ANALYSIS AND MODELING OF DEPLETION-MODE MOS TRANSISTORS

Depletion mode MOSFETs are widely used in MOS—LSI/VLSI circuits as load elements. The main advantages offered by these devices are:


INTRODUCTION
MOSFETs are classified as depletion-type MOSFETs or enhancement-type MOS- FETs, depending on the operation principles.Burried channel MOSFETs are not new.These are obtained by introducing within the surface region impurities of opposite type to that of the substrate impurities.Thus, a conducting channel between the source and drain contacts exists in a direction parallel to the interface but below it.The width of the neutral channel region is restricted by a surface depletion region and a bulk depletion region.Thus, a junction of depletion regions is formed around the metallurgical junction, whose local width depends on the externally applied voltages.The operation of buried-channel depletion-mode MOS transistors is explained in Fig. 1.
Depletion/enhancement mode.Normal depletion mode and Depletion mode with complete/partial surface inversion., , Vsu "charge layer between channel and substrate FIGURE 1 Cross-section of a buried N-channel MOS transistor.

OPERATION OF BURIED CHANNEL DEPLETION MOSFETS
In order to describe the different operating modes of a buried-channel depletion- mode MOSFET, the exact profile is approximated by a one step profile with a junction depth "X" as shown in Fig. 2 such that, 1 / xj N(x) dx.

Complete Enhancement Mode
In this mode, the applied voltage relationship V6s -> VDS > 0 holds good.For large positive values of 'V6' in excess of the drain voltage 'VD', electrons accumulate near the semiconductor surface over the entire channel length between the source and drain electodes (Refer Fig. 3(a)).
The local width of the channel is only limited by the depletion region extending around the subtrate/channel p-n junction (XL <--Xj -< Xr).Due to the accumulation of the carriers on the surface, the channel conductance increases with larger positive values of V6.The current flowing between the source and drain increases Actual NDI (x) --/ \ \ non-linearly for larger positive values of VDS since the depletion region of the p-n junction becomes larger.A similar effect may result from modifying the subtrate polarization.One may expect a lower electron mobility in the surface region than in the buried channel region due to surface scattering.

Depletion/Enhancement MOde
In this mode, (VDs > VGS > 0) holds good.For smaller positive values of VGs compared to the previous mode, electron accumulation only occurs between the U. KUMAR source contact (y 0) and some specific point (Ya < L) along the channel.The rest of the channel is now depleted.The local width of the buried channel for y > y is thus restricted as shown in Fig. 3(b).

Normal Depletion Mode
This mode is valid for the condition (Vs VFB) < 0. Thus, for a negative value of Vs, (more exactly for negative values of (Vs VFB)), the surface depletion of the n-region extends over the entire channel length.The width of the buried channel decreases for increasing values of VDS and 'y' due to local potential 'V Y along the channel.

Depletion Mode with (Complete Surface Inversion
For further increase in negative potential 'Vs', a partial surface inversion may take place due to the formation of a hole inversion layer between the surfaces of source contact (y 0) and any point (Yi < L) along the channel length.The rest of the channel length Yi < Y < L is still surface depleted.This is shown in Fig. 3(c).
For still more negative values of 'V', the surface region of the n-surface becomes inverted over the entire channel length and the surface depletion region attains its maximum width.The width of buried channel is no longer a function of the gate potential 'V'.

CLASSIFICATION OF BURIED CHANNEL MOSFETS
The depletion-mode buried-channel MOSFETs in general can be placed in to the following two broad categories depending upon the thickness and doping level of the implanted channel.
Type-A; Complete pinch off devices, Type-B; Non-pinch off or deep depletion devices.

Type-A Devices
In these type of devices, the buried channel is shallow implanted and lightly doped.
The thickness of the channel (xj), (Refer Fig 3(a), (b),(c)) is less than the maximum depletion layer width (Xd max) for inversion at the interface.Assuming the one step profile of the channel, the maximum thickness of the channel for complete pinch off versus the doping for different substrate concentrations are shown in Fig. 4. The allowed pinch-off voltage for various channel doping and substrate bias for various channel thickness and also the limiting thickness of the channel for various substrate doping are shown in Fig. 5, 6. (The parameter calculations are done using depletion approximation and a step junction profile).These figures are quite informative for selection of required depth, channel implant, and pinch-off voltage for typical depletion-load characteristics.

Type-B Devices
These devices are deep implanted and heavily doped such that the thickness of the channel (x) is greater than the maximum depletion layer width (Xd max) (Fig. 3(a), (b), (c)) at the time of inversion at the inversion.This is because of the incomplete pinch off for which the inversion layer is formed at the Si/SiO2 interface.Inversion layer formed at the interface is floating in nature.Hence, there is very little work done in this aspect and this paper also does not deal with the inversion mode of operation of these devices.

MOSFETS
In this paper, an analysis has been made for deriving the I D V D characteristics for the two types of devices in the selected modes of their operations.To account for the various modes of operation, the basic equations are derived explicitly for the desired conditions.Another important consideration that has been taken into account is the field dependance of the surface mobility irrespective of channel length.The following assumptions are made in the process of analysing the operation of each device in the selected modes.

Assumptions
The conventional gradual channel approsimation is assumed.The doping profile of the channel region is assumed to be uniform (box-type).
The depletion approximation is used to calculate the density of electrons depleted from the channel region.All the derivations are based around the grounded source operation for p-channel devices and are equally applicable to n-channel devices with cor- responding proper signs.

ANALYSIS OF TYPE-A DEVICES
Fig. 7 shows the charge density and potential drop across the channel in the conduction region of such a device.Using gradual channel approximations we write for the charge density, which causes conduction in the channel at any point in the x-direction as Q(x) Qi + Qj (x) + QD (x) + Qs (x) (1) Where Qi Implanted charge q N A Xj, depletion charge on p-side of the junction.K (2 s q NE) 1/2 N E NA ND/(NA + ND) Q(x) surface charge in the Si/SiO2 interface which depends on the particular mode.
QD(X) Surface depletion charge qNA Xd.The drain current at any point along the y-direction in the channel where the potential V(y) is given by, d V(y) los + W Q (x) For this mode, the surface charge density Q(x) is given by, Substitution of this in equation ( 1) and (4) gives, Where lab bulk mobility, effective surface mobility, depend on gate bias.
The effect of gate field on la is not negligible and the effective mobility is obtained through an averaging procedure.Thus, U. KUMAR s (7) 1 + 0 (Vs-VFB 2 The value of lab can be taken to be fairly constant for a given implant.Using equations ( 6) and (7), the ID VD characteristics for this mode is plotted.

Type-A Device in Accumulation Mode
In this mode of operation, the channel is partially accumulated over a distance 'L 1' near the source and depleted over a distance 'L2' near the drain such that (L + L2) L, as shown in Fig. 8.The I D V D characteristic can therefore be modelled as a combination of two devices; one of channel length 'L' as in the accumulation mode and the other of channel length 'L2' in depletion mode.The surface/channel potential at the transition is given by V c VGS VFB (8) Assuming the charge densities for lengths La and L2 as Os(X) --Cox [VGs-VFB V(y)] and QD(X) q NA Xo, respectively, we write the equation for current in the two sections as, 2 Vc)3/2 (Vsub "+" qtB)3/2] 1 IDS" L labW QiVc K1 (Vsub + B "['-lsCoxW [(VGs VFB) Vc c2 ] (9) IDS" L 2 VDS J W [Qi + Qj (X) + Qo K2 {VGs VFB V(y) + Vo}1/2] dv procedure is fast enough to be coupled to an online Data Acquisition system as it does not require any change in circuit configuration during measurements.

EXTRACTION OF VFB VGS
From this equation, a plot of (Vos Vs) (Vs + B) 1/2 is obtained, the intercept of which on the (Vos Vs ) axis gives (Vra + Ca).Assuming some value for B (0.6V), VFB can be calculated.This method has the advantage that the identification of the transition points (T) is more precise than in Haken's method.
EXTRACTION OF NA, Xj

Qi
The value of implanted dose efe is obtained from Cefe N A Xj q F (V VFB ) controller (HP 2240 A).The process controller measures gds and Vsub by triggering a ramp generator.The gate voltage is changed by a programmable power supply (e.g., HP 6002 A) after every ramp.The output of the lock-in amplifier and that of the ramp appearing at the substrate are fed to the process controller.Once the measurement is complete on one device, the prober is automatically stepped up by the computer through the HP 2240 A.

CONCLUSION
A detailed analysis has been offered about the type, mode o operation, measure- ment set up and, parameter extraction principles for the buried-channel depletion- mode MOSFETs.Their use as the load transistor to replace the conventional enhancement-mode MOSFET in an inverter for obtaining improved performancewith added features like Jarger power handling ability, faster response, smaller die area, low power loss, etc., are noteworthy.
Basic equations for drain current have been deduced for every mode of operation.A simple averaging procedure for deriving surface mobility of carders from the considerations of gate field effect on long channel devices is incorporated.
Finally, a very compreh.ensivestudy has been made of various parameters to be extracted and a compact, simple, fast acting, and on-line extraction method has been proposed.

FIGURE 4 FIGURE 5 3 FIGURE 6
FIGURE 4 Plot of maximum allowed channel thickness vs. channel doping for complete Pinchoff for different substrate dopings.
c) Charge density and (d) Potential drop across the channel for BC MOSFET in depletion mode (a) and (b).
can be otherwise written as VD .wf o(x) d V(y)

FIGURE 9
FIGURE 9 Typical gds Vsub plots of buried channel MOSFET exhibiting various modes Vds 0 (plotted by the data acquisition system).
data  acquisition system for fast On-line parameter measurements.