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Journal of The Electrochemical Society, 157 �3� H272-H277 �2010�H272
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Self-Consistent Technique for Extracting Density of Statesin Amorphous InGaZnO Thin Film TransistorsJun-Hyun Park, Kichan Jeon, Sangwon Lee, Sangwook Kim,* Sunil Kim,Ihun Song, Jaechul Park,z Youngsoo Park, Chang Jung Kim,Dong Myong Kim, and Dae Hwan Kimz
School of Electrical Engineering, Kookmin University, Seongbuk, Seoul 136-702, Korea
The self-consistent technique for extracting density of states �DOS: g�E�� in an amorphous indium gallium zinc oxide �a-IGZO�thin film transistor is proposed and demonstrated. The key parameters are the g�E� of the a-IGZO active layer and the intrinsicchannel mobility ��ch�. While the energy level �E� is scanned by the photon energy and gate-to-source voltage �VGS� sweep, itsdensity is extracted from an optical response of capacitance–voltage characteristics. Using the VGS-dependent �ch as anotherboundary condition, a linearly mapped DOS assuming a linear relation between VGS and E is translated into a final DOS by fullyconsidering a nonlinear relation between VGS and E. The final DOS is finally extracted and verified by finding the self-consistentsolution satisfying both the linearly mapped DOS and the measured VGS dependence of �ch with the numerical iteration of aDOS-based �ch model. The extracted final DOS parameters are NTA = 1.73 � 1017 cm−3 eV−1, NDA = 3.5 � 1015 cm−3 eV−1,kTTA = 0.023 eV, kTDGA = 1.2 eV, and EO = 1.7 eV with the formula of exponential tail states and Gaussian deep states.© 2010 The Electrochemical Society. �DOI: 10.1149/1.3273203� All rights reserved.
Manuscript submitted August 12, 2009; revised manuscript received November 9, 2009. Published January 4, 2010. This wasPaper 774 presented at the San Francisco, California, Meeting of the Society, May 24–29, 2009.
0013-4651/2010/157�3�/H272/6/$28.00 © The Electrochemical Society
Recently, multicomponent amorphous oxide semiconductor-based thin film transistors �TFTs� �i.e., amorphous InGaZnO �a-IGZO�, a-InZnO, and a-GaZnO� have been under active researchand development because of their room-temperature fabrication pro-cess, low cost, higher mobility than those of covalent semiconductorTFTs, and compatibility with transparent and rollable electronicsapplications. The density of states �DOS, g�E�� is a critical param-eter playing a significant role in the electrical property of a-IGZO.However, the extraction of g�E� in the a-IGZO TFTs has been rarelyinvestigated or recently studied by some groups.1-3 Also very re-cently, we proposed the a-IGZO DOS extraction method based on anoptical response of capacitance–voltage �C-V� curve4 assuming alinear relation between the gate-to-source voltage VGS and energylevel E. In this work, the self-consistent g�E� extraction technique,including a complicated nonlinear relation between E and VGS, isproposed by combining an optical response of the C-V curve and theVGS-dependent intrinsic channel mobility ��ch�.
The integrated IGZO TFTs have the most commonly used back-channel-etch staggered bottom gate structure for active matrix liquidcrystal displays and/or active matrix organic light emitting diodedisplays. Devices are fabricated as follows: On a thermally grownSiO2/Si substrate, the first sputtered deposition at room temperatureand the patterning of molybdenum �Mo� gate are followed byplasma-enhanced chemical vapor deposition �PECVD� deposition ofa 100 nm thick SiO2 at 300°C �TGI = 100 nm�. A 70 nm thickactive layer �In2O3:Ga2O3:ZnO = 2:2:1 atom %� is then sputteredby the radio frequency �rf� magnetron sputtering at room tempera-ture in a mixed atmosphere of Ar/O2 �100:1 at sccm� and wet etchedwith diluted HF �TIGZO = 70 nm�. For the source/drain �S/D� pat-tern, Mo is sputtered at room temperature and then patterned by dryetching. After N2O plasma treatment on the channel surface of theIGZO active layer, a SiO2 passivation layer without a vacuum breakis continuously deposited at 150°C by PECVD, and finally, all thesamples �W/L/LOV = 200/50/10 �m� were annealed at 250°C for 1h in the furnace. The fabricated IGZO layer is verified to have anamorphous phase by XRD and transmission electron microscopy�TEM� views and shows the nature of an n-type amorphous oxidesemiconductor. Figure 1 shows the device schematic, XRD pattern,and TEM image.
* Electrochemical Society Active Member.z E-mail: soppia0121@paran.com; drlife@kookmin.ac.kr
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Model Parameter Extraction Method
To extract and validate g�E�, including the complicated nonlinearrelation between the VGS and the surface potential �S �eventually E�,the critical model parameters ��ch and g�E� assuming the linearrelation between �S and VGS� should be extracted from the mea-sured data.
The extraction of �ch plays a significant role in confirming thevalidity of g�E� of a-IGZO TFT because we can consider that the�ch is related to the electrons moving on the condition of a specificpotential distribution. The extraction of �ch is started from the ac-quisition of a total on-resistance �RT� and an intrinsic channel resis-tance �Rch� of TFTs. The drain-to-source current �IDS� in the linearregion is given by
IDS � �FECoxW
L�VGS − VT� � VDS �A� �1�
where �FE, Cox, VT, and VDS are the field-effect mobility, gate oxidecapacitance per unit area, threshold voltage, and drain-to-sourcevoltage, respectively. RT and parasitic resistance �RP� are defined inthe following equation5
RT = limVDS→0
� � VDS
� IDS�
constant VGS
= Rch + RP = rchL + RP ��� �2�
where rch is the intrinsic channel resistance per unit channel length.RP includes both the contact resistance �RC� and the S/D spreadingresistance �RS and RD�, as shown in Fig. 2.
By using the basic transistor equation from the gradual channelapproximation like the crystalline semiconductor, we can determinerch. The rch is represented as
rch =1
�chCoxW�VGS − VT� � �
�m� �3�
By substituting Eq. 3 with Eq. 2, we obtain
RT = RP +L
�chCOX�VGS − VT�= RP + Rch ��� �4�
Then, based on a transmission line model �TLM� method, therch�VGS� can be extracted from the slope of the RT − L plot withvarious VGS. The RT is measured from the linear region of the outputcharacteristics �IDS-VDS� of TFTs. In our case, various L’s �L = 2, 6,10, 30, and 50 �m� under a fixed W �W = 200 �m� were utilized
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H273Journal of The Electrochemical Society, 157 �3� H272-H277 �2010� H273
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for extracting RT. Figure 3a and b shows the IDS-VDS characteristicof a-IGZO TFT with W/L = 200/50 �m and the RT − L plot as thefunction of VGS. The slope of the RT − L plot is independent of L, asseen in Fig. 3b, as predicted by Eq. 4. Therefore, according to Eq. 3,the �ch can be obtained by plotting the reciprocal of the rch as afunction of VGS. The extracted �ch is used for the purpose of com-
Figure 1. �Color online� �a� Schematic cross section of the fabricateda-IGZO TFT, �b� XRD pattern, and �c� TEM image of a-IGZO active layer.
Figure 2. �Color online� The schematic of cross section of a-IGZO TFT withthe definitions of various resistances �R , R , R , and R �.
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paring the measured �ch with the calculated one by the DOS-based�ch model �as seen in Fig. 6a�. Needless to say, the �ch is thefunction not only of VGS but also of g�E� parameters because theVGS dependence of �ch results from the trap filling of a-IGZO g�E�.Therefore, by comparing the measured �ch with the one calculatedfrom the �ch model, we can verify g�E�, including the nonlinearrelation between VGS and E.
Because the potential distribution along the vertical direction x isa function of both the free charges and localized charges, we caneasily consider the �ch as a function of g�E� parameters. Therefore,to calculate the �ch model described in the Model Derivation sec-tion, we should know the g�E� parameters. Furthermore, becauseboth the electron concentration n and DOS of a-IGZO TFTs makesignificant roles in electrical properties, extracting n and g�E� isvery important in the modeling and characterization of their devicesand circuits. While n is determined by process conditions �i.e., oxy-gen vacancies6,7 and rf power in sputtering8� and has been experi-mentally extracted by many groups6-10 �e.g., Hall measurement orelectrical characteristics�, the extraction of g�E� has been rarely in-vestigated or recently studied by some groups.1-3
To extract g�E� of the a-IGZO layer, in our previous work theoptical C-V response between the gate and S/D electrodes in thea-IGZO TFT is employed by utilizing the difference in measuredcapacitance between the dark and photoilluminated states as a func-tion of VGS. A detailed procedure has been shown in Ref. 4. Here,we define the linearly mapped g�E�. The terminology “linearlymapped g�E�” means that the g�E� assumes the linear relation be-tween the �S �consequently E� and the VGS as in Ref. 4. Figure 4aand b shows the measured C-V curve under both the dark and pho-toilluminated conditions and the extracted linearly mapped g�E�,respectively. In other words, in Fig. 4b, the linear relation betweenVGS and �S �eventually E� is assumed. In terms of translating the Elevel from VGS, two transition points in the dark C-V curve areassumed to correspond to Ei �midgap� and EC, as shown in Fig. 4c.Then, the relation between E and VGS is given, as shown in Fig. 4d.
Therefore, the nonlinear relation between �S and VGS in g�E� isnot yet considered in this section. The final g�E�, as the final resultof our proposed technique, is completed through a procedure forfinding self-consistent parameters described in the Results and Dis-cussion section. Here, only the lateral location of data points in thelinearly mapped g�E� �in Fig. 4b� is changed even after reflectingthe nonlinear relation between the �S and the VGS.
Model Derivation
In this section, we introduce the �ch model based on the nonlin-ear relation between the VGS and the E. This �ch model equation isapplied to find self-consistent g�E� parameters, as described in theResults and Discussion section.
First, to calculate the �ch model, the calculation of the relationbetween the VGS and the E is begun with solving both the chargedensity and the electric field �EIGZO� along the x direction in thea-IGZO active layer. Then, the localized trapped electron density perunit volume �nloc� is expressed as
nloc�x� = EV
EC
g�E� � f�E�dE = ndeep�x� + ntail�x� �cm−3� �5�
where f�E� is the Fermi–Dirac distribution function.As shown in Fig. 4b, a deep state of extracted g�E� can be
approximated to be the Gaussian distribution function. However,because the VGS-dependent trap filling above VT is mainly deter-mined by tail states, we assumed that the deep state can be approxi-mated to an exponential function for convenience in terms of calcu-lating �ch. Our assumption is verified later. Then, the localizedelectron densities of the deep and tail states per unit volume areexpressed as11
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H274 Journal of The Electrochemical Society, 157 �3� H272-H277 �2010�H274
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ndeep�x� = NDA � g�T/TDA� �kT
q
��
sin� �T
TDA� expq���x� − �ch − �FO�
kTDA� �cm−3�
�6�
ntail�x� = NTA � g �kT
q
�1
� T
TTA− 1� expq���x� − �ch − �FO�
kT� �cm−3�
�7�
where g, �ch, �FO, kTDA/kTTA, and NDA/NTA are the degeneracyfactor, electron quasi-Fermi potential, bulk Fermi potential underthermal equilibrium condition, characteristic energy of acceptor-likedeep/tail states, and density of deep/tail states, respectively. In addi-tion, the free carrier density per unit volume �nfree� is represented as
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nfree�x� = NC � expq���x� − �ch − �FO�kT
� �cm−3� �8�
where NC is the conduction band effective DOS. Then, Poisson’sequation along the x direction from the interface between thea-IGZO/gate insulator oxide is redescribed as
�2��x�� x2 = −
��x��IGZO
=q
�IGZO�nfree�x� + nloc�x�� �V/cm2� �9�
where �IGZO, �, and q are the permittivity of the a-IGZO material,the volume charge density, and the magnitude of the single electroncharge, respectively. Therefore, the EIGZO of the a-IGZO active layerat a specific x is given as follows. Here, the � at the a-IGZO/passivation layer interface, i.e., �B = ��x = TIGZO�, is assumed tobe negligible in comparison with �S at the a-IGZO/gate insulatoroxide interface
Figure 3. �Color online� �a� TheVGS-dependent IDS-VDS characteristics�W/L = 200/50 �m� and �b� the RT-Lplot of a-IGZO TFT for extracting �ch.
Figure 4. �Color online� �a� MeasuredC-V curve under both the dark and photo-illuminated conditions �S/D electrodes areground�, �b� the linearly mapped g�E� as-suming the linear relation between �S andVGS, �c� the schematic diagram illustratingtwo points �in the dark C-V curve� used incorrelating E with VGS, �d� the VGS depen-dence of E in linearly mapped g�E�.
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H275Journal of The Electrochemical Society, 157 �3� H272-H277 �2010� H275
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EIGZO = �2��x=TIGZO�
��x�q
�IGZO�nloc�x� + nfree�x��d��x� � V
cm��10�
To calculate the nonlinear relation between VGS and E, we applyGauss law to the interface of the a-IGZO/gate insulator oxide. Whenwe apply Eq. 10, the continuity of dielectric displacement across theinterface between the a-IGZO/gate insulator oxide gives
VGS = VFB + �S +Qinduced
Cox= VFB + �S +
�IGZOEIGZO��S�Cox
�V�
�11�
where Qinduced and VFB are the VGS-dependent field-induced chargeper unit area within the entire a-IGZO active layer and flatbandvoltage, respectively. Because the EIGZO is a function of g�E�, onecan infer that the final g�E� parameters �NTA, NDA, kTTA, and kTDA�should be known to completely calculate the nonlinear relation be-tween the �S and the VGS. Therefore, the relation between the VGSand the �S should be calculated by self-consistent numerical itera-tions. The kTTA and kTDA �characteristic energy of the tail/deep� aresignificantly changed by employing the nonlinear relation betweenthe VGS and the �S, while NTA and NDA �tail/deep state density�would be nearly unchanged even after applying that nonlinear rela-tion. Therefore, kTTA and kTDA are such unknown variables in thelinearly mapped g�E�. However, because the �ch is a function ofboth the g�E� and VGS, we can use the �ch model as another bound-ary condition to extract the final g�E� parameters, kTTA and kTDA.
Here, based on the nonlinear relation between the VGS and �S inEq. 11, the DOS-based �ch model is calculated. In contrast to field-effect mobility �FE, the �ch is the intrinsic parameter connected onlywith the Rch. Thus, the VGS-dependent �ch is the most suitable pa-rameter for verifying the intrinsic properties of the a-IGZO activematerial, i.e., DOS, g�E�. Because the ��x� is a function of both freeand localized charges, we can easily infer that the �ch is also modu-lated by those charges. In detail, the �ch, as in hydrogenated amor-phous silicon �a-Si:H� TFT, is expressed as the function of the con-duction band mobility �band, the free charge density per unit areaQfree, and the localized trapped charge density per unit area Qloc asfollows12
�ch���x�� = �band �Qfree���x��
Qinduced���x��= �band
�Qfree���x��
Qfree���x�� + Qloc���x��� cm2
V s� �12�
where Qfree and Qloc are represented as
Qfree���x�� = qx
x=TIGZO
nfree�x�dx = qx
x=TIGZO
NC
� expq���x� − �ch − �FO�kT
�dx � C
cm2� �13�
Qloc���x�� = qx
x=TIGZO
nloc�x�dx = qx
x=TIGZOEV
EC
g�E�
� f�E�dEdx �C/cm2� �14�
Inasmuch as the energy band bending would be calculated based onthe total Qloc from x to the back interface of the a-IGZO/passivationlayer, Qfree���x�� and Qloc���x�� can be derived by integratingnfree�x� and nloc�x� from x to the end of the active layer �x= TIGZO� throughout the entire a-IGZO active layer.
By unifying Eq. 5, 8, 10, and 12-14, �ch�x� can be calculated asthe model equation consisting of DOS parameters. Consequently,the � of free electrons at the surface channel is given by � �x
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= 0� = �ch���x = 0�� = �ch��S�. Then, �ch��S� can be translatedinto �ch�VGS� by using Eq. 11. Therefore, it can be directly com-pared with the measured �ch�VGS�.
Results and Discussion
In this section, the self-consistent technique, including the pa-rameter extraction methods and model equations, is proposed, asshown in Fig. 5. The proposed procedure is as follows: �i� Theexperimental C-V curve, I-V curve, and Hall measurement data areused as the inputs. �ii� The �band, NC, and q�FO are extracted fromHall measurement data. They are conceptually the first-fixed param-eters �In this work, NC, q�FO, and �band are assumed to be appro-priate values without Hall measurement�. �iii� The measuredIDS-VDS characteristic is used to experimentally extract the �ch as afunction of VGS. �iv� The measured C-V response under the dark andphotoilluminated conditions is used to extract the linearly mappedg�E� assuming the linear relation between the VGS and the E. �v� The�ch�x = 0, ��x� = �S� in Eq. 12 is calculated from the DOS param-eters of linearly mapped g�E� and translated into �ch�VGS� model byusing Eq. 10 and 11. �vi� Only the lateral location of data points inlinearly mapped g�E� is adjusted by a numerical iteration until sat-isfying the self-consistency between the �ch�VGS� model and themeasured �ch�VGS�. In this way, the extraction of final DOS param-eters is completed.
Figure 6 shows the final results of our self-consistent �ch modelof a-IGZO TFTs. By applying the nonlinear relation between theVGS and the �S �or E�, the linearly mapped g�E� �Fig. 4b� is trans-lated into the final g�E� �Fig. 6b�. The final g�E� can be modeled as�analogous to that of a-Si:H TFTs�13
g�E� = NTA � exp�E − EC
kTTA� + NDA
�exp − �EO − E
kTDGA�2� �cm−3 eV−1� �15�
where kT and E are the standard deviation and average value of
Figure 5. �Color online� Schematic diagram illustrating the proposed proce-dure of self-consistent technique including the parameter extraction methodsand model equations. Acquired final g�E�, the �ch model guaranteeing theconsistency among the correlation between the VGS and the �S in Eq. 11, themeasured linearly mapped g�E�, and the measured �ch �VGS�.
DGA O
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H276 Journal of The Electrochemical Society, 157 �3� H272-H277 �2010�H276
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the Gaussian deep states, respectively. The final DOS parameters areNTA = 1.73 � 1017 cm−3 eV−1, NDA = 3.5 � 1015 cm−3 eV−1,kTTA = 0.023 eV, kTDGA = 1.2 eV, and EO = 1.7 eV. However, asmentioned above, in the DOS-based �ch model, the �ch is calculatedfrom g�E� as follows �g�E� used in the �ch model, as seen in Fig.6b�
g�E� = NTA � exp�E − EC
kTTA� + NDA � exp�E − EC
kTDA� �cm−3 eV−1�
�16�To verify our assumption, i.e., deep state can be expressed as anexponential function instead of a Gaussian function without a largeerror, we point out that the E corresponded with a specific VGS.Here, we particularly chose VGS = 0 V because the measured �FEand/or �ch �Fig. 6a� start/s to increase when the VGS is positive. Asshown in Fig. 7, the dashed line corresponding to VGS = 0 V islocated in the tail state, which indicates that the VGS-dependent trapfilling above VT is mainly determined by the tail state. Therefore,our assumption is valid in a-IGZO TFTs.
Conclusively, in Fig. 6b and 7, the nonlinear relation betweenVGS and �S �eventually E� is self-consistently calculated by chang-ing the lateral positions of data points in Fig. 4b until satisfying theconsistencies among Eq. 10-12 and the measured �ch�VGS�. Thefinally calculated nonlinear relation between VGS and �S is shown inFig. 8. As the VGS increases, the �S increases and is eventuallysaturated.
Table I summarizes the DOS parameters used in calculating boththe �ch model in Eq. 12 and the nonlinear relation between VGS andE in Eq. 11. The g�E� used in the �ch model is also shown in Fig. 6b
Figure 7. �Color online� The final g�E� where the dashed line correspondingwith VGS = 0 V is plotted to verify our assumption of exponential deepstates in the � model’s g�E�.
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by a dashed line. The form of the deep state of the final g�E��Gaussian function� is much different from that of the g�E� used inthe �ch model �exponential function� that each value of NDA showsa slight difference. As shown in Fig. 6a, the �ch model calculatedwith the parameters in Table I agrees well with the measured �ch.Because the ratio of RP/RT is reduced only under the condition ofthe larger Rrh at a long channel length �L = 50 �m�, it is noticeablethat the measured �ch is analogous to the �FE.
Actually, the �ch�VGS� is extracted at VDS = 0.1 V, as shown inFig. 6a. A low value of VDS guarantees the I-V characteristic oper-ated in the linear region such as that in Eq. 1. The value of VDSquantitatively affects the proposed method in terms of calculatingnfree and nloc �Eq. 6-8� with the quasi-Fermi potential �ch. In addi-tion, the RP�VGS� extracted by the TLM method14 is used in acquir-ing the internal channel voltage VDS� as follows
VDS� = VDS − �IDS � RP�VGS�� �17�
Therefore, in the proposed g�E� extraction technique, the relationbetween VGS and �S �eventually E� is influenced by RP�VGS�. In ourcase, the VDS� was 0.093 V at VDS = 0.1 V, as shown in Fig. 8. Thus,VDS� = 0.093 V was used in calculating �ch�VGS�. In addition, theratio of RP/RT increases as the channel length L decreases. In ourcase, the a-IGZO TFT with L = 50 �m was used. However, theproposed technique is independent of L because the L-independent�ch�VGS� is utilized in extracting the final g�E�.
Figure 6. �Color online� �a� The calcu-lated �ch model compared with the mea-sured �ch and �FE. �b� The final g�E� ex-tracted from the proposed self-consistentprocedure. It can be mathematically de-scribed as in the equation in the inset.
Figure 8. �Color online� The nonlinear relation between VGS and �S, whichis used in the energy mapping in the final g�E� �as seen in Fig. 6b and 7�.
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H277Journal of The Electrochemical Society, 157 �3� H272-H277 �2010� H277
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Compared with the case of a-Si:H TFT, the tail and deep statedensities at EC �NTA and NDA� of the a-IGZO TFT are so muchlower. Furthermore, kTTA = 23 meV is much lower than a roomtemperature thermal energy 25 meV, which indicates that the Fermilevel EF easily moves up to near the EC with the increase in VGS. Itis consistent that the �ch of the a-IGZO TFT is much higher thanthat of the a-Si:H TFT. Consequently, high performance of thea-IGZO TFT, i.e., bandlike conduction, relies on the low NTA andkTTA.
Conclusion
A previously proposed g�E� extraction method based on an op-tical response of the C-V curve in a-IGZO TFTs is improved byfully considering the nonlinear relation between the E and the VGS.By finding the solution satisfying both the linearly mapped DOS andthe measured VGS dependence of �ch with the numerical iteration,the self-consistent technique for extracting the DOS of a-IGZOTFTs is proposed and verified by comparing the measured �ch andthe calculated one from the DOS-based �ch model. Our results showthat the proposed technique and the �ch model are very useful forthe device design and modeling of a-IGZO TFTs as a representativeof multicomponent amorphous oxide semiconductor TFTs.
Acknowledgments
This work was supported by the Korea Science and Engineering
Table I. DOS parameters used to calculate the �ch model.
Parameter Value Parameter
NC�cm−3� 4 � 1018 NTA�cm−3 eV−1�NDA�cm−3 eV−1� 2.3 � 1015 kTTA�eV�kTDA�eV� 3 q�FO�eV�
Foundation �KOSEF� grant funded by the Korean government
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�MEST� �no. 2009-0080344�. CAD software was supported by Sil-vaco and IC Design Education Center �IDEC�.
Kookmin University assisted in meeting the publication costs of this ar-ticle.
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