffusion from the quasi-neutral regions), it will be swept across the junction by the built-in electric field “collection” of minority carriers  reverse current I D (A) V D (V)

8. Slide 8EE40 Fall 2007Prof. Chang-Hasnain quasi-neutral p region Charge Density Distribution + + + + + – – – – – p n acceptor ions donor ions depletion regionquasi-neutral n region charge density (C/cm 3 ) distance Charge is stored in the depletion region.

9. Slide 9EE40 Fall 2007Prof. Chang-Hasnain Two Governing Laws Gauss’s Law describes the relationship of charge (density) and electric field. Poisson’s Equation describes the relationship between electric field distribution and electric potential

10. Slide 10EE40 Fall 2007Prof. Chang-Hasnain Depletion Approximation 1 Gauss’s Law p n p n

11. Slide 11EE40 Fall 2007Prof. Chang-Hasnain Depletion Approximation 2 p n P=10 18 n=10 4 n=10 17 p=10 5 x E 0 (x) s nod s poa xqN x E      )0( 0 x no -x po 22 22 po s a no s d x qN x    0 (x) x x no -x po Poisson’s Equation

12. Slide 12EE40 Fall 2007Prof. Chang-Hasnain EE40 Lecture 33 Prof. Chang-Hasnain 11/26/07 Reading: Supplementary Reader

13. Slide 13EE40 Fall 2007Prof. Chang-Hasnain Depletion Approximation 3

14. Slide 14EE40 Fall 2007Prof. Chang-Hasnain Effect of Applied Voltage The quasi-neutral p and n regions have low resistivity, whereas the depletion region has high resistivity. Thus, when an external voltage V D is applied across the diode, almost all of this voltage is dropped across the depletion region. (Think of a voltage divider circuit.) If V D > 0 (forward bias), the potential barrier to carrier diffusion is reduced by the applied voltage. If V D < 0 (reverse bias), the potential barrier to carrier diffusion is increased by the applied voltage. p n + + + + + – – – – – VDVD

15. Slide 15EE40 Fall 2007Prof. Chang-Hasnain Depletion Approx. – with V D <0 reverse bias p n P=10 18 n=10 17 x E 0 (x) s nod s poa xqN x E      )0( 0 x no -x po 22 22 po s a no s d x qN x    0 (x) x x no -x po  bi Built-in potential  bi = -x p xnxn xnxn  bi -qV D Higher barrier and few holes in n- type lead to little current! p=10 5 n=10 4

16. Slide 16EE40 Fall 2007Prof. Chang-Hasnain Depletion Approx. – with V D >0 forward bias Poisson’s Equation p n n=10 4 n=10 17 p=10 5 x E 0 (x) s nod s poa xqN x E      )0( 0 x no -x po 22 22 po s a no s d x qN x    0 (x) x x no -x po  bi Built-in potential  bi = -x p xnxn  bi -qV D Lower barrier and large hole (electron) density at the right places lead to large current! -x p xnxn P=10 18

17. Slide 17EE40 Fall 2007Prof. Chang-Hasnain Forward Bias As V D increases, the potential barrier to carrier diffusion across the junction decreases*, and current increases exponentially. I D (Amperes) V D (Volts) * Hence, the width of the depletion region decreases. p n + + + + + – – – – – V D > 0 The carriers that diffuse across the junction become minority carriers in the quasi-neutral regions; they then recombine with majority carriers, “dying out” with distance.

18. Slide 18EE40 Fall 2007Prof. Chang-Hasnain Reverse Bias As |V D | increases, the potential barrier to carrier diffusion across the junction increases*; thus, no carriers diffuse across the junction. I D (Amperes) V D (Volts) * Hence, the width of the depletion region increases. p n + + + + + – – – – – V D < 0 A very small amount of reverse current ( I D < 0) does flow, due to minority carriers diffusing from the quasi-neutral regions into the depletion region and drifting across the junction.

19. Slide 19EE40 Fall 2007Prof. Chang-Hasnain Light incident on a pn junction generates electron-hole pairs Carriers are generated in the depletion region as well as n- doped and p-doped quasi-neutral regions. The carriers that are generated in the quasi-neutral regions diffuse into the depletion region, together with the carriers generated in the depletion region, are swept across the junction by the electric field This results in an additional component of current flowing in the diode: where I optical is proportional to the intensity of the light Optoelectronic Diodes

20. Slide 20EE40 Fall 2007Prof. Chang-Hasnain Example: Photodiode An intrinsic region is placed between the p-type and n-type regions  W j  W i-region, so that most of the electron-hole pairs are generated in the depletion region  faster response time (~10 GHz operation) I D (A) V D (V) with incident light in the dark operating point

21. Slide 21EE40 Fall 2007Prof. Chang-Hasnain Planck Constant Planck’s constant h = 6.625·10 -34 J·s E=h  hc  eV-  m/  m) C is speed of light and h  is photon energy The first type of quantum effect is the quantization of certain physical quantities. Quantization first arose in the mathematical formulae of Max Planck in 1900. Max Planck was analyzing how the radiation emitted from a body was related to its temperature, in other words, he was analyzing the energy of a wave. The energy of a wave could not be infinite, so Planck used the property of the wave we designate as the frequency to define energy. Max Planck discovered a constant that when multiplied by the frequency of any wave gives the energy of the wave. This constant is referred to by the letter h in mathematical formulae. It is a cornerstone of physics.

22. Slide 22EE40 Fall 2007Prof. Chang-Hasnain Bandgap Versus Lattice Constant Si