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Special Issue on the nano devices 서울대 나노 협동과정 & 나노 응용시스템 연구센터 (NSI_NCRC). The 2 nd lecture: MOS operational principle Prof. Young June Park. - 나노 물리소자 특강 부제 “ 한글 ; 나노반도체와 분자소자 결합 목요일 오후 1 시 -4 시 교수학습개발센터 1 층 스튜디오 강의실 전기신호를 이용해서 신호 및 에너지를 변환하거나 , 전환하는 소자가
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Special Issue on the nano devices서울대 나노 협동과정&나노 응용시스템 연구센터(NSI_NCRC) The 2nd lecture: MOS operational principle Prof. Young June Park
- 나노 물리소자 특강 부제“한글; 나노반도체와 분자소자 결합 목요일 오후 1시-4시 교수학습개발센터 1층 스튜디오 강의실 전기신호를 이용해서 신호 및 에너지를 변환하거나, 전환하는 소자가 나노 분야에서 사용되고 있다. 빛, 화학, 분자와 전자소자의 interaction 등에 대해서 콜로키움 형태로 특강을 진행한다. Syllabus (updated)
1. Introduction: motivation of the lecture 1주: 박 영준교수 2. Nano semiconductor Device operational principle 2주(3/14): MOSFET operational principle(박 영준교수) 3주(3/22): 1. IV characteristics of MOSFET(박 영준교수) 2,3: Nanowire MOSFET(박병국교수) 4주(3/29): Single Electron Transistor and its molecular interaction (박 병국, 박영준교수) Syllabus (updated)
3. Lecture from Max Plank(Germany): Dr. S. Roth 5주(4/5): Introduction into the physics of low-dimensionsal materials: 6주(4/12) Conducting Polymers 7주(4/19) Carbon Nanotubes 8주(4/26) Graphene Layers 4:30~6:00 교재: VCH: One dimensional conductor available from http://www.wiley-vch.de/publish/en/books/ISBN3-527-30749-4/http://www.amazon.com/One-Dimensional-Metals-Physics-Materials-Science/dp/3527268758 8주 : review and midterm Syllabus (updated)
4. 전기화학의 기초( 성영은교수) 9주(5/3): 전기화학의 기초 10주(5/10): characterization techniques (cyclo voltametry) - may be shifted to 9th 11주(5/17): Electric double layer structure Faradaic interface Non Faradaic interface Syllabus (updated)
5. ISFET and molecule-insulator surface 12주(5/31) ISFET: Molecular and insulator interface (박영준교수) 13주(6/7): molecule to insulator(electrode) interface(강헌교수) 6. Others 14주(6/14) : 1. Charge transport in Organic device(이창희교수) Syllabus (updated)
MOS eq:quantum and classical model C-V characteristics Long channel IV characteristics MOS equation and CV characteristics Ref :Y.J.Park, B.G.Park, H.C. Shin, H.S.Min, VLSI device with NANOCAD, chapter 2, (Korean) Grove, Chap. 4, Physics and Technology of Semiconductor Dev., John Wiley & Sons, 1967
MOS Equations(1) (1) • describes the voltage across the gate, oxide and semiconductor surface with respect some references • is when so that is called "the Flat Band Voltage" • : voltage applied in the gate caused by the poly depletion effect : voltage applied across the oxide : Semiconductor surface potential w,r,t some reference voltage (see next page for the reference)
MOS Equations(2) From simple D continuity consideration between interfaces; Gate- oxide and oxide semiconductor interface, Vox = QG/Cox ( notice that Qs=-QG due to charge conservation) • Find the relation , with a single variable , then we can solve the MOS equations with respec to . • This can be achieved by using the "semiconductor areal charge density", represented by Vox (so ) Ex) Draw the rho(****) and field relation in the depth direction as you did in the case of PN junction.
Qs and relationships There are several models to find Qs and relationships - classical with MB statistics - classical with FD statistics - Quantum mechanical model
relationship: classical model • Assuming that the surface is not quantized in x direction, and MB statistics is valid, the general relation can be found as, (2) where Then (from the continuity in electric flux, D) (3) and (4)
Vertical Electric Fields • Important physical quantities related with vertical fields : Es and Eox, and Eeff • Eox : determines the tunneling current in thin oxide, limiting the minimum thickness of gate oxide. • Eeff : determines the effective vertical field which carriers see in vertical direction. Ex) relationship Draw relationship from Eq. (1)
Classical VTtheory • is value in which is appreciable so that drain current is detectable. • Eq.(2) states that is exponentially increasing function of whereas is increasing function in the power of 0.5. • So, as we do approximate I-V of diode such that I=0 when where is around 0.7V even though I flows continuously as increases from 0V, we assume that until becomes a certain value ( ). • Also assume that is fixed to the value and does not increase further. • With this assumptions, classical expression for MOS VT and can be found.
Classical VTtheory(2) • Assume , for , Eq. (1) becomes, so that where . For , since is fixed to Eq.(1) becomes, so after inversion can be written found as, .
quantum mechanical model Eq. For Qn for 2 D gas as function of Ei and Ef. Schrodinger eq. For Ei and the Poisson equation for Vp Equation for n(x): n(x) determines Vp => Ei and Ni(Qn)
One of the most powerful experimental method to know the MOS surface is measurement of gate capacitance CG vs VG. Here, DC VG is applied and a small signal is applied with a certain frequency so that the current through the gate is measured and transformed to Capacitance. DC VG is scanned so that C-VG can be plotted. C-V Characteristics
C-V Characteristics(2) • The applied frequency is so low that the electron concentration can be responded so that Eq. (1) with relation always hold. • If high frequency is applied so that electron cannot be responded to the applied signal, high frequency characteristics is observed. • Differentiating Eq.(1) with respect to ,
C-V Characteristics(3) • Notice that this Eq. can be written as
C-V Characteristics • Above Fig. shows that approximate Cs behavior. The following feature should be noticed. and . • Notice that from , can be found, so the • Then can be obtained from .
C-V Characteristics(4) • Let us first consider Cs. From Eq. (2), Cs can be easily found as, • Fig. 2 shows that approximate Cs behavior. The following feature should be noticed. and . • Notice that from , can be found, so be . Then can be obtained from .
Effects of quantum mechanical model on CV From C. Richter's, EDL p.35, Jan 2001)
1-1. MOSFET current : General Band diagram VGS VS VDS y VBS x
1-2.Classical approximation above threshold Above threshold, current is mainly due to the drift.
Classical approximation above threshold (pinch off voltage) The equation for VDS,sat due to pinch off is
1-3. below threshold (Subthreshold characteristics) Current in the subthreshold region is assumed to be due to diffusion,
Classical approx. below threshold (Subthreshold characteristics) Now the relationship between and VGS-VT is,
Classical approx. below threshold (Subthreshold characteristics)
1-4. Mobility in the inversion layer S. Takaki et. al, "On the universality of inversion layer mobility in N- and P- channel MOSFET's," IEDM, pp.398-401, 1988.
Mobility enhancement • Enhancement of the MOS mobility is one of the key • Issues to enhance the CMOS circuit performance. • Lowering the vertical field • Using the strained layer to change the effective mass • Stress induced mobility change is used as the molecular sensor.
Mobility enhancement( from Tagaki, IEDM short lecture , 2003) Using the strained layer to change the effective mass. [5] J. J. Welser, J. L. Hoyt and J. F. Gibbons, IEDM Tech. Dig., 1000 (1992)