hw2 solution

hw2 solution - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF...

This preview shows pages 1–3. Sign up to view the full content.

ECE 3080: Homework #2, Solution June 23, 2005 Page 1 of 6 G EORGIA I NSTITUTE OF T ECHNOLOGY S CHOOL OF E LECTRICAL AND C OMPUTER E NGINEERING ECE 3080: Semiconductor Devices for Computer Engineering and Telecommunication Systems Summer Semester 2005, Homework #2 SOLUTION 1. Carrier Transport: Continuity Equation (40 points) Assume a 1-dimensional silicon crystal, which has been doped with 10 17 cm -3 phosphorous atoms. Using a high-energy light source, 10 14 cm -3 additional electron-hole pairs are generated at x = 0 in the stationary state (dp/dt = dn/dt = 0). (a) Can we consider low-level injection or do we have to assume high-level injection? Justify your answer. (b) Calculate analytical expressions for the minority carrier distribution p n (x) in the stationary state for x > 0 for the following two cases: (i) Infinitely long semiconductor with p n (x= ) = p n0 (see sketch (i)) (ii) Semiconductor with length W and p n (x=W) = p n0 (see sketch (ii)) (c) In case of the semiconductor with length W: give an approximate solution of the minority carrier distribution in the case L p = (D p τ p ) 1/2 >> W (hint: do a Taylor expansion of the resulting sinh function, i.e. sinh(x) x, e x 1 + x, and e -x 1 – x for small x) Case (i): Case (ii): Comment: Use the 1-D continuity equation, L p = (D p τ p ) 1/2 , and sinh(x) = (e x - e -x )/2.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECE 3080: Homework #2, Solution June 23, 2005 Page 2 of 6 Solution: (a) Low-level injection can be considered, because the number of injected carriers Δ p = Δ n = 10 14 cm -3 is far smaller than the majority carrier density n n0 = N D = 10 17 cm -3 . This way, the majority carrier concentration remains basically unchanged, while the minority carrier concentration strongly increases. (b)
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/28/2010 for the course ECE 3080 taught by Professor Staff during the Fall '08 term at Georgia Tech.

Page1 / 6

hw2 solution - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online