# Berkeley ELENG 130 - Semiconductor Fundamentals Lecture 5 (25 pages)

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## Semiconductor Fundamentals Lecture 5

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## Semiconductor Fundamentals Lecture 5

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Lecture Notes

Pages:
25
School:
University of California, Berkeley
Course:
Eleng 130 - Integrated-Circuit Devices
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Unformatted text preview:

EECS130 Integrated Circuit Devices Professor Ali Javey 9 11 2007 Semiconductor Fundamentals Lecture 5 Reading Chapter 3 Announcements 1st HW due right now 2nd HW due next Tuesday Professor Javey s OH for tomorrow is cancelled He will have an extra OH next week Ereference Ec and Ev vary in the opposite direction from the voltage That is Ec and Ev are higher where the voltage is lower Ec Ereference qV V x Ec E Ev x Variation in Ec with position is called band bending Einstein Relationship between D and Consider a piece of non uniformly doped semiconductor n N ce N typesemiconductor semiconductor n type Decreasing donor concentration Ec x Ef dn N E E kT dEc ce c f dx kT dx n dEc kT dx Ev x Ec E f kT n q kT Einstein Relationship between D and dn n q dx kT dn 0 at equilibrium dx qDn qn kT J n qn n qDn 0 qn n kT n Dn q kT Similarly Dp p q These are known as the Einstein relationship EXAMPLE Diffusion Constant What is the hole diffusion constant in a piece of silicon with p 410 cm2 V 1s 1 Solution kT D p p 26 mV 410 cm 2 V 1s 1 11 cm 2 s q Remember kT q 26 mV at room temperature Excess Carriers and Charge Neutrality Equilibrium Excess n n0 n p p0 p Charge neutrality n p If not neutral then built in field causes drift until neutrality is achieved Recombination Lifetime Assume light generates n and p If the light is suddenly turned off n and p decay with time until they become zero The process of decay is called recombination The time constant of decay is the recombination time or carrier lifetime Recombination is nature s way of restoring equilibrium n p 0 Recombination Lifetime ranges from 1ns to 1ms in Si and depends on the density of metal impurities contaminants such as Au and Pt These deep traps capture electrons or holes to facilitate recombination and are called recombination centers Ec Ev Rate of recombination s 1cm 3 Consider recombination only dn n dt n p n p dp dn dt dt EXAMPLE Photoconductors A bar of Si is doped with boron at 1015cm 3 It is exposed to light

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