CN102254072A - Analytical model for threshold voltage of fence-structured MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) - Google Patents

Analytical model for threshold voltage of fence-structured MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) Download PDF

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CN102254072A
CN102254072A CN2011102192375A CN201110219237A CN102254072A CN 102254072 A CN102254072 A CN 102254072A CN 2011102192375 A CN2011102192375 A CN 2011102192375A CN 201110219237 A CN201110219237 A CN 201110219237A CN 102254072 A CN102254072 A CN 102254072A
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threshold voltage
mosfet
voltage
fence
analytical model
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梅光辉
李佩成
胡光喜
倪亚路
刘冉
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Fudan University
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Abstract

The invention belongs to the technical field of semiconductors, and particularly relates to an analytical model for calculating a threshold voltage of a fence-structured metal-oxide-semiconductor field effect transistor (MOSFET). In the invention, the analytical model for the threshold voltage is obtained by the steps: solving the electric potential distribution of the fence-structured MOSFET, solving the surface charge density of the fence-structured MOSFET according to the electric potential distribution, and then obtaining the threshold voltage which is the corresponding gate voltage when the surface charge density on a device virtual electrode is equal to critical charge density according to a threshold value definition method in the invention. The analytical model for the threshold voltage has the characteristics of concise form, clear physical conception and high calculation precision, and provides a rapid and accurate tool for circuit simulation software during researches on novel fence devices.

Description

A kind of grid structure MOSFET threshold voltage analytic model that encloses
Technical field
The invention belongs to technical field of semiconductors, be specifically related to the model that grid structural metal-oxide-semiconductor field effect transistor (MOSFET) threshold voltage is enclosed in a kind of calculating.
Background technology
Along with the integrated circuit (IC) chip integrated level improves constantly and constantly the dwindling of device geometries, in the evolution of nanoscale MOSFET device, progressively develop to the on-plane surface spatial structure from planar technology.And in all kinds of non-traditional planer device structures, enclose grid structure MOSFET, because grid can surround raceway groove fully, its integration density is the highest, and grid control ability is the strongest, can better suppress short-channel effect, reduce the quiescent dissipation of device, make subthreshold current minimize.It is optimal structure that the MOSFET device enters nanoscale.Therefore to this fense MOSFET structure, create analytic model and become particularly important.Being subjected to industry member day by day with this threshold voltage extraction model that encloses grid structure MOSFET simultaneously pays close attention to.Can not adapt to for the body silicon MOSFET threshold voltage model of conventional planar technology in the past, bring new challenge for the modeling and the simulation of this novel multiple-grid nano-device.
Threshold voltage
Figure 298096DEST_PATH_IMAGE001
Be MOSFET one of important parameter the most, threshold voltage is defined as: needed grid voltage when reaching threshold value transoid point, work as the accurate Fermi's electromotive force of electronics that surface potential equals 2 times for n type device
Figure 906932DEST_PATH_IMAGE002
The time device state, the perhaps accurate Fermi's electromotive force in hole that equals 2 times when surface potential for p type device
Figure 893474DEST_PATH_IMAGE003
The time device state.In order to use correctly mimic channel characteristic of circuit simulation software, it is very important setting up accurate threshold voltage model.
Summary of the invention
In view of this, the object of the invention is to provide a kind of form succinct, clear physics conception, and precision high enclose grid structure MOSFET threshold voltage model.
The present invention proposes encloses grid structure MOSFET threshold voltage analytic model, for circuit simulation software when gate device is enclosed in research, a kind of quick accurate Analysis model is provided.
For exhausting fense MOSFET entirely, Potential Distributing mainly is because by immovable ionized impurity decision when being operated in depletion region and weak transoid and also not reaching strong inversion, can ignore the influence of free carrier, the threshold voltage model that the present invention proposes has been made the depletion approximation hypothesis here.Seldom can ignore in threshold zone and the removable electric charge of sub-threshold region, before the raceway groove strong inversion begins, exhaust entirely for the fense MOSFET raceway groove, when the doping of channel region P type, so its channel region Potential Distributing can be represented by the Poisson equation under the cylindrical coordinate:
Figure 904155DEST_PATH_IMAGE004
(1)
Figure 934428DEST_PATH_IMAGE005
，
Figure 30560DEST_PATH_IMAGE006
， ，
Figure 918936DEST_PATH_IMAGE008
(2)
In the formula, gate oxide
Figure 120110DEST_PATH_IMAGE009
, aBe the fense MOSFET device radius, t Ox Be thickness of grid oxide layer;
Figure 516588DEST_PATH_IMAGE010
With
Figure 828620DEST_PATH_IMAGE011
Specific inductive capacity for silicon and gate oxide; LBe channel length;
Figure 813894DEST_PATH_IMAGE012
Be the Potential Distributing function; qBe electron charge;
Figure 452815DEST_PATH_IMAGE013
Be the channel region doping content;
Figure 523539DEST_PATH_IMAGE014
,
Figure 639263DEST_PATH_IMAGE015
Be the electromotive force of source S ource,
Figure 479043DEST_PATH_IMAGE016
Be built-in electromotive force;
Figure 772752DEST_PATH_IMAGE017
Be that drain D rain is with respect to source voltage;
Figure 127510DEST_PATH_IMAGE018
,
Figure 984608DEST_PATH_IMAGE019
Be the voltage of grid G ate with respect to source electrode;
Figure 990479DEST_PATH_IMAGE020
Be flat-band voltage.
In order to find the solution the Potential Distributing Poisson equation, electromotive force is decomposed into the one dimension electromotive force that only is applicable under the long channel case
Figure 642040DEST_PATH_IMAGE021
With the two-dimentional electromotive force that utilizes Laplace's equation to find the solution to comprise all boundary conditions
Figure 749673DEST_PATH_IMAGE022
So total electromotive force equation just is:
Figure 144882DEST_PATH_IMAGE023
(3)?。
So equation (1) is decomposed into about the one dimension electromotive force
Figure 506725DEST_PATH_IMAGE024
Equation:
Figure 594766DEST_PATH_IMAGE025
(4)
With about two-dimentional electromotive force Laplace's equation:
Figure 123017DEST_PATH_IMAGE027
(5)?。
Finding the solution the one dimension electromotive force
Figure 526316DEST_PATH_IMAGE028
Analytic method in, according to the boundary condition at one dimension oxide layer and body silicon interface place:
Figure 96844DEST_PATH_IMAGE029
(6)
(7)
Separate for:
Figure 650502DEST_PATH_IMAGE031
(8)
Wherein
Figure 49253DEST_PATH_IMAGE032
,
Figure 790682DEST_PATH_IMAGE033
So
Figure 766728DEST_PATH_IMAGE034
(9)
Find the solution two-dimentional Laplace's equation:
Figure 369748DEST_PATH_IMAGE035
(10)
Figure 13219DEST_PATH_IMAGE036
Figure 161435DEST_PATH_IMAGE037
Figure 348932DEST_PATH_IMAGE039
(11)?。
Utilize the separation of variable to find the solution top two-dimentional Laplace's equation and provide separating of its progression form:
Figure 909226DEST_PATH_IMAGE040
(12)
Figure 228343DEST_PATH_IMAGE041
(13)
Figure 444561DEST_PATH_IMAGE042
(14)
Figure 389383DEST_PATH_IMAGE043
(15)?。
It is eigenwert;
Figure 995999DEST_PATH_IMAGE045
Be n rank Bessel's functions;
Figure 496251DEST_PATH_IMAGE046
Be Bezier-Fourier coefficient, eigenwert satisfies:
Figure 729917DEST_PATH_IMAGE047
The definition of tradition threshold voltage model: the electromotive force of surface potential minimum point equal 2 times the channel surface electromotive force promptly
Figure 202487DEST_PATH_IMAGE048
The time pairing gate voltage.Define thus, obtain the position of electromotive force minimum point earlier, can obtain threshold voltage then.The threshold voltage definition that the present invention adopts: the gate voltage of correspondence when equaling critical charge density according to the empty electrode of device place surface charge density.The position of empty electrode is the electromotive force minimum point of device along channel direction.
When device surface inversion layer charge density equaled ionized impurity electric charge equivalent face density, doping exhausted channel device entirely for the p type, and critical charge density equals to be subjected to main ionized impurity electric charge equivalent face density
Figure 424259DEST_PATH_IMAGE049
Empty electrode place surface inversion layer electric density can obtain by inversion layer charge is assigned to the surface from the raceway groove central product:
Figure 349489DEST_PATH_IMAGE050
(16)?。
The position of empty electrode wherein
Figure 636114DEST_PATH_IMAGE051
According to:
Figure 776240DEST_PATH_IMAGE052
(17)
Figure 122907DEST_PATH_IMAGE053
(18)
Obtain the electromotive force minimum point
Figure 535434DEST_PATH_IMAGE051
,
Figure 609438DEST_PATH_IMAGE054
Be empty electrode place Fermi level, Fermi level
Figure 853338DEST_PATH_IMAGE055
,
Figure 121639DEST_PATH_IMAGE056
Be intrinsic carrier concentration,
Figure 83779DEST_PATH_IMAGE057
Be thermal voltage, can think in weak inversion regime:
Figure 649889DEST_PATH_IMAGE058
(19)?。
Therefore obtaining empty electrode place surface inversion layer electric density is:
Figure 991704DEST_PATH_IMAGE059
(20)
When The time, threshold voltage equals added grid voltage:
Figure 67293DEST_PATH_IMAGE061
(21)?。
In the time of the threshold voltage numerical evaluation,, get because the higher order term decay is exceedingly fast to not influence of result n=3,
Figure 984565DEST_PATH_IMAGE062
Can ignore, can reduce computing cost like this.
Formula (21) is the analytical expression of the threshold voltage model of calculating fense MOSFET, and advantage is by parsing the fense MOSFET threshold voltage, simplifying computation model and make computing cost little.
Description of drawings
Fig. 1 is the fense MOSFET tomograph.
Fig. 2 is that fense MOSFET is along the channel direction sectional view.
Fig. 3 different radii threshold voltage is with the variation of channel length.
The gate oxide threshold voltage of Fig. 4 different-thickness is with the variation of channel length.
Fig. 5 is a threshold voltage modeling schematic flow sheet.
Embodiment
At the problem that background technology is mentioned, existing TCAD simulation software intermediate computations fense MOSFET threshold voltage calculates by numerical simulation.Analytic model by us calculates, and n type fense MOSFET threshold voltage of the present invention as shown in Figure 3 is with the analysis result and the TCAD simulation curve of changes in channel length, at identical thickness of grid oxide layer
Figure 203056DEST_PATH_IMAGE063
Under the condition, choose the device of 3 kinds of different radii size types, wherein the raceway groove radius 5,7.5,10 and channel length be respectively 20,30,40,50,60,70,80,90,100, unit is nanometer nm.As shown in Figure 4, at the raceway groove radius
Figure 111DEST_PATH_IMAGE064
Under the condition, choose the device of 3 kinds of different radii gate oxide types, wherein radius 1,2,5 and channel length be respectively 20,30,40,50,60,70,80,90,100, unit is nanometer nm.For every kind of device
Figure 920531DEST_PATH_IMAGE065
,
Figure 156341DEST_PATH_IMAGE066
, normal temperature
Figure DEST_PATH_IMAGE067
Calculate with TCAD software in come out result contrast of numerical simulation, TCAD calculates threshold voltage by current/voltage I/V family curve.

Claims (2)

1. one kind is enclosed grid structure MOSFET threshold voltage analytic model, it is characterized in that the analytic expression of this threshold voltage model is:
Figure 2011102192375100001DEST_PATH_IMAGE001
Wherein, gate oxide
Figure 377148DEST_PATH_IMAGE002
, aBe the fense MOSFET device radius, t Ox Be thickness of grid oxide layer; With
Figure 231971DEST_PATH_IMAGE004
Specific inductive capacity for silicon and gate oxide; LBe the fense MOSFET device channel length; qBe electron charge;
Figure 11709DEST_PATH_IMAGE006
,
Figure 2011102192375100001DEST_PATH_IMAGE007
Be the electromotive force of source electrode,
Figure 2011102192375100001DEST_PATH_IMAGE009
Be built-in electromotive force; Be that drain electrode is with respect to source voltage;
Figure 2011102192375100001DEST_PATH_IMAGE013
, Be the voltage of grid with respect to source electrode;
Figure 656185DEST_PATH_IMAGE016
Be flat-band voltage,
Figure 2011102192375100001DEST_PATH_IMAGE017
Be empty electrode place Fermi level, Fermi level
Figure 2011102192375100001DEST_PATH_IMAGE019
,
Figure 595191DEST_PATH_IMAGE020
Be intrinsic carrier concentration,
Figure 2011102192375100001DEST_PATH_IMAGE021
Be the channel region doping content,
Figure 604605DEST_PATH_IMAGE022
Be thermal voltage,
Figure 2011102192375100001DEST_PATH_IMAGE023
Position for empty electrode;
Figure 809321DEST_PATH_IMAGE024
In the formula,
Figure 2011102192375100001DEST_PATH_IMAGE027
Figure 801734DEST_PATH_IMAGE028
Figure 2011102192375100001DEST_PATH_IMAGE029
Be the one dimension Potential Distributing,
Figure 982048DEST_PATH_IMAGE030
It is eigenwert;
Figure 2011102192375100001DEST_PATH_IMAGE031
Be n rank Bessel's functions;
Figure 674061DEST_PATH_IMAGE032
Be Bezier-Fourier coefficient, eigenwert satisfies:
Figure 2011102192375100001DEST_PATH_IMAGE033
2. the grid structure MOSFET threshold voltage analytic model that encloses according to claim 1 is characterized in that n=3.
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Publication number Priority date Publication date Assignee Title
CN102692543A (en) * 2012-06-01 2012-09-26 西安邮电大学 Method for extracting flat-band voltage and threshold voltage of MOSFET (metal-oxide-semiconductor field effect transistor) based on current generation of grid-control drain electrode
CN102779205A (en) * 2012-06-20 2012-11-14 上海华力微电子有限公司 Threshold voltage analytical model of short channel ring fence structure metal oxide semiconductor field effect transistor (MOSFET)
CN105005663A (en) * 2015-07-24 2015-10-28 集美大学 Resolving model for two-dimensional threshold voltage of body contact potential PD-SOI MOSFET, building method of resolving model for two-dimensional threshold voltage of body contact potential PD-SOI MOSFET and method for calculating threshold voltage
CN108388697A (en) * 2018-01-23 2018-08-10 华北水利水电大学 A kind of asymmetric double grid structure MOSFET threshold voltage analytic modell analytical models

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CN101464919A (en) * 2008-12-30 2009-06-24 上海集成电路研发中心有限公司 BSIM3 HCI reliability model used in MOSFET electrical simulation
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102692543A (en) * 2012-06-01 2012-09-26 西安邮电大学 Method for extracting flat-band voltage and threshold voltage of MOSFET (metal-oxide-semiconductor field effect transistor) based on current generation of grid-control drain electrode
CN102779205A (en) * 2012-06-20 2012-11-14 上海华力微电子有限公司 Threshold voltage analytical model of short channel ring fence structure metal oxide semiconductor field effect transistor (MOSFET)
CN105005663A (en) * 2015-07-24 2015-10-28 集美大学 Resolving model for two-dimensional threshold voltage of body contact potential PD-SOI MOSFET, building method of resolving model for two-dimensional threshold voltage of body contact potential PD-SOI MOSFET and method for calculating threshold voltage
CN105005663B (en) * 2015-07-24 2018-02-16 集美大学 A kind of body connects current potential PD SOI MOSFET Two Dimensional Thresholding voltage analytic modell analytical models and its method for building up and threshold voltage computational methods
CN108388697A (en) * 2018-01-23 2018-08-10 华北水利水电大学 A kind of asymmetric double grid structure MOSFET threshold voltage analytic modell analytical models
CN108388697B (en) * 2018-01-23 2021-08-10 华北水利水电大学 Threshold voltage analysis method for MOSFET with asymmetric double-gate structure

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