Chapter 3 Quantum-Confinement Model for Ultra-Thin-Body MOSFETs with
3.4 Various Channel Materials and Surface Orientations
Fig 3.2 shows the calculated quantized n th eigenenergy (E ) in Ge-channel n devices with various T . We can find that as ch T =5nm, ch
E2 E1
0.35eV ismuch larger than kT 0.026eV . From equation (3.6), it can be expected that the first eigenenergy (E ) will be dominant in the determination of the electron density when 1 quantum-confinement effect is strong.
In Fig. 3.3, we show the square of the first eigenfunction (1 2) with T =5nm ch and 10nm. Fig 3.4 shows the electron density across half L for the UTB devices.
Although the square of the first eigenfunction with T =5nm is larger than the one ch with T =10nm, the electron density with ch T =5nm is smaller than the one with ch T =10nm as shown in Fig 3.4. From equation (3.6), the ch T =5nm ch UTB device is expected to have smaller electron density since it possess large
E 1 EC,min
as shown in Fig 3.2. Our quantum-mechanical model is fairly accurate compared with TCAD simulations.3.4 Various Channel Materials and Surface Orientations
Changing channel materials may improve device performance through the enhancement of carrier mobility. In this chapter, we will use Si, Ge, and In0.53Ga0.47As as channel materials to examine our quantum-mechanical model. In addition, since Si and Ge have three common surface orientations (100), (110), and (111), we will discuss the impact of surface orientation considering quantum mechanism.
To consider quantum mechanism, the first thing is that different channel material or surface orientation may have different corresponding effective mass (m*x). The effective mass will determine the degree of quantization. The channel with lighter effective mass will have stronger quantum-mechanical effects. For a given surface orientation, Si or Ge may have two distinct effective masses with corresponding degeneracy (d ) and effective density-of-state mass ( md,). Table 3.1 shows m*x, d , and md, of the three channel materials considering various surface orientations [24]-[26].
In this work, we use our parabolic channel potential model for different channel materials. Then based on our quantum-mechanical model, we can use the parameters in Table 3.1 to solve the Schrödinger equation and to calculate the electron density considering the impact of surface orientation.
Fig 3.5 shows the channel potentials of Si and In0.53Ga0.47As, respectively. It can be seen that our parabolic channel potential model is accurate. Fig. 3.6 shows the
E 1 EC,min
for Si with (100) and (110) surface orientations. Because theseorientations have two types of valley (two effective mass m*x ), there exists two
E 1 EC,min
. We can find that the difference between the two
E 1 EC,min
becomes large (>>kT 0.026eV) when T about 3nm. It means that the valley with smaller ch
E 1 EC,min
will determine the electron density in ultrathin T devices. Similarly, chFig 3.7 shows the
E E
for Ge with (110) and (111) surface orientations.When T about 5nm, the difference becomes obvious and hence we can treat the ch valley with smaller
E 1 EC,min
as the dominant type for calculating the electron density. From Fig 3.6 and Fig 3.7, we can find that in ultrathin T devices ch (Tch 3nm for Si, Tch 5nm for Ge), the type of valley with heavier effective mass will determine the electron density.
Table 3.2 collects the critical effective masses (m*x,crit) which dominate the electron density. The table can help us understand what critical effective mass may affect the degree of quantization and corresponding electrostatic characteristics in ultrathin T devices. Fig 3.8 shows the dominant ch
E 1 EC,min
of Si-channel with (100) orientation, Ge-channel with (100) orientation, and In0.53Ga0.47As-channel UTB devices, respectively. We can find that the In0.53Ga0.47As-channel UTB device has the largest
E 1 EC,min
and thus experiences the strongest quantum-mechanical effects.Fig. 3.9 shows the square of the first eigenfunction (12 ) for Si- and In0.53Ga0.47As-channel UTB devices. Note that Si-channel UTB device with (100) orientation has two types of 1 2. In Fig 3.10, we show the electron density for different channel materials in the UTB devices. It can be seen that for Si-channel UTB device with (100) orientation, the electron density of the dominant type of valley (2-fold valley) essentially determines the total electron density for the T =5nm ch device. This supports our use of the critical effective mass to determine the degree of quantization.
3.5 Summary
In this chapter, we present the UTB MOSFET model considering quantum mechanism based on our previous parabolic channel potential model. Using the model, we can obtain eigenenergy, eigenfuction, and quantum electron density. Besides, we have demonstrated that
E 1 EC,min
will be the dominant term to determine the electron density, especially for ultrathin T devices. chWe have also discussed the impacts of different channel materials and surface orientations considering quantum mechanism. We find that the channel material which experiences the strongest quantum-mechanical effects has the lightest effective mass (m*x). We have constructed the table (Table 3.2) of the critical effective masses (m*x,crit) which determine the degree of quantum confinement.
Fig. 3.1 The conduction band edge and corresponding eigenenergies for T =10nm devices with (a) ch L=60nm and (b) L=30nm.
Fig. 3.2 The calculated quantized n th eigenenergy (E ) for the devices with n various T . ch
Fig. 3.3 The square of the first eigenfunction (1 2) for T =5nm and 10nm in ch the Ge-channel UTB devices.
Fig. 3.4 The electron density for T =5nm and 10nm in the Ge-channel UTB ch devices.
Table 3.1 m*x, d , and md, of three channel materials considering surface
Fig. 3.5 The potential distribution of (a) Si-channel UTB device, and (b) In0.53Ga0.47As-channel UTB device for model and TCAD results.
Fig. 3.6 The
E 1 EC,min
of Si-channel UTB devices with (a) (100) and (b) (110) surface orientations with model and TCAD results.Fig. 3.7 The
E 1 EC,min
of Ge-channel UTB devices with (a) (110) and (b) (111) surface orientations with model and TCAD results.Table 3.2 The critical m*x,crit of three channel materials considering surface orientations when quantum-mechanical effect is strong in ultrathin T ch devices.
(100) (110) (111)
Si
* ,crit
mx
0.916m 0 0.316m 0 0.259m 0
Ge
* ,crit
mx
0.117m 0 0.218m 0 1.57m 0
In0.53Ga0.47As
* ,crit
mx
0.041m 0
Fig. 3.8 The dominant
E 1 EC,min
for UTB devices with various channelFig. 3.9 The square of the first eigenfunction (1 2) for (a) Si-channel with (100) surface orientation and (b) In0.53Ga0.47As-channel UTB devices.
Fig. 3.10 The electron density of Si-channel with (100) surface orientation and In0.53Ga0.47As-channel UTB devices.
Chapter 4
Impact of Quantum-Mechanical Effects on Threshold-Voltage Roll-Off
in UTB GeOI MOSFETs
4.1 Introduction
Germanium as a channel material has been proposed to enable mobility scaling.
However, its higher permittivity makes it very susceptible to Short Channel Effects (SCEs). To improve the electrostatic integrity, ultra-thin-Body (UTB) Germanium-On-Insulator (GeOI) MOSFET has been proposed as a promising device architecture and shows better control of SCEs than the bulk counterpart [27]-[28]. By scaling down the channel thickness, UTB GeOI MOSFETs can show comparable subthreshold swing as compared with the UTB SOI counterparts [29]. As the channel thickness scales down, the quantum-mechanical effect becomes more significant and its impact on the threshold-voltage (V ) roll-off in UTB SOI MOSFETs has been T reported in [30]. However, the impact of quantum-mechanical effect on the V T roll-off in UTB GeOI MOSFETs has rarely been examined.
In this chapter, we investigate the impact of quantum-mechanical effect on the V roll-off characteristics for UTB GeOI MOSFETs by the developed model in T
Chapter 3 and numerical solution of coupled Poisson and Schrödinger equations.
4.2 UTB GeOI Devices and Simulation
The schematic cross section of UTB structure was shown in Fig 2.1. In this study, the gate oxide thickness (T ) is 1nm, the channel thickness (ox T ) ranges from 4nm to ch 10nm, the channel length (L) ranges from 2.4 to 10 times the T (proportional to ch T ), and the buried oxide thickness (ch TBOX) ranges from 10nm to 20nm. The channel doping concentration ( N ) is 1x10A 15cm-3. Besides, we use the heavily-doped (1x1020cm-3) silicon substrate and treat it as ground plane.
For UTB devices, our TCAD simulations self-consistently solves the Poisson’s equation (for channel potential) and 1-D Schrödinger equation (for eigenenergy and eigenfunction) at each slice perpendicular to the interface between oxide and channel.
The process of the numerical calculations doesn’t have approximations. Therefore, the TCAD simulations can be exactly to assess quantum-mechanical effects for UTB GeOI devices.
In this study, the V is defined as the T VGS at which the average electron density of the cross-section at y ycrit exceeds the channel doping concentration.
The ycrit stands for the position from the source of highest potential barrier for carrier flow. The ycrit is about L 2 for VDS=0.05V, and about L 3 for VDS=1V.
4.3 Results and Discussion
4.3.1 Channel Thickness
Fig. 4.1(a) and Fig 4.1(b) show the V roll-off of Ge- and Si-channel UTB T devices with quantum-mechanical (QM) and classical (CL) considerations for T =10nm and 5nm, respectively. In Fig 4.1(a), both the Ge- and Si-channel devices ch
with QM consideration show larger V roll-off than that with the CL one. However, T in Fig 4.1(b), the Si-channel UTB MOSFET with QM consideration shows comparable V roll-off as compared with that using the CL one. The Ge-channel T UTB MOSFET with QM consideration even shows smaller V roll-off than that T with the CL one.
In [30], Y. Omura reported that the V roll-off would be increased by QM effect T in UTB SOI MOSFETs. Their study used the simulator with density-gradient model (DGM) [31]-[32]. In our study, we can see the same trend of increased V roll-off in T UTB SOI MOSFET. However, the V roll-off is suppressed by QM effect for UTB T GeOI MOSFET with T =5nm. ch
Fig 4.1 can be explained by [33]-[34]
QM QM
T m
V
(4.1) , where m is the subthreshold slope factor, QM is the surface potential shift, and
QM
VT
is the V shift due to QM effects. In this work, we choose the peak of the T channel potential at y ycrit cross-section as the reference potential. Therefore, the
E 1 EC,min
at y ycrit can stand for the qQM when considering QM effects.
Fig 4.2 shows the
E 1 EC,min
for GeOI devices with T =10nm and 5nm. Fig ch 4.2(a) shows that for GeOI devices with T =10nm, the ch
E 1 EC,min
of the long-channel (L6Tch) GeOI device is about 2.5
E 1 EC,min
the short-channel(L2.4Tch) one. In other words, the short-channel GeOI device with T =10nm ch shows much smaller
E 1 EC,min
and thus smaller QM as compared with the long-channel one. This leads to larger V roll-off observed in Fig 4.1(a). On the T other hand, Fig 4.2(b) shows that for the T =5nm GeOI devices, the ch QM of thelong-channel (L6Tch) GeOI MOSFET is only ~1.3
E 1 EC,min
the short-channel ( L2.4Tch ) one. The m factor of the T =5nm short-channel GeOI device, ch however, is about 2.5 the long-channel one. Therefore, for the T =5nm GeOI ch devices, the VTQM of the short-channel device is larger than that of the long-channel one which results in the suppression of V roll-off observed in Fig 4.1(b). T4.3.2 Surface Orientation
Fig 4.3 shows the V roll-off of three surface orientations in UTB GeOI T MOSFET for T =4nm with QM and CL considerations. It can be seen that the ch V T of the three orientations are (100)>(110)>(111). In Chapter 3, we have pointed out that the UTB GeOI device with T =4nm has a critical effective mass (ch m*x,crit). From Table 3.2, we can find that the critical effective masses of (100), (110), and (111) are 0.117m , 0.2180 m , and 1.570 m , respectively. This means that the degree of QM 0 effect is (100)>(110)>(111). It explains why the surface potential shifts (QM ) shown in Fig 4.3(b) are (100)>(110>(111). In other word, the (100) orientation GeOI devices have the largest VTQM and thus the largest V as shown in Fig 4.3(a). T
Fig 4.3(b) also shows the VTSCE of the three surface orientations. The VTSCE can be expressed as
VTSCE
mQM
long
mQM
short
VT,long VT,short
CL (4.2)Since the QM shown in Fig 4.3(b) is almost the same for long- and short-channel GeOI devices, the equation (4.2) can be approximated as
VTSCE QM
mlong mshort
VT,long VT,short
CL (4.3)Because the (100) orientation GeOI devices possess the largest QM, they have the smallest VTSCE. That is, the improvement of the V roll-off is the most significant T for the (100) orientation GeOI devices. Note that
mlongmshort
is a negative number due to short channel effects (SCEs).4.3.3 Drain Bias and Buried Oxide Thickness
Fig 4.4(a) illustrates the V roll-off of the GeOI devices at T VDS=1V. Its worse SCEs shows lower V and larger T V roll-off than that with T VDS=0.05V. The VTQM in the long-channel (L6Tch=30nm) GeOI devices are comparable between VDS=1V and 0.05V as shown in Fig 4.4(a). Fig. 4.4(b) shows that for the short-channel (L2.4Tch=12nm) devices, high-drain-bias GeOI device shows larger improvement of roll-off (~0.3V) than the low-drain-bias one (~0.1V). This is because the high-drain-bias device shows both larger
E 1 EC,min
(thus QM) and m factor than the low-drain-bias device as shown in Fig 4.5. For T =5nm GeOI devices, the ch suppression of the V roll-off caused by the QM effect is more significant at high T drain bias than at low drain bias.Fig 4.6 shows the V roll-off of the T T =5nm GeOI devices with QM and CL ch considerations for TBOX =20nm and 10nm. The long-channel (L6Tch=30nm) device with TBOX=20nm has comparable VTQM as compared with the TBOX=10nm device as shown in Fig 4.6(a). Fig 4.6(b) shows that at L=12nm, the GeOI device with TBOX=20nm shows larger improvement of roll-off than that with TBOX=10nm. This is because the TBOX=20nm device shows both larger
E 1 EC,min
(thus QM) and m factor than the TBOX =10nm device as shown in Fig 4.7. In other words, for the T =5nm GeOI devices, the suppression of the ch V roll-off caused by the QM effect T is more significant for TBOX =20nm than for TBOX=10nm. It should be noted that the GeOI device with TBOX =20nm shows larger V roll-off with CL consideration due T to the drain field penetration through the buried oxide, which may be compensated by the more significant suppression of the V roll-off due to QM effects. Therefore, T when considering QM effect, the Tch =5nm device with TBOX =20nm shows comparable V roll-off as compared with the T TBOX=10nm device as shown in Fig 4.6.In Fig 4.8, we show the difference between VTQMlong and VTQMshort for devices design with different buried oxide thicknesses and drain biases. The long-channel GeOI device is L6Tch and the short-channel one is L2.4Tch. Then we make the intersections of the line
short channel
QM channel T
long QM
T V
V
=0 and the
curves in Fig 4.8 and define the T locations of these intersections as the critical ch channel thicknesses (Tch,crit). Therefore, for GeOI devices with T >ch Tch,crit, the V T roll-off is enhanced by QM effect, while for GeOI devices with T <ch Tch,crit, the V T
show larger Tch,crit than those with low drain bias and thin TBOX .
4.4 Summary
We have investigated the impact of QM effects on the V roll-off in UTB GeOI T MOSFETs. It shows two opposite trends for different ranges of T . For GeOI ch devices with T >ch Tch,crit, the QM effect may increase the V roll-off. For GeOI T devices with T <ch Tch,crit, the QM effect is found to suppress the V roll-off. We also T
find that the value of Tch,crit increases with drain bias and TBOX . This quantum-mechanical impact on short channel V roll-off should be considered when T designing/evaluating UTB GeOI devices.
Fig. 4.1 The V roll-off of Ge- and Si-channel UTB devices with (a) T T =10nm ch and (b) T =5nm.
Fig. 4.2
E 1 EC,min
and mQM comparisons between short- and long-channel devices with (a) T =10nm and (b) ch T =5nm. chFig. 4.3 (a) The V , (b) the T V roll-off (T VTSCE), and the QM of (100), (110), and (111) surface orientations for T =4nm GeOI devices..
Fig. 4.4 (a) The V and (b) The T V roll-off of the T Tch=5nm GeOI devices at VDS=0.05V and 1V.
Fig. 4.5 The GeOI device (Tch=5nm, L=12nm) with VDS=1V shows larger m and mQM than that with VDS=0.05V.
.
Fig. 4.6 (a) The V and (b) The T V roll-off of the T Tch=5nm GeOI devices with TBOX=20nm and 10nm.
Fig. 4.7 The GeOI device (Tch=5nm, L=12nm) with TBOX =20nm shows larger m and mQM than that with TBOX=10nm.
.
Fig 4.8 The (VTQMlongchannel VTQMshortchannel) for TBOX=20nm and 10nm GeOI devices at (a) VDS=0.05V and (b) VDS=1V.
Chapter 5 Conclusions
We have theoretically investigated the impact of quantum-confinement effects on V roll-off for UTB GeOI MOSFETs with thin BOX under subthreshold region. T To determine V of UTB devices, we derived a quantum-confinement model base on T a parabolic form of channel potential. This parabolic channel potential is simplified from the series solution of Poisson’s equation and has the correct dependence of channel length. Therefore, this quantum-confinement model can accurately reveal the subthreshold characteristics of UTB devices when considering short channel effects (SCEs) such as V roll-off. T
By using the quantum-confinement model and TCAD simulations which self-consistently solve the Poisson’s equation and Schrödinger equation, we find that in UTB GeOI MOSFETs, there exists two trends of V roll-off for different ranges T of T , either increased or suppressed ch V roll-off caused by quantum confinement. T The critical channel thickness (Tch,crit) represents the crossover point between the two
trends. For GeOI devices with T >ch Tch,crit, the QM effect increases the V roll-off. T On the other hand, the QM effect is found to suppress the V roll-off when T T <ch Tch,crit. The value of Tch,crit increases with the drain bias and TBOX . For a given TBOX, the Tch,crit for Ge-channel devices is larger than that for Si-channel ones. The impact of quantum-confinement on the V roll-off must be considered when T
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