670
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 36, NO. 4, APRIL 1989
`
`Potential and Electron Distribution Model for the
`Buried-Channel MOSFET
`
`MICHAEL J. VAN DER TOL AND SAVVAS G. CHAMBERLAIN, SENIOR MEMBER, IEEE
`
`the literature, the relationships between the modes of
`Abstract-In
`operation of the buried-channel MOSFET and the potential and signal
`electron distribution within the device is unclear. In this paper we
`present a new analytic model for the potential and electron distribution
`in the channel-depth direction for the buried-channel MOSFET. The
`purpose of our model is to aid in the fundamental physical understand-
`ing of the operational modes of the BC-MOSFET and the mechanisms
`affecting these modes. Using Poisson’s equation individual analytic
`expressions are formulated to predict the potential distribution and
`electron concentration profile under conditions of depletion, inversion,
`pinchoff, and accumulation as a function of the gate bias, substrate
`bias, and the applied channel potential. The model is general and is
`used here to represent the potential distributions for both the nor-
`mally-on and normally-off type BC-MOSFET under various bias con-
`ditions. While the potential distribution in the channel depth direction
`enables one to visualize the band-bending within the device, the signal
`electron concentration profile leads to an easy physical interpretation
`of the modes of operation and the location of mobile charge relative to
`the channel surface: this is important for mobility and device speed
`considerations. In addition, our developed model can be used for de-
`vice design. It predicts the effects of doping density concentration both
`in the substrate and in the channel region, channel implant depth, and
`oxide thickness on the operating regimes of the device.
`
`I. INTRODUCTION
`HE buried-channel MOSFET is typically realized by
`
`T implanting a surface layer of impurities into a sub-
`
`strate of opposite doping. This implant not only alters the
`threshold voltage, but significantly changes the operating
`characteristics of the device. In the past, the BC-MOS-
`FET was typically used as a depletion load device in basic
`NMOS inverters; this was done in an attempt to increase
`packing densities, increase switching speeds, and im-
`prove the power-delay product [l]. In order to take ad-
`vantage of the inherent high mobilities and reduced sur-
`face state effects, the BC-MOSFET has been used in a
`variety of other applications such as high-speed logic cir-
`cuits [2].
`Many authors have presented current-voltage models
`for the BC-MOSFET [3]-[20]. Hara [3] analyzed the fun-
`
`damental characteristics of p-channel BC-MOSFET’s.
`Edwards and Marr [4] used a weighted average profile to
`replace the Guassian channel implant profile. To properly
`model the effective channel length, the Z-V model in-
`cluded a channel-length modulation factor. Huang [5] fol-
`lowed by Huang and Taylor [6] presented a four-terminal
`model for the Z-V characteristics of the depletion-mode
`MOSFET using an average semiconductor capacitance
`method. DeMoulin and Van de Wiele [7] followed by
`Chiang et al. [18] discussed, in detail, the various modes
`of operation for the BC-MOSFET and derived a complete
`set of Z-V characteristics to model these modes. The de-
`pletion-mode MOSFET and its application as a load de-
`vice in an inverter configuration was addressed by Merckel
`[8]. El-Mansy [ l l ] , [12] developed a four-terminal model
`for the depletion-mode IGFET. The current-voltage
`equations were derived for all modes of operation neglect-
`ing the diffusion component in the analysis. To account
`for the surface scattering of electrons in the accumulation
`mode of operation, Baccarani et al. [14] included the ef-
`fect of surface mobility degradation due to the transverse
`electric field. Haque-Ahmed and Salama [ 151 expanded
`upon this work and the work done by El-Mansy and pre-
`sented a simple long-channel depletion-mode MOSFET
`model that included saturation currents and a transverse
`field-dependent mobility. Turchetti and Masetti [ 171 and
`then Parikh and Vasi [ 191 included the effects of diffusion
`currents in their analysis. In the linear and saturation re-
`gimes of operation, Parikh and Vasi demonstrated that the
`diffusion component of the current was insignificant.
`Weng er al. [20] presented an analytical CAD model that
`predicted the threshold shift of a short-channel BC-MOS-
`FET and model the Z-V characteristics suitable for CAD
`integration.
`In the literature, the relationship between the modes of
`operation of the buried-channel MOSFET and the poten-
`tial distribution within the device is unclear. Current-
`voltage relationships cannot provide a fundamental un-
`derstanding of the relationship between the potential dis-
`tribution and the applied terminal voltages, nor can such
`models predict the location of mobile charge in relation
`to these modes. In order to predict the electrical charac-
`teristics of the BC-MOSFET, it is necessary to understand
`its modes of operation. Depending on the doping density
`distribution, physical dimensions, and bias conditions, the
`device can enter into a number of operating modes in-
`cluding inversion, depletion, pinchoff, and accumulation.
`0018-9383/89/0400-0670$01 .OO 0 1989 IEEE
`
`Manuscript received March 14, 1988; revised October I , 1988. This
`work was supported by an individual operating research grant awarded to
`S. G. Chamberlain by the Natural Science and Engineering Research Coun-
`cil of Canada. M. J . Van der To1 was supported by the Natural Sciences
`and Engineering Council of Canada under a post-graduate scholarship pro-
`gram and by the Bell-Northem Research Scholarship Program. A GPX 11
`computer was supplied through a UW-DEC agreement. Partial support was
`provided by ITRC.
`The authors are with the Department of Electrical Engineering, Univer-
`sity of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
`IEEE Log Number 8825920.
`
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`VAN DER TOL AND CHAMBERLAIN: POTENTIAL AND ELECTRON DISTRIBUTION MODEL
`
`67 1
`
`An insight into these modes of operation becomes evident
`when one considers the potential distribution and the elec-
`tron profile in the channel-depth direction within the de-
`vice. However, to date, the potential and signal electron
`distribution in the channel-depth direction has not been
`addressed.
`In this paper, using Poisson’s equation, we develop a
`one-dimensional potential distribution model in the chan-
`nel-depth direction for the buried-channel MOSFET.
`Using the potential distribution model, a profile of the
`electron concentration in the channel-depth direction is
`determined. The purpose of our model is to aid in the
`fundamental physical understanding of the device opera-
`tion and the mechanisms affecting its operating modes.
`The potential distribution enables one to visualize the
`band-bending within the device, while the electron con-
`centration profile leads to an easy physical interpretation
`of the mode of operation. The model is useful for device
`design; to predict the effects of doping density concentra-
`tion (both in the substrate and the channel regions), chan-
`nel-implant depth, and oxide thickness on the operating
`regimes of the device and the location of mobile charge.
`Separate analytic expressions are derived to model the po-
`tential distribution under conditions of depletion, inver-
`sion, pinchoff, and accumulation as a function of the gate
`bias, substrate bias, and channel potential. The model is
`general and can be used to obtain the potential distribution
`and electron concentration profiles in both normally-on
`and normally-off type BC-MOSFET’s.
`A brief introduction into the modes of operation for the
`buried-channel MOSFET is presented in Section 11. A de-
`tailed derivation of the potential distribution model in the
`channel-depth direction is given in Section 111. In Section
`IV, the flat-band voltage for a BC-MOSFET is high-
`lighted and is used in conjunction with the one-dimen-
`sional potential distribution model to design normally-on
`and normally-off buried-channel MOSFET’s. The poten-
`tial distribution and electron concentration profile for these
`devices are illustrated to emphasize the relationship be-
`tween the device biasing, energy-band bending, the modes
`of operation, and the location of mobile charge. The re-
`sults of the potential distribution model are compared with
`the results obtained using a two-dimensional semiconduc-
`tor device simulator. These are in good agreement.
`
`11. MODES OF OPERATION
`The terms depletion-mode MOSFET and buried-chan-
`ne1 MOSFET have been used synonymously in the liter-
`ature. This, however, is not entirely valid and a clear dis-
`tinction between the two is necessary. The depletion-mode
`MOSFET refers to a device that under zero gate bias ex-
`hibits a significant channel conductance. The threshold
`voltage of such an n-channel device is less than zero volts
`and a gate voltage, less than the threshold voltage, is re-
`quired to reduce the channel conductance to zero. On the
`other hand, the buried-channel MOSFET refers to a de-
`vice structure and not a device designed to operate in a
`particular mode 1201. Strictly speaking, the buried-chan-
`
`SOU
`
`n
`
`b substrate
`
`vES
`(a)
`
`azide
`
`/substrate region
`
`gage
`
`‘ channel region
`
`(b)
`Fig. I . Buried-channel MOSFET structure. (a) Cross section of a typical
`buried-channel MOSFET device. The channel region is doped with N D
`donors and the substrate region is doped with NA acceptors. The channel-
`depth is increasing in the x direction with x = 0 at the oxide-semicon-
`ductor interface. (b) The doping density profile in the x direction for the
`buried-channel MOSFET. The device is subdivided into the following
`regions: 1) gate region: x < -x,,,, 2) oxide region: -x,,, < x < 0, 3)
`implanted channel region: 0 < x < x,, and 4) substrate region: x > x , .
`
`ne1 MOSFET can be fabricated to operate as a normally-
`on (depletion-type) device or a normally-off (enhance-
`ment-type) device, both of which are considered to be
`buried-channel MOSFET’s. In the analysis that follows,
`we direct our discussion to n-channel BC-MOSFET’s and
`we will use the term depletion mode only when it applies
`to a particular operating regime.
`Let us consider the buried-channel device shown in Fig.
`l(a). In practice the buried-channel device is formed by
`ion implanting a donor impurity in to a p-type substrate.
`The resulting doping profile in the channel can be char-
`acterized by a Gaussian function [ 11.
`Q.
`N ( x ) = J2.lra exp
`where Qj is the implant dose, U is the implant straggle,
`and Rp is the implant projected range. It has been shown
`by Karmalkar and Bhat [21] that the Gaussian implant
`profile can be represented by a correct equivalent box pro-
`file. This has also been substantiated by other authors
`1121, [13], [22]. The channel doping may be approxi-
`mated by a uniformly doped channel region of doping
`density [21]
`
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`

`672
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 36, NO. 4. APRIL 1989
`
`and that the depth of this uniformly doped buried layer is
`
`20 Jz
`x . = -
`m
`In our analysis, we have assumed an equivalent box pro-
`file given by Fig. l(b). The implanted channel region and
`the substrate region are assumed to be uniformly doped
`with N o donors and NA acceptors, respectively. A metal-
`lurgical junction exists at the abrupt interface between the
`channel region and the substrate at a distance xi from the
`oxide-semiconductor interface. A built-in voltage V,; is
`formed across the junction equal to
`
`(3)
`
`(4)
`
`The gate oxide that separates the gate material from the
`semiconductor has a thickness of xox. The device has a
`flat-band voltage denoted by V F B due to the presence of
`surface states and the work function difference between
`the gate and the substrate materials. The source and sub-
`strate voltages are denoted by Vs and VBS, respectively,
`while the gate bias and the drain bias are given by V , and
`V,. We will assume that the source is the reference volt-
`age and that both the source and substrate voltages are
`held at ground potential.
`With VG - VFB > V, + Vb,, the buried-channel MOS-
`FET is said to be operating in the surface channel mode
`(Fig. 2(a)). Under these conditions, electrons from the
`n +-type diffusion regions accumulate near the semicon-
`ductor surface across the channel. As the gate voltage V,
`becomes more positive, the channel conductance in-
`creases due to the injection of electrons into the surface
`region from the source and drain diffusion regions. Cur-
`rent flowing between the drain and the source will in-
`crease nonlinearly with an increase in VD.
`Operating the BC-MOSFET in the surface channel re-
`gime does not exploit the buried-channel’s higher mobil-
`ity. Since electrons will prefer to reside near the oxide-
`semiconductor interface, there is a marked decrease in
`electron mobility due to the presence of surface states.
`When V, is reduced such that V ( y ) + V,, > V, - VFB,
`where V ( y ) is the applied channel potential at some point
`y along the channel, a partial depletion region develops
`beneath the gate. Electron accumulation only occurs be-
`tween the source contact and a point y . The region de-
`pleted of electrons extends from the point y to the drain
`contact. As a result, the conducting channel in the prox-
`imity of the drain is removed from the surface and forms
`a buried channel.
`As VG is reduced further, the surface depletion region
`will extend over the entire channel length. This combined
`with the space-charge region at the metallurgical junction
`serves to form a true buried channel from the source to
`the drain (Fig. 2(b)). Further reduction in the gate voltage
`can lead to punchthrough of the opposing depletion re-
`gions. Under such circumstances the buried channel be-
`comes pinched off (Fig. 2(c)).
`
`When the gate voltage of the BC-MOSFET is reduced
`in such a way that the surface potential at the oxide-semi-
`conductor interface becomes sufficiently negative, a sig-
`nificant number of holes will be attracted to the surface.
`In a practical device, these holes originate from the pt
`channel stops beneath the field oxide. If a sufficiently neg-
`ative gate voltage is applied, the density of holes at the
`surface will exceed the doping density of the implanted
`channel region; the entire surface region of the BC-MOS-
`FET can become inverted (Fig. 2(d)).
`Clearly, both the punchthrough and the inversion con-
`ditions are implant doping density dependent. Both the
`dose and the implant depth will ultimately determine if a
`particular device has the ability to punchthrough before
`the surface becomes completely inverted. If the metal-
`lurgical junction is driven too deep into the substrate dur-
`ing implantation, the space-charge region of the n-side
`may be unable to assist in pinching off the channel before
`the surface region of the BC-MOSFET inverts. Alterna-
`tively, if the implant dose is made too large, the resulting
`space-charge width may again be insufficient to assist in
`pinchoff before a reduction in gate voltage leads to surface
`inversion. In both instances, the device cannot be turned
`off using a gate bias. These modes can be defined and
`clarified if the potential and electron distributions in the
`channel-depth direction are available.
`
`111. THE MODEL: POTENTIAL AND ELECTRON
`IN THE CHANNEL DEPTH DIRECTION
`DISTRIBUTION
`Recall that the BC-MOSFET can operate as a surface-
`channel MOSFET or a buried-channel MOSFET depend-
`ing upon the applied biasing. These modes of operation
`can be directly inferred from the potential distribution in
`the x direction within the channel of the device. The po-
`tential distribution can be determined by making use of
`the depletion approximation and solving Poisson’s equa-
`tion in one dimension [23]. In the following sections the
`potential distribution in the x direction is derived for con-
`ditions of depletion, inversion, pinchoff, and accumula-
`tion (surface-channel mode).
`
`A. Potential Distribution Under Depletion Conditions
`Under depletion conditions, the charge distribution in
`the x direction at a point y along the channel may be ap-
`proximated by Fig. 3(a). The applied biasing is such that
`VTf - VFB < VG -
`< V ( Y ) + Vbi
`( 5 )
`where V,, is the gate voltage required to invert the sur-
`face, VG is the gate potential, VFB is the flat-band voltage,
`V ( y ) is the applied channel potential, and Vb, is the built-
`in potential. The surface depletion region (0 < x < x , )
`and the space-charge layer (x, < x < x,) serve to form a
`channel through which mobile electrons flow in relation
`to an applied drain bias. The amount of mobile charge in
`the channel region (x, < x < x,) is exactly neutralized
`by the charge contribution due to the background doping
`density,
`
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`

`VAN DER TOL AND CHAMBERLAIN: POTENTIAL AND ELECTRON DISTRIBUTION MODEL
`
`673
`
`P
`
`N A
`
`Fig. 2 . Mode of operation for a BC-MOSFET. (a) Complete surface accumulation: (surface-channel mode): VG - VFR > Vr, + V,2,. (b) Complete
`surface depletion mode: VG - VFB < VS + V,,,. (c) Pinchoff. (d) Channel pinchoff with complete surface inversion,
`
`VG
`
`Potential ( V )
`300
`
`2 5 0
`
`2 0 0
`
`I 5 0
`
`1 0 0
`
`0 50
`
`I
`
`OW
`-1 00
`
`OW
`
`IW
`
`2 0 0
`x (am)
`(a)
`(b)
`Fig. 3. (a) The buried-channel MOSFET under depletion conditions. Charge distribution in the x direction at a pointy along the channel. The device is
`partitioned into the following regions: 1) oxide region: -x,,, < x < 0, 2 ) surface depletion region: 0 < x < x,, 3) channel region: x , < x < x,,, 4)
`n-side space-charge region: x , < x < x , , 5 ) p-side space-charge region: x , < x < x,,. and 6 ) bulk region: x,, < .r < OD. (b) The buried-channel
`MOSFET under depletion conditions. Potential distribution in the x direction at a pointy along the channel using (9) through (14). VG - VFB is set to
`0 V while V ( v ) is varied from 0 to 2 V. The oxide region is defined over the range -0.1 pm < x < 0; the implant region is 0 < II < 0.5 pm; and,
`the bulk region is defined as x > 0.5 pm.
`
`300
`
`4 W
`
`5 0 0
`
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`

`614
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 36, NO. 4, APRIL 1989
`
`In our analysis, the device cross section depicted in Fig.
`3(a) is partitioned into the following regions:
`1) oxide region: -xox < x < 0;
`2) surface depletion region: 0 < x < x,;
`3) channel region: x, < x < x,;
`4) n-side space-charge region: x,, < x < x,;
`5 ) p-side space-charge region: x, < x < x,,;
`6) bulk region: x,, < x < 00.
`In order to determine the potential distribution, we must
`solve Poisson's equation within each of the above six re-
`gions subject to the appropriate boundary conditions.
`& - - -e.
`dx2
`e,
`At the region boundaries the potential distribution must
`be continuous, giving the following conditions:
`
`(6)
`
`= VG - vFB
`
`-
`* ( x ) l A = o - - + ( x ) l . ~ 0 4
`+(4 Irq = + ( x ) l x = x ;
`+(4 Ix=<; = + ( x ) I.=,:
`lr=.,
`= + ( x ) l x = x ;
`
`$ ( x )
`
`=
`
`Applying Gauss's law at the interfaces between regions,
`we have the additional conditions
`EoxE(4 lx=o- =
`
`;
`r=r
`l
`% E ( x ) I r = r , = &)
`%E(X) Ix=., = € A X )
`
` lr=.,
`
`+ ( x ) = +d, - 9% ( x - x,) 9
`2%
`
`2
`
`x, < x I xi
`
`where
`
`(F),
`
`-
`
`The potential distribution given by (9) through (14) is
`shown in Fig. 3(b).
`The effective gate voltage VG - V F B , is held at 0 V
`while the channel potential V ( y ) is varied from 0 to 2 V .
`It is clear from Fig. 3(b) that this particular device is being
`operated in its depletion mode. Both the surface depletion
`width and the n-side space-charge layer increase with an
`increasing channel potential and further deplete the chan-
`nel of mobile electrons. Moreover, the position of the mo-
`bile electrons in the neutral channel region moves further
`away from the silicon-oxide interface with increasing ap-
`plied channel potential V ( y ) .
`
`B. Potential Distribution Under Inversion Conditions
`When the gate voltage of our BC-MOSFET is reduced
`in such a way that the surface potential at the oxide-semi-
`conductor interface becomes sufficiently negative, a sig-
`nificant number of holes will be attracted to the surface.
`In a practical device, these holes originate from the pf
`channel stops beneath the field oxide.
`If a sufficiently negative gate voltage is applied, the
`density of holes at the surface will exceed the doping den-
`sity of the implanted channel region. The surface poten-
`at which this occurs is given by
`tial
`+ ( x ) l , = o = $x = +,Il".
`
`(19)
`
`% E ( X )
`
`( 8 )
`
`= %E(X) Ix=.$
`Solving Poisson's equation in each of the six regions
`(see Appendix I), we can determine the potential distri-
`bution in the channel depth under conditions of depletion
`as
`+ ( x ) = V G - VFB - E ~ x ( x + X o x ) ,
`
`-& < x I 0
`(9)
`
`o < x 5 x ,
`
`
`
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`

`VAN DER TOL AND CHAMBERLAIN: POTENTIAL AND ELECTRON DISTRIBUTION MODEL
`
`675
`
`C. Surface Potential Pinning
`Once the surface inversion becomes strong, the surface
`potential will not change appreciably with a further de-
`crease in gate voltage; the surface potential becomes
`pinned. A consequence of this surface potential pinning
`is that the surface depletion region, shielded by the in-
`version layer of holes at the surface, also remains rela-
`tively constant and is given by
`
`If a buried channel exists between the surface depletion
`region and the n-side space-charge region at the onset of
`strong inversion, it becomes impossible to pinch off the
`device with the gate bias. Pinchoff can only be achieved
`by increasing the channel potential V ( y ) until the n-side
`space-charge region widens and touches the surface de-
`pletion region.
`The potential distribution in the channel depth direction
`under conditions of inversion is essentially a special case
`of depletion and can be determined by the following:
`$ ( X ) = VG - VFB - E o x ( X + X,,),
`-Xox < X I 0
`( 2 9 )
`
`x, c x I x;
`
`x; < x I xp
`
`where
`
`We can determine an expression for $inv by relating the
`hole concentration at the surface to the equilibrium hole
`concentration in the substrate. The hole concentration at
`the surface is given by
`
`where P = q / k T . In the bulkpp, = NA. At inversion, the
`surface hole concentration will become equal to the dop-
`ing density of the implant.
`
`ND.
`Ps
`Therefore, the surface potential at inversion is
`
`(21 1
`
`In order to determine that gate voltage at which inver-
`sion occurs, we need to determine a relationship between
`V, and the surface potential $ S . From (10) the surface
`potential can be expressed as
`
`where xs is given as
`
`(2).
`
`-
`
`For inversion, $S = $inv and (23) can be expressed as
`
`(F).
`
`-
`
`Solving for V,, the gate voltage at inversion Vn is
`1
`VT/ = vFB + $in" - - (2qcsND($eh -
`
`( 2 6 )
`
`c o x
`
`where
`
`cox = E,,
`
`X O X
`
`$ch = V ( y ) + Vbi.
`( 2 7 )
`Thus, when V , < V,,, the surface at a point y along the
`channel will become inverted. The charge distribution in
`the x direction at a point y along the channel under inver-
`sion conditions may be approximated by Fig. 4(a).
`
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`

`gate
`\
`
`, ozide
`
`676
`
`VG
`
`inversion
`layer of holes
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 36. NO. 4, APRIL 1989
`
`1
`
`O.lpm
`Gate oxide:
`0.5pm
`Implant depth:
`Implant doping: 1.0 x 10"'(cm-3)
`Substrate d0ping:l.O x lO"(~m-~)
`
`Potential ( V )
`
`Fig. 4. (a) The buried-channel MOSFET under inversion conditions. Charge distribution in the x direction at a pointy along the channel under inversion
`conditions. The device is partitioned into the following regions: 1) oxide region: -xox < x < 0, 2) surface depletion region including the inversion
`layer of holes: 0 < x < x$n7ax, 3) channel region: x,,~, < x < x,, 4) n-side space-charge region: x , < x < x , , 5) p-side space-charge region: x, < x
`< x,,. and 6) bulk region: xp < x < W . (b) The buried-channel MOSFET under inversion conditions. Potential distribution in the x direction at a
`is varied from - 1 to - 3 V. The
`point y along the channel under inversion conditions using (29) through (34). V ( y ) is set to 0 V while VG - V,,
`oxide region is defined over the range -0.1 pm < x < 0; the implant region is 0 < x < 0.5 pm; and, the bulk region is defined as x > 0.5 pm.
`
`(38 )
`
`The potential distribution given by (29) through to (34) is
`shown in Fig. 4(b).
`The applied channel potential V ( y ) is held at zero volts
`while the effective gate voltage VG - VFB is vaned from
`- 1 to -3 V . Under this variation, it is easy to see that
`the device is operating in an inversion mode. The poten-
`tial at the oxide-semiconductor interface remains pinned
`and the potential variation throughout the semicon-
`at
`ductor is independent of the gate voltage. The number of
`mobile electrons per unit area that are in the neutral chan-
`ne1 region remains unchanged for gate voltages below VT,.
`The only means by which the channel depth and number
`of electrons can be modified under inversions conditions,
`is by varying the applied channel potential V ( y ) .
`
`D. Potential Distribution Under
`Conditions
`Pinchoff in the BC-MOSFET is characterized by the ab-
`sence of mobile charges at a point y in the channel region.
`When the gate voltage is reduced such that the surface
`depletion region and n-side space-charge region merge,
`the channel becomes pinched off at some pointy along the
`channel. The charge distribution in the x direction under
`pinchoff conditions can be approximated by Fig. 5(a).
`Let us consider the BC-MOSFET at the onset of pinch-
`
`off. There are no mobile charges at a point y along the
`channel. The edge of the surface depletion region x, is
`coincident with the boundary of the n-side space charge
`layerx,. Thus, x, = x,. The device can be partitioned into
`the following regions:
`1) oxide region: -xox < x < 0;
`2) depleted channel region: 0 < x < xi;
`3) p-side space-charge region: xi < x < x,,;
`4) bulk region: x,, < x < M.
`The potential must be continuous at the region bounda-
`ries, giving
`
`~ ( x ) ( x = - x , , x = vG - VFB
`
`= V S S .
`
`(39)
`
`Ix=o- = +(x) lx=O+
`+b)Ixrr; = +(x)Ix=.:
`+(x) lx=xp
`From Gauss's law we can formulate the additional re-
`quirements
`E o x W lr=
`-Iox = o
`t s E ( n - ) l x = x p = 0
`%w)lr=.;
`= t,E(x)lx=r;
`
`toxE(x)
`
`= f,E(X)
`
`(40)
`
`Authorized licensed use limited to: Bucknell University. Downloaded on June 01,2020 at 17:24:58 UTC from IEEE Xplore. Restrictions apply.
`
`Micron Ex. 1016, p. 7
`Micron v. Godo Kaisha IP Bridge 1
`IPR2020-01008
`
`

`

`VAN DER TOL AND CHAMBERLAIN: POTENTIAL AND ELECTRON DISTRIBUTION MODEL
`
`677
`
`Potential ( V )
`
`s=o
`
`600
`
`500
`
`Implant depth:
`0.5pm
`Implant doping: 1.0 x lO"(~m-~)
`
`\
`
`gate \ /
`
`VG
`
`I
`
`Qc
`
`Fig. 5 . (a) The buried-channel MOSFET under pinchoff conditions. Charge distribution in the x direction at a point y along the channel under pinchoff
`conditions. The device is partitioned into the following regions: I ) oxide region: -x,,, < .r < 0, 2 ) depleted channel region: 0 < x < x ~ , 3 ) p-side
`space-charge region: x, < x < x,,, 4) bulk region: x,, < x < m. (b) The buried-channel MOSFET under pinchoff conditions. Potential distribution in
`the x direction at a point y along the channel under pinchoff conditions using (41) through (44). Vti - VAS is varied from 0 to 2 V . V ( r ) represents
`the applied channel potential required to completely deplete the channel at a point y along the channel. The oxide region is defined over the range
`-0.1 p n < x < 0; the implant region is 0 < x < 0.5 +m; and. the bulk region is defined as .x > 0.5 pn.
`
`Using the one-dimensional form for Poisson's equation
`and the depletion approximation, along with the above
`boundary conditions, we can determine the potential dis-
`tribution in the x direction at a point y along the channel
`where pinchoff occurs (see Appendix 11).
`-xox < x < 0
`
`= vBS>
`
`where
`
`O < X < X i
`
`
`
`(41)
`
`(42)
`
`xi < x < x,,
`
`(43)
`x p < x < 0 3
`(44 1
`
`XI, = xi + - ( X i - x,,).
`N D
`NA
`The potential distribution given by (41) through (44) is
`shown in Fig. 5(b).
`As the effective gate voltage VG - VFB is varied from
`0 to 2 V, the maximum channel potential increases. It is
`clear from Fig. 5(b) that the device is being operated un-
`der pinchoff conditions. The channel region is completely
`depleted of any mobile charges at a point y along the
`channel.
`
`E. Potential Distribution Under Accumulation
`Conditions
`A somewhat more complicated approach is required to
`determine the potential distribution in the channel depth
`direction under the conditions of electron accumulation.
`For the BC-MOSFET, accumulation occurs at the semi-
`conductor surface when
`v, - VFB > V ( y ) + v,,i.
`
`(49)
`
`Authorized licensed use limited to: Bucknell University. Downloaded on June 01,2020 at 17:24:58 UTC from IEEE Xplore. Restrictions apply.
`
`Micron Ex. 1016, p. 8
`Micron v. Godo Kaisha IP Bridge 1
`IPR2020-01008
`
`

`

`678
`
`gate
`\
`
`, ozide
`
`IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 36, NO. 4. APRIL 1989
`
`Potential ( V )
`
`Gate oxide:
`Implant depth:
`0.5pm
`Implant doping: 1 0 x 10'~(cm-~)
`
`'r ' 8.
`
`accumulated
`
`electrons
`
`I
`I
`
`channel
`
`(a)
`Fig. 6. (a) The buried-channel MOSFET under accumulation conditions. Charge distribution in the x direction at a point y along the channel under
`accumulation conditions. The device is partitioned into the following regions: 1) oxide region: -xc)x < x < 0, 2 ) surface accumulation region: 0 <
`x < x , , 3) neutral channel region: x , < x < x,, 4) n-side space-charge region: x,, < x < x , , 5 ) p-side space charge region: x , < x < x,~, and 6) bulk
`region: xp < x < W . (b) The buried-channel MOSFET under accumulation conditions. Potential distribution in the x direction at a pointy along the
`channel under accumulation conditions using (52) through (57). V, - VFB is held at 5 V while V ( y ) is varied from 0 to 3 V . The oxide region is
`defined over the range -0.1 p n < x < 0; the implant region is 0 < x < 0.5 p n , and the bulk region is defined as x > 0.5 pm.
`
`mann relation we get
`
`d211/ - p ( x ) - 4%
`
`dx2 -
`
`( 1 - e!3(+(r)-+dd),
`
`-xOx < x < 0
`( 5 2 )
`112
`( K - x ) ) + 1) + $,/!,
`
`qPND
`
`1
`P
`
`Tc determine the potential distribution in the channel
`dept direction a hybrid approach is followed. First, using
`the L*pletion approximation, the potential distribution in
`the regions outside the accumulation layer is determined.
`E ,
`6 ,
`Secondly, the potential distribution within the accumula-
`0 < x < x,.
`(51)
`tion region is derived using the Boltzmann relations.
`For the analysis the device cross-section shown in Fig. Using the above expression, the potential distribution
`6(a) is partitioned in the following manner:
`within the accumulation region can be determined (see
`1) oxide region: -xox < x < 0;
`Appendix 111).
`2) surface accumulation region: 0 < x < x,;
`Under conditions of accumulation, we obtain the fol-
`3 ) neutral channel region: x,? c: x < x,;
`lowing set of equation to describe the potential distribu-
`4) n-side space-charge region: x, < x < x i ;
`tion in the x direction.
`5 ) p-side space-charge region: xi < x < xp;
`$(x) = V G - V,q - E,,(x + xOx),
`6) bulk