( )! N D ( x) ) and equilibrium

Size: px
Start display at page:

Download "( )! N D ( x) ) and equilibrium"

Transcription

1 ECE 66: SOLUTIONS: ECE 66 Homework Week 8 Mark Lundstrom March 7, 13 1) The doping profile for an n- type silicon wafer ( N D = 1 15 cm - 3 ) with a heavily doped thin layer at the surface (surface concentration, N S = 1 cm - 3 ) is sketched below. Answer the following questions. 1a) Assume approximate space charge neutrality ( n x! N D ( x) ) and equilibrium conditions and compute the position of the Fermi level with respect to the bottom of the conduction band at x = and as x!. n ( ( x) = N C e E F!E C ) k T B N D x E F! E C ( x) = k B T ln N x D ' N C ' E F! E C = k B T ln N D N C ' ' E F E C N C = 3.3!1 19 cm - 3 = k B T ln = +1.13k B T ECE- 66 1

2 ECE 66: = k B T ln N x D E F! E C x N C 1 E F E C ( x ) 15 = k B T ln = 1.4k B T ' ) () 1b) Using the above information, sketch E C ( x) vs. x. Be sure to include the Fermi level. 1c) Sketch the electrostatic potential vs. position. 1d) Sketch the electric field vs. portion. ECE- 66

3 ECE 66:, in terms of ( x). HINT: Use the electron current 1e) Derive an expression for the position dependent electric field, E x the position- dependent doping density, N D equation and assume equilibrium conditions. J n = nqµ n E + k B T µ n dn dx = E = k B T q! E = k T B q 1 dn n dx = k T B q N D 1 x N D dn D dx 1 x ( x) dn D x dx ( Another way is to begin with n N D = N C e E F E C ) k T B and differentiate. ) A silicon diode is symmetrically doped at N D = = 1 15 cm - 3. Answer the following questions assuming room temperature, equilibrium conditions, and the depletion approximation. a) Compute. = k T B q ln! N D! 13 =.6ln 1 =.6 V =.6 b) Compute x n,x p and W. x n =! S q N D + N D ( '( 1/ =.65 µm x n = x p =.65 µm (because N and P regions are symmetrical) W = x n + x p = 1.5 µm ECE- 66 3

4 ECE 66: c) Compute V ( x = ) and E ( x = ). By symmetry: V ( ) = =.3 V or use V ( x = ) = q x! S p E ( x = ) = q x! S p = E ( ) =! V/cm d) Sketch!( x) vs. x. ρ N = +qn D = C/cm 3! P = q = C/cm 3 3) Your textbook (Pierret, SDF) presents the classic expressions for PN junction electrostatics. Simplify these expressions for a one- sided P + N junction for which >> N D. Present simplified expressions (when possible) for: 3a) The built- in potential,, from Pierret, Eqn. (5.1). = k BT q ln! N D no simplification possible ECE- 66 4

5 ECE 66: 3b) The total depletion layer depth, W, from Pierret, Eqn. (5.31). ) W =! S + q * + N D N D ' ( V, bi. - 1/ >> N D W =! S qn D ( ' 1/ 3c) The peak electric field, E ( ), from Pierret, Eqn. (5.19) or (5.1). E ( ) = W = q N D! s + N D ' ( E = qn D! s 3d) The electrostatic potential, V ( x) from Pierret, Eqn. (5.8) V ( x) =! qn D ( x n! x) V ( x) = V S bi qn D ( W x) κ S ε Now use the expression for W above to find: = 1 ( 1 x W ) V x 4) A silicon diode is asymmetrically doped at = 1 19 cm - 3 and N D = 1 15 cm - 3 Answer the following questions assuming room temperature, equilibrium conditions, and the depletion approximation. 4a) Compute. = k T B q ln! N D =.6ln! 15 ' =.84 V =.84 ECE- 66 5

6 ECE 66: 4b) Compute x n,x p and W. x p! x n! W = S qn D ' ) ( 1/ = 1.5 µm W = 1.5 µm (depletion region mostly on the N- side, the lightly doped side) 4c) Compute V ( x = ) and E ( x = ). V ( )! V E ( ) = qn D W = V/cm! S E ( ) = 1.6!1 4 V/cm (plus sign assumes N regios on the left) 4d) Sketch!( x) vs. x. The charge on the P- side is essentially a delta function with the total charge in C/cm equal in magnitude and opposite in sign to the charge on the N- side. ECE- 66 6

7 ECE 66: 5) Repeat problem 4) using the exact solution to PN junction electrostatics. V N = + k BT q ln V P =! k T B q ln N D 115 =.6 ln 1 1 = ' =.6ln 1 1 ' =!.54 = V N!V P =.84 V =.84 V ( ) = C! C N P a N! a P a N = N D = 1 15 a P =! =!1 19 C N = a N V N! ( k B T q)cosh( qv N k B T ) C N = 1 15!.3!1 1 (.6)cosh 11.5 =.74!1 14 C P = a P V P! ( k B T q)cosh( qv P k B T ) C P =!1 19! 1 1 (.6)cosh!.7!.54 = V ( ) = C! C N P =!.518 a N! a P V ( )! V P =!.54!.51 =.8 k B T q The potential drop across the heavily doped side is about kbt/q. E = q! S k B T q Putting in numbers, we find: E ( )! V/cm V/cm ( e qv () kbt + ( k B T q)e qv () kbt a N V() + C N ) 1/ which is about 1X the electric field we found in prob. 4. ECE- 66 7

8 ECE 66: = e qv = e!qv n p! k BT = 7 cm - 3 = q p q !! + k BT = cm - 3 n ( ) + N D = q.37 ' ( q.37 '1 19 ' ( (depletion approximation would give! = q p ( ) n = q ! + = q.37 ' ' (depletion approximation would give! + q 1 15 ' ) q 1 19 ' ) 6) Semiconductor devices often contain high- low junctions for which the doping density changes magnitude, but not sign. The example below shows a high- low step junction. Answer the questions below. ECE- 66 8

9 ECE 66: 6a) Sketch an energy band diagram for this junction. 6b) Sketch V ( x) 6c) Sketch E ( x) ECE- 66 9

10 ECE 66: 6d) Sketch!( x) vs. x. 6e) Name the charged entities responsible for!( x) in 6d). For x <, the charge is a depletion charge. Mobile electrons leave the heavily doped side of the junction leaving behind a concentration, ND1, of ionized donors. For x >, the charge is due to the additional mobile electrons that have spilled over from the heavily doped side. This is NOT a depletion region. 6f) Explain why the depletion approximation cannot be used for this problem. Because, as explained above, there is a depletion region on only ONE side of the junction. We could use the depletion approximation there, but not on the lightly doped side. 6g) Calculate for this high- low junction assuming silicon at room temperature. First, consider the two sides of the junction separately: ( n 1 = N C e E F 1!E C ) k B T ( n = N C e E F!E C ) k B T n 1 ( = e E F 1!E F ) k B T n The built- in potential develops to align these two Fermi levels: ( E F1! E F ) = q = k B T ln n 1 ' = k T B q ln N D1 N D n ECE- 66 1

11 ECE 66: 7) Consider an N + P diode with the length of the quasi- neutral P- region being, WP. Answer the following questions assuming that recombination the space- charge region can be neglected. 7a) Derive a general expression for I D ( V A ) valid for a P region of any length, WP. In HW7, problem 1c, we solved the minority carrier diffusion equation for a region of any length and found:!n( x)=!n sinh ( W x) / L P n sinh W P / L n Let x = be the edge of the neutral P- region. The electron current is: J n = +qd n d!n dx x= = q D n L n!n cosh ( W L P n ) (minus sign means that the electron sinh W P L n current is flowing in the minus x direction. Since this is a one- sided junction, and we are ignoring recombination the space- charge region, this is the total diode current, ID. Let s define the forward biased current to be positive. I D =! AJ n = qa D n L n n cosh ( W L P n ) sinh W P Finally, use the Law of the Junction for the boundary condition:!n = n i to find: e qv A k BT 1 L n! I D = qa D n L n cosh W P sinh W P ( L n ) kbt '1 eqva L n 7b) Simplify the expression derived in 7a) for a long diode. Explain what long means (i.e. WP is long compared to what?) A long diode is one with the quasi- neutral regios much longer than the diffusion length, W P >> L n. ECE

12 ECE 66: cosh( x)! ex sinh ( x )! ex! I D = qa D n L n e qv A k B T '1 and we find 7c) Simplify the expression derived in 7a) for a short diode. Explain what short means. A short diode is one with the quasi- neutral regios much shorter than the diffusion length, W P << L n. cosh x! 1 sinh( x)! x and we find! I D = qa D n W P e qv A k B T '1 8) Consider a P + N diode that is illuminated with light, which produces a uniform generation, GL, of electron- holes pairs per cm 3 per second. The N- regios long compared to a diffusion length. 8a) Consider first a uniform, infinitely long N- type semiconductor with a uniform generation rate and solve for the steady- state excess minority carrier density,!p. We have solved this problem before, in HW7. The answer is:!p = G L p 8b) Now consider the illuminated P+N diode. What are the boundary conditions at!p n ( x n ) and!p n ( x )? Assume that the Law of the Junction still applies.!p n x n = n i N D e qv A k BT 1!p n ( x ) = G L n ECE- 66 1

13 ECE 66: 8c) Use the boundary conditions developed in 8b), neglect recombination- generation in the SCR and in the P+ layer, and solve for I D ( V A ) for this illuminated diode. Having solved the MDE so many times, we can see that the solutios:!p x = Ae x/ L p + G L p This satisfies the b.c. for x! = A + G L p A = G L! p p( ) so the solutios: =!p( )e x/ L p + G L p 1 e x/ L p!p!p x The current is: dp J p =!qd p = q D p p( )! q D p G dx x= L p L L p p Use the Law of the Junction: J p = J D = q D n p i e qv A k BT L p! q D p G L L p p Note that the first term is just the diode current in the dark, J DARK and the second term is the photo- generated current, which is bias- independent and what we measure under short circuit conditions. J D = J DARK ( V A )! J SC J DARK ( V A ) = q D n p i J SC = q D p L p G L! p L p e qv A k BT 1 This result is the classical way of describing a solar cell the approach is called superposition we add the dark current and the current due to collection of photo- generated carriers. Note that superposition assumes that the collected photocurrent is independent of bias and that the Law of the Junctios valid under illumination. ECE

14 ECE 66: 8d) Sketch I D ( V A ) for G L =, G L = G and G L = G. ECE

ECE-305: Spring 2018 Exam 2 Review

ECE-305: Spring 2018 Exam 2 Review ECE-305: Spring 018 Exam Review Pierret, Semiconductor Device Fundamentals (SDF) Chapter 3 (pp. 75-138) Chapter 5 (pp. 195-6) Professor Peter Bermel Electrical and Computer Engineering Purdue University,

More information

Semiconductor Physics fall 2012 problems

Semiconductor Physics fall 2012 problems Semiconductor Physics fall 2012 problems 1. An n-type sample of silicon has a uniform density N D = 10 16 atoms cm -3 of arsenic, and a p-type silicon sample has N A = 10 15 atoms cm -3 of boron. For each

More information

EECS130 Integrated Circuit Devices

EECS130 Integrated Circuit Devices EECS130 Integrated Circuit Devices Professor Ali Javey 9/18/2007 P Junctions Lecture 1 Reading: Chapter 5 Announcements For THIS WEEK OLY, Prof. Javey's office hours will be held on Tuesday, Sept 18 3:30-4:30

More information

SOLUTIONS: ECE 606 Homework Week 10 Mark Lundstrom. Purdue University. (Revised 3/29/13)

SOLUTIONS: ECE 606 Homework Week 10 Mark Lundstrom. Purdue University. (Revised 3/29/13) ECE- 66 SOLUTIOS: ECE 66 Homework Week 1 Mark Lundstrom (Revised 3/9/13) 1) In a forward- biased P junction under low- injection conditions, the QFL s are aroximately flat from the majority carrier region

More information

Semiconductor Junctions

Semiconductor Junctions 8 Semiconductor Junctions Almost all solar cells contain junctions between different materials of different doping. Since these junctions are crucial to the operation of the solar cell, we will discuss

More information

Lecture-4 Junction Diode Characteristics

Lecture-4 Junction Diode Characteristics 1 Lecture-4 Junction Diode Characteristics Part-II Q: Aluminum is alloyed into n-type Si sample (N D = 10 16 cm 3 ) forming an abrupt junction of circular cross-section, with an diameter of 0.02 in. Assume

More information

Lecture 15 - The pn Junction Diode (I) I-V Characteristics. November 1, 2005

Lecture 15 - The pn Junction Diode (I) I-V Characteristics. November 1, 2005 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 15-1 Lecture 15 - The pn Junction Diode (I) I-V Characteristics November 1, 2005 Contents: 1. pn junction under bias 2. I-V characteristics

More information

For the following statements, mark ( ) for true statement and (X) for wrong statement and correct it.

For the following statements, mark ( ) for true statement and (X) for wrong statement and correct it. Benha University Faculty of Engineering Shoubra Electrical Engineering Department First Year communications. Answer all the following questions Illustrate your answers with sketches when necessary. The

More information

n N D n p = n i p N A

n N D n p = n i p N A Summary of electron and hole concentration in semiconductors Intrinsic semiconductor: E G n kt i = pi = N e 2 0 Donor-doped semiconductor: n N D where N D is the concentration of donor impurity Acceptor-doped

More information

6.012 Electronic Devices and Circuits

6.012 Electronic Devices and Circuits Page 1 of 1 YOUR NAME Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology 6.12 Electronic Devices and Circuits Exam No. 1 Wednesday, October 7, 29 7:3 to 9:3

More information

Holes (10x larger). Diode currents proportional to minority carrier densities on each side of the depletion region: J n n p0 = n i 2

Holes (10x larger). Diode currents proportional to minority carrier densities on each side of the depletion region: J n n p0 = n i 2 Part V. (40 pts.) A diode is composed of an abrupt PN junction with N D = 10 16 /cm 3 and N A =10 17 /cm 3. The diode is very long so you can assume the ends are at x =positive and negative infinity. 1.

More information

Semiconductor Physics and Devices

Semiconductor Physics and Devices The pn Junction 1) Charge carriers crossing the junction. 3) Barrier potential Semiconductor Physics and Devices Chapter 8. The pn Junction Diode 2) Formation of positive and negative ions. 4) Formation

More information

ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 2/25/13) e E i! E T

ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 2/25/13) e E i! E T ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 2/25/13) 1) Consider an n- type semiconductor for which the only states in the bandgap are donor levels (i.e. ( E T = E D ). Begin with

More information

Solar Cell Physics: recombination and generation

Solar Cell Physics: recombination and generation NCN Summer School: July 2011 Solar Cell Physics: recombination and generation Prof. Mark Lundstrom lundstro@purdue.edu Electrical and Computer Engineering Purdue University West Lafayette, Indiana USA

More information

Semiconductor Physics Problems 2015

Semiconductor Physics Problems 2015 Semiconductor Physics Problems 2015 Page and figure numbers refer to Semiconductor Devices Physics and Technology, 3rd edition, by SM Sze and M-K Lee 1. The purest semiconductor crystals it is possible

More information

Ideal Diode Equation II + Intro to Solar Cells

Ideal Diode Equation II + Intro to Solar Cells 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

More information

Spring Semester 2012 Final Exam

Spring Semester 2012 Final Exam Spring Semester 2012 Final Exam Note: Show your work, underline results, and always show units. Official exam time: 2.0 hours; an extension of at least 1.0 hour will be granted to anyone. Materials parameters

More information

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. EECS 130 Professor Ali Javey Fall 2006

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. EECS 130 Professor Ali Javey Fall 2006 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Professor Ali Javey Fall 2006 Midterm I Name: Closed book. One sheet of notes is allowed.

More information

Chapter 7. The pn Junction

Chapter 7. The pn Junction Chapter 7 The pn Junction Chapter 7 PN Junction PN junction can be fabricated by implanting or diffusing donors into a P-type substrate such that a layer of semiconductor is converted into N type. Converting

More information

Minority Carrier Diffusion Equation (MCDE)

Minority Carrier Diffusion Equation (MCDE) ECE-305: Spring 2015 Minority Carrier Diffusion Equation (MCDE) Professor Mark undstrom Electrical and Computer Engineering Purdue University, West afayette, IN USA lundstro@purdue.edu Pierret, Semiconductor

More information

Semiconductor Physics fall 2012 problems

Semiconductor Physics fall 2012 problems Semiconductor Physics fall 2012 problems 1. An n-type sample of silicon has a uniform density N D = 10 16 atoms cm -3 of arsenic, and a p-type silicon sample has N A = 10 15 atoms cm -3 of boron. For each

More information

Session 6: Solid State Physics. Diode

Session 6: Solid State Physics. Diode Session 6: Solid State Physics Diode 1 Outline A B C D E F G H I J 2 Definitions / Assumptions Homojunction: the junction is between two regions of the same material Heterojunction: the junction is between

More information

Department of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Due on Feb. 15, 2018 by 7:00 PM

Department of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Due on Feb. 15, 2018 by 7:00 PM Department of Electrical and Computer Engineering, Cornell University ECE 3150: Microelectronics Spring 018 Homework 3 Due on Feb. 15, 018 by 7:00 PM Suggested Readings: a) Lecture notes Important Note:

More information

Section 12: Intro to Devices

Section 12: Intro to Devices Section 12: Intro to Devices Extensive reading materials on reserve, including Robert F. Pierret, Semiconductor Device Fundamentals Bond Model of Electrons and Holes Si Si Si Si Si Si Si Si Si Silicon

More information

ECE-305: Spring Carrier Action: II. Pierret, Semiconductor Device Fundamentals (SDF) pp

ECE-305: Spring Carrier Action: II. Pierret, Semiconductor Device Fundamentals (SDF) pp ECE-305: Spring 015 Carrier Action: II Pierret, Semiconductor Device Fundamentals (SDF) pp. 89-104 Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA

More information

ECE 305 Exam 2: Spring 2017 March 10, 2017 Muhammad Alam Purdue University

ECE 305 Exam 2: Spring 2017 March 10, 2017 Muhammad Alam Purdue University NAME: PUID: : ECE 305 Exam 2: Spring 2017 March 10, 2017 Muhammad Alam Purdue University This is a closed book exam You may use a calculator and the formula sheet Following the ECE policy, the calculator

More information

Semiconductor Device Physics

Semiconductor Device Physics 1 Semiconductor Device Physics Lecture 3 http://zitompul.wordpress.com 2 0 1 3 Semiconductor Device Physics 2 Three primary types of carrier action occur inside a semiconductor: Drift: charged particle

More information

Schottky Rectifiers Zheng Yang (ERF 3017,

Schottky Rectifiers Zheng Yang (ERF 3017, ECE442 Power Semiconductor Devices and Integrated Circuits Schottky Rectifiers Zheng Yang (ERF 3017, email: yangzhen@uic.edu) Power Schottky Rectifier Structure 2 Metal-Semiconductor Contact The work function

More information

Fundamentals of Semiconductor Physics

Fundamentals of Semiconductor Physics Fall 2007 Fundamentals of Semiconductor Physics 万 歆 Zhejiang Institute of Modern Physics xinwan@zimp.zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Transistor technology evokes new physics The objective of

More information

ECE 305 Fall Final Exam (Exam 5) Wednesday, December 13, 2017

ECE 305 Fall Final Exam (Exam 5) Wednesday, December 13, 2017 NAME: PUID: ECE 305 Fall 017 Final Exam (Exam 5) Wednesday, December 13, 017 This is a closed book exam. You may use a calculator and the formula sheet at the end of this exam. Following the ECE policy,

More information

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. Professor Chenming Hu.

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. Professor Chenming Hu. UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Spring 2009 Professor Chenming Hu Midterm I Name: Closed book. One sheet of notes is

More information

This is the 15th lecture of this course in which we begin a new topic, Excess Carriers. This topic will be covered in two lectures.

This is the 15th lecture of this course in which we begin a new topic, Excess Carriers. This topic will be covered in two lectures. Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture - 15 Excess Carriers This is the 15th lecture of this course

More information

Lecture 16 The pn Junction Diode (III)

Lecture 16 The pn Junction Diode (III) Lecture 16 The pn Junction iode (III) Outline I V Characteristics (Review) Small signal equivalent circuit model Carrier charge storage iffusion capacitance Reading Assignment: Howe and Sodini; Chapter

More information

ECE 305 Exam 3: Spring 2015 March 6, 2015 Mark Lundstrom Purdue University

ECE 305 Exam 3: Spring 2015 March 6, 2015 Mark Lundstrom Purdue University NAME: PUID: : ECE 305 Exam 3: March 6, 2015 Mark Lundstrom Purdue University This is a closed book exam You may use a calculator and the formula sheet at the end of this exam Following the ECE policy,

More information

ECE-305: Fall 2016 Minority Carrier Diffusion Equation (MCDE)

ECE-305: Fall 2016 Minority Carrier Diffusion Equation (MCDE) ECE-305: Fall 2016 Minority Carrier Diffusion Equation (MCDE) Professor Peter Bermel Electrical and Computer Engineering Purdue University, West Lafayette, IN USA pbermel@purdue.edu Pierret, Semiconductor

More information

ECE 340 Lecture 21 : P-N Junction II Class Outline:

ECE 340 Lecture 21 : P-N Junction II Class Outline: ECE 340 Lecture 21 : P-N Junction II Class Outline: Contact Potential Equilibrium Fermi Levels Things you should know when you leave Key Questions What is the contact potential? Where does the transition

More information

Solid State Electronics. Final Examination

Solid State Electronics. Final Examination The University of Toledo EECS:4400/5400/7400 Solid State Electronic Section elssf08fs.fm - 1 Solid State Electronics Final Examination Problems Points 1. 1. 14 3. 14 Total 40 Was the exam fair? yes no

More information

collisions of electrons. In semiconductor, in certain temperature ranges the conductivity increases rapidly by increasing temperature

collisions of electrons. In semiconductor, in certain temperature ranges the conductivity increases rapidly by increasing temperature 1.9. Temperature Dependence of Semiconductor Conductivity Such dependence is one most important in semiconductor. In metals, Conductivity decreases by increasing temperature due to greater frequency of

More information

Numerical Example: Carrier Concentrations

Numerical Example: Carrier Concentrations 2 Numerical ample: Carrier Concentrations Donor concentration: N d = 10 15 cm -3 Thermal equilibrium electron concentration: n o N d = 10 15 cm 3 Thermal equilibrium hole concentration: 2 2 p o = n i no

More information

PN Junctions. Lecture 7

PN Junctions. Lecture 7 Lecture 7 PN Junctions Kathy Aidala Applied Physics, G2 Harvard University 10 October, 2002 Wei 1 Active Circuit Elements Why are they desirable? Much greater flexibility in circuit applications. What

More information

Electronic Devices and Circuits Lecture 5 - p-n Junction Injection and Flow - Outline

Electronic Devices and Circuits Lecture 5 - p-n Junction Injection and Flow - Outline 6.012 - Electronic Devices and Circuits Lecture 5 - p-n Junction Injection and Flow - Outline Review Depletion approimation for an abrupt p-n junction Depletion charge storage and depletion capacitance

More information

EE105 Fall 2015 Microelectronic Devices and Circuits: Semiconductor Fabrication and PN Junctions

EE105 Fall 2015 Microelectronic Devices and Circuits: Semiconductor Fabrication and PN Junctions EE105 Fall 2015 Microelectronic Devices and Circuits: Semiconductor Fabrication and PN Junctions Prof. Ming C. Wu wu@eecs.berkeley.edu 511 Sutardja Dai Hall (SDH) 1 pn Junction p-type semiconductor in

More information

Lecture 17 - p-n Junction. October 11, Ideal p-n junction in equilibrium 2. Ideal p-n junction out of equilibrium

Lecture 17 - p-n Junction. October 11, Ideal p-n junction in equilibrium 2. Ideal p-n junction out of equilibrium 6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 17-1 Lecture 17 - p-n Junction October 11, 22 Contents: 1. Ideal p-n junction in equilibrium 2. Ideal p-n junction out of equilibrium

More information

Lecture 20 - p-n Junction (cont.) October 21, Non-ideal and second-order effects

Lecture 20 - p-n Junction (cont.) October 21, Non-ideal and second-order effects 6.70J/3.43J - Integrated Microelectronic Devices - Fall 00 Lecture 0-1 Lecture 0 - p-n Junction (cont.) October 1, 00 Contents: 1. Non-ideal and second-order effects Reading assignment: del Alamo, Ch.

More information

Effective masses in semiconductors

Effective masses in semiconductors Effective masses in semiconductors The effective mass is defined as: In a solid, the electron (hole) effective mass represents how electrons move in an applied field. The effective mass reflects the inverse

More information

Lecture 2. OUTLINE Basic Semiconductor Physics (cont d) PN Junction Diodes. Reading: Chapter Carrier drift and diffusion

Lecture 2. OUTLINE Basic Semiconductor Physics (cont d) PN Junction Diodes. Reading: Chapter Carrier drift and diffusion Lecture 2 OUTLIE Basic Semiconductor Physics (cont d) Carrier drift and diffusion P unction Diodes Electrostatics Caacitance Reading: Chater 2.1 2.2 EE105 Sring 2008 Lecture 1, 2, Slide 1 Prof. Wu, UC

More information

Sample Exam # 2 ECEN 3320 Fall 2013 Semiconductor Devices October 28, 2013 Due November 4, 2013

Sample Exam # 2 ECEN 3320 Fall 2013 Semiconductor Devices October 28, 2013 Due November 4, 2013 Sample Exam # 2 ECEN 3320 Fall 203 Semiconductor Devices October 28, 203 Due November 4, 203. Below is the capacitance-voltage curve measured from a Schottky contact made on GaAs at T 300 K. Figure : Capacitance

More information

FYS 3028/8028 Solar Energy and Energy Storage. Calculator with empty memory Language dictionaries

FYS 3028/8028 Solar Energy and Energy Storage. Calculator with empty memory Language dictionaries Faculty of Science and Technology Exam in: FYS 3028/8028 Solar Energy and Energy Storage Date: 11.05.2016 Time: 9-13 Place: Åsgårdvegen 9 Approved aids: Type of sheets (sqares/lines): Number of pages incl.

More information

ECE 440 Lecture 20 : PN Junction Electrostatics II Class Outline:

ECE 440 Lecture 20 : PN Junction Electrostatics II Class Outline: ECE 440 Lecture 20 : PN Junction Electrostatics II Class Outline: Depletion Approximation Step Junction Things you should know when you leave Key Questions What is the space charge region? What are the

More information

The Law of the Junction Revisited. Mark Lundstrom Network for Computational Nanotechnology and Purdue University ( ). (1)

The Law of the Junction Revisited. Mark Lundstrom Network for Computational Nanotechnology and Purdue University ( ). (1) The Law of the Junction Revisited Mark Lundstrom Network for Computational Nanotechnology and Purdue University Consider a one-sided, short base diode like that shown in Fig.. We usually analyze the I-V

More information

Carriers Concentration and Current in Semiconductors

Carriers Concentration and Current in Semiconductors Carriers Concentration and Current in Semiconductors Carrier Transport Two driving forces for carrier transport: electric field and spatial variation of the carrier concentration. Both driving forces lead

More information

Department of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Due on March 01, 2018 at 7:00 PM

Department of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Due on March 01, 2018 at 7:00 PM Department of Electrical and Computer Engineering, Cornell University ECE 3150: Microelectronics Spring 2018 Homework 4 Due on March 01, 2018 at 7:00 PM Suggested Readings: a) Lecture notes Important Note:

More information

Final Examination EE 130 December 16, 1997 Time allotted: 180 minutes

Final Examination EE 130 December 16, 1997 Time allotted: 180 minutes Final Examination EE 130 December 16, 1997 Time allotted: 180 minutes Problem 1: Semiconductor Fundamentals [30 points] A uniformly doped silicon sample of length 100µm and cross-sectional area 100µm 2

More information

ECE 340 Lecture 27 : Junction Capacitance Class Outline:

ECE 340 Lecture 27 : Junction Capacitance Class Outline: ECE 340 Lecture 27 : Junction Capacitance Class Outline: Breakdown Review Junction Capacitance Things you should know when you leave M.J. Gilbert ECE 340 Lecture 27 10/24/11 Key Questions What types of

More information

Lecture 16 - The pn Junction Diode (II) Equivalent Circuit Model. April 8, 2003

Lecture 16 - The pn Junction Diode (II) Equivalent Circuit Model. April 8, 2003 6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 16-1 Lecture 16 - The pn Junction Diode (II) Equivalent Circuit Model April 8, 2003 Contents: 1. I-V characteristics (cont.) 2. Small-signal

More information

Recitation 17: BJT-Basic Operation in FAR

Recitation 17: BJT-Basic Operation in FAR Recitation 17: BJT-Basic Operation in FAR BJT stands for Bipolar Junction Transistor 1. Can be thought of as two p-n junctions back to back, you can have pnp or npn. In analogy to MOSFET small current

More information

Quiz #1 Practice Problem Set

Quiz #1 Practice Problem Set Name: Student Number: ELEC 3908 Physical Electronics Quiz #1 Practice Problem Set? Minutes January 22, 2016 - No aids except a non-programmable calculator - All questions must be answered - All questions

More information

ECE-342 Test 2 Solutions, Nov 4, :00-8:00pm, Closed Book (one page of notes allowed)

ECE-342 Test 2 Solutions, Nov 4, :00-8:00pm, Closed Book (one page of notes allowed) ECE-342 Test 2 Solutions, Nov 4, 2008 6:00-8:00pm, Closed Book (one page of notes allowed) Please use the following physical constants in your calculations: Boltzmann s Constant: Electron Charge: Free

More information

PN Junction and MOS structure

PN Junction and MOS structure PN Junction and MOS structure Basic electrostatic equations We will use simple one-dimensional electrostatic equations to develop insight and basic understanding of how semiconductor devices operate Gauss's

More information

PHYS208 P-N Junction. Olav Torheim. May 30, 2007

PHYS208 P-N Junction. Olav Torheim. May 30, 2007 1 PHYS208 P-N Junction Olav Torheim May 30, 2007 1 Intrinsic semiconductors The lower end of the conduction band is a parabola, just like in the quadratic free electron case (E = h2 k 2 2m ). The density

More information

1 Name: Student number: DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY MEMORIAL UNIVERSITY OF NEWFOUNDLAND. Fall :00-11:00

1 Name: Student number: DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY MEMORIAL UNIVERSITY OF NEWFOUNDLAND. Fall :00-11:00 1 Name: DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY MEMORIAL UNIVERSITY OF NEWFOUNDLAND Final Exam Physics 3000 December 11, 2012 Fall 2012 9:00-11:00 INSTRUCTIONS: 1. Answer all seven (7) questions.

More information

V BI. H. Föll: kiel.de/matwis/amat/semi_en/kap_2/backbone/r2_2_4.html. different electrochemical potentials (i.e.

V BI. H. Föll:  kiel.de/matwis/amat/semi_en/kap_2/backbone/r2_2_4.html. different electrochemical potentials (i.e. Consider the the band diagram for a homojunction, formed when two bits of the same type of semicondutor (e.g. Si) are doped p and ntype and then brought into contact. Electrons in the two bits have different

More information

Diodes. anode. cathode. cut-off. Can be approximated by a piecewise-linear-like characteristic. Lecture 9-1

Diodes. anode. cathode. cut-off. Can be approximated by a piecewise-linear-like characteristic. Lecture 9-1 Diodes mplest nonlinear circuit element Basic operation sets the foundation for Bipolar Junction Transistors (BJTs) Also present in Field Effect Transistors (FETs) Ideal diode characteristic anode cathode

More information

Review Energy Bands Carrier Density & Mobility Carrier Transport Generation and Recombination

Review Energy Bands Carrier Density & Mobility Carrier Transport Generation and Recombination Review Energy Bands Carrier Density & Mobility Carrier Transport Generation and Recombination The Metal-Semiconductor Junction: Review Energy band diagram of the metal and the semiconductor before (a)

More information

Midterm I - Solutions

Midterm I - Solutions UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Spring 2008 Professor Chenming Hu Midterm I - Solutions Name: SID: Grad/Undergrad: Closed

More information

FYS3410 Condensed matter physics

FYS3410 Condensed matter physics FYS3410 Condensed matter physics Lecture 23 and 24: pn-junctions and electrooptics Randi Haakenaasen UniK/UiO Forsvarets forskningsinstitutt 11.05.2016 and 18.05.2016 Outline Why pn-junctions are important

More information

The 5 basic equations of semiconductor device physics: We will in general be faced with finding 5 quantities:

The 5 basic equations of semiconductor device physics: We will in general be faced with finding 5 quantities: 6.012 - Electronic Devices and Circuits Solving the 5 basic equations - 2/12/08 Version The 5 basic equations of semiconductor device physics: We will in general be faced with finding 5 quantities: n(x,t),

More information

Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium September 20, 2005

Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium September 20, 2005 6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-1 Contents: Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium September 20, 2005

More information

Semiconductor Devices and Circuits Fall Midterm Exam. Instructor: Dr. Dietmar Knipp, Professor of Electrical Engineering. Name: Mat. -Nr.

Semiconductor Devices and Circuits Fall Midterm Exam. Instructor: Dr. Dietmar Knipp, Professor of Electrical Engineering. Name: Mat. -Nr. Semiconductor Devices and Circuits Fall 2003 Midterm Exam Instructor: Dr. Dietmar Knipp, Professor of Electrical Engineering Name: Mat. -Nr.: Guidelines: Duration of the Midterm: 1 hour The exam is a closed

More information

Consider a uniformly doped PN junction, in which one region of the semiconductor is uniformly doped with acceptor atoms and the adjacent region is

Consider a uniformly doped PN junction, in which one region of the semiconductor is uniformly doped with acceptor atoms and the adjacent region is CHAPTER 7 The PN Junction Consider a uniformly doped PN junction, in which one region of the semiconductor is uniformly doped with acceptor atoms and the adjacent region is uniformly doped with donor atoms.

More information

Semiconductor Device Physics

Semiconductor Device Physics 1 emiconductor Device Physics Lecture 8 http://zitompul.wordpress.com 2 0 1 3 emiconductor Device Physics 2 M Contacts and chottky Diodes 3 M Contact The metal-semiconductor (M) contact plays a very important

More information

Section 12: Intro to Devices

Section 12: Intro to Devices Section 12: Intro to Devices Extensive reading materials on reserve, including Robert F. Pierret, Semiconductor Device Fundamentals EE143 Ali Javey Bond Model of Electrons and Holes Si Si Si Si Si Si Si

More information

(Refer Slide Time: 03:41)

(Refer Slide Time: 03:41) Solid State Devices Dr. S. Karmalkar Department of Electronics and Communication Engineering Indian Institute of Technology, Madras Lecture - 25 PN Junction (Contd ) This is the 25th lecture of this course

More information

PART III SEMICONDUCTOR DEVICES

PART III SEMICONDUCTOR DEVICES PART III SEMICONDUCTOR DEVICES Chapter 3: Semiconductor Diodes Chapter 4: Bipolar Junction Transistors (BJT s) Chapter 5: Field Effect Transistors (FET s) Chapter 6: Fabrication technology for monolithic

More information

Lecture 04 Review of MOSFET

Lecture 04 Review of MOSFET ECE 541/ME 541 Microelectronic Fabrication Techniques Lecture 04 Review of MOSFET Zheng Yang (ERF 3017, email: yangzhen@uic.edu) What is a Transistor? A Switch! An MOS Transistor V GS V T V GS S Ron D

More information

1st Year-Computer Communication Engineering-RUC. 4- P-N Junction

1st Year-Computer Communication Engineering-RUC. 4- P-N Junction 4- P-N Junction We begin our study of semiconductor devices with the junction for three reasons. (1) The device finds application in many electronic systems, e.g., in adapters that charge the batteries

More information

2.626 Fundamentals of Photovoltaics

2.626 Fundamentals of Photovoltaics MIT OpenCourseWare http://ocw.mit.edu 2.626 Fundamentals of Photovoltaics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Charge Separation:

More information

Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction, and the transistors.

Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction, and the transistors. - 1-1/15/02C:\lec320.doc H.L.Kwok SEMICONDUCTOR MATERIALS AND DEVICES by H.L. Kwok Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction,

More information

Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction, and the transistors.

Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction, and the transistors. - 1-3/4/02C:\lec320.doc H.L.Kwok SEMICONDUCTOR MATERIALS AND DEVICES by H.L. Kwok Objective: The purpose of these notes is to familiarize students with semiconductors and devices including the P-N junction,

More information

CHAPTER 4: P-N P N JUNCTION Part 2. M.N.A. Halif & S.N. Sabki

CHAPTER 4: P-N P N JUNCTION Part 2. M.N.A. Halif & S.N. Sabki CHAPTER 4: P-N P N JUNCTION Part 2 Part 2 Charge Storage & Transient Behavior Junction Breakdown Heterojunction CHARGE STORAGE & TRANSIENT BEHAVIOR Once injected across the junction, the minority carriers

More information

EE 130 Intro to MS Junctions Week 6 Notes. What is the work function? Energy to excite electron from Fermi level to the vacuum level

EE 130 Intro to MS Junctions Week 6 Notes. What is the work function? Energy to excite electron from Fermi level to the vacuum level EE 13 Intro to S Junctions eek 6 Notes Problem 1 hat is the work function? Energy to ecite electron from Fermi level to the vacuum level Electron affinity of 4.5eV Electron affinity of Ge 4.eV orkfunction

More information

PHYSICAL ELECTRONICS(ECE3540) CHAPTER 9 METAL SEMICONDUCTOR AND SEMICONDUCTOR HETERO-JUNCTIONS

PHYSICAL ELECTRONICS(ECE3540) CHAPTER 9 METAL SEMICONDUCTOR AND SEMICONDUCTOR HETERO-JUNCTIONS PHYSICAL ELECTRONICS(ECE3540) CHAPTER 9 METAL SEMICONDUCTOR AND SEMICONDUCTOR HETERO-JUNCTIONS Tennessee Technological University Wednesday, October 30, 013 1 Introduction Chapter 4: we considered the

More information

The pn junction. [Fonstad, Ghione]

The pn junction. [Fonstad, Ghione] The pn junction [Fonstad, Ghione] Band diagram On the vertical axis: potential energy of the electrons On the horizontal axis: now there is nothing: later we ll put the position qf s : work function (F

More information

CLASS 3&4. BJT currents, parameters and circuit configurations

CLASS 3&4. BJT currents, parameters and circuit configurations CLASS 3&4 BJT currents, parameters and circuit configurations I E =I Ep +I En I C =I Cp +I Cn I B =I BB +I En -I Cn I BB =I Ep -I Cp I E = I B + I C I En = current produced by the electrons injected from

More information

PN Junction

PN Junction P Junction 2017-05-04 Definition Power Electronics = semiconductor switches are used Analogue amplifier = high power loss 250 200 u x 150 100 u Udc i 50 0 0 50 100 150 200 250 300 350 400 i,u dc i,u u

More information

Getting J e (x), J h (x), E(x), and p'(x), knowing n'(x) Solving the diffusion equation for n'(x) (using p-type example)

Getting J e (x), J h (x), E(x), and p'(x), knowing n'(x) Solving the diffusion equation for n'(x) (using p-type example) 6.012 - Electronic Devices and Circuits Lecture 4 - Non-uniform Injection (Flow) Problems - Outline Announcements Handouts - 1. Lecture Outline and Summary; 2. Thermoelectrics Review Thermoelectricity:

More information

ECE-305: Spring 2018 Final Exam Review

ECE-305: Spring 2018 Final Exam Review C-305: Spring 2018 Final xam Review Pierret, Semiconductor Device Fundamentals (SDF) Chapters 10 and 11 (pp. 371-385, 389-403) Professor Peter Bermel lectrical and Computer ngineering Purdue University,

More information

Electrical Characteristics of MOS Devices

Electrical Characteristics of MOS Devices Electrical Characteristics of MOS Devices The MOS Capacitor Voltage components Accumulation, Depletion, Inversion Modes Effect of channel bias and substrate bias Effect of gate oide charges Threshold-voltage

More information

Mark Lundstrom 2/10/2013. SOLUTIONS: ECE 606 Homework Week 5 Mark Lundstrom Purdue University (corrected 3/26/13)

Mark Lundstrom 2/10/2013. SOLUTIONS: ECE 606 Homework Week 5 Mark Lundstrom Purdue University (corrected 3/26/13) SOLUIONS: ECE 606 Homework Week 5 Mark Lundstrom Purdue University corrected 6/13) Some of the problems below are taken/adapted from Chapter 4 in Advanced Semiconductor Fundamentals, nd. Ed. By R.F. Pierret.

More information

Semiconductors CHAPTER 3. Introduction The pn Junction with an Applied Voltage Intrinsic Semiconductors 136

Semiconductors CHAPTER 3. Introduction The pn Junction with an Applied Voltage Intrinsic Semiconductors 136 CHAPTER 3 Semiconductors Introduction 135 3.1 Intrinsic Semiconductors 136 3.2 Doped Semiconductors 139 3.3 Current Flow in Semiconductors 142 3.4 The pn Junction 148 3.5 The pn Junction with an Applied

More information

PN Junction. Ang M.S. October 8, Maxwell s Eqautions Review : Poisson s Equation for PNJ. Q encl S. E ds. σ = dq ds. ρdv = Q encl.

PN Junction. Ang M.S. October 8, Maxwell s Eqautions Review : Poisson s Equation for PNJ. Q encl S. E ds. σ = dq ds. ρdv = Q encl. PN Junction Ang M.S. October 8, 0 Reference Sedra / Smith, M icroelectronic Circuits Maxwell s Eqautions Review : Poisson s Equation for PNJ. Gauss Law for E field The total enclosed charge Q encl. insde

More information

Department of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Exam 1 ` March 22, 2018

Department of Electrical and Computer Engineering, Cornell University. ECE 3150: Microelectronics. Spring Exam 1 ` March 22, 2018 Department of Electrical and Computer Engineering, Cornell University ECE 3150: Microelectronics Spring 2018 Exam 1 ` March 22, 2018 INSTRUCTIONS: Every problem must be done in the separate booklet Only

More information

Metal Semiconductor Contacts

Metal Semiconductor Contacts Metal Semiconductor Contacts The investigation of rectification in metal-semiconductor contacts was first described by Braun [33-35], who discovered in 1874 the asymmetric nature of electrical conduction

More information

Lecture 10 - Carrier Flow (cont.) February 28, 2007

Lecture 10 - Carrier Flow (cont.) February 28, 2007 6.720J/3.43J Integrated Microelectronic Devices - Spring 2007 Lecture 10-1 Lecture 10 - Carrier Flow (cont.) February 28, 2007 Contents: 1. Minority-carrier type situations Reading assignment: del Alamo,

More information

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. EECS 130 Professor Ali Javey Fall 2006

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. EECS 130 Professor Ali Javey Fall 2006 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Professor Ali Javey Fall 2006 Midterm 2 Name: SID: Closed book. Two sheets of notes are

More information

Devices. chapter Introduction. 1.2 Silicon Conductivity

Devices. chapter Introduction. 1.2 Silicon Conductivity chapter 1 Devices 1.1 Introduction The properties and performance of analog bicmos integrated circuits are dependent on the devices used to construct them. This chapter is a review of the operation of

More information

Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium. February 13, 2003

Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium. February 13, 2003 6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 4-1 Contents: Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium February 13, 2003

More information

ECE 440 Lecture 28 : P-N Junction II Class Outline:

ECE 440 Lecture 28 : P-N Junction II Class Outline: ECE 440 Lecture 28 : P-N Junction II Class Outline: Contact Potential Equilibrium Fermi Levels Things you should know when you leave Key Questions What is the contact potential? Where does the transition

More information

PHYS485 Materials Physics

PHYS485 Materials Physics 5/11/017 PHYS485 Materials Physics Dr. Gregory W. Clar Manchester University LET S GO ON A (TEK)ADVENTURE! WHAT? TRIP TO A MAKER S SPACE IN FORT WAYNE WHEN? THURSDAY, MAY 11 TH @ 5PM WHERE? TEKVENTURE

More information

B12: Semiconductor Devices

B12: Semiconductor Devices B12: Semiconductor Devices Example Sheet 2: Solutions Question 1 To get from eq. (5.70) of the notes to the expression given in the examples sheet, we simply invoke the relations n 0 p 0, n 0 n 0. In this

More information