Results and Discussion

In this study, the V is defined as the _T V_GS at which the average electron density of the cross-section at y  y_crit exceeds the channel doping concentration.

The y_crit stands for the position from the source of highest potential barrier for carrier flow. The y_crit is about L 2 for V_DS=0.05V, and about L 3 for V_DS=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  y_crit cross-section as the reference potential. Therefore, the



E 1 EC,min



at y  y_crit can stand for the q^QM 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 (L6T_ch) GeOI device is about 2.5



E 1 EC,min



the short-channel

(L2.4T_ch) 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 the

long-channel (L6T_ch) GeOI MOSFET is only ~1.3



E 1 EC,min



the short-channel ( L2.4T_ch ) 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 V_T^QM 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). _T

4.3.2 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 V_T^QM and thus the largest V as shown in Fig 4.3(a). _T

Fig 4.3(b) also shows the V_T^SCE of the three surface orientations. The V_T^SCE can be expressed as

^V_T^{SCE }

 

^m^QM



_long ^



^m^QM



_short



^



^V_T,long ^V_T,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

^V_T^{SCE }^{QM }



^m_long ^m_short

 

^{ V}_T,long ^V_T,short



^CL (4.3)

Because the (100) orientation GeOI devices possess the largest ^QM, they have the smallest V_T^SCE. That is, the improvement of the V roll-off is the most significant _T for the (100) orientation GeOI devices. Note that



mlongmshort



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 V_DS=1V. Its worse SCEs shows lower V and larger _T V roll-off than that with _T V_DS=0.05V. The V_T^QM in the long-channel (L6T_ch=30nm) GeOI devices are comparable between V_DS=1V and 0.05V as shown in Fig 4.4(a). Fig. 4.4(b) shows that for the short-channel (L2.4T_ch=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 T_BOX =20nm and 10nm. The long-channel (L6T_ch=30nm) device with T_BOX=20nm has comparable V_T^QM as compared with the T_BOX=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 T_BOX=10nm. This is because the T_BOX=20nm device shows both larger



E 1 EC,min



(thus ^QM) and m factor than the T_BOX =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 T_BOX =20nm than for T_BOX=10nm. It should be noted that the GeOI device with T_BOX =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 T_ch =5nm device with T_BOX =20nm shows comparable V roll-off as compared with the _T T_BOX=10nm device as shown in Fig 4.6.

In Fig 4.8, we show the difference between V_T^QM_long and V_T^QM_short for devices design with different buried oxide thicknesses and drain biases. The long-channel GeOI device is L6T_ch and the short-channel one is L2.4T_ch. 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 (T_ch,crit). Therefore, for GeOI devices with T >_ch T_ch,crit, the V _T roll-off is enhanced by QM effect, while for GeOI devices with T <_ch T_ch,crit, the V _T

show larger T_ch,crit than those with low drain bias and thin T_BOX .

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 T_ch,crit, the QM effect may increase the V roll-off. For GeOI _T devices with T <_ch T_ch,crit, the QM effect is found to suppress the V roll-off. We also _T

find that the value of T_ch,crit increases with drain bias and T_BOX . 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 m^QM comparisons between short- and long-channel devices with (a) T =10nm and (b) _ch T =5nm. _ch

Fig. 4.3 (a) The V , (b) the _T V roll-off (_T V_T^SCE), 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 T_ch=5nm GeOI devices at V_DS=0.05V and 1V.

Fig. 4.5 The GeOI device (T_ch=5nm, L=12nm) with V_DS=1V shows larger m and m^QM than that with V_DS=0.05V.

.

Fig. 4.6 (a) The V and (b) The _T V roll-off of the _T T_ch=5nm GeOI devices with T_BOX=20nm and 10nm.

Fig. 4.7 The GeOI device (T_ch=5nm, L=12nm) with T_BOX =20nm shows larger m and m^QM than that with T_BOX=10nm.

.

Fig 4.8 The (V_T^QM_{longchannel} V_T^QM_{shortchannel}) for T_BOX=20nm and 10nm GeOI devices at (a) V_DS=0.05V and (b) V_DS=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 (T_ch,crit) represents the crossover point between the two

trends. For GeOI devices with T >_ch T_ch,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 T_ch,crit. The value of T_ch,crit increases with the drain bias and T_BOX . For a given TBOX, the T_ch,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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簡 歷

姓名：謝欣原

生日：74 年 8 月 19 日 出生地：台灣省雲林縣

地址：高雄縣鳳山市誠義路 185 巷 1 號 學歷：

高雄市立高雄高級中學畢 (89 年 9 月~92 年 6 月)

國立交通大學電子工程學系畢 (93 年 9 月~97 年 6 月)

國立交通大學電子研究所碩士班畢 (97 年 9 月~99 年 8 月)

碩士論文題目：

超薄絕緣鍺金氧半場效電晶體在量子侷限下的 短通道效應模型與分析

Modeling and Investigation of Short-Channel Effects for Ultra-Thin-Body Germanium-On-Insulator MOSFETs Considering Quantum Confinement

在文檔中 超薄絕緣鍺金氧半場效電晶體在量子侷限下的短通道效應模型與分析 (頁 49-0)