Книги+1 / 2013 [Chandan_Kumar_Sarkar]_Technology_CAD
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Basic Semiconductor and Metal-Oxide-Semiconductor (MOS) Physics |
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Channel |
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inversion layer |
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Depeletion |
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Gate |
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Oxide |
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Poly |
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n+ Source |
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n+ Drain |
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p-substrate |
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Imaged by gate |
Imaged by the |
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source the drain |
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FIGURE 2.66
Charge sharing between the source/drain depletion regions and the channel depletion region.
depletion regions of the source and the drain are very close to each other. Through a charge sharing mechanism as in Figure 2.66, this phenomenon can be explained as in [48]. In case of a short-channel device, a considerable portion of the field lines emanating from the bulk charge terminate in the source and the drain regions instead of the gate. It is easier for the gate to deplete the amount of channel charge, lowering the threshold voltage of the device.
To sum up,
•Long-channel MOS transistor: The depletion is only due to the electric field created by the gate voltage.
•Small-geometry transistor: In addition to the previous contribution, the depletion charge near n+ regions contributes a significant amount of the depletion charge.
The expression of the threshold voltage in long-channel MOSFET thus overestimates the depletion charge supported by the gate voltage. Thus the amount of the gate voltage required to offset the depletion charge reduces. The estimated threshold voltage value from the threshold voltage expression of long-channel MOSFET will be larger than the actual value of the shortchannel MOSFET.
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The deeper depletion region is accompanied by larger surface potential, making the channel more attractive for electrons. Thus the device can conduct more current. This effect may be considered as the reduction of Vth, as the drain current is the function of (VGS – Vth). Increase in VDS and reduction of channel length will decrease the effective threshold voltage. In other words, the bulk depletion charge contributed by the gate is smaller than the expected charge, controlled solely by the gate, as a significant portion of the total depletion region charge under the gate is actually due to the source and the drain depletion junction. As the threshold voltage is a function of bulk depletion charge induced by the gate, the expression must be modified to account for this reduction in the bulk depletion charge. The threshold
voltage of the short-channel MOSFET can be expressed as Vth (SC) = Vth – VthO, where VthO is the change in threshold voltage from the long to the short-
channel MOSFET.
The depletion due to the source and the drain contacts encroaches substantially underneath the gate, decreasing the additional gate voltage required to create the strong inversion compared to the long-channel case. This is shown in Figure 2.67 where the source and the drain regions are assumed to be cylindrical with radius xj and the depletion depth of
extent xd.
The amount of charge imaging on the gate electrode is assumed by a trapezoidal approximation to be
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Q/B = −qNAxd |
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In the long-channel case,
QB = −qNAxdL
L
n+ xj
xd
L´
FIGURE 2.67
Schematic of the channel region of a short-channel MOSFET.
(2.143)
(2.144)
n+
Basic Semiconductor and Metal-Oxide-Semiconductor (MOS) Physics |
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The charge in the shaded regions image is on the gate and not on the contacts. Thus the reduced bulk charge is the source of the reduced threshold voltage from
Now as L/ → L, then QQ/BB
VT = 2ΦF + VFB − QB
COX
Q/
V/T = 2ΦF + VFB − B
COX
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QB − Q/B |
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QB |
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◊ 1 (i.e., the long-channel case).
2.33 Hot Electron Effects
(2.145)
(2.146)
(2.147)
The longitudinal electric field in the channel increases from the source to the drain ends. For abrupt source and drain junctions, the peak field is at the drain- to-channel junction, and its value depends on VDS and L. When carriers move in the electric fields that exceed the value of the onset velocity saturation, they continue to acquire kinetic energy from the electric field, but their velocity is randomized by the excessive collision such that their velocity along the electric field direction no longer increases but their random kinetic energy does. Depending on the statistics of scattering, a small fraction of the overall carrier population acquires a significant energy, and these are called hot carriers. The electric field heats the normal lattice electrons coming into the pinch-off region [49].
The carriers crossing from the inverted channel pinch-off point to the drain travel at their maximum saturated speed, and so gain their maximum kinetic energy in saturation. These carriers having high energy are called hot carriers. They travel from the source to the drain along the channel gaining kinetic energy at the expense of electrostatic potential energy in the pinchoff region, and they behave as a hot electron. Some of them obtain energy to create impact ionization with silicon lattice atoms, as a result of which new electrons and holes are created: this effect is referred to as weak avalanche. The new electrons created join the other channel electrons and move toward the drain. Some hot carriers in small numbers can acquire enough energy so as to surmount the Si-SiO2 interface barrier and thus move into the gate oxide as in Figure 2.68. Most of the injected carriers are collected by the gate electrode resulting in the gate current IG, reducing the input impedance. Because the barrier potential for this process is very high, the number of hot carriers injected into the gate will be much smaller compared to those
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barrier |
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tunneling |
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Direct |
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FIGURE 2.68
Three types of carrier injection into the gate causing hot carrier effects.
causing impact ionization. Therefore, the gate current will be smaller than the substrate current by a few orders of magnitude. It must be noted that carriers can also enter the gate oxide by tunneling. For direct tunneling, the oxide has to be very thin and the field is high. Even for the thicker oxide, the carrier with energy less than the energy barrier can tunnel through the barrier. This effect is called Fowler-Nordheim tunneling.
A small fraction of the high energy carriers create damage at the siliconoxide interface which manifests itself as an increase in the interface state density, and yet another fraction becomes trapped in the oxide. The traps in the oxide significantly affect reliability. The accumulation of such traps behaves as a fixed oxide charge, causing a change in the threshold voltage of the device, and this affects the gate’s control, giving rise to oxide breakdown.
A lightly doped drain (LDD) structure can reduce this hot-carrier effect. This is because, in such a case, part of the depletion region would be inside the drain, absorbing some of the potential that otherwise would exist in the pinch-off region, and lowering the maximal electric field.
2.34 Avalanche Breakdown and Parasitic Bipolar Action
An undesirable short-channel effect that occurs due to the high velocity of electrons in the presence of a large longitudinal electric field generates electron-hole pairs by impact ionization of the silicon atoms as in [50]. The presence of high longitudinal fields in a short-channel MOSFET can accelerate electrons that can ionize silicon atoms by impacting against them.
Basic Semiconductor and Metal-Oxide-Semiconductor (MOS) Physics |
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When the electric field in the channel is increased, due to high energetic hot electrons, avalanche breakdown occurs in the channel at the drain end. This increases the flow of current. The electrons are attracted by the drain, while the holes enter the substrate to form part of the parasitic substrate current.
There is also parasitic bipolar action taking place. The region between the source and the drain can act like the base of an n-p-n transistor, with the source playing the role of the emitter and the drain that of the collector. Holes generated by the avalanche breakdown move from the drain to the substrate underneath the inversion layer. The hole current forward biases the sourcebody p-n diode. Also if the holes coming from avalanche are collected by the source and the corresponding hole current creates a voltage drop in the substrate material of the order of 0.6V, the normally reverse biased substrate source p-n junction will conduct appreciably. The electrons are also injected as the minority carriers into the p-type substrate underneath the inversion layer from the forward biased junction, similar to the injection of electrons from the emitter to the base. They can obtain enough energy as they move toward the drain to create new e-h pairs. These electrons arrive at the drain and create further electron-hole pairs through the avalanche multiplication. The positive feedback between the avalanche breakdown and the parasitic bipolar action results in breakdown at lower drain voltage. The process is shown in Figure 2.69, and the steps are as follows:
Process 1: Hot carriers having sufficient energy to overcome the oxideSi barrier are injected from the channel to the gate oxide (process 1) causing the gate current to flow. Trapping of some of this charge can change Vth permanently.
Process 2: Avalanching can take place producing electron-hole pairs.
Process 3: The holes produced by avalanching are collected by the substrate contact causing parasitic substrate current Isub.
Process 4: Voltage drop due to Isub can cause the substrate-source junction to be forward biased.
Process 5: The forward biased substrate-source junction causes the minority electrons to be injected from the source into the substrate. Some of them are collected by the reverse biased drain and cause a parasitic bipolar action.
2.35 DIBL (Drain-Induced Barrier Lowering)
The population of channel carriers in the long channel devices is controlled by the gate voltage that creates the vertical electric field, whereas the horizontal field controls the current between the drain and the source. The current flow in the channel depends on creating and maintaining an inversion layer on
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FIGURE 2.69
Impact ionization and parasitic bipolar action in a short-channel MOSFET.
the surface. If the gate voltage is not sufficient to invert the surface (VG < Vth), the carriers (electrons) in the channel face a potential barrier that blocks the flow. Increasing the gate voltage reduces this potential barrier and eventually allows the flow of carriers under the influence of the channel electric field.
In long-channel devices, the horizontal and the vertical electric fields can be treated as having separate effects on the device characteristics. When the device is scaled down, the drain region moves closer to the source, and its electric field influences the whole channel. The drain-induced electric field also plays a role in attracting carriers to the channel without the control from the gate terminal. This effect is known as drain-induced barrier lowering (DIBL) because the drain lowers the potential barrier for the source carriers to form the channel. The threshold voltage lowers to feel the impact of this effect. DIBL attracts carriers with a loss in the gate control resulting in increased off-state leakage current.
2.36 Velocity Saturation in MOSFET
Velocity saturation due to the mobility reduction is important in the submicron devices. In the derivation of I-V relationship of the long-channel MOSFET, we explicitly assume that the mobility is a constant. However, this
Basic Semiconductor and Metal-Oxide-Semiconductor (MOS) Physics |
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assumption must be modified for two reasons. Two effects are combined in the transistors to account for this mobility; reduction due to the horizontal electric field, and the mobility reduction due to the vertical electric field.
The performance of short-channeled devices is also affected by the velocity saturation, which reduces the transconductance in the saturation mode. At low electric field, the electron drift velocity Vd in the channel varies linearly with the electric field intensity [51]. However, as the electric field increases above 104 V/cm, the drift velocity tends to increase more slowly, and approaches a
saturation value of Vd(sat) = 107 cm/s around the electric field = 105 v/cm at 300 K. For a MOS device, if VDS = 5 V and the channel length L = 1 µm, the aver-
age electric field is 5 * 104 V/cm, and thus velocity saturation is more likely to occur in the short-channel devices for length L < 1 µm because drift velocity saturates around electric field = 105 V/cm.
Due to very high longitudinal electric field (drain bias) in the pinch-off region in long-channel devices, the carrier velocity saturates. This is more prominent in the short-channel devices as the corresponding horizontal electric field is generally even larger than long-channel MOSFET. For an ideal long-channel I-V relationship, the current saturation occurs when the inversion charge density becomes zero at the drain terminal or when VDS = VDS(sat) = VGS – Vth.
However, velocity saturation can change this condition. Velocity saturation will yield an ID(sat) value smaller than that predicted in an ideal relation, and it will yield a smaller VDS (sat) value than predicted. In a short-channel MOSFET before attaining pinch off, carrier drift velocity saturates and thus the current saturation occurs at a low value of VDS. ID will be linear with VGS. The short-channel devices therefore experience an extended saturation region and tend to operate more often in saturation conditions than their long-channel counterparts, as shown in Figure 2.70.
IDS
In mA
Long channel
MOSFET
Short channel
MOSFET
0 |
VDSsat VGS – Vth |
FIGURE 2.70
Current saturates in short-channel devices for small VDS.
VDS
In volts
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2.37 Mobility Degradation
There are two reasons for mobility reduction in MOSFET:
1.Due to the vertical electric field
2.Due to the horizontal electric field
2.37.1 Vertical Electric Field Mobility Degradation
A vertical electric field exists in MOSFET due to the applied gate voltage, which creates the conduction channel. When carriers move within the channel under the effect of the horizontal electric field, they feel the effect of the gate-induced vertical electric field, pushing carriers toward the gate oxide. This causes the carriers to collide with the oxide-channel interface. The oxide-channel interface is rough and imperfect, and carriers thus lose mobility. This effect is called surface scattering. It reduces mobility. If there is a positive fixed oxide charge near the oxide-semiconductor interface, the mobility will be further reduced due to additional coulomb attraction.
The effective inversion charge mobility is a strong function of temperature because of lattice scattering. As temperature decreases, mobility increases. The mobility used in the MOSFET model is not the mobility of electrons in the silicon crystal, called bulk mobility. Rather, it is a surface mobility. The surface mobility is lower than the bulk mobility because of increased scattering of the electrons at the silicon-oxide interface, as shown in Figure 2.71. The surface mobility depends on how much the electrons interact with the interface and, therefore, on the vertical electric field that “pushes” the electrons against the interface. The higher the electric field, the lower is the surface mobility.
2.37.2 Surface Scattering
The mobility is reduced in a small dimension compared to a larger dimension due to an increase in the average vertical field in the inversion layer. As the channel length becomes smaller due to the lateral extension of the depletion layer into the channel region, the longitudinal electric field component Ey increases, and the surface mobility becomes field dependent. Because the carrier transport in a MOSFET is confined within the narrow inversion layer, and the surface scattering (the collisions suffered by the electrons that are accelerated toward the interface by Ey) causes reduction of the mobility, the electrons move with great difficulty parallel to the interface, so that the average surface mobility, even for small values of Ey, is about half as much as that of the bulk mobility. The mobility in the inversion layer is distinctly lower than in bulk material. This is due to the fact that the electron wave-function
Basic Semiconductor and Metal-Oxide-Semiconductor (MOS) Physics |
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+VGS
VDS
Vertical E-Field
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Inversion charge layer
Induced space charge
Inversion layer
Oxide
Drain
Space charge
Carrier Surface Scattering
FIGURE 2.71
Vertical electric field in a short-channel MOSFET and due to that, surface scattering is seen.
extends into the oxide and the carrier mobility is lowered due to the lower mobility in the oxide.
2.37.3 Horizontal Electric Field Mobility Degradation
The mobility degradation due to the lateral field Ey (drain voltage) plays a more significant effect on the device current equations than does the normal field Ex (gate voltage). This is because an increase in the lateral field eventually causes velocity saturation of the carriers. For a given normal field, the velocity v of a carrier is proportional to Ey, at low lateral fields, and the proportionality constant is the surface mobility µs. However, as Ey increases, the carrier velocity tends to saturate. Carriers in the short-channel devices reach the velocity saturation at lower values of VDS than for the long-channel
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devices. This effect is due to the channel length reduction that implies higher horizontal electric fields for equivalent drain to-source voltages than the long-channel MOSFETs. The horizontal electric field within the channel is due to the voltage applied to the drain terminal. Due to this horizontal electric field, horizontal mobility also decreases.
References
1.Bart Van Zeghbroeck, Principles of Semiconductor Devices, Department of ECE, University of Colorado, 2007.
2.H.J. Juretschke, Crystal Physics, W.A. Benjamin, New York, 1974.
3.J.F. Nye, Physical Properties of Crystals, Oxford University Press, New York, 1979.
4.C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1976.
5.R.H. Bube, Electrons in Solids, 3rd ed., Academic Press, New York, 1992.
6.B.G. Streetman, Solid State Electronic Devices, 4th ed., Prentice Hall, Upper Saddle River, NJ, 1995.
7.W.A. Harrison, Solid State Theory, Dover, New York, 1974.
8.W. VanRoosbroeck, Theory of flow of electrons and holes in germanium and other semiconductors, Bell Syst. Techn. J., vol. 29, pp. 560–607, 1950.
9.R. Entner, Modeling and Simulation of Negative Bias Temperature Instability, dissertation, Technical Universität Wien, Vienna, Austria, 2007.
10.M.S. Lundstrom, Fundamentals of Carrier Transport, 1st ed., Addison-Wesley, Reading, MA, 1990.
11.G. Baccarani, F. Odeh, A. Gnudi, and D. Ventura, Semiconductors Part II, A critical review of the fundamental semiconductor equations, The IMA Volumes in Mathematics and its Applications, vol. 59, pp. 19–32, Springer-Verlag, New York, 1994.
12.Dragica Vasilesca and Stephen M. Goodnick, Computational Electronics, 1st ed., Morgan and Claypool, San Rafael, CA, 2006.
13.E.M. Conwell, High Field Transport in Semiconductors, Academic Press, New York, 1967.
14.D.L. Rode, Low field transport in semiconductors, Semiconductors and Semimetals, vol. 10, pp. 1–90, Academic Press, New York, 1972.
15.C. Jacoboni and L. Reggiani, The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials, Rev. Mod. Phys., vol. 55, pp. 645–705, 1983.
16.M.V. Fischetti and S.E. Laux, Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects, Phys. Rev. B, vol. 38, pp. 9721–9745, 1988.
17.T. Kunikiyo et al., A Monte Carlo simulation of anisotropic electron transport in Silicon including full band structure and anisotropic impact-ionization model, J. Appl. Phys., vol. 75, pp. 297–312, 1994.
18.A. Pacelli and U. Ravaioli, Analysis of variance reduction schemes for ensemble Monte Carlo simulation of semiconductor devices, Solid S. Electronics, vol. 41, pp. 599–605, 1997.