Modelling of capacitance and threshold voltage for ultrathin normally-off AlGaN/GaN MOSHEMT

Transcription

1 Pramana J. Phys. (07) 88: 3 DOI 0.007/s y c Indian Academy of Sciences Modelling of capacitance and threshold voltage for ultrathin normally-off AlGaN/GaN MOSHEMT R SWAIN, K JENA and T R LENKA Microelectronics and VLSI Design Group, Department of Electronics & Communication Engineering, National Institute of Technology Silchar, Silchar , India Corresponding author. t.r.lenka@ieee.org; trlenka@ece.nits.ac.in MS received January 05; revised 6 February 06; accepted 6 May 06; published online December 06 Abstract. A compact quantitative model based on oxide semiconductor interface density of states (DOS) is proposed for Al 0.5 Ga 0.75 N/GaN metal oxide semiconductor high electron mobility transistor (MOSHEMT). Mathematical expressions for surface potential, sheet charge concentration, gate capacitance and threshold voltage have been derived. The gate capacitance behaviour is studied in terms of capacitance voltage (CV) characteristics. Similarly, the predicted threshold voltage (V T ) is analysed by varying barrier thickness and oxide thickness. The positive V T obtained for a very thin 3 nm AlGaN barrier layer enables the enhancement mode operation of the MOSHEMT. These devices, along with depletion mode devices, are basic constituents of cascode configuration in power electronic circuits. The expressions developed are used in conventional long-channel HEMT drain current equation and evaluated to obtain different DC characteristics. The obtained results are compared with experimental data taken from literature which show good agreement and hence endorse the proposed model. Keywords. Two-dimensional electron gas; density of state; high electron mobility transistor; metal oxide semiconductor high electron mobility transistor; normally-off; quantum capacitance. PACS Nos 60; 70. Introduction AlGaN/GaN devices are promising candidates for microwave and power electronic applications because of their unique properties such as high two-dimensional electron gas (DEG) density of 0 3 cm,maximum oscillation frequency (f max )of9ghzandoutput power density of 3.65 W mm at 8 GHz []. The DEG concentration in the conventional AlGaN/GaN high electron mobility transistor (HEMT) device plays a vital role [,3] and it has a strong dependence on the Al-content of the AlGaN layer [4]. Scaling of the barrier layer has a risk of increase in gate leakage current, current collapse and hot electron effect [5]. The metal oxide semiconductor high electron mobility transistors (MOSHEMTs) have thin dielectric layers such as Al O 3 [6] under the gate to minimize the leakage current. Very low gate leakage current of 0 Amm is achieved in AlGaN/GaN MOSHEMTs [7]. Charges occupying oxide/algan interface traps, depending upon the position of Fermi energy level, help to deplete the DEG density in the quantum well at AlGaN/GaN interface and hence shift V T towards positive values [8]. MOSHEMT with atomic layer deposition (ALD) of SiO as gate dielectric on 7.5 nm thick Al 0.6 Ga 0.74 N barrier possesses a V T of.5 V with fixed oxide/algan interface charge concentration of.6 0 cm [9]. For Al-mole fraction of 0.5 the critical barrier thickness is around 6 nm for the formation of DEG in the well [0]. Ultrathin subcritical AlGaN barrier layer is ideal for the realization of normally-off (E-mode) devices because thin barrier forms negligible DEG density at zero gate bias (V gs ). With only 3 nm thick Al 0.5 Ga 0.75 N barrier and 0 nm thick SiO layer, V T of 4 V is obtained []. Compact charge-based model for current voltage and capacitance voltage characteristics in AlGaN/GaN HEMTs is presented by considering all the nonideal factors as in refs [,3]. However,

2 3 Page of 7 Pramana J. Phys. (07) 88: 3 there is no suitable model which illustrates the effect of charge trapping at oxide/barrier interface in case of MOSHEMTs. Therefore, our present work focusses on a proper model for MOSHEMTs by considering oxide/ barrier interface DOS to achieve normally-off operation. The organization of this paper is as follows. The model is developed by considering necessary energy band diagrams and HEMT physics in. The MATLABbased simulation results of the developed model are compared graphically with the experimental results from the literature presented in 3. Finally the conclusion has been drawn in 4.. Model development The basic expression for sheet charge concentration in HEMT device is given by [4] n s = σ pol ε AlGaN [φ s + E F (n s ) E C ], () qd AlGaN where σ pol is the total spontaneous and piezoelectric polarization induced charge concentration, ε AlGaN and d AlGaN are permittivity and thickness of AlGaN, q is the charge of the electron, E F (n s ) is the difference between the Fermi level and the bottom of conduction band in GaN layer which is again a function of sheet charge density, φ s is the surface potential and E C is the discontinuity in the conduction band at AlGaN/GaN interface. For enhancement mode device the surface potential φ s can be represented as φ s = φ s0 V gs where φ s0 is the surface potential at zero gate bias. So eq. () becomes n s0 = σ pol ε AlGaN [φ s0 + E F (n s0 ) E C ]. () qd AlGaN. Dependence of n s on oxide/algan interface DOS The oxide/barrier interface energy states are continuous having a charge neutral state (E NL )towardsthe centre. All the levels above this state are acceptor states and levels below it are donor states [5]. As per the definition of Fermi level (E F ) all the levels above it are empty while those below it are filled with electrons. This results in the ionized donor states between E NL and E F while the acceptor states are neutral. Assuming all the states between E NL and E F are ionized, the interface charge is given by Charge concentration = DOS electronic charge energy Q it = D it q(e NL E F ). (3) Here D it represents the interface DOS and Q it represents the interface charge. The barrier depletion charge along with the oxideinterface charge results in a potential drop V ox which can be given by V ox = Q D + Q it, (4) where Q D is the depletion charge and is the oxide capacitance. The depletion charge is formed in the barrier due to the polarization-driven movement of free electrons from the barrier to the triangular quantum well and can be formulated as Q D = qn D d AlGaN, (5) where N D is the unintentional doping concentration in AlGaN barrier. Making use of eqs (3 5) we get V ox = qn Dd AlGaN + D it q(e NL E F ). (6) From figure it can be written as φ s0 = φ M + V ox χ AlGaN and E NL E F = q(φ s0 φ 0 ), where φ M is the work function of the metal, χ AlGaN is the electron affinity for AlGaN and φ 0 is the potential difference between the neutral level and the conduction band edge. Introducing these relations in eq. (6) we get the dependence of surface potential on DOS as in eq. (7). φ s0 = γ(φ M χ AlGaN ) + ( γ)φ 0 γqn Dd AlGaN, (7) where γ = + D it q. / Substituting eq. (7) in eq. () we shall get the DEG sheet charge density at zero gate potential as in eq. (8). n s0 = σ pol ε [ AlGaN γ (φ M χ AlGaN ) + ( γ )φ 0 qd AIGaN γqn ] Dd AlGaN + E F (n s0 ) E C. (8) However, the Fermi level can be expressed as a secondorder expression [6 8], which gives a good fitting to the numerical solution of eq. (8), where E F (n s0 ) is given by E F (n s0 ) = k + k n / s0 + k 3n s0, (9) where k, k and k 3 are constants defined in [6]. Making use of eqs (8) and (9) and solving for n s0 we get [9] n s0 = [ A + A (B + Cφ s0 F)], (0)

3 Pramana J. Phys. (07) 88: 3 Page 3 of 7 3 qv OX Vacuum level qv OX Vacuum level q AlGaN q AlGaN q M q S0 q 0 q M E F E NL C E F (n S) E F q S q 0 E NL C E F (n S ) Metal SiO d AlGaN GaN Metal SiO d AlGaN GaN (a) (b) Figure. Conduction band profile for metal/oxide/algan/gan interface for (a) V g = 0and(b) V g >V T. where ε AlGaN k A = (ε AlGaN k 3 + qd AlGaN ), () B = ε AlGaN(k E C ) (ε AlGaN k 3 + qd AlGaN ), () ε AlGaN C = (ε AlGaN k 3 + qd AlGaN ), (3) d AlGaN qσ pol D = (ε AlGaN k 3 + qd AlGaN ). (4) The DEG charge density at any gate voltage is denoted as n s and can be obtained by replacing φ s0 with φ s + V gs in eq. (0) and can be written as in eq. (5). [ n s = A + A (B + C(φ s + V gs ) D)].. Electric field (5) The near-surface electric field across the barrier can be predicted by [0] E s = q(σ pol n s ), (6) ε AlGaN where n s is a function of the gate voltage..3 Quantum capacitance The total capacitance across the MOSHEMT junction is given by [] as follows: [ ] C eq = + C it + ( ), (7) /C b + /C q where C it is the capacitance due to interface traps, C b is the capacitance due to barrier layer and C q represents the quantum capacitance formed in DEG. If we neglect the variation in interface states and assume that C b is much greater than C q, the total capacitance becomes C eq = C q + C q, (8) where = ε oxide /t oxide and C q = (qn s )/ φ s. Quantum capacitance is formed at the DEG region due to the penetration of Fermi level into the conduction band. It can be obtained by differentiating the sheet charge density with respect to the surface potential as in eq. (9) []. C C q = q.4 Threshold voltage [ A + ] A (B + Cφ s D) A (B + Cφ s D). (9) To make the device off, DEG must be completely depleted (n s = 0). As can be seen in figure, under this condition, E F (n s ) reduces to zero. Putting these conditions in eq. () and replacing φ s with φ s0 + V T where φ s0 is given by eq. (7), the expression for V T can be obtained as in eq. (0). V T = γ(φ M χ AlGaN )+( γ)φ 0 γqn Dd AlGaN E C σ polqd AlGaN ε AlGaN. (0)

4 3 Page 4 of 7 Pramana J. Phys. (07) 88: 3 3. Simulation results and discussion E F S E NL Metal SiO dalgan C GaN Figure. Conduction band at pinch-off. Now C eq and V T from eqs (8) and (0) respectively can be used in drain current equation for HEMT in linear mode [3]. I d,linear = μ GaN C eq ( ) Z [(V gs V T )V ds Vds L ], SD () where μ GaN is the electron mobility in GaN, L SD is the source to drain distance, V ds is the voltage applied between the drain and the source and Z is the width of the channel. Similarly, the saturation mode current equation is given by I d,sat = μ GaN C eq ( ) Z (V gs V T ). () L SD The parameters for AlGaN/GaN heterostructure used for solving the model equations in MATLAB are taken from the existing literatures and indicated in table. Equation (0) is plotted in MATLAB to realize the variation of sheet charge density with respect to barrier thickness at zero gate bias as shown in figure 3. The figure confirms that the minimum barrier thickness beyond which DEG is formed is 6 nm as per ref. [0] and therefore taking 3 nm barrier is subcritical in accordance with ref. []. Further, it can be observed from the figure that for a DEG density of 0 7 m,30 nm thick barrier is required. Similarly, the electric field across AlGaN barrier obtained from eq. (6) is plotted against gate voltage as shown in figure 4. Until threshold voltage is reached, the electric field remains constant at.5 MV cm due to negligible DEG density as compared to polarization charges. Increasing gate voltage beyond threshold voltage increases DEG density at AlGaN/GaN interface, and so there is a linear decay in the electric field and at 3.5 V it becomes zero. Further increase in V g makes the electric field negative due to the accumulation of more negative charges inside the quantum well. In figure 5 the graph of gate capacitance vs. gate voltage is shown. The model results obtained from eqs (8) and (9) are correlated with the experimental results taken from ref. [7] for a device having a gate length of 6 μm. It shows a maximum capacitance of.5 pf across the gate beyond V T. For gate voltage Table. List of model parameters. Parameter Value Unit References ε AlGaN 8.8ε 0 Fm ε oxide 3.9ε 0 Fm k [6] k [6] k [6] σ pol m [4] t oxide 0, 0, 30 nm φ M (Ni) 5. ev χ AlGaN.5 ev φ 0 ev [4] N D 0 m 3 D it.5 0 cm ev [5] E C.4 ev [6] Z/L SD 00 μm/6 μm [] μ GaN 0. m V s Sheet charge Density (x0 m ) AlGaN Barrier Thickness (nm) Figure 3. DEG sheet charge density (n s ) with the variation of AlGaN barrier thickness.

5 Pramana J. Phys. (07) 88: 3 Page 5 of Electric Field (MV/cm) Gate Voltage (V) Figure 4. Electric field across AlGaN/GaN interface with the variation of gate voltage. below V T the capacitance is very small, i.e. 0.9 pf due to negligible sheet charge density. Figure 6 demonstrates the variation of V T with barrier thickness as per eq. (0). It shows a linearly decaying V T with increase in barrier thickness similar to the behaviour obtained in ref. [6]. Due to the unavailability of sufficient experimental data in literature demonstrating the above behaviour for AlGaN/GaN MOSHEMT, comparison with TCAD [8] results is preferred as illustrated in figure 6 showing good agreement. It is observed here that to attain positive V T,very thin barrier below 0 nm is required. This is in good agreement with the argument presented in ref. [0] Figure 6. Variation of threshold voltage with barrier thickness. for a device with barrier having 5% Al content. Barrier thickness of 3 nm and oxide thickness of 0 nm are considered to achieve a V T of.6 V. Figure 7 shows a plot between threshold voltage and oxide thickness. The modelled threshold voltage values are compared with the experimental values taken from ref. [9]. As per the model, V T decreases linearly with increase in oxide thickness which is also evident from experimental results. Finally, the drain current in eqs () and () are plotted with respect to V gs and V ds to obtain I d V gs and I d V ds characteristics respectively. The oxide thickness considered to obtain I d V gs characteristics is 0 nm Figure 5. Gate capacitance with the variation of gate voltage. Figure 7. Threshold voltage variation with oxide thickness.

6 3 Page 6 of 7 Pramana J. Phys. (07) 88: 3 values obtained from the model presented in are appropriate. 4. Conclusion Figure 8. Drain current characteristics with respect to gate voltage for t ox = 0 nm. In this paper, the authors have attempted to establish an analytical model for predicting capacitance and threshold voltage characteristics of ultrathin Al 0.5 Ga 0.75 N/GaN MOSHEMT by developing suitable models for surface potential and sheet charge concentration in the DEG formed at AlGaN/GaN heterointerface. It is evident that a positive V T of.6 V is obtained by decreasing the barrier thickness below the critical value, i.e., 3 nm which leads to normally-off operation of MOSHEMT. The predicted C g V g, I d V gs,andi d V ds characteristics consistently agree with the experimental results available in the literature. and for I d V ds the thickness is 0 nm. The characteristics obtained from the developed models are compared with the respective experimental results taken from ref. [] and are shown in figures 8 and 9. In figure 8 we obtained a threshold voltage of.6 V and drain current of 90 ma mm at V gs = 6Vfor V ds = V. In figure 9 the saturation drain currents of 460 ma mm at V gs = 6 V, 300 ma mm at V gs = 5V,80mAmm at V gs = 4 V are obtained. This also proves that the capacitance and threshold voltage Figure 9. Drain current characteristics with respect to drain voltage for t ox = 0 nm. Acknowledgements The authors acknowledge the Microelectronics Computational Lab in the Department of Electronics & Communication Engineering of National Institute of Technology Silchar, India for providing all necessary facilities to carry out the research work. References [] Z H Feng et al, Electron Device Lett. 3(), 386 (00) [] T R Lenka and A K Panda, Semiconductors 45(9), (0) [3] T R Lenka and A K Panda, Semiconductors 45(5), 660 (0) [4] M Miyoshi, M Sakai, S Arulkumaran, H Ishikawa, T Egawa, M Tanaka and O Oda, Jpn J. Appl. Phys. 43(), 7939 (004) [5] M Higashiwaki, R Chu and U K Mishra, IEEE Trans. Electron Device 58(), 68 (0) [6] P Ye, B Yang, K Ng, J Bude, G Wilk, S Halder and J Hwang, Int. J. High Speed Electron. Systems 4(3), 79 (004) [7] A Colon and J Shi, Solid State Electron. 99, 5 (04) [8] R Swain, J Panda, K Jena and T R Lenka, J. Comput. Electron. 4(03), 754 (05) [9] C J Kirkpatrick et al, Electron Device Lett. 33, 40 (0) [0] A Endoh et al, Jpn J. Appl. Phys. 43(4B), 55 (004) [] R Brown et al, Electron Device Lett. 35(9), 906 (04) [] S Khandelwal and T A Fjeldly, Solid State Electron. 76, 60 (0) [3] F M Yigletu and S Khandelwal, IEEETrans.ElectronDevices 60(), 3746 (03) [4] O Ambacher et al, Appl. Phys. Lett. 85(6), 3 (999) [5] M Tapajna and J Kuzmík, Jpn. J. Appl. Phys. 5, o8jn08-5 (03) [6] S Kola, J M Golio and G N Maracas, IEEE Electron Device Lett. 9(30), 36 (988)

7 Pramana J. Phys. (07) 88: 3 Page 7 of 7 3 [7] M Li and Y Wang, IEEE Trans. Electron Devices 55(), 6 (008) [8] X Cheng, M Li and Y Wang, IEEE Trans. Electron Devices 56(), 88 (009) [9] K Jena, R Swain and T R Lenka, Pramana J. Phys. DOI:0.007/s (05) [0] D Yan, H Lu, D Cao, D Chen, R Zhang and Y Zheng, Appl. Phys. Lett. 97(5), (00) [] D A Deen and J G Champlain, Appl. Phys. Lett. 99, 5350 (0) [] K Jena, R Swain and T R Lenka, J. Semiconductors 36(3), (05) [3] S M Sze, Physics of semiconductor devices, 3rd edn (John Wiley & Sons, 007) [4] J Robertson and B Falabretti, J. Appl. Phys. 00, 04-8 (006) [5] S Arulkumaran, T Egawa and H Ishikawa, Jpn J. Appl. Phys. 44, 8 (005) [6] Z Wang, B Zhang, W Chen and Z Li, IEEE Trans. Electron Devices 60(5), 607 (03) [7] J H Bae, I Hwang, J M Shin, H-I Kwon, C H Park, J Ha, J Lee, H Choi, J Kim, J B Park, J Oh, J Shin, U I Chung and J H Lee, Proceedings of IEEE IEDM, 303 (0) [8] SILVACO, International Incorporated, ATLAS User s Manual, Version 5..0.R. USA, Silvaco inc. (00) [9] R Brown, A Al-Khalidi, D Macfarlane, S Taking, G Ternent, I Thayne and E Wasige, Phys. Status Solidi C, 844 (04)