www.elsevier.com/locate/eswa

Expert Systems with Applications 32 (2007) 358–363

Expert Systemswith Applications

Neural network based modeling of HfO2 thin film characteristicsusing Latin Hypercube Sampling

Kyoung Eun Kweon a, Jung Hwan Lee a, Young-Don Ko a, Min-Chang Jeong b,Jae-Min Myoung b, Ilgu Yun a,*

a Semiconductor Engineering Laboratory, Department of Electrical and Electronics Engineering, Yonsei University,

134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Koreab Information and Electronic Materials Research Laboratory, Department of Materials Science and Engineering, Yonsei University,

134 Shinchon-Dong, Seodaemun-Gu, Seoul 120-749, Republic of Korea

Abstract

In this paper, the neural network based modeling for electrical characteristics of the HfO2 thin films grown by metal organic molecularbeam epitaxy was investigated. The accumulation capacitance and the hysteresis index are extracted to be the main responses to examinethe characteristics of the HfO2 dielectric films. The input process parameters were extracted by analyzing the process conditions and thecharacterization of the films. X-ray diffraction was used to analyze the characteristic variation for the different process conditions. Inorder to build the process model, the neural network model using the error back-propagation algorithm was carried out and those initialweights and biases are selected by Latin Hypercube Sampling method. This modeling methodology can allow us to optimize the processrecipes and improve the manufacturability.� 2005 Elsevier Ltd. All rights reserved.

Keywords: HfO2; Process modeling; Neural networks; Latin Hypercube Sampling

1. Introduction

The industrial demands for highly integrated and multi-functional circuits lead to increase circuit density and scal-ing down the size of semiconductor devices. According tothe technology roadmap of the semiconductor industryassociation (SIA) (Semiconductor Industry Association,2000), a gate oxide thickness is reduced less than 1 nmfor the application of the 0.05-lm metal-oxide-semiconduc-tor field-effect-transistors (MOSFETs) in the near future.In this scale, MOSFETs cannot work properly because ofthe physical limits such as the excessive gate tunneling leak-age and the gate oxide reliability (Wilk, Wallace, &Anthony, 2001). Therefore, the high-k dielectric materials,such as Al2O3, ZrO2, and HfO2, have a great attention as

0957-4174/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.eswa.2005.11.032

* Corresponding author. Tel.: +82 2 2123 4619; fax: +82 2 313 2879.E-mail address: iyun@yonsei.ac.kr (I. Yun).

candidates to replace the current gate oxides such as SiO2

(Cho et al., 2003; Cho, Wang, Sha, & Chang, 2002; Gusevet al., 2000; Lee, Kang, Nieh, Qi, & Lee, 2000; Lee, Kang,et al., 2000; Qi et al., 2000; Zhu, Li, & Liu, 2004). Amongthese candidates, HfO2 has risen as the one of the promis-ing dielectric materials due to the large band-gap energy,the high dielectric constant and the high breakdown field.

The application of the neural networks in the semicon-ductor manufacturing has been researched and successfullyimplemented in the area of the process modeling such asthe molecular beam epitaxy and plasma-enhanced chemicalvapor deposition processes (Han, Ceiler, Bidstrup, Kohl, &May, 1994; Lee, Ko et al., 2000, 2000).

In this paper, the electrical properties of HfO2 thin filmcharacteristics, such as the accumulation capacitance (Cacc)and the hysteresis index, were investigated via the neuralnetwork model using the error back-propagation algo-rithm. The accumulation capacitance (Cacc) is defined asthe capacitance at the strong accumulation region and

Table 1Summary of process conditions

Process variables Range

Substrate temperature 450–550 �CBubbler temperature 130 �C (Fixed)Nozzle temperature 270 �C (Fixed)Base pressure 10�9 TorrWorking pressure 10�7 TorrGas flow (Ar) 3–5 sccmGas flow (O2) 3–5 sccmGrowth time 30 min

K.E. Kweon et al. / Expert Systems with Applications 32 (2007) 358–363 359

the hysteresis index is defined as the width of the hysteresisloop generated by the bi-directional voltage sweep. TheLatin Hypercube Sampling (LHS) was used to generatethe weights and the biases of the neural networks and themodeling results were verified using statistical analysis.

2. Experiments

HfO2 thin film was grown on a p-type Si (100) sub-strate, of which the native oxide was chemically eliminatedby (50:1) H2O:Hf solution prior to the growth byMOMBE. Hafnium-tetra-butoxide [Hf (O � t-C4H9)4] waschosen as the MO precursor because it has an appropriatevapor pressure and relatively low decomposition tempera-ture. High-purity (99.999%) oxygen gas was used as theoxidant. Hf-t-butoxide was introduced into the main cham-ber using Ar as a carrier gas through a bubbling cylinder.The bubbler was maintained at a constant temperature tosupply the constant vapor pressure of Hf-source. The appa-ratus of the system is schematically shown in Fig. 1.High-purity Ar carrier gas passed through the bubbler con-taining the Hf-source. The gas line from the bubbler to thenozzle was heated to the same temperature. The mixture ofAr and metal-organic gases heated at the tip of the nozzleflows into the main chamber. The introduced Hf-sourcedecomposed into Hf and ligand parts when it reached asubstrate maintained at high temperature and Hf ion wascombined with O2 gas supplied from another nozzle. Thebase pressure and working pressure were �10�9 and�10�7 Torr, respectively. The HfO2 films grown byMOMBE were annealed at 700 �C for 2 min in N2 ambient.The process conditions are summarized in Table 1.

Au dots were deposited to evaluate the electrical proper-ties of grown HfO2 sample. The stainless shadow mask wasused to make regular Au dots and the hole diameter in themask was 0.2 mm. The determination of the electrode

PrPrPrPrgagagaga

Substrateholder

TurboMolecularpump

Viewport Leak

valveMassflowcontroller

O2

Substrateheater

No

Mainchamber

Shutter

Substrateholder

TurboMolecularpump

Viewport Leak

valveMassflowcontroller

O2

Substrateheater

No

Mainchamber

Shutter

Substrateholder

TurboMolecularpump

Viewport Leak

valveMassflowcontroller

O2

Substrateheater

No

Mainchamber

Shutter

Substrateholder

TurboMolecularpump

Viewport Leak

valveMassflowcontroller

O2

Substrateheater

No

Mainchamber

Shutter

Fig. 1. The schematic o

metal and accurate definition of electrode area has influ-ence on the analysis of the electrical properties of HfO2.

3. Modeling scheme

3.1. Design of experiments

In order to characterize the high-k dielectric properties,the input factors are extracted with respect to the control-lable process variables of MOMBE equipment. Those fac-tors are the substrate temperature (Tsub), Ar gas flow (Ar)and O2 gas flow (O2). Generally, the factorial design createstwo levels of each factor, which are called ‘high’ and ‘low’,respectively. The full factorial design specifies factorialdesign with all possible high (+)/low (�) combination ofall the input factors. Considering the curvature effect, thedesign of two-level factors with center points is carriedout (Montgomery, Keats, Perry, Thompson, & Messina,2000). The full factorial design matrix with one center pointis summarized in Table 2.

3.2. Latin Hypercube Sampling

The Latin Hypercube Sampling (LHS) is used in thisstudy to select randomized values for the weights and the

uuuu

Loadlockchamber

essurege

Bubblervalves

Mass flowcontroller

Ar

zzle

Loadlockchamber

essurege

Bubblervalves

Inlet

Outlet

Mass flowcontroller

Ar

zzle

BubblerHeater

Loadlockchamber

essurege

Bubblervalves

Mass flowcontroller

Ar

zzle

Loadlockchamber

essurege

Bubblervalves

Inlet

Outlet

Mass flowcontroller

Ar

zzle

BubblerHeater

f MOMBE systems.

Table 2Factorial design matrix

Run Tsub [�C] Ar [sccm] O2 [sccm] Remark

1 450 3 3 Full factorial design2 450 3 53 450 5 34 450 5 55 550 3 36 550 3 57 550 5 38 550 5 5

9 500 4 4 Center point

y1 yj yn

h1

x1

hk

xi

ho

xm

W11

W1j Woj

Wmo

Responses

Inputs

Output Layer

Hidden Layer(s)

Input Layer

. . . . . . . .

. . . . . . . .

. . . . . . . .

Fig. 3. Typical feed-forward neural networks.

360 K.E. Kweon et al. / Expert Systems with Applications 32 (2007) 358–363

biases, which are parameters of neural networks. The LHSmethod is a stratified sampling technique where therandom variable distributions are divided into equal prob-ability intervals. The LHS method generates a sample sizeN from the n variables. A 1/N probability is randomlyselected from within each interval that is partitioned intoN nonoverlapping ranges for each basic event (Swidzinski& Chang, 2000). Unlike the simple random sampling, theLHS method can describe a full coverage of the samplingrange by maximally satisfying each marginal distribution.The distributions of sampling with respect to the selectingmethod are illustrated in Fig. 2. The 100 samples were gen-erated in the range of (�0.5, 0.5). It is presented that thesampling values of the LHS method are uniformly distrib-uted comparing to that of the random sampling. Therefore,the unbiased random values of the weights and biases forthe neural networks were selected via the LHS method.

3.3. Neural networks

Neural networks are utilized to model the nonlinearrelationship between inputs and outputs in semiconductorprocess modeling. The networks consist of the three layersthat are the input layer, the hidden layer and the outputlayer. That is comprised of simple processing units calledneurons, interconnection, and weights that are assignedto the interconnection between neurons (May, 1994). Eachneuron contains the weighted sum of its inputs filtered by anonlinear sigmoid transfer function.

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

12

14

Fre

quen

cy

Value(a) (

Fig. 2. Two difference distributions of the sampling va

The neural networks in this work carried out with theerror BP algorithm. The error BP neural networks consistof several layers of neurons which receive, process andtransmit critical information regarding the relationshipsbetween the input parameters and correspondingresponses. Generally, the weight mechanism of the BPalgorithm is defined by the following (Chen, 1996):

wijkðnþ 1Þ ¼ wijkðnÞ þ gDwijkðnÞ ð1Þwhere wijk is the connection strength between the jth neu-ron in the layer (k � 1) and the ith neuron in layer k, Dwijk

is the calculated change in that weight which reduces theerror function of the networks, and g is the learning rate.

This algorithm has been shown to be very effective inlearning arbitrary nonlinear mappings between noisy setsof input and output factors. The schematic of generalfeed-forward neural networks are shown in Fig. 3. The neu-ral networks parameters used in this study are summarizedin Table 3. These networks were trained on nine experi-mental runs. The two trials were used for testing data inorder to verify the fitness of the NNet outputs for the

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

12

14

Fre

quen

cy

Valueb)

lues: (a) the simple random sampling and (b) LHS.

Table 3Summary of the neural network parameters

NNets parameters

NNet structure 3-4-3-2NNet learning rate 0.0003NNet momentum 0.04

Table 4Statistical significance level

Factor Significance level

Cacc Hysteresis

Tsub 0.002 0.416Ar 0.007 0.011O2 0.088 0.039

K.E. Kweon et al. / Expert Systems with Applications 32 (2007) 358–363 361

results of the training data. The root mean square errors(RMSEs) of the training for Cacc and the hysteresis are0.76 and 0.03, respectively. The RMSEs for the testingare 0.76 and 0.03, respectively.

4. Results and discussion

The neural network model results and the residual plotsfor Cacc and the hysteresis are illustrated in Figs. 4 and 5,where the squares represent the training data and the trian-gles represent the testing data for prediction. The modelingresults exhibit a good agreement with the values betweenthe predicted and the measured responses, respectively. Itis observed that the residual plots for all responses arerandomly distributed and there are no special patterns

0-0.10

-0.05

0.00

0.05

0.10

Res

idua

ls

0.0 0.4 0.8 1.2 1.6 2.0

0.0

0.4

0.8

1.2

1.6

2.0

: training data : testing dataH

yste

resi

s (N

etw

ork

Out

puts

) [V

]

Hysteresis (Experimental Data) [V]0

-0.10

-0.05

0.00

0.05

0.10

0.0 0.4 0.8 1.2 1.6 2.0

0.0

0.4

0.8

1.2

1.6

2.0

: training data : testing dataH

yste

resi

s (N

etw

ork

Out

puts

) [V

]

Hysteresis (Experimental Data) [V](a) (b)

Fig. 5. The neural network modeling results for the hysteresis: (a)

10 12 14 16 18 20 2210

12

14

16

18

20

22

: training data : testing data

Cac

c (N

etw

ork

Out

puts

) [p

F]

C (Experimental Data) [pF]0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Res

idua

ls

10 12 14 16 18 20 2210

12

14

16

18

20

22

: training data : testing data

C (

Net

wor

k O

utpu

ts)

[pF]

Cacc (Experimental Data) [pF]0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Res

idua

ls

(a) (b)

Fig. 4. The neural network modeling results for Cacc: (a) the m

and features indicating that the results are satisfied withthe statistical assumption for the residuals (Mayers &Montgomery, 1995).

The statistical significances of three input factors arelisted in Table 4 under the significance level (a = 0.05).For the accumulation capacitance (Cacc), Tsub and Ar aresignificance factors and Ar and O2 are considered as signif-icance factors for the hysteresis index.

The response surface plots of the accumulation capaci-tance are shown in Fig. 6 when O2 is fixed at the 4 sccmand Tsub is fixed at 500 �C, respectively. The accumulationcapacitance is proportional to the dielectric constant andinversely proportional to the equivalent oxide thickness

2 4 6 8 10

Run Order2 4 6 8 10

Run Order

the measured vs. the predicted values and (b) the residual plot.

2 4 6 8 10

Run Order

2 4 6 8 10

Run Order

easured vs. the predicted values and (b) the residual plot.

Fig. 6. The response surface plots for Cacc: (a) O2 = 4 sccm and (b) Tsub = 500 �C.

362 K.E. Kweon et al. / Expert Systems with Applications 32 (2007) 358–363

(EOT). With increasing Tsub, fully decomposed Hf source[Hf (O Æ t-C4H9)4] makes the hydrocarbon-rich circum-stances. The incorporation of them limits the crystallite sizeand causes the dominant tetragonal phase in the film. Itwas found that small O2/Ar ratio causes the hydrocar-bon-rich plasma and limits crystal size. As small O2/Arratio causes the hydrocarbon-rich plasma and limits crystalsize, the accumulation capacitance (Cacc) is increased (Kimet al., 2004). As the substrate temperature (Tsub) isincreased, the oxide thickness is decreased and Cacc isincreased. Based on the results for 2h XRD scan shownin Fig. 7, the tetragonal phase is observed at 30.3�. Thetetragonal phase means that crystallite size is limited andsmall because the tetragonal phase can be stabilized in verysmall crystallites (Garvie, 1978; Garvie & Gross, 1985). Asshown in Fig. 7, the intensity of the tetragonal phase isincreased as the substrate temperature is increased from450 �C to 550 �C. It can be interpreted that the tetragonalphase affects the reduction of the oxide thickness (Kimet al., 2004).

The response surface plots of the hysteresis are shown inFig. 8 when Tsub is fixed at 500 �C and O2 is fixed at 4 sccm,

20 30 40 5010

100

1000

t(1 1 1)

m(1 1 1)m(-1 1 1)

Au

Inte

nsit

y (a

.u.)

2Θ20 30 40 50

10

100

1000

m(2 0 0)

Au

(a)

Fig. 7. The 2h XRD scan: (a) Tsub = 450 �C, Ar = 5 sccm, and O2 =

respectively. As shown in Fig. 8 (a), the hysteresis that isproportional to the interfacial trap density (Dit) increaseswith decreasing O2/Ar ratio because the formation of asuperior interface of the oxide layers decreases Dit withincreasing O2/Ar ratio (Wilk et al., 2001). During thegrowth of HfO2 on a Si substrate, Hf is deposited andreacts with the oxygen.

HfObulk2 þHf þO2 ! HfObulk

2 ð1ÞHowever, the oxygen is not enough to react with Hf, theoxygen vacancy (VO) is created.

HfObulk2 þHf ! HfObulk

2 þ 2V O ð2ÞAs shown in Fig. 8 (b), sufficient oxygen vacancy mobil-

ity decomposes the interfacial layer of SiO2 and creates theinterfacial silicate. It was found that these decompositionreactions take place actively when Tsub is lower than500 �C (Copel & Reuter, 2003). In addition, the chargesare trapped by the oxygen vacancies as voltage sweep bi-directionally. The interfacial trap density and the hysteresisindex are increased due to the trapped charges. As Tsub

increases from 450 �C to 550 �C, the decomposition does

Inte

nsit

y (a

.u.)

20 30 40 5010

10

10

m(-1 1 1)m(2 0 0)

Au

t(1 1 1)

2Θ20 30 40 50

100

1000

m(-1 1 1)m(2 0 0)

Au

t(1 1 1)

(b)

5 sccm and (b) Tsub = 550 �C, Ar = 5 sccm, and O2 = 5 sccm.

Fig. 8. The response surface plots for the hysteresis: (a) Tsub = 500 �C and (b) O2 = 4 sccm.

K.E. Kweon et al. / Expert Systems with Applications 32 (2007) 358–363 363

not happen actively and the hysteresis index is decreased.Based on this analysis, the modeling results reveal a goodagreement with the physical mechanism.

5. Conclusion

The electrical characteristics of HfO2 thin films wereinvestigated via the error BP neural network model usingThe Latin Hypercube Sampling and the neural networkmodels to correlate between the process conditions andthe electrical characteristics were developed. The LatinHypercube Sampling method used to generate the weightsand the biases with equal probability distribution withina specific interval statistically randomly. From theseresults, the neural network modeling can explain the com-prehensive effects of the response on the varying processconditions in accordance with the physical mechanisms.The methodology can allow us to predict electrical proper-ties with respect to process conditions as well as it canimprove the manufacturability.

Acknowledgement

This work was supported by the Brain Korea 21 Projectin 2005.

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