As we mentioned in Chapter 1, with aggressive scaling of operation voltage, devices become increasingly more sensitive to the fluctuations in the device characteristics. In this Chapter, we investigate the issue associated with the multiple-gated TFTs devices with nanowire (NW) channels. These devices were provided from seniors of our group. The cross-sectional transmission electron microscopic (TEM) images of two types of such devices with triangular-shaped NW channel are shown in Fig. 4-1. Figure 4-1(a) shows the one with larger NW dimensions of around 40nm, 50nm and 80nm. This type is denoted as NW-A. The other type, denoted as NW-B, is with smaller NW dimensions of around 20nm, 30nm and 45nm. In the following fluctuation analysis, we measure around 25 to 30 devices for each split of device structures.
Figure 4-2 shows the transfer characteristics of 25 NW-A type devices with various channel length. Figure 4-3 shows the VTH distribution of these splits shown in Fig. 4-2. From the figures it is obviously seen that the range of VTH distribution
becomes wider as the channel length is shortened. The trend is consistent with the data reported in previous papers [26-32]. Figure 4-4 shows characteristics of the NW-B devices. Trends are similar to those observed in the NW-A devices (Fig. 4-2 and Fig. 4-3), albeit with tighter distribution, thanks to the smaller dimensions in the NW-B type.
To more deeply understand the experimental results, a simple VTH fluctuation model considering the random-dopant-fluctuation (RDF) is adopted in this study [42].
Figure 4-5 shows the vertical electric field, E, as a function of depth, x, in the channel region. If there is an extra charge sheet ΔQ placed within the channel depletion layer,
E(x) will be modified from the solid line to the dashed line so that the voltage drop between surface and the depletion region edge (x=WDEP) is constant. A change in the surface electric field will result in a VTH shift, expressed as
1 ) )(
(
DEP OX
TH W
x C
V = ΔQ −
Δ (4-1),
which is valid for both uniform doping and non-uniform doping.
Assuming that the extra charge sheet (ΔQ) volume is LWΔx, the standard deviation of ΔQ is expressed as
x LW x LW N
Q= q Δ
Δ ( ) (4-2)
where N(x) is the doping concentration, L and W are channel length and width, respectively. Standard deviation of VTH can be obtained by integrating the charge
sheet from x=0 to x= WDEP, expressed as
This expression results in
LW
where NEFF is a weighted average of N(x), defined as
∫
−From Eq. (4-4), we can obtain the relationship between standard deviation of VTH, channel length, and width,
LW
VTH 1
σ ∝ (4-6).
It should be noted that, the above model considers the dopant fluctuation effect in bulk CMOS devices. It is well known that threshold voltage is dependent on the channel dopant concentration since the channel dopants need to be depleted first in order to effectively shift the surface potential with the applied gate voltage. In the present case, no intentional doping was implemented in the poly-Si NW channels of the fabricated devices. However, similar situation happens to poly-Si NW channels.
Note that there are many defects presenting in the grain boundaries. These defects act as trap centers and a large portion of them are occupied by electrons before the channel potential is inverted. As a result the threshold voltage can be expressed as
[43]
2 Trap d
TH FB F
OX
qN W
V V
φ C
≅ + + (4-7),
where NTrap and Wd are trap states density and effective depletion width, respectively.
The equation above is valid for partially depleted body (Tsi>Wd). Figure 4-6 shows the schematics of VTH dependence of trap density at poly-Si grain boundaries. When the body is fully depleted, Wd is simply Tsi. For a multiple-gated configuration Wd is smaller than Tsi. For example, the double-gated configuration shown in Fig.4-6(c), Wd
is a half of Tsi.
As stated above, similar to the dopants in the channel of bulk devices, the defects presenting in the grain boundaries of the poly-Si films affect the threshold voltage and subthreshold swing of devices, so it is assumed that the defects also play a similar role as the dopants in affecting the device performance fluctuation. So in the following analysis the NEFF in Eqs. (4-4) and (4-5) is considered to be the effective defect concentration, NTrap, contained in the poly-Si NW layer.
Figure 4-7 shows the VTH deviation as a function of LW . The trend is very well described by the model mentioned above. In Fig. 4-7, it is obvious that VTH
deviation in thicker NW body (NW-A) is larger than that in thinner NW body (NW-B).
This is reasonable according to Eq. 4-4, since a larger depletion width leads to more dopant fluctuation. Figure 4-8 shows the VTH deviation after normalizing the effective
depletion width where the depletion width (Wd) is estimated to be half of maximum poly-Si NW thickness in Fig. 4-1, which is around 4nm-thick for NW-B and 12nm-thick for NW-A. After the treatment the two curves becomes very close to each other, confirming the suitability of the model for fluctuation analysis.
Since the grain size and grain number vary from cell to cell, such effective trap states at grain boundaries will lead to VTH-fluctuation. In order to study the impact drawn by the trap density, we have investigated and compared the characteristics of VTH-fluctuation before and after NH3-plasma treatment. The VTH distributions before and after NH3-plasma treatment are shown in Fig. 4-9. It can be seen that the mean value and standard deviation of VTH before NH3-plasma treatment is larger than those after treatment. This indicates that the NH3-plasma treatment can effectively passivate the trap states and result in a significantly reduced trap density. The effective trap states density per unit area, TTrap, in the poly-Si NW channel can be extracted from the subthreshold swing with the following equation.
C ) 1 C ( q ) (kT 10 ln SS
ox
+ dm
×
×
= , where Cdm = q×TTrap (4-7)
For the thicker poly-Si channel fabricated in this chapter, the SS for fresh device is around 350mV/dec (see Fig. 4-10), which is equivalent to TTrap=5.2×1012 cm-2. The SS after NH3-plasma treatment is about 150mV/dec, converting to TTrap=1.6×1012 cm-2. And the effective trap-state concentration (NTrap = TTrap /Wd) can be calculated.
The TTrap extracted from the SS and effective trap states concentration are summarized and listed in Table 4-1.
For effective trap states, it should follow a Gaussian distribution in the NW channel. The standard deviation of NT, σNT is equal to the square root of NT [27].
Thus, the standard deviation of VTH due to σNT is proportional to NT . Figure 4-11 shows VTH standard deviation as a function of NT for the NW-A devices, which confirms the inference. Another expression is shown in Fig. 4-12. In Fig. 4-11(a), the VTH standard deviation is expressed as a function of 1
LW . The curve for the devices before plasma treatment exhibits a much steeper slope, owing to a higher trap density. When the trap density is taken into account, as shown in Fig. 4-12(b) in
which the VTH standard deviation is expressed as a function of Ttrap
LW , the two lines tend to converge each other. The same phenomenon is also observed in NW-B devices, as shown in Fig. 4-13. Figure 4-14 shows the standard deviation of VTH as a function
of W Td trap
LW for the two types of NW devices. The two curves coincide each other, as predicted by Eq. (4-5).