The understanding of the drain-current fluctuation in a silicon-carbon source-drain
strained n-channel metal-oxide-semiconductor field-effect transistors
E. R. Hsieh and Steve S. Chung
Citation: Applied Physics Letters 104, 203503 (2014); doi: 10.1063/1.4879244 View online: http://dx.doi.org/10.1063/1.4879244
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/20?ver=pdfcov Published by the AIP Publishing
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The understanding of the drain-current fluctuation in a silicon-carbon
source-drain strained n-channel metal-oxide-semiconductor field-effect
transistors
E. R. Hsieh and Steve S. Chunga)
Department of Electronics Engineering and Institute of Electronics, National Chiao Tung University, Hsinchu, Taiwan
(Received 12 March 2014; accepted 5 May 2014; published online 22 May 2014)
In a certain class of strained n-channel metal-oxide-semiconductor field effect transistor (MOSFET) with silicon-carbon (Si:C) as a stressor in its source/drain, it serves as good candidate for high mobility and drain current device. However, its drain current (Id) fluctuation and the threshold voltage (Vth) fluctuation, have not been clarified. This paper reports a systematic method to analyze the sources of the above two different fluctuations represented by rIdand rVth, respectively. The dominant sources of the rIdand rVthhave been clarified on experimental n-channel Si:C source/drain FETs. The Id fluctuation relies on the dopant fluctuation or the mobility factors related to the conductions at various biases. Results show that the Idfluctuation at low field or low gate bias, i.e., near the threshold, is dominated by the RDF (Random Dopant Fluctuation) effect, while at high field, it is dominated by the channel conduction and scattering events which can be adequately described by the changes of mobility. The abnormal increase in the RDF effect in the Si:C was induced by the carbon out-diffusion from the drain into the channel. A dopant profiling technique has been developed to validate the out-diffusion effect.
VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4879244]
For the scaling of complementary metal-oxide semicon-ductor field effect transistor (MOSFET) to extend the Moore’s Law,1the enhancement of the channel mobility by various strain techniques has been the most successful one which has lasted for several generations.2–5 Among them, the process-induced strain has gained more popularity.6–12In p-channel MOSFET, the usage of silicon-germanium (SiGe) in the source/drain(S/D)6–9 has been in the production. In n-channel MOSFET, silicon-carbon (Si:C) in S/D with a tensile-strain effect becomes feasible as a counter part in the CMOS architecture.6,10–12On the other hand, in the further scaling of these devices, one of the major issues is the thresh-old voltage fluctuation caused by the random dopant fluctua-tion (RDF) because the electrical characteristics of the device become more sensitive to the number of dopants in the channel as we reduce the device area further.13Different configurations of dopant positions will affect the local threshold voltage, Vth, in the channel, and the electrical char-acteristics will not be uniform any more while the numbers of dopants are reduced to quite a few.14
To probe into the random dopant induced fluctuation, the most simplest way is to use the standard deviation of measurable Vth, such as the Pelgrom plot15 or Takeuchi plot,16by the using of rVth, the standard deviation of thresh-old voltage, versus the device area plot as a gauge of the RDF induced effect. Also, in more recent years, more atten-tions have been focused on how to reduce the Vthfluctuation through the process or transistor architecture improvement.17 However, the understanding of the strain effect on the drain-current (Id) fluctuation is more important and has been rather limited. Therefore, we are really in short of a
systematic approach to analyze the random dopant distribu-tion and to understand fully the correladistribu-tion between the ran-dom dopant and the fluctuations of the drain current (Id), especially for the strain-silicon devices.
In this paper, it is of interest to understand the origin which induces the Vthor Idfluctuation and to investigate the associated physical mechanisms. The Vthfluctuation depends on the random dopant fluctuation, while the Id fluctuation depends on the carrier conduction or the applying field, which will both be justified experimentally. The study has been demonstrated on the strained n-channel Si:C source/ drain devices.
Figures 1(a) and 1(b) are the schematics of a control and a strained Si:C source/drain n-channel MOSFET formed by the solid phase epitaxy implanted with Si:C18in the source/drain (S/D) region. The substitutional carbon concentrations with 1.1% in the Si:C were prepared at the condition of 950C and 1 ms. The dimensions of both devi-ces are 100 nm in width, 50 nm in length, and the gate oxide is oxynitride (SION), whose equivalent oxide thickness (EOT) is 2 nm. Based on the experimental observations of the Id Vgscharacteristics in Fig.1(c)for the control (con-ventional silicon S/D) and strained Si:C devices, these curves exhibit a horizontal shift and a vertical shift with the change of slopes. The horizontal shift is regarded as the Vth fluctuation (rVth), while the vertical shift comes from the changes of transconductance (gm). In the subthreshold region, the horizontal shift, rVth¼ 26 mV for Si:C and rVth¼ 18 mV for the control, reveals that the shift in rIdof strained devices is larger than that of control ones. This is believed to the difference in the Vth fluctuation of two devices. On the contrary, in the linear region as we increase the bias, Vgs, rId of strained devices (¼8%) is adversely
a)
0003-6951/2014/104(20)/203503/5/$30.00 104, 203503-1 VC2014 AIP Publishing LLC
smaller than that of control devices (¼13%), which cannot be adequately described by the rVthapparently. To under-stand their discrepancies, the current Idin the linear region can be represented by
Id¼ ðW=LÞlef fCoxðVgs VthÞVds; (1a)
¼ gmðVgs VthÞ; (1b)
where W and L are the width and length of devices, respec-tively, leffis the effective mobility, Coxis the gate-oxide ca-pacitance, and gmis defined as the derivative of Ids to Vgs, e.g., gm¼ @Ids=@Vgs¼ (W/L) leffCoxVds. Therefore, Id can be expressed in terms of gm and Vthas shown in Eq. (1b). Both factors are responsible for the horizontal and the verti-cal shift of the Idshown in Fig.1(c). Furthermore, the stand-ard deviation of normalized Id(rId) can be further
represented by rId ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a rVth 2 þ b rgð mÞ2; q (2) in which a is the dependent factor of rId and b is the
depend-ent factor of rgm. Figs.2(a)and2(b)are the scattering plots
of normalized Idversus Vth and gmmax, respectively, in the subthreshold regime at Vgs¼ 0.1 V, whose slopes represent a and b. In comparison, the plots show a stronger dependency on a in comparison to the b, i.e., the dominant fluctuation source of Idin the subthreshold region is Vth, corresponding
to the parallel shift in Fig. 1(c). Moreover, it is noted that rVth of strained devices (jaj ¼ 4.14) is larger than that of control one (jaj ¼ 2.335), as given in Fig. 2(a). This is believed to be the specific Si:C structure which induces larger rVth.
In order to understand why Si:C S/D devices raised a larger rVth, which results in a severe rIdin the subthreshold region, Fig. 3(a) shows Pelgrom plot, where the standard deviation of Vthagainst the inverse of square-root of device area, and its slope, Avt, can be considered as the degree of rVth. In other words, larger slope exhibits much larger RDF. It shows that rVthis getting worse when the strain is intro-duced in the drain/source with carbon. In lieu of the method-ology that authors demonstrated,19 a so-called discrete dopant profiling technique (DDP) can be used to examine why Si:C device has higher RDF induced Vth fluctuation. The main idea of DDP is described as below. If the discrete dopant is treated as a delta function located in the channel randomly, only those discrete dopants at the channel barrier peak will contribute to the Vthvariation, i.e.,
FIG. 1. The schematic of (a) a strained Si:C source/drain n-channel FET and (b) a conventional Si source/drain as a control sample, for comparison pur-pose. (c) The comparison of drain currents for two devices in (a) and (b). The curves on the left shows the comparison of rVth measured at
Vgs Vth¼ 0 V or Vgs¼ Vth, indicating a larger fluctuation of rVthfor the
Si:C device. Those curves on the right show the comparison at Vgs Vth¼ 1 V and Si:C device exhibits a reduced Idcurrent fluctuation.
FIG. 2. The scattering plots to show the dependency of (a) the normalized drain current on the threshold voltages (normalized), (b) the normalized drain current on the maximum transconductance (normalized), at low field with Vgs¼ 0.1 V.
203503-2 E. R. Hsieh and S. S. Chung Appl. Phys. Lett. 104, 203503 (2014)
rVth¼ ðq=CoxÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðWd 0 DniðxÞdðx xiÞdx ! LW; v u u t (3) ¼ ðq=CoxÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X DniðxÞ=LW q : (4)
Here, q is a constant value, 1.6 1019with unit of cou-lomb, Dni(x) is the varying amount of dopant density, ni, and d((x – xi)) is Dirac delta function, with unity of its integral at xibut zero elsewhere. Since the rVthis directly related to the summation of each discretized varying amount, Dni(xi), the variation of dopant density at a specified location, i.e., DNi(x), can be derived as
DNiðxÞ ¼ ðCoxrVth=qÞ 2
ðunit: number=cm3Þ: (5)
Experimentally, by increasing the source-to-drain voltage, Vsd, the channel barrier peak will be moved from the middle of the channel to the region near the drain side in Fig.3(b), from which the location of dopant density can be determined along the channel direction by calculating the barrier peak position. In other words, from the calculation of channel bar-rier peak position, we can calculate the variation of dopant density as a function of the channel position from the meas-ured rVth. Fig.3(c)shows the results of the dopant densities along the channel. There are high peaks of the dopant den-sities in the channel in the Si:C device. This is believed to be the carbons out-diffused into the channel from the Si:C S/D region, which induces the RDF effect. In other words, these
carbons in the channel do not occupy the substitutional sites but are considered to be the defects in the channel and cause the perturbation of the channel potential, resulting in a larger boron atom fluctuation or Vth variation. This is consistent what we measured in the Pelgrom plot, Fig. 3(a), that Si:C device shows a larger AVTvalue. Meanwhile, in Fig. 3(c), we also found that huge peaks close to the drain edge were observed. It is due to the fact that not only the carbons but also the impurities in the drain, e.g., arsenic (As), are dif-fused into the channel. Because the relative heavy atomic mass of arsenic, the distance of arsenic out-diffusion is very short and just around the corner of the drain edge. These high peaks are an indication of the arsenic induced fluctuation.
Furthermore, when we increase the gate bias above Vth, the vertical drain-current variation becomes more fluctuated than the horizontal one, as can be clearly seen from the right hand side curves in Fig. 1(c) where Si:C device exhibits a small rId, which is no longer dominated by Vth, and rather there would have another factor which creates the differen-ces. Figures4(a)and4(b)are the scattering plots of normal-ized Vth and gmmax versus Id at Vgs¼ 1 V, respectively. In
FIG. 3. (a) The Pelgrom plot of the tested samples with different channel widths but a fixed channel length. Note that the slope AVTis a measure of
the rVth. (b) The schematic to describe the profiling of channel dopant
den-sities. (c) The experimental results of dopant distributions for both the Si:C S/D device (blue color) and the control (green color). The high peaks in the channel are the carbon out-diffusion enhanced RDF.
FIG. 4. The scattering plots to show the dependency of (a) the normalized drain current on the threshold voltages (normalized), (b) the normalized drain current on the maximum transconductance (normalized), at high field with Vgs¼ 1 V.
contrast to Fig.2, it was found that gmmax exhibits stronger dependency on Id, but Vthshows weaker dependency. Thus, gmmax is more significant than Vthin terms of their contribu-tions to rIdat higher field. To justify the above observations, Fig.5(a)shows the comparisons of normalized standard devi-ations of gmmax for two devices. It was found that the Si:C exhibits a smaller rgmmax value such that its rIdis smaller. This is consistent with the comparison in Fig.4(b). Moreover, the curves of rgm in Fig. 5(a) show a three-segment trend, which corresponds to a three-segment trend of mobility char-acteristics as Vgsis varied in Fig.5(b). Therefore, the fluctua-tion source of gm can be considered to be mainly from the scattering of mobility. When the channel is in weak-inversion at low Vgs, impurity scattering is dominant, which determines the carrier scattering and exhibits a very higher rgm. While at Vgs just slightly higher than Vth, the channel impurity is shielded by the inversion-charge, the phonon scattering takes place and dominates rgm. Because the mobility is the highest in this region, rgm is the lowest with relatively low scattering events. When Vgs is raised much higher than Vth, mobility decreases while surface roughness scattering increases and rgm is increased simultaneously. In other words, the fluctua-tion source of gm is believed to be from phonon scattering or surface scattering of the mobility at high filed, i.e., Vgs> Vth.
In short, the addition of carbon in the Si:C introduced the strain and provides a current gain of 41% (Fig.1(c)) and a bet-ter rId in the device operating voltage ranges of inbet-terest, nevertheless the penalty is a higher Vthvariation in the sub-threshold region of Id. Extra efforts may be taken to have a good control of the incorporation of carbon in the source/drain through the process improvement.
In conclusion, an experimental methodology has been provided to analyze the fluctuation sources of Id systemi-cally. It was demonstrated on a specific class of strained devices with Si:C source/drain structure. The Idfluctuation can be decoupled into gmand Vthfluctuations depending on the device operating regions. The Vthdominates rIdat low field (subthreshold region), while gmdominates at high field (linear region). By introducing the carbon in the Si:C struc-ture, it has been able to suppress the carrier scattering and reduce the gm fluctuation dramatically, leading to a much lower Idfluctuation in comparison to the control devices at high field.This is good for a device by using the strain in the enhancement of mobility. However, it has adversely induced larger Vth fluctuation at low field, i.e., Vth served as the dominant fluctuation source of Idin the subthreshold region. This was attributed to the carbon-out-diffusion enhanced dopant fluctuation in the channel, which can be reasonably justified by the proposed dopant profiling technique. Although the methodology was demonstrated specifically on the strained devices, it can also be very useful and to be applied to any miniaturized MOSFETs to examine their Id and Vthfluctuations.
This work was support in part by the National Science Council, Taiwan, under Contract NSC100-2221-E009-016-MY3 and NCTU-UCB I-RiCE program, Ministry of Science and Technology, Taiwan, under Grant No. MOST 103-2911-I-009-302.
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