Compact Modeling of TFTs for Flexible and Large Area Electronics

Transcription

1 Compact Modeling of Fs for Flexible and Large Area Electronics Benjamin Iñiguez Department of Electronic Engineering (DEEEA), Universitat Rovira i irgili, arragona, Catalonia, Spain. benjamin.iniguez@urv.cat

2 Goals Review of compact modeling issues affecting different types of Fs: a-si, poly- Si, nc-si, oxide, organic, polymer F Presentation of universal modeling and parameter extraction techniques for all types of Fs

3 Outline Introduction F modeling issues n n n n n Amorphous F Polycristalline F Nanocrystalline F Organic F Oxide F Unified F modeling and parameter extraction techniques Results Conclusions

4 Introduction Fs are the essential devices in large area low cost circuits (drivers of AMLCDs, transistors for flexible electronics,...) a-si Fs are the most commonly used Fs n Advantages: Possibility for deposition over large surfaces at a relatively low temperature. n Disadvantages: Low mobility, and degradation under illumination and bias stress. Poly-Si Fs do not present the disadvantages of a- Si Fs, and have higher mobility. n Disadvantages: High temperatures are used for the crystallization of the a-si:h material.

5 Introduction a-si F structure Source Drain Source Polymer Drain Polymer d Insulator d Insulator Gate Gate organic F structures

6 Introduction An alternative to both a-si and poly-si Fs are nanocrystalline Si Fs (nc-si Fs), which can obtained at low substrate temperatures and over large areas n nc-si films consist of small Si crystallites, embedded in amorphous silicon. herefore, properties of nc-si Fs lay between those of a-si and poly-si Fs Organic Fs have emerged as potential challengers to a-si Fs, because of their low power consumption and cost, compatibility with flexible substrates and printing processes n hey combine the electrical properties of inorganic semiconductors with the simple technological processing of plastics hey allow flexible, light and low cost applications in large areas

7 Introduction Another alternative: oxide semiconductor Fs, such as ZnO Fs, GIZO and HIZO Fs: hey can be amorphous, nanocrystalline or polycrystalline hey can be deposited over large and flexible substrates at low temperatures, and also can be printed hey can be applied in transparent electronics Source ZnO Drain Gate Source SiO 2 SI GaAs

8 Introduction he huge increase of the applications of hin-film ransistors (Fs) for large-area and flexible electronics makes it necessary to have accurate compact models of these devices However, accurate F modeling is a quite complex task: n presence of many special physical phenomena n bias and geometry dependence of many parameters

9 Introduction Examples of special effects n n n oltage drop at the series resistance Nonlinear contact effects Bias-dependences of several key parameters Field-effect mobility hreshold voltage Series resistance n Frequency dispersion

10 Introduction Mobility discussion first requires on accurate extraction method. Difference with SOI: large gap between and g m peak! Mobility expression in SOI cannot explain this gap µ eff 2µ W = 0, Y = CoxD µ 1+ θ ( G ) L 0 ( ) he Y-function, Y = I D / g m, cannot be applied as in SOI! G

11 Introduction Example: F field effect mobility is a power law of gs ii( x2) iii( n) jj( x2) jjj( m) a x2, n a+ c x2, m 5 a-si F above threshold ii 1 /( γ + 1) ( ) = I gs a-si F below threshold jj ( ) 1 /( γ b + 1) = I gs

12 Poly-Si F Conduction mechanisms in poly-si Fs: driftdiffusion in the grains, and thermionic emission in the grain boundaries Effective medium approach: in order to derive a charge control model, in Poisson s equation the nonuniform poly-si sample can be treated as some uniform effective medium with effective material properties Poly-Si F modeling is developed using a driftdiffusion formulation, in which the effect of the grain boundary potential barrier is included in the expression of the field-effect mobility

13 Poly-Si F In the subthreshold regime, diffusion dominates: W 2 gs ( ) ds Isub = µ scox ηth exp 1 exp L ηth ηth Above threshold there is a significant number of free carriers and the drain current is given by an expression similar to that used for crystalline MOSFEs. W dse Ia = µ FECox gt dse L 2α sat where µ FE is the gate voltage dependent field-effect mobility that includes the effects of the trap states, α sat is the body effect parameter. It increases with the gate voltage until it saturates. he leakage well below threshold is due to thermionic field emission through the grain boundary trap sites and is modeled using an additional term

14 Poly-Si F = + m µ eff k( G ) µ 0 wo limiting mechanisms: potential barriers + regular transport he model also accounts for mobility degradation at high field = + [ 1 ( )] m + θ G µ eff k( G ) µ = I C D oxw D µ eff ( G ) L k : low field mobility constant : related to grain boundaries barriers m : low field mobility power law exponent µ 0 : low field mobility (as in SOI) Θ accounts for high field mobility degradation (surface roughness scattering)

15 Poly-Si F We use a unified expresion of the drain current valid from subthreshold to above threshold (RPI model): I d where g = ch chds( 1+ λds ) ( g I ) m g [ ] 1 1+ m = 1+ ch g ds chi g sat chi ( R + R ) s d ( W L) gchi = qnsµ eff / n s is a unified expression of the sheet carrier density at the source end of the channel

16 Poly-Si F he expression of the saturation current I sat is derived using an appropriate velocity-field relationship. he DIBL effect is included in the threshold voltage expression. λ accounts for channel length modulation he impact ionization is modeled by an additional term to the drain current: ID = Id + ΔI kink = Id 1+ ( M ) M = L L kink m kink ds kink dse exp ds kink dse

17 a-si F Conduction a-si Fs is due to the drift of the induced free charge As the gate voltage is increased, both trapped and free charge are induced. he field-effect mobility is proportional to the fraction of free charge, n free /(n free +n trapped ), and has the form, above threshold: µ FE gs 0 = µ n AA γ

18 a-si F Above threshold, the current is written as: I a W µ L = FE C ox 0 ( gs α SA dse ) dse Below threshold, the current is a power law of gs - fb : I sub 1+γ b ( ) gs fb µ µ FE GS GS ) oo γ a (, ) = ( At large negative gate bias, a hole-induced drain leakage current caused by thermionic diffusion at the contacts, is accounted for γ a aa

19 nc-si F Modeling of nc-si Fs is based on the a-si:h F modeling Using the a-si:h F model, he modeled good agreement with the experimental curve up to a certain high voltage. Above a certain value of GS we observe a dramatic increase on the experimental drain current and transconductance, which are not reproduced by the model

20 nc-si F 1x10-6 1x10-6 Experiment a-si:h model DS = 5 7x10-8 6x10-8 Experiment a-si:h model DS = 5 I DS, A 8x10-7 6x10-7 g m = di DS /d GS 5x10-8 4x10-8 3x10-8 4x10-7 2x10-8 2x10-7 1x GS, GS, Experimental and modeled transfer and transconductance characteristics using the a-si:h F model

21 nc-si F his high GS regime is called the transitional (to crystalline behaviour) regime the traps are almost completely filled, n trapped remains constant and n free increases with increasing GS similarly to crystalline MOSFE As a consequence, the field-effect mobility µ fet will increase linearly with increasing GS In nc-si:h the DOS is lower than in a-si:h because of the higher internal atomic order, and we can expect that the transition to crystalline-like regime occurs at significantly lower gate voltages than in a-si Fs

22 nc-si F o model this regime, added to the a-si:h F model an abovethreshold drain current term, I tr, to account for the transitional regime. I tr = th W = µ nci 2 L Gtre Gtr th DSe + 2 δ D ( 1+ λ ) M DS Gtr th 1 2 Gtre n where Gtr = GS - tr, th is thermal voltage and δ is a transition width parameter which ensures the good behavior of Gtre. We use the following unified expression of the channel current: I DS = I leak 1 + I sub + I abv 1 + I tr 1

23 nc-si F 7x10-8 6x10-8 Experiment nc-si:h model DS = 5 3x10-6 Experiment nc-si:h model opmost curve GS = 36, Step = -4 g m = di DS /d GS 5x10-8 4x10-8 3x10-8 2x10-8 I DS, A 2x10-6 2x10-6 1x10-6 1x10-8 5x GS, DS,

24 Organic F l l Organic and polymer Fs will probably become essential devices in niche applications, related to flexible, printed or large ara electronics: electronic tags, drivers in AMLCDs, sensors Organic and polymer electronics allow flexible and low-cost substrates for large-area applications by relatively simple and lowtemperature fabrication for disposable electronics Source Drain Source Polymer Drain Polymer d Insulator d Insulator Gate Gate

25 Organic F In organic Fs transport is due to hopping between localized states An analytical solution is possible assuming an exponential DOS and neglecting dopants and free charge With these assumptions, well above threshold (linear regime), we obtain: I DS W = Cdiel µ 0 L 20 [( ) ( ) ] 20 / 20 / GS FB his expression has the same form as the current in a-si:h F, although the assumed transport mechanism is different. It is equivalent to use a crystalline MOSFE model with a fieldeffect mobility: 20 / 2 ( ) 2 2 µ FE GS = µ DS FB GS FB = µ ( ) 0 FE o GS FB aa 0 /

26 Organic F he current expression can be written in a more general way: I DS = W L Cdiel 1+ W R L µ FE Cdiel ( ) µ GS FE ( ) ( 1+ λ ) where DSsat = αs ( GS ) R is source plus drain resistance, I 0 is the leakage current and m and λ are adjustment parameters related to the sharpness of the knee region and to the channel length modulation respectively, and α S is the nonideal saturation parameter GS DS DS 1 m m DS 1+ DSsat + Io

27 Organic F l he localized charge in the organic semiconductor in above threshold was considered to be much larger than the free charge, as it is done for inorganic amorphous Fs in the subthreshold region: I DS = β (, o) C β (, o) = i W L 2 σo 0 [ Bc( 2α ) ] ( ) GS l We can identify OF parameters with those of a-si Fs FB 2o GS kb sin( π / o) k 1 bo o o 3 2 o o DS FB 2o 2 ( Ci ) o 1 ( ε ) S 2o

28 Organic F l In a-si Fs above threshold: l Where an exponential DOS was assumed: l β(,o) turns to be equal to P(,o). ( ) = o DS FB GS o FB GS i o L W C o P DS I ), ( ( ) = ), ( ' ), ( o S o C i o P o P ε o b o o b Fo do b b k E Fo E b o k o o k E E g k q N k q o P = 2 ) / sin( exp exp ), ( ' π π = o k E g E g b do d exp ) (

29 Organic F l he field-effect mobility in organic Fs can be related to the parameters of the exponential DOS: µ FE 2o 2 C 2o i = P' (, o) o GS FB 1 ( ε S ) 2 ( ) 1 ( ) ( ) γ µ = γ FE ' GS FB aa 2o 2 1 C i = P'(, o) 2 o γ γ = 2 aa εs o ( ) 1 ( )

30 Organic F o Subthreshold regime o model the subthreshold region of devices with high on/off ratio in subthreshold, the drain current can be represented as an exponential function of the gate voltage as:

31 Organic F 1E-9 1 type device measured modeled I DS [A] 1E-10 DS = GS []

32 I DS [A] Organic F 1 type device 1E-8 modeled measured DS = GS []

33 Amorphous Oxide F Distribution of acceptor type traps g a = g at Conduction band energy E C E + 0 exp gad 0 exp k1 EC E k 2 1 ( a + 2) = γ 2 ail acceptor density of states Deep acceptor density of states 2 ( b + 2) = γ 2 he GS variation above threshold modifies the population of the tail states. he GS variation in subthreshold modifies the population of the deep states.

34 Amorphous Oxide F ABOE HRESHOLD Channel length modulation I ab where (, ) GS DS = W L C µ i FE 1+ W R L C µ i ( )( 1+ λ ) FE GS ( ) GS Saturation parameter Empirical parameters defining the variation of mobility with gs above threshold DS DS 1+ ( GS α DS ) m 1/ m Sharpness of the knee region µ FE µ = 0 ( ) GS aa γa γa 34

35 Amorphous Oxide F o model the subthreshold region of devices, the drain current can be described as: SUBHRESHOLD γ b depends on the temperature and on the characteristic temperature of the deep states distribution ( 2 ) 2 γb =

36 Amorphous Oxide F DEEP SUBHRESHOLD Well below, in deep subthreshold regime, diffusion becomes the predominant charge transport mechanism and the current shows an exponential dependence with the gate voltage for GS which can be expressed as: he region where a hump may be present in stressed devices corresponds to a part of the deep subthreshold region where the slope is different due to the presence of the back interface charges, can be represented by another exponential behavior with an inverse slope S 2 where ( FB + 2 ) is the gate voltage below where the hump starts. 36

37 Unified F Model Parameter Extraction Since a universal model formulation is possible for most types of Fs, a unified extraction procedure can be applied to extract most parameters

38 Unified F Model Parameter Extraction Unified formulation of the drain current model above threshold g ch = 1+ β γ + 1 β ( gt / aa ) ( R + R )( / ) γ s d gt aa I sat 2 βgt = 1 gt βrsgt + + βrsgt + L 2 ( 1+ λ ) ch ds ds I = m 1/ m 1+ g g ch ( 1+ λ ) ds ds I sat Basic parameters: m,, γ, λ, β / γ + 1 aa = W L C ox µ / γ + 1 aa, L = v L / µ, R, R s s d GS DS = = gs ds IR I s ( R + R ) s d

39 Unified F Model Parameter Extraction Simple extraction methods are used for the basic model parameters he threshold voltage and γ are extracted using the integral gs I( operator: H ( ) gs = gs I( ) d gs ) gs gs = γ Ha( n) 10 HHa( n) a n a+ c his method is independent of the mobility Ha(n): H( gs ) from a-si F measurements HHa(n): fitted H( gs )

40 Unified F Model Parameter Extraction he rest of parameters are obtained from specific equations of each type of device Subthreshold n In a-si F, I sub 1+γ b ( ) GS fb Using the integral operator we extract fb and γ b n In poly-si F I sub e gt /η th From a log(i) vs gt plot we extract η

41 Unified F Model Parameter Extraction Saturation threshold voltage (with the DIBL effect) iik( x4) ipc( x4) iik(x4): H( gs ) from measurements ipc(x4): fitted H(gs) H ( ) gs = gs I sat I ( sat gs ( ) d gs ) gs = o + K ds gs γ + 3 s as x4 cs Current dependent resistance: R si = R so + I I o R sio +α Rs Kink effect (in short-channel poly-si Fs)

42 Unified F Model Parameter Extraction After extracting all the parameters, we complete the final basic compact model gchds formulation: ( 1+ λds ) = g g I m 1/ m 1+ g ch ( 1+ λ ) = chi ch W 1 + gchi ( Rs + Rd ) g chi = µ qn s he unified expression of n s, valid from below to above threshold, depends on the type of device L ds ds I sat n s = 2n o ln 1 + Poly-Si F 1 exp 2 η gt th n s = a-si F n n sa sa n sb + n sb sa ox γ +1 gt n = C / n sb = C ox γ aa 1+ γ b γ b ( ) / gs fb bb

43 Unified F Model Parameter Extraction In a-si:h and amorphous oxide Fs, the subthreshold current is also a power law of the gate voltage overdrive: FB is obtained by applying the H operator γ b is obtained using the H operator and it depends on the temperature and on the characteristic temperature of the deep states distribution ( 2 ) 2 γb = 2 2

44 Unified F Model Parameter Extraction ( ) ( ) ( ) ( ) m m GS S DS GS FE i DS DS GS FE i DS C L W R C L W I = α µ λ µ ( ) + = + + γ γ γ γ α µ α µ ) ( log log2 S Dsat AA o i DSsat DSsat DSsat S AA o i C L W R I C L W m m is calculated from this equation for DSsat1 =α S ( GS1 - ) at GS1 equal or near GSmax, considering λ=0. Above threshold

45 Unified F Model Parameter Extraction ( ) ( ) ( ) DS GS AA o i m GS s DS GS AA o i DS DS C L W C L W R I m + + = + + γ γ γ γ µ α µ λ λ is evaluated using the same expression, for the same value GS1 and a value of DS2 near the maximum value measured. I DS2 is the current measured at DS2.

46 Unified F Model Parameter Extraction Deep subthreshold regime in organic and amorphous oxide Fs: I S = Io + I DS ( + D, DS ) e GS S 2.3 S is extracted from the slope of log(i S ) vs ( GS - ). he total drain current is the sum of the two components, in above and below threshold regimes. he tahh function is used to sew both terms. I DSt = I s ( + D ) Q) 1+ tanh( ( + D ) ) 1 tanh( GS Q + I GS DS 2 2

47 Results Measured (dots) and calculated (solid lines) characteristics of a-si F Fs

48 Results x10-4 Measurements MOF in Mathcad MOF erilog-a GS = 20 I DS ( DS = 20 ) Measurement MOF in Mathcad MOF erilog-a I DS (A) 4.0x x GS = 16 GS = 12 GS = GS () GS () GIZO F W=160 µm L=20 µm ds=20

49 Results 4x10-5 Measurements GS =4 8x10-6 I DS (A) 2x10-5 GS =5 GS =8 Model Output conductance (S) 6x10-6 4x10-6 2x10-6 Measurements GS =4 GS =5 GS =8 Model DS () DS () GIZO F W=160 µm L=20 µm

50 Results tip Pentacene OF L=50 µm W=200 µm DS = I DS (µa) 0.10 measured modeled I DS (A) GS [] 10-11

51 Results 6 GS = I DS (na) GS = -20 GS = -10 GS = DS Experimental (simbols) and modeled (straight lines) I- characteris9cs of the PMMA/P3H OF with insulator thickness di PMMA =330 nm and ds P3H =80 nm.

52 Quasi-static capacitance modeling n A quasi-static (QS) charge model is developed by integrating the mobile charge sheet density (per unit area) over the channel Q CH = W I 2 DS Ci 2 µ 0 3+ γ ( ) ( ) GS 3+ γ n he QS capacitances are obtained by differentiating the total charges with respect to the applied voltages DS GS 3+ γ C GG Q = G GS Q = CH GS

53 Quasi-static capacitance modeling n he extrinsic capacitance effect due to the overlap of the gate with the source and drain regions (C OR ) is added to the calculated intrinsic capacitance above: n L OR is the overlapping length between gate and drain contacts and between gate and source ones. n he total gate-to-channel capacitance in accumulation regime and below threshold close to accumulation is: n he image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

54 Quasi-static capacitance modeling n he equivalent capacitance in depletion regime is obtained then from the sum of the series arrange of C i and the depletion capacitance CD. n Where, in partial depletion conditions:

55 Quasi-static capacitance modeling n In conditions of full depletion, the organic layer thickness replaces W D n he unified expression of the capacitance is: where Δ is the shift of the threshold voltage of the C- characteristic at different frequencies, and Q2 is a transition parameter of the tanh function

56 Improved capacitance modeling ofrequency dependence In OFs, it has been observed that the value of the capacitance in accumulation condition is affected as the frequency of the applied AC signal increases. As similarly done in [*] for modeling the MIS capacitor, but assuming that the interface traps are negligible, we applied the empirical formula proposed by Cole and Cole ** to represent the variation of the dielectric constant for a considerable number of liquids and solids: ε i ( εi0 εi ) [ 1+ jωτ ] p = εi + where ε i0 and ε i are the permittivity at very low and very high frequencies, respectively. τ is the relaxation time and 1>p>0. [*] M. Estrada, F. Ulloa, M. Avila, A. Cerdeira, A. Castro- Carranza, B. Iñiguez, L. Marsal, J. Pallarés, Frequency and voltage dependence of the capacitance of MIS structures fabricated with polymeric materials IEEE rans. Electron. Dev (in press) ** J. Chem. Phys., vol, 9, no. 4 pp , Apr

57 Improved capacitance modeling -I DS (na) GS = -30 GS = -20 GS = -10 C G-CH (pf) Measurement 500Hz 1KHz 10KHz Model 500Hz 1KHz 10KHz 0 GS = DS G-CH Experimental (simbols) and modeled (straight lines) I- and C- characteris9cs of the PMMA/P3H OF with insulator thickness di PMMA =330 nm and ds P3H =80 nm.

58 Improved capacitance modeling -I DS (na) GS = -20 GS = -10 GS = 0 GS = DS G-CH C G-CH (pf) Measurements 500Hz 1KHz 5KHz 10KHz Model 500Hz 1KHz 5KHz 10KHz Experimental (simbols) and modeled (straight lines) I- and C- characteris9cs of the PMMA/PCDB OF with insulator thickness di PMMA =390 nm and ds PCDB =50 nm.

59 Frequency dispersion effects n he capacitance of polymeric MIS structures fabricated with polymers as dielectric and semiconductor layers can behave quite different as function of frequency, depending not only on the characteristics of the polymers, the thickness of the semiconductor layer but also on the properties of its interface with the insulator and with the metal contact. n he dielectric constant ki of polymeric insulators can vary with frequency at relatively low frequencies, even below 1 MHz. his effect reduces the accumulation capacitance as the frequency increases, so C curves shift down. n he effect of the non depleted part of the polymeric layer introduces a frequency dependent impedance that reduces additionally the measured capacitance, specially, in accumulation. his effect is more important as the active layer is thicker or its resistivity is higher

60 Frequency dispersion effects he presence of the high density of interface states can shift and deform the C curves. Both positively and negatively charged interface states can be observed, depending on the polymers used as dielectric and semiconductor. As frequency increases, interface traps will no longer be able of changing their charge with the measurement frequency so the shift they produce is lower Although polymers have high density of bulk states, their effect was only observed at high frequencies and in MIS structures where the density of interface states was sufficiently small he presence of a non-linear contact resistance related to the barrier formed at the polymer-metal contact due to the energy difference between the polymer HOMO and metal contact workfunction, can significantly modify the form of the C curves.

61 Frequency dispersion effects Study of MIS structures with different materials using C measurements at different frequencies. 2 main behaviors are observed [1]: 1. C min /C max is constant, and the increase in capacitance was due to the increase of the dielectric constant of the dielectric used he main properties of the materials used in the MIS structures can be determined even at relatively high frequencies, eg. 1 MHz used in MOSFEs

62 Frequency dispersion effects

63 Frequency dispersion effects 2. Cmin/Cmax reduces as the frequency increases, producing a deformation of the C curve only low frequency measurements can be used to determine the properties of the materials used [1] M. Estrada, F. Ulloa, J. Sanchez, A. Cerdeira, B. Iñiguez, Differences on the frequency dependence of capacitance in MIS structures with different organic materials, ICOE 2012, invited presentation

64 Frequency dispersion effects Frequency and voltage dependence of the capacitance of MIS structures fabricated with polymeric materials 3 structures are considered: Structure 1: 395 nm of PMMA and 95 nm of P3H layer Structure 2: 437 nm of PMMA on top of 30 nm thick PCDB layer Structure 3: 332 nm of PMMA on top of 22 nm of F82 layer

65 Frequency dispersion effects he reduction of C accum is due to the reduction in the dielectric constant Structure 1: for f > 100 KHz, C aacum decreases more rapidly IF only the variation of k i vs. f is considered Structure 3: the same behavior starts at f > 80 KHz

66 Frequency dispersion effects An equivalent circuit, based on a RC network, has been developed to model the capacitances at different frequencies C I the capacitance of the dielectric C D the capacitance of the depleted layer R B resistance of the not yet depleted polymer C B capacitance associated with the non depleted layer C SS / R SS effect of the interface states C / R effect of the bulk traps in the semiconductor layer R 0 / C 0 effect of the contact resistance between the polymer and the back metal contact

67 Frequency dispersion effects Measured and calculated C- characteristics for a MIS with 437 nm of PMMA on top of 30 nm thick PCDB layer

68 Frequency dispersion effects Measured and calculated C- characteristics for a MIS with 332 nm of PMMA on top of 22 nm thick F82 layer

69 Conclusions We have reviewed compact modeling issues for the different types of Fs: amorphous, polycristalline, nanocrystalline, oxide and organic Fs We have presented unified F modeling and parameter extraction techniques he parameters of the basic model formulation can be obtained from I- measurements using an extraction method valid for all F types Direct extraction techniques are possible for the rest of parameters, including those who are specitic to certain F types Good agreement with measurements have been found for different types of Fs

70 Acknowledgements his research is supported in the last years by contract hin Oxide F SPICE Model, with Silvaco Inc., and by the FlexNet Network of Excellence (7 th Framework Programme of the European Union)