Equivalent Correlation between Short Channel DG & GAA MOSFETs
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1 Equivalent Correlation between hort Channel DG & GAA FETs K. Yılmaz 1,2, G. Darbandy 1, B. Iñíguez 2, F. Lime 2 and A. Kloes 1 1 NanoP, THM-University of Applied ciences, Giessen, Germany 2 DEEEA, Universitat Rovira i Virgili, Tarragona, pain - at EDERC/ECIRC eptember 3 rd, 2018, Dresden, Germany
2 Motivation tatus quo: Concept of equivalent thickness and capacitance (long channel) [1]. Goal: Extend 2-D DG compact model [2] to short channel GAA FETs. Challenge: tretch the channel length to equalize electrostatics & short channel behavior. Methods: 1. Theory derived from the Laplace s & Poisson s equation. 2. Concept of equivalent channel length due to equiv. capacitance. n++ Ch G r Oxide z intrinsic D n++ [1] N. Chevillon et al., IEEE TED, Vol. 59, no. 1, pp , January [2] A. Kloes et al., IEEE TED, Vol. 59, no. 2, February Dresden ept.3, /23
![Motivation tatus quo: Concept of equivalent thickness and capacitance (long channel) [1]. Goal: Extend 2-D DG compact model [2] to short channel GAA FETs.](/docs-images/90/101382440/images/3-4.jpg "Challenge: tretch the channel length to equalize electrostatics & short channel behavior. Methods: 1. Theory derived from the Laplace s & Poisson s equation. 2.")
3 Motivation tatus quo: Concept of equivalent thickness and capacitance (long channel) [1]. Goal: Extend 2-D DG compact model [2] to short channel GAA FETs. Challenge: tretch the channel length to equalize electrostatics & short channel behavior. Methods: 1. Theory derived from the Laplace s & Poisson s equation. 2. Concept of equivalent channel length due to equiv. capacitance. n++ Ch G r Oxide z intrinsic D n++ [1] N. Chevillon et al., IEEE TED, Vol. 59, no. 1, pp , January [2] A. Kloes et al., IEEE TED, Vol. 59, no. 2, February Dresden ept.3, /23
4 Outline 1. Introduction 2. Device dimensions dependent equivalent length 3. imulation & Compact Model Results 4. Conclusion Dresden ept.3, /23
5 1. Introduction ubthreshold equivalent potential theory: Current model [3]: I D nn2 ii Φ ee min NN AA VV tt dddd Assumption: Potential barrier through channel thickness is parabolic. Φ mmmmmm xx = Φ CC xx2 RR 2 Φ CC Φ Modified current model: I D nn2 ii NN AA ΦCC ππ R e VV tt erf (Φ CC Φ ) VV tt 2 (Φ CC Φ ) VV tt [3] Q. Chen et al., IEEE TED, Vol. 49, no. 6, pp , June Dresden ept.3, /23
6 2. Device dimensions dependent equivalent length Two independent derivation methods: 1. Method (=> slightly complicated): Φ mmmmmm parabolic olve 2-D Poisson s equation channel surface cylindrical coordinates Φ mmmmmm sinusoidal olve 2-D Laplace s equation channel center Cartesian coordinates Equate the potential drops Φ mmmmmm rr = Φ mmmmmm xx and compare the potential drops along the channel Φ rr, zz ee ± zz/λλ with the so-called natural length λλ [4,5,6]. Result for Φ if Φ mmmmmm is sinusoidal [7]: Φ DDDD Φ CC CCCCCC( xx λλ DDDD ) CCCCCCC( zz DDDD λλ DDDD ) Φ GGGGGG Φ CC JJ 0 ( rr λλ GGGGGG ) CCCCCCC( zz GGGGGG λλ GGGGGG ) zz DDDD λλ DDDD λλ GGGGGG zz GGGGGG 1.53 zz GGGGGG [4].-H. Oh et al., IEEE EDL, Vol. 21, no. 9, pp , eptember [5] R. H. Yan et al., IEEE TED, Vol. 39, no. 7, pp , Jul [6] K. uzuki et al., IEEE TED, Vol. 40, no. 12, pp , Dec [7] C. P. Auth et al., IEEE EDL, Vol. 18, no. 2 pp , Feb Dresden ept.3, /23
![subthreshold slopes: DDDD GGGGGG sssss = sssss Lundstrom [8]: sssss = ηη log 10 VV TT ηη 1 = Φ VV GGGG =](/docs-images/90/101382440/images/7-4.jpg "Ratio of capacitances must be equal!")
7 2. Device dimensions dependent equivalent length Two independent derivation methods: 2. Method (=> simpler): Device's electrostatics are represented by the subthreshold slope Equalize subthreshold slopes: DDDD GGGGGG sssss = sssss Lundstrom [8]: sssss = ηη log 10 VV TT ηη 1 = Φ VV GGGG = Ratio of capacitances must be equal! 1 CC DD 1 = CCoooo + 1 CC DD 1 CC DD 1 + CCoooo [8] Lecture: Lundstrom EE-612 F08 Dresden ept.3, /23
8 2. Device dimensions dependent equivalent length Two independent derivation methods: Capacitance DG GAA C,D C ox εε ww tt ccc LL DDDD /2 2 εε oooo ww tt oooo LL DDDD 2ππ εε ππ RR 2 LL GGGGGG /2 εε oooo ln 1 + tt oooo RR LL GGGGGG Equivalent channel length: LL DDDD = LL GGGGGG with ββ = 2 ββ tt oooo RR llll 1+ tt oooo RR In addition: Equivalent channel width due to equivalent capacitances: WW ccc = ππ RR 2 2 ββ Dresden ept.3, /23
9 2. Device dimensions dependent equivalent length imulation results match for the center potential: CC Φ GGGGGG CC = Φ DDDD imulation results don t match for the surface potential Φ, subthreshold swing and DIBL. Capacitance model of Lundstrom has its limitations. The first method helps out: olve the Laplace equation by assuming a sinusoidal shape through the channel thickness! Combining both methods lead to the best match for Φ, swing and DIBL. Equivalent channel length: LL DDDD = LL GGGGGG 1.53 ββ with ββ = tt oooo RR llll 1+ tt oooo RR Equivalent channel width: WW ccc = ππ RR ββ Dresden ept.3, /23
10 3. imulation & Compact Model Results Center potential Φ CC vs. channel length LL GGGGGG VV DD = 0 VV, VV GG = 0 VV o TCAD (GAA) TCAD (DG) + Model Dresden ept.3, /23
11 3. imulation & Compact Model Results Center potential Φ CC vs. channel length LL GGGGGG VV DD = 0 VV, VV GG = 0 VV o TCAD (GAA) TCAD (DG) + Model Dresden ept.3, /23
12 3. imulation & Compact Model Results Center potential Φ CC vs. channel length LL GGGGGG VV DD = 0 VV, VV GG = 0 VV o TCAD (GAA) TCAD (DG) + Model Dresden ept.3, /23
13 3. imulation & Compact Model Results urface potential Φ vs. channel length LL GGGGGG VV DD = 0 VV, VV GG = 0 VV o TCAD (GAA) TCAD (DG) + Model Dresden ept.3, /23
14 3. imulation & Compact Model Results urface potential Φ vs. channel length LL GGGGGG VV DD = 0 VV, VV GG = 0 VV o TCAD (GAA) TCAD (DG) + Model Dresden ept.3, /23
15 3. imulation & Compact Model Results urface potential Φ vs. channel length LL GGGGGG VV DD = 0 VV, VV GG = 0 VV o TCAD (GAA) TCAD (DG) + Model Dresden ept.3, /23
16 3. imulation & Compact Model Results ubthreshold wing vs. channel length LL GGGGGG sth [V/dec] L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
17 3. imulation & Compact Model Results ubthreshold wing vs. channel length LL GGGGGG sth [V/dec] L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
18 3. imulation & Compact Model Results ubthreshold wing vs. channel length LL GGGGGG sth [V/dec] L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
19 3. imulation & Compact Model Results ubthreshold wing vs. channel length LL GGGGGG sth [V/dec] L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
20 3. imulation & Compact Model Results Drain-induced barrier lowering (DIBL) vs. channel length LL GGGGGG DIBL [V] V D = 1.0 V 0.1 V = 0.9 V L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
21 3. imulation & Compact Model Results Drain-induced barrier lowering (DIBL) vs. channel length LL GGGGGG DIBL [V] V D = 1.0 V 0.1 V = 0.9 V L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
22 3. imulation & Compact Model Results Drain-induced barrier lowering (DIBL) vs. channel length LL GGGGGG DIBL [V] V D = 1.0 V 0.1 V = 0.9 V L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
23 3. imulation & Compact Model Results Drain-induced barrier lowering (DIBL) vs. channel length LL GGGGGG DIBL [V] V D = 1.0 V 0.1 V = 0.9 V L GAA [nm] o TCAD (GAA) TCAD (DG) + 1 Model + 2 Φ-TCAD & Model Dresden ept.3, /23
24 4. Conclusion The equivalent capacitance concept is presented to capture short channel GAA FET electrostatic & behavior by DG FET. It is shown that the method is working properly for subthreshold region in intrinsic and lightly doped channel. The center and surface potential (φ C & φ ) need different equivalent values for the channel length. In subthreshold region where the leakage current mainly flows in the center, not only φ C but also φ has significant influence on the electrostatic and characteristics. Outlook: The method is under development for above threshold short channel devices. Dresden ept.3, /23
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