IEEE ELECTRON DEVICE LETTERS, VOL. 17, NO. 3, MARCH 1996 85
A Novel Method
for
Extracting
the
Metallurgical
Channel Length of MOSFET's Using a Single Device
Hsin-Hsien Li,
Student Member, IEEE,Yu-Lin
Chu,
Student Member, IEEE,and Ching-Yuan Wu,
Member, IEEEAbstract-A new charge-pumping method with dc sourcddrain
biases and specified gate waveforms is proposed to extract the metallurgical channel length of MOSFET's by using a single device. Using two charge-pumping currents of a single nMOSFET measured under different VGL (VGH for pMOSFET's), the metallurgical channel length can be easily extracted with an accuracy of 0.02 pm. It is shown that the proposed novel method is self-consistent with the results obtained by the charge-pumping current measured from multidevices under different gate pulse waveforms and bias conditions.
I. INTRODUCTION
HE metallurgical channel length (L,,t) is an important
T
physical parameter for MOSFET characterization and modeling and is usually used to monitor lithography, etching and diffusion processes. Many efforts [ 11-[5] have been made to determine the metallurgical channel length, based on the turn-on I-V characteristics of MOSFET's operated at low drain bias. The charge-pumping measurement technique is a reliable tool for MOS interface characterization [6]-[lo], and the related experimental and analytical procedures are simple and fast. Recently, the charge-pumping current measurement has been applied to extract the metallurgical channel length ofMOSFET's with very high accuracy (0.01 pm resolution) [9].
In this paper, a novel charge-pumping method using only one MOSFET device is proposed to determine the metallurgical channel length. It is shown that the accuracy of the new method is slightly worse than the multidevice method [9], however, the new method is simple and is feasible to deal with a large number of samples.
11. MODEL DERIVATIONS AND EXTRACTION METHOD Using the effective area approach [9] and assuming the constant interface-trap density along the channel direction, the charge-pumping current can be expressed as
where L,, is the length of the effective area, W is the channel width, and Qsat is the recombined charges per cycle and can Manuscript received September I , 1995; revised November 3, 1995. This work was supported by the National Science Council, Taiwan, ROC, under Contract NSCSS-2215-E009-041.
The authors are with the Advanced Semiconductor Device Research Labo- ratory and Institute of Electronics, National Chiao-Tung University, Hsin-Chu, Taiwan, ROC.
Publisher Item Identifier S 0741-3106(96)01958-1.
be approximately expressed as [7] Ez Qsat N q L l N z t ( E ) dE = q Z ( @ 2 - El) (2) with (3) k T 4
EI
= E, f - In (cppo'%hnztemh) and (4) kT QEa
= E, - - In (onovthntteme)where
E,
is the intrinsic Fermi energy, k is the Boltzmann constant, T is the absolute temperature, aPo (ono) is the hole (electron) capture-cross-section, vth is the thermal velocity,n, is the intrinsic carrier concentration, and t e m h
(terne)
is the nonsteady-state hole (electron) emission time, which is a function of rising/falling slopes of the gate-pulses(SRISF)
and substrate bias (VSUB).
The setup and applied waveform are shown in Fig. 1. If we measure the charge-pumping current with the waveforms of the same S E , S,, and V S ~ B but different VGL or TL,
we can derive the charge-pumping currents related to the same Qsat but different Lcp. Measuring the charge-pumping currents for two applied low gate voltages
V G L ~
and V G L ~ , the metallurgical channel length can be derived from the following equation:A& f - %(VGLI) - y(vG'L2) ( 5 ) where A ( I c p / f ) is the difference of charge-pumping current per cycle; z1 (Q) is at the edge of the effective area near the
source under V G L ~ ( V G L ~ ) , as shown in Fig. 1 (x = 0 is located at the source junction). Note that xl(x2) is located at the position where the surface hole concentration is p c under
V G L ~ ( V G L ~ ) ,
and p , is the critical surface hole concentration related to half-maximum of I c p / f versus VGL curves. The extraction method for p , had been mentioned in [9] and p , is 1.65 x l O I 5 ~ c m - ~ whenTL
= 1 ,us. From [lo], we know that the product of p L andTL
is a constant, therefore the edges of the effective area with respect to any VGL, V&B, and T tcan be obtained by calculating the surface hole concentration of a MOSFET operated with VGL and V S ~ B using a 2-D numerical simulator.
Comparing with the multidevice method [9], the metallur- gical channel length can be extracted from only two charge- pumping currents of a single device and can also be applied to
-
~ ( X I
-
5 2 ) Lmet - 2x1 Lmet - 2x286 E E E ELECTRON DEVICE LETTERS, VOL. 17, NO. 3, MARCH 1996 I I P-substrate
I
A Current Meter0
Fig. 1. The experimental setup and the applied gate pulse waveform for charge-pumping current measurement and a schematic device cross-section showing the definition of Lmet, L m a s k , 2 1 . and z2.
interface-trap uniformity analysis. However, there are several points to be noted while using (5). 1) The VGL, VSUS, and
TL used for charge-pumping current measurement should be chosen to keep x1 and xz located in the channel region with constant interface-trap density, because the interface-trap density i s larger near the sourceldrain region and decreases to
a constant value in the center of the channel. In general, I G ~ and 2 2 should be kept away from the junction more than 0.02 pm, otherwise, the Lmet will be underestimated. 2)
A ( I c p / f )
in ( 5 )should be derived from two charge-pumping currents measured under the same S R ,
S,,
and V&B, otherwise, further error will be induced. The error can be approximated aswhere A E is the difference of the effective interface-trap range in the bandgap for different S R ,
SF,
and V ~ T J B . IfSR,
S F ,and VSUB are unchanged, A E approaches zero and the error can be ignored. 3 ) To reduce the error, x1 and 2 2 should not be too close. For example, the charge-pumping current error induced by measurement is I,,,,,, then the induced error in the extracted Lmet using (5) can be expressed as
It is clear that ($1 - 22) becomes small, L,,,,, will become serious. Because the interface-trap density of an unstressed device is low (around 1 x lo1' cm-'
.
eV-'), so the measured charge-pumping current is small, andI,,,,,
becomes the major error source of this method.111. EXPERIMENTAL RESULTS
The experimental transistor used to demonstrate the novel method proposed in this paper is an n-channel MOSFET with
0
-0.02 0.00 0.02 0.04 0.06 0.08
Distance to source junction (urn)
I &U,= -0.2V
-
-2.4V VGL,. %LZ = 0.8V 0 T, = 500 nsec ?x TL = 1000 nsec a T, = 2000 nsec Source junction L x 0 ' I -0.02 0.00 0.02 0.04 0.06 0.08Distance to source junction (urn)
Fig. 2. The metallurgical channel length derived from (a) different
(VGL - V&TS), and (b) different T L . Note that the data point along the z-direction is calculated by defining z = (z1
+
s z ) / 2 .the mask channel length ( L m a s k ) of 0.8 pm and the channel width of 100 pm. The I c p ( V ~ ~ , V S U B ) / ~ data are measured with VGL varying from -3.8
+
VSUB to -1.2+
VSUB V andVSUB varying from -0.2 to -2.4 V. TL varies from 0.5 to 2
ps and both SR(O) and s ~ ( 0 ) are 2 x 106 VIS. As shown in Fig. 2(a), the saturation value in the channel is about OS8 pm and
A L = 0.22 pm ( A L = L m a s k - Lmet) is equal to the value derived from the multidevice method [5]. As mentioned in the previous section, when 2 1 and x2 are near the junction, the interface-trap density is higher than that in the middle of the channel and the extracted Lmet is underestimated. Using V,,
difference of 0.8 V, the Lmet deviations (L,,,,,) are smaller than 0.01 pm. Besides, the Lmet derived from different TL are also self-consistent, as shown in Fig. 2(b). Note that the TLITF
value for measurement should not be too small to make the real
TL value generated by the pulse generator much smaller than expected, otherwise, serious error will appear. In this paper,
LI et al.: NOVEL METHOD FOR EXTRACTING THE METALLURGICAL CHANNEL LENGTH 87
the charge-pumping currents measured under TL = 0.5 ps
and larger IVSUB are slightly smaller than expected (the pulse generator generated TL is smaller than 0.5 ps), therefore, the calculated Lmet is slightly larger than those derived from
TL
= 1 ps and 2 ps. The accuracy of the proposed new method becomes worse than the multidevice method (0.01,um accuracy)
[ 5 ] ,
because theLe,,,,
induced by the charge- pumping current measurement cannot be ignored. However, the current measurement induced deviations are smaller than0.01 pm, 0.02 pm accuracy still can be achieved easily using the proposed new method.
IV. CONCLUSIONS
In this paper, a novel charge-pumping method using a single device is proposed to determine the metallurgical channel length of MOSFET’ s, in which the charge-pumping current related to the local area of an n-channel MOSFET can be derived from the charge-pumping currents measured with dif- ferent VG, and
TL.
Comparing with the multidevice method, the newly developed method is shown to be relatively simple because only a single MOSFET and its measurement are needed. Moreover, the proposed method is shown to be accurate and self-consistent. In addition, the novel method can be applied to p-channel MOSFET’s by determining the edges of the effective area from the critical surface electronconcentration (n,) at VGH, and A ( I c p / j ) in ( 5 ) should be derived from the charge-pumping currents measured under different VGH and TH with the same S R , S F , and V ~ U B .
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