Modelling the Vertical PNP - Transistor using ICCAP and VBIC

Transcription

1 Modelling the ertical PNP - Transistor using AP and Jörg erkner nfineon Technologies AG Munich, Germany 1 Abstract: This paper deals with modelling the vertical pnp-transistor (PNP) using the 95 model. The vertical pnp-transistor is an important element in modern imo technologies. t reaches higher transit frequencies and higher current driver capabilities as the usual lateral or substrate pnp-transistor. On the other hand, based on it s complicated structure, several parasitic effects may occur, which are investigated in this article. Furthermore, measurement and simulation results in comparison of the and the iemens Q3 model are presented. 1 ntroduction PNP Transistor ross ection Parasitic Effects Latch Up ollector urrent ompliance Quasisaturation Measurement ircuits PNP Modelling Model Depletion harge Model Normalised ase harge Transport urrents ollector Resistance and Quasisaturation Transit Time Q3 - Model Normalised ase harge Transit Time ubcircuit Models PNP Measurement and imulation Results ummary References This paper is intended for the HP AP User Meeting, June 1999 in Marseille, Rev: UM150.DO, ,

2 1 ntroduction The model [1] became more and more public during the last years and several papers were published, referring to model the npn transistor using [3][4][5][10]. On the other hand, so far no results announced regarding to the pnp version of the model. ased on it s equivalent circuit, the model seems to be especially suitable to model the PNP transistor. That is why, this paper is concerned with modelling the PNP using in comparison to the iemens Q3 model. ection 2 of this paper outlines some details of the PNP transistor and the appropriate measurement circuits. n ection 3, important features for the and the Q3 model are explained. Finally, in ection 4 D- and A- measurement and simulation results are presented. 2 PNP Transistor 2.1 ross ection n contrast to the well known integrated npn-transistor, the vertical bipolar transistor (PNP) consists of five technological layers: p-emitter, n-base, p-collector, n-pocket and p-substrate (Fig. 1). The PNP reaches higher transit frequencies and current driver capabilities as a lateral pnp- or substrate pnp-transistor. n comparison to the substrate pnp-transistor, the PNP collector is not grounded, resulting in a more flexible usage in the circuit design. NP p-emitter E n-ase p-ollector PARN PNP REX PARP n-pocket p-ubstrate Fig. 1: PNP cross section onsidering the PNP structure it is obviously, that there are two parasitic transistors additional to the main PNP transistor: the parasitic npn-transistor PARN (consisting of n-base, p-collector and n- pocket) and the parasitic pnp-transistor PARP (consisting of p-collector, n-pocket and p-substrate). oth these transistors, together with high collector resistance values, may cause several parasitic effects, explained in the next section in detail. The occurrence of these effects depends on technological parameters (e.g. collector sheet resistance), on geometrical parameters (transistor design) and the operation point conditions. 2

3 2.2 Parasitic Effects Latch Up f Latch Up occurs, we can observe a steep increase of both the n-pocket- and the substrate currents in the Gummel plot (Fig. 3). Here the inner R voltage drop biases the N-junction in forward direction. The parasitic npn-transistor (PARN) enters the active inverse mode, it s emitter current gains the PNP base current. oth the collector current and the R voltage drop increase. This results in a positive feedback. PARN creates the n-pocket current, whereas the parasitic pnp-transistor (PARP) creates the substrate current, working in the active forward mode. oth currents are limited only by external sources. That is why, the operating points of an integrated circuit may be affected, if Latch Up occurs. A high collector resistance value is a prerequisite for Latch Up. t is caused by the -depletion layer extension into the collector. onsequently Latch Up appears only at high collector voltages (Fig. 4). NP p-emitter E PNP n-ase -Depletion Layer REX PARN p-ollector p-ubstrate N PARP n-pocket Fig. 2: Latch UP, R is pinched by the -depletion layer Fig. 3: Gummel Plot,, N, U = f ( ), N = + 4, = - 10, Latch Up is indicated by the steep increase of both N and ub at E = 0.85 Fig. 4: Gummel Plot,, N, U = f ( ), N = + 4, = - 5, No Latch Up occurs at lower 3

4 2.2.2 ollector urrent ompliance Another parasitic effect is the collector current compliance. This effect may occur, if the N-depletion layer extension into the collector is high enough to pinch off the collector resistance. The current path through the collector is pinched off similarly to a JFET. onsequently the collector current is limited. Fig. 5 illustrates the situation in the cross section. Fig. 6 shows a typical output characteristic [15]. This effect may be avoided using a constant offset voltage at the N-depletion layer ( Fig. 7 ). NP p-emitter E n-ase PNP REX p-ollector PARN N-Depletion Layer PARP n-pocket p-ubstrate Fig. 5: ollector resistance pinch off, R is pinched by N-depletion layer Fig. 6: Output characteristic = f ( ), = parameter ; collector current compliance is caused by R pinch off Fig. 7: Output characteristic = f ( ), = parameter; using an offset voltage off = + 4 no collector current compliance appears 4

5 2.2.3 Quasisaturation Quasisaturation does not occur only for PNP transistors, however, a PNP is particularly affected by this effect. Generally, quasisaturation occurs, if the outer base-collector junction is reverse biased ( vpnp > 0, as in the active forward mode), while the inner base-collector junction is already forward biased ( vpnp < 0, as in saturation). Quasisaturation is caused by a current and voltage dependent collector resistance. At high collector currents the internal voltage drop R is high enough to drive the transistor into quasisaturation. onsidering an forward output characteristic, Q appears as an increase of the output conductance with decreasing collector voltage ( Fig. 9). Fig. 8: Output characteristic = f ( ), = Par. ; no Quasisaturation at low collector currents Fig. 9: Output characteristic = f ( ), = Par. Quasisaturation occurs at high collector currents 2.3 Measurement ircuits According to the PNP equivalent circuit, a number of measurement circuits is necessary to characterize the main PNP and the two parasitics PARN and PARP. n Fig. 10 and Fig. 11 the general D- and A- measurement circuits are shown for an AP environment, where MU s 2 are available. The appropriate MU settings for the particular circuit are defined in Table MU = ource Monitor Unit (e.g. in HP4142) 3 This table does not contain definite values, because they depend on the used technology. 5

6 E PNP MU E NWA PORT1 E PNP MU E MU PARN MU PARN NWA PORT2 N MU N MU PARP MU N MU N MU PARP MU Fig. 10: General PNP D- measurement circuit Fig. 11: General PNP A- measurement circuit Table 1: MU settings for PNP measurement circuits ircuit MU1 E MU2 MU3 MU4 N MU5 PNP PAR N PAR P fg_vpnp 0 - = sweep fwd off off -1 fwd off off fg_vpnp 0 - = sweep - + ( N = offset) offset rg_vpnp - E - = sweep rev fwd off fg_parp = sweep 0-1 off rev fwd rg_parp off off fwd =sweep re_vpnp 0 - = sweep = 0 N = 0 = 0 at off off rc_vpnp 0 - = sweep = F * N = 0 = 0 at off off fo_vpnp 0 - = sweep1 - = sweep2 0-1 fwd off off -1 fwd off off fo_vpnp 0 - = sweep1 - = sweep2 + ( N = offset) offset ro_vpnp - E = - = sweep rev off off sweep2 fo_parn = sweep1 + N = - 1 off fwd off sweep2 ro_parn 0 + = sweep2 + = sweep1 0-1 fwd off off acmf_vpnp f M = sweep1 acsf_vpnp f M = const. 0 - = sweep2 - = sweep3 0-1 fwd off off 0 - = sweep1 - = sweep2 0-1 fwd off off 6

7 3 PNP Modelling Model The 95 was developed by a committee of U semiconductor companies to overcome the deficiencies of the GP 4 model, which has remained unchanged in the last 20 years. The main features of the 95 model are [1] [3] [5]: ase current definitions independent of the transfer currents, no beta parameters are used First order distributed-base model Early effect model is based on the junction depletion charge Modified Kull model for quasisaturation Parasitic substrate transistor ingle piece depletion capacitance model mproved temperature scaling Weak avalanche for junction Parasitic overlap capacitances elf heating model A complete description of the model equations is behind the scope of this paper (see [2][6]), we will focus on the equations, describing the Early effect, the quasisaturation and the transit time Depletion harge Model The 95 model is focused on charges, not capacitances. Normalised charges are used both for D - and A equations. Given the voltage dependent capacitance of a reverse biased junction as JO ( ) = (1) M 1 P where are P and M the built-in potential and the grading coefficient, respectively, we have after integration the following relation for the voltage dependent charge: (1 M ) Q( ) = 0 ( ) d = JO (1 P M 1 1 ) n 95 the second factor of eqn (2) is realised as a function, called qj. This function represents a normalised charge 5. Using this normalised charge, the charge itself is given by multiplication with the zero bias capacitance, given as model parameter: (, P M ) Q ( ) = JO * qj, ased on this principles, the normalised depletion charges are calculated in the model as fundamental values 6. Note, that the normalised charge depends on the voltage across the junction and on both the model parameters P, M as well, whereas the parameter JO does not affect qj. P (2) (3) 4 GP = pice - Gummel Poon Model 5 Note, that the dimension of this normalised charge is olt. 6 The 95 model includes two depletion charge models: the regional model (GP model) and a new singlepiece model, which limits the capacitance to a constant value for bias values greater than the built in potential. The appropriate model is selected using AJ as a flag: if AJ <= 0, the regional model is used, otherwise the single-piece model. 7

8 3.1.2 Normalised ase harge The normalised base charge is defined as where 2 [ ] q = 1 b q + q + q2 (4) 2 q qdbe = + + ER 1 1 qdbc (5) EF tf q2 = + KF tr KR (6) The Early voltages ER, EF and the knee currents KF, KR are the model parameters. Note, that for q 1 the normalised charges q dbe and q dbc (unit ) are used, instead of branch voltages be and bc, as in the GP model. As explained before, the normalised charges q deb and q dbc are dependent on the internal voltages bei and bci again Transport urrents The forward and reverse ideal transport currents are defined as 7 tf tr bei = exp 1 NF t bci = exp 1 NR t (7) (8) where are the transport saturation current, NF and NR the emission coefficients and t the temperature voltage. ased on these equations we have the forward and reverse nonideal transfer currents tzf and tzr as 8 and = tzf = tzr q q tf b tr b (9) (10) where q b is the normalised base charge. n this way a voltage dependent output conductance is realised in. 7 The index i denotes a voltage between the internal nodes. 8 The separate definition of tzf and tzr is necessary, because the zero phase current tzf is used in the additional excess phase network of the 95 model as the control current. Using this network, the current txf with an additional excess phase is calculated. f the excess phase parameter TD is specified, the current txf is used in the model instead of tzf. 8

9 3.1.4 ollector Resistance and Quasisaturation The collector resistance consists of two parts: the constant external resistance R X and the epi layer resistance. The epi layer resistance depends on both the collector current and the epi layer voltage drop. According to the KULL model [7], the current through the epi layer ohm is calculated as: with K ohm bci = = rci + t K bci K bcx R 1+ GAMM exp bci t 1 + log 1 + K K bci bcx (11) (12) K bcx = 1+ GAMM exp bcx t (13) where R (the epi resistance under equilibrium condition) and GAMM (the epi charge coefficient) are the model parameters. Eqn (11) takes into account the epi layer resistance reduction, if the transistor enters quasisaturation in the range of ohmic behaviour. Examining the effect of the quasisaturation parameters GAMM and R, it is useful to consider eqn (11) more in detail. Rearranging this relationship, it reduces to a simple equation of the form = / R: where and ohm rci cor rci+ = R = = bci t K bci cor bcx K bcx (14) (15) 1 + K bci log (16) 1 + K bcx OR here is a correction voltage, depending on both the epi layer doping parameter GAMM and the epi layer voltage drop rci. This correction voltage is added to rci. n the active normal case ( bcx < 0, bci < 0) OR is zero, but in quasisaturation OR increases. For a given R value this results in an increasing value for the current ohm. n this way the effective collector resistance is reduced. Additional to the epi layer resistance reduction, the effect of carrier velocity saturation (nonohmic behaviour) may occur in quasisaturation. Eqn (17) takes into account this effect by modifying the current ohm : rci = 1+ O 1+ ohm R ohm rci + O HRF 2 (17) 9

10 where O (saturation velocity voltage) and HRF (high current R factor) are the new model parameters. Eqn (17) shows, that the 95 model modifies the value of R using the factor sqrt(1+ R * ohm / O) instead of the factor (1+ ( rci / O) 2 ) used by the KULL model. rci = ohm R ohm 1+ O 2 (18) onsidering the simplified eqn (18), we can see: if the voltage drop R * ohm is lower than O, rci and ohm are nearly identical. f the voltage drop reaches O, the denominator increases and rci decreases ( rci < ohm ). Additional, eqn (17) shows that the value of O is changed depending on rci and the model parameter HRF. Thus the effect of rci reduction increases with rci. To avoid numerical problems rci is calculated in eqn (17) as ( rci ) ½ Transit Time The forward transit time is defined as: t ff = TF 2 1 (19) tf bci ( 1+ QTF q ) 1+ XTF exp tf + TF 1.44 TF This definition is identical to the GP model, except the additional term (1+ QTF * q1). Note, that q1 includes a dependence on the internal branch voltages bei and bci using the normalised charges q dbe and q dbc and the ideal current tf is used in eqn.(19). 10

11 3.2 Q3 - Model The iemens Q3 model is an improved pice Gummel Poon model (GP). The main advantages over the GP model are: base current definitions independent of the transfer currents, no beta parameters are used improved temperature scaling improved transit time equation A detailed description of the Q3 model is again behind the scope of this paper (see [13][14]). We will consider here only the Q3 base charge and the transit time equation Normalised ase harge The used normalised base charge definition is identical to the GP: Q Q = * 1 1 4Q2 2 where 1 Q1 = ' ' ' E ' 1 AF AR and Q = F R 2 KF + KR (20) (21) (22) This base charge definition results in an voltage independent output conductance Transit Time The Q3 transit time formulation is different to the model: T FF = 1 TF bc TA MTA 1+ cb TK * 1 TK * 1+ bc TG * 1 TG implifying this equation as T FF = A (24) we can consider the terms A, and more closely (Fig. 12). Term A describes the voltage dependence of T FF, using the well known space charge capacitance formulation (model parameters TA, MTA). Term is used to describe the T FF increase with increasing collector current. Again, the space charge capacitance formulation is used to introduce an additional voltage dependence of the knee current parameter TK, using the parameters TK, MTK. MTK MTG KTK KTK (23) 11

12 At very high collector currents the increase of T FF attenuates and T FF approaches a limiting value. This behaviour may be modelled using term and the model parameters TG, TG, MTG. T FF TG,TG, MTG, KTK TK,TK, MTK, KTK TA, MTA Fig. 12: Effect of Q3 - parameters on T FF Equation (23) allows a good fit for various types of T FF curves, but it may be complicated determine the model parameters, because the terms A, and affect each other. The Q3 model does not take into account the Quasisaturation and, moreover, it does not contain parasitic devices. That is why a subcircuit model is always necessary to model integrated transistors using Q ubcircuit Models The model contains one parasitic transistor, sufficient for npn modelling. For PNP modelling however, a subcircuit model is necessary to take into account the parasitic substrate transistor PARP (Fig. 13). The Q3 subcircuit model consists of three transistors, each one modelled by an Q3 model, and an external collector resistance (Fig. 14). E E PNP PNP (Q3) NP PARN PARN (Q3) REX PARP (GP) NP PARP (Q3) Fig. 13: subcircuit model for PNP Fig. 14: Q3 subcircuit model for PNP 12

13 4 PNP Measurement and imulation Results n this section some measurement and simulation results are presented. For the sake of an practical assessment we will consider the simulation results in comparison to the Q3 subcircuit model, used so far for the PNP transistor at nfineon Technologies [15] [16]. The simulations are made using AP 5.2 and pectre for the model respectively aber for the Q3 model. Gummel Plot (Fig. 15) Fig. 15 shows forward Gummel characteristics for various collector voltages. At = -3 the transistor is in the active forward mode, at = -1 the device enters saturation at = -0.9, indicated by the increasing n-pocket current and at = -0.2 the device is in saturation during the whole sweep. The simulated n-pocket current N is for both the models good in agreement with the measurement. The substrate current does not appear under active forward and saturation operating conditions, as explained in section 2.2. n the case of Latch Up both the models are not able to model substrate current exactly, because the R parameter value, sufficient for active forward and saturation operating conditions, is to low. Output haracteristic (Fig. 16, Fig. 17) The output characteristics were measured at various base current (- = µa) and collector voltage sweeps (- max = 2.5 and - max =15 ). As can be seen from Fig. 16, in the low current range simulations and measurements in agreement for both the models. n the mid current range (- = µa), delivers betters results, because the Q3 does take into account the quasisaturation. This statement is true in the high current range (- = µa) as well, however only in the low voltage range up to - = 5. onsidering Fig. 17 we have to note, that the output conductance in the high current range for - > 5 is modelled badly by. ontrary to an npn transistor, there is no way to model the output conductance both in the low and high current range exactly using, despite it s improved Early voltage formulation (eqn(5)). The strong increase of the output conductance vs. collector current seems to be typical for PNP transistors. Note, that this is not caused by self heating or avalanche effect. That is why, there is no possibility to model the effect by the appropriate self heating or avalanche parameters of the model. urprisingly, on the other hand, the Q3 model delivers better results in the high voltage range (- = ) as the, despite it uses the simple GP Early voltage formulation (21). Transit Frequency haracteristic (Fig. 18, Fig. 19) The Transit frequency characteristics where measured at various collector voltages: - = 0.2, 0.5, 1, 3, 5, 10. Modelling these characteristics, we are faced with two problems: a strong dependence of f T vs. and a steep decrease of f T vs. at higher currents As expected, the Q3 model is able to simulate the transit frequency from - = 1 up to - = 10 sufficiently in agreement with the experimental data (Fig. 18). n the saturation range (- = 0.2, 0.5 ), however, considerable deviations appear (Fig. 19). The model is, contrary to the Q3 model, not able to simulate the f T dependence of f T vs.. The simulated f Tmax -value at - = 10 is nearly 20% lower than the measured value and, moreover, the f T decrease at high currents is not modelled. Although for the model the GP f T equation is modified by QTF (eqn(19)), it is not possible to get a better fit of f T vs. using the parameter QTF. n the saturation range, similarly to the Q3 model, considerable deviations appear 13

14 Q3 = - 3 = - 3 = - 1 = - 1 = = Fig. 15: Gummel Plot,, N, ub, N = f ( ), = Parameter 14

15 Q3 - = 50, 100, 150, 200, 250 µa - = 50, 100, 150, 200, 250 µa - = 10, 20, 30, 40, 50 µa - = 10, 20, 30, 40, 50 µa - = 1, 2, 3, 4, 5 µa - = 1, 2, 3, 4, 5 µa Fig. 16: Output characteristic = f ( ), = Parameter, max =

16 Q3 - = 50, 100, 150, 200, 250 µa - = 50, 100, 150, 200, 250 µa - = 10, 20, 30, 40, 50 µa - = 10, 20, 30, 40, 50 µa - = 1, 2, 3, 4, 5 µa - = 1, 2, 3, 4, 5 µa Fig. 17: Output characteristic = f ( ), = Parameter 16

17 Q3 = - 10 = - 5 = - 3 Fig. 18: Transit frequency characteristic f T = f ( ), - = 3, 5, 10 17

18 Q3 = - 1 = = Fig. 19: Transit frequency characteristic f T = f ( ), - = 0.2, 0.5, 1 18

19 5 ummary n this paper the suitability of the model for PNP modelling was investigated. The PNP structure and typical parasitic effects as Latch Up, collector current compliance and quasisaturation were explained. D- and A- measurement circuits suitable for an AP environment where shown. ome main features of the 95 and the Q3 model where explained using the appropriate equations. Measurement and simulation results are presented in comparison to the Q3 model, resulting in the following conclusions: The main advantage of Q3 model is the transit time equation. Although this equation is not physical based, it allows to fit transit time characteristics of various shapes. The main disadvantage of Q3 model is the lack of a quasisaturation model. The main advantage of the model is the quasisaturation model. The main disadvantage of model is the inaccurate modelling of the transit time at higher collector voltages. Table 2: omparison of and Q3 for PNP modelling topic Q3 quasisaturation good not available transit time poor at higher collector voltages good output conductance good up to mid currents, poor at sufficient higher collector currents n-pocket current good good ummarising we can say, that the model delivers better D-results as the Q3, at least up to mid currents, because it takes into account the quasisaturation. The A-results, however, are bad at higher collector voltages. Taking into account the fact, that in modern RF circuits low supply voltages (e.g. 3) are usual, the deficiencies of the model at higher voltages are less important. From this point of view, is the preferred model for PNP modeling. Nevertheless an improved pnp-version of the model is necessary, including at least an improved transit time equation. 19

20 6 References Model [1] ertical ipolar nter ompany 1995: "An mproved ertical, ipolar Transistor Model". n: Proceedings of the EEE ipolar ircuits and Technology Meeting, 1995, pp [2] "95 Model Definition, Release 1.1.5, Jul 28, 1996". [3] McAndrew,.. et.al. : "95, The ertical ipolar nter-ompany Model". EEE Journal of olid tate ircuits, ol.31, No.10, October 1996 [4] McAndrew,.. et.al. : " Fundamentals for JT Design". n: Proceedings of the EEE ipolar ircuits and Technology Meeting, 1998, pp [5] anfield, L.; Dunn, M.; Lynch, D. : " and MEXTRAM: Two state-of-the-art JT models". Proceedings of the 1996 HP Eesof High -Frequency imulation and Device Modeling eminar, Fall1996 [6] erkner, J.: "A Review of the 95 ipolar Transistor Model". iemens AG HL D M PX1,.Laborbericht L143 vom [7] Kull, G.M., et. al.: "A Unified ircuit Model for ipolar Transistors ncluding Quasi aturation Effects". EEE Transactions on Electron Devices, ol. ED - 32, No. 6, JUNE 1985, pp [8] erkner, J.: "Parameter Extraction for JT Quasisaturation Models". n: European -AP User Meeting Proceedings, Oct.1997 erlin [9] HP : AP 5.01, Model File,.../iccap/examples/model_files/bjt/vbic_npn.mdl [10] innesbichler, F.X., Olbrich, G.R. : " - The ertical ipolar ntercompany Model, Ein Überblick über das Modell und über zugehörige Parameterextraktionen". AP Workshop - Reihe 1997 / 98 [11] innesbichler, F.X.*, Olbrich, G.R.*, ischka, F.** : " - The ertical ipolar ntercompany Model, Overview About the Model, Relationship to the Gummel - Poon Model, Parameter Extraction, Modeling Reference ook , Hewlett Packard GmbH öblingen; * Technical University Munich, nstitute of High Frequency Techniques ** Hewlett Packard GmbH öblingen [12] erkner, J.: Parameterextraktion für das - Modell". iemens AG HL D M PX1,.Laborbericht L136 vom Q3 Model [13] Meiser, P. : "ipolar level 3 model". iemens AG HL AD TF, [14] erkner, J., Kevni üyüktas, K. : "Modellparameter des Q3 - Modells". nfineon Technologies HF D, 5/99 [15] erkner, J.: Messung und Modellierung der PNP - Transistoren P852, P8532, P8543, P1172, P1492, P12 und P100 der 6A - Technologie. iemens AG HL D M PX1,.Laborbericht L135 vom [16] erkner, J.: " Q3 - ubcircuitmodell für die vertikalen PNP - Transistoren P1, P4 und P12 der 6HF - Technologie ". iemens AG HL D M PX1,.Laborbericht L 138 vom