On the transit time of polysilicon emitter transistors

PERGAMON

Solid-State Electronics 43 (1999) 189±197

On the transit time of polysilicon emitter transistors Sukla Basu, R.N. Mitra, A.N. Daw * Institute of Radio Physics and Electronics, 92 Acharya Prafulla Chandra Road, Calcutta 700 009, India Received 12 October 1997; received in revised form 1 June 1998

Abstract Polysilicon emitter transistors are now being widely used in high speed bipolar circuits because of their extremely low emitter transit time tE. A model has been developed here to predict the relative contributions of the neutral polysilicon and monosilicon regions of the emitter to tE, for various device parameters. Studies have been made for both uniform and exponential doping pro®les in the mono-emitter region. Relative contributions of tE and base transit time tB towards the total forward transit time tF for various device parameters have also been studied. # 1998 Elsevier Science Ltd. All rights reserved.

1. Introduction The speed of a bipolar transistor is determined by the carrier transit time t, which is given by

that in the polysilicon region (tEP). A model has been developed here to predict the emitter transit time tE of a PET. Relative contributions of tEM and tEP to tE and that of tE and tB to tF have also been studied.

t ˆ tE ‡ tB ‡ tC ‡ tjEB ‡ tjBC : The ®rst three terms viz. tE (emitter transit time), tB (base transit time) and tC (collector transit time) are due to contributions from minority carrier charge stored in the emitter, base and collector regions respectively. The last two terms arise due to contributions from emitter±base and base±collector junction capacitances respectively. Recently polysilicon emitter transistors (PETS) have been widely used in high speed bipolar circuits for their better switching speed than conventional transistors. The emitter of a PET consists of a polysilicon region and a monosilicon region separated by an interfacial oxide layer of few angstrom thickness. Since the capacitance terms are reduced due to reduction of dimensions and new isolation techniques, the speed performance of a PET is primarily characterised by forward transit time tF which is the sum of tE and tB. tB of a PET is the same as that of a conventional transistor, while tE has two components viz. transit time in the monosilicon region (tEM) and

* Corresponding author. Tel.: +91-350-9115; Fax: +91-33241-3222.

2. Theory In order to determine the transit time tEM and tEP in the monosilicon and polysilicon emitter regions respectively, di€usion capacitances due to minority carrier charge storage in these regions are calculated and the product of emitter±base diode resistance and di€usion capacitance in the respective regions gives the transit time tEM and tEP. Although Suzuki [1] has also followed the same approach for calculating transit time, the di€erence lies in the fact that the model of hole current ¯ow used by him is basically di€erent from the model proposed by us earlier [2] and used here for calculating the charge stored in the poly- and mono-emitter regions of a PET. Also Suzuki did not take into consideration the e€ect of concentration dependent band gap narrowing e€ect and the e€ect of presence of break-up in the interfacial oxide layer. In our expression for transit time these two e€ects have also been included.

0038-1101/98/$ - see front matter # 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 8 - 1 1 0 1 ( 9 8 ) 0 0 2 4 3 - 3

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S. Basu et al. / Solid-State Electronics 43 (1999) 189±197

Fig. 1. Plot of injected minority carrier concentration in the emitter and base regions of an n±p±n PET with uniform interfacial oxide layer.

2.1. Transit time in the monosilicon emitter region of a PET The hole current density JpM in n-type monosilicon emitter region of an n±p±n PET (Fig. 1) with an arbitrary doping concentration ND(x) in the emitter region is given by [3] JpM

dpM …x† ‡ qmpM …x†E…x†pM …x† ˆ ÿqDpM …x† dx

where the electric ®eld E(x) is given by   kT 1 dND …x† 1 dn2ieE …x† E…x† ˆ ÿ ÿ 2 : q ND …x† dx nieE …x† dx

then JpM is constant in this region and solution of Eq. (1b) is given by [5] …x N …x† dx C JpM 0 Deff pM …x† ˆ ÿ NDeff …x† NDeff qDpM

…1a†

where C is the integration constant. Recalling that at the emitter±base junction pM(0) = n2i exp(qVj/kT)/ NDe€(0), the expression for hole distribution comes out to be

…1b†

pM …x† ˆ

DpM, mpM and pM represent di€usion constant, mobility and concentration of holes in the monosilicon emitter region respectively, nieE is the e€ective intrinsic carrier concentration in the emitter region and the other terms have their usual signi®cances. The ®rst component in the r.h.s of the above expression is due to non-uniform doping concentration and the second is due to non-uniform band gap narrowing in the monosilicon region. Following [4] Eq. (1a) can be written as   kT 1 dNDeff …x† E…x† ˆ ÿ …2† q NDeff …x† dx where NDe€(x) = n2i /n2ieE
ND(x). DpM and mpM are assumed to be constant in this region. If recombination in the monosilicon region is assumed to be negligible,

ÿ

n2i

NDeff …x† …x JpM qDpM

0

exp…qVj =kT † NDeff …x† dx NDeff …x†

:

…3†

Integrating the injected minority carriers in the monosilicon emitter region, the injected minority carrier charge density (charge per unit area) in this region is obtained as … WEM QpM ˆ q pM …x† dx ˆ q: 0

… WEM 0

…x 0

n2i

NDeff …x†

exp…qVj =kT † dx ÿ

NDeff …x† dx NDeff …x†

dx:

… WEM 0

JpM : DpM

…4†

S. Basu et al. / Solid-State Electronics 43 (1999) 189±197

191

Di€erentiating Eq. (4) with respect to Vj, the di€usion capacitance per unit area associated with the monosilicon region is obtained as … q2 WEM n2i d CpM ˆ exp…qVj =kT † dx ÿ dVj kT 0 NDeff …x† …x … WEM N …x† dx JpM 0 Deff dx: …5† NDeff …x† DpM 0

cs and DVgI are respectively band bending and bandgap narrowing at the interface in the mono-emitter region. For a broken interfacial oxide layer, the hole current density ¯owing through the oxide covered region, JpM,ox, is given by the same expression as in Eq. (8). Since the interfacial oxide layer is absent, the tunneling probability of holes ( ph) through the oxide free region is unity and Ge becomes very small compared to GE and GP and the current density ¯owing through the oxide free region can be written as

Noting that the emitter±base diode resistance is given by kT/q(JpM + Jn) where Jn is the electron current density, tEM can be written as

JpM,oxf ˆ

tEM

kT q CpM ˆ ˆ q…JpM ‡ Jn † …JpM ‡ Jn † … WEM … WEM n2i JpM
exp…qVj =kT † dx ÿ N …x† D Deff pM 0 0 …x  NDeff …x† dx 0 dx : NDeff …x†

…6†

In the presence of a broken-up oxide layer JpM is given by JpM ˆ …1 ÿ rox †JpM,oxf ‡ rox JpM,ox

…7†

where, rox represents percentage of oxide covered interfacial area and JpM,oxf (JpM,ox) hole current density ¯owing through the oxide free (covered) area. For a uniform interfacial oxide layer, JpM can be given by [2] JpM ˆ

qn2i ‰exp…qVj =kT †Š …GE ‡ Gp ‡ Ge †

…when Vj  kT=q†

…8†

where … WEM GE ˆ ‰…ni =nieE †2 ND …x†=DpM Š dx 0 … WEM ˆ NDeff …x†=DpM dx 0

Gp ˆ ˆ

… …WEM ‡WEP † WEM

… …WEM ‡WEP † WEM

‰…ni =nieE †2 ND …x†=DpP Š dx NDeff …x†=DpP dx

and  Ge ˆ ND …WEM †

2pmh * kT

1=2

exp‰q…cs ÿ DVgI †=kT Š=ph

  2pmh * 1=2 ˆ NDeff …WEM † exp‰q…cs †=kT Š=ph : kT

qn2i ‰exp…qVj =kT †Š …GE ‡ Gp †

…when Vj  kT=q†:

Using Eqs. (7)±(9), JpM can be written as  1 ÿ rox JpM ˆ qn2i exp…qVj =kT † …GE ‡ Gp †  rox ‡ ˆ qn2i exp…qVj =kT †=M …GE ‡ Gp ‡ Ge †

…9†

…10†

where  ÿ1 1 ÿ rox rox Mˆ : ‡ …GE ‡ Gp † …GE ‡ Gp ‡ Ge † Replacing qn2i exp(qVj/kT) by MJpM, Eq. (6) is rewritten as … WEM JpM M tEM ˆ dx NDeff …x† …JpM ‡ Jn † 0 …x  … WEM NDeff …x† dx 0 ÿ dx : …11† NDeff …x†DpM 0 For uniform doping distribution in the mono-emitter region, using the relation Jn = qn2i exp( qVj/kT)/GB where,„ GB is the base Gummel number and is given by W GB ˆ 0 EM NDe€(x)/Dn dx, tEM is written as (for Jn/ JpM>>1)   GB WEM M W 2EM tEM ˆ ÿ : …12† M NDeff 2DpM Considering exponential distribution of the form ND(x) =ND (WEM)exp m(xÿ WEM) in the mono-emitand ter region, using JpM/Jn = GB/M NDe€(x) = A[ND(x)]a, where A = 6.792  1011 and a = 0.304 [7], Eq. (11) reduces to  GB M tEM ˆ …exp maWEM ÿ 1† M ‰ND …WEM †Ša ma   1 1 ÿ exp…ÿmaWEM † ÿ WEM ÿ …13† maDpM ma Thus from Eqs. (12) and (13), transit time in the monosilicon emitter region can be calculated for uniform and exponential doping distributions respectively in the presence of a broken oxide layer.

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… WE pP …x† dx QpP ˆ q

2.2. Transit time in the polysilicon emitter region of a PET

WEM

In order to ®nd the hole concentration in the polysilicon region, steady state continuity equation is used which is given by 2

d pP …x† pP …x† ˆ 2 : dx 2 LpP Using the boundary conditions pP(x = WEM + WEP) = 0 and pP(x = WEM) = phpM(x = WEM), the above equation is solved and pP(x) is obtained as 1 pP …x† ˆ ph pM …WEM †cosech…WEP =LpP †‰expg…WE 2 ÿx†=LpP †g ÿ expf…x ÿ WE †=LpP Š

…14†

where WE = WEM + WEP. Stored minority carrier charge density in the poly region is then given by

ˆ qLpP ph pM …WEM †tanh…WEP =2LpP † for a uniform interfacial oxide layer. In presence of a broken oxide, the charge density can be considered to be composed of two parts: one is due to the holes injected through the oxide free region and the other due to those injected through the oxide covered region. In the oxide free region, probability of tunneling ph = 1. Therefore, QpP can be written as QpP ˆ QpP jox ‡ QpP joxf ˆ qLpP ph pM …WEM †tanh…WEP =2LpP †rox ‡ qLpP pM …WEM †tanh…WEP =2LpP †…1 ÿ rox † where pM(WEM) from Eq. (5) is given by

Fig. 2(a).

…15†

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193

Fig. 2. Dependence of transit time on emitter junction depth, WEM (with WEP = 300 nm and WB = 100 nm) for (a) HF device with no interfacial oxide layer and (b) RCA device with 1.4 nm thick interfacial oxide layer. Dashed line represents Suzuki's plot [1].

n2i exp…qVj =kT † NDeff …WEM † … WEM NDeff …x† dx JpM 0 ÿ : qDpM NDeff …WEM †

tEP ˆ

pM …WEM † ˆ

 …16†

Using Eqs. (15) and (16), tEP comes out to be tEP

kT dQpP ˆ  q…JpM ‡ Jn † dVj

 qLpP ph tanh…WEP =2LpP † n2i exp…qVj =kT † …JpM ‡ Jn † NDeff …WEM † … WEM JpM NDeff …x† dx  0 ÿ …17† ‰rox ph ‡ …1 ÿ rox †Š: qDpM NDeff …WEM †

ˆ

Using the relation GE ˆ cing

qn2i exp(qVj/kT)

„ WEM 0

[NDe€(x)/DpM] dx, repla-

by MJpM and using the relation

JpM/Jn = GB/M, we have

GB ; M

LpP tanh…WEP =2LpP † …M ÿ GE †‰rox ph ‡ …1 NDeff …WEM †  ÿ rox †Š :

…18†

Thus, for uniform distribution in the mono-emitter region, the total emitter transit time tE is obtained by taking the sum of tEM and tEP as given by Eqs. (12) and (18) and for exponential distribution in the monoemitter region, tE is obtained by taking the sum of Eqs. (13) and (18).

3. Discussion In order to study the dependence of transit time on the polysilicon and monosilicon regions of a PET on di€erent parameters involved in Eqs. (12), (13) and (18), RCA (rox = 1) and HF cleaned (rox = 0) devices

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S. Basu et al. / Solid-State Electronics 43 (1999) 189±197

are considered. Typical values of some of the parameters are taken as follows. mh* = 0.41.m0, LpP = 100 nm, interfacial oxide layer thickness, D = 14 AÊ for RCA cleaned device and 0 AÊ for HF cleaned device, potential barrier height, Kh = 0.5 eV for RCA cleaned device and di€usion coecient of electrons in the base region Dn = 7.7 cm2/s [1]. Di€usion coecients of holes in mono and poly regions are taken as DpM = 1.27 cm2/s and DpM/ DpP = 3 [6], respectively. Uniform doping concentration in the emitter and base regions are taken as 1020/cm3 and 2  1018/cm3 respectively. 3.1. Dependence of transit time on monosilicon thickness (WEM) of emitter region having uniform doping concentration In Fig. 2(a) the variation of tEM as calculated from Eq. (12) has been plotted by continuous line for HF cleaned devices, taking WEP = 300 nm and WB = 100 nm. It is seen from this ®gure that tEM increases

almost linearly with WEM while tEP decreases, although the rate of decrease of tEP is quite small. It is interesting to note that at low values of WEM, tEP may be larger than tEM. In this particular case, tEP is larger than tEM up to about 70 nm of WEM. Fig. 2(b) shows the dependence of transit time tE on WEM for RCA cleaned device. Here tEP is negligible compared to tEM and tE is almost wholly controlled by tEM. Also, since tEM is directly related to WEM, tE10 when WEM = 0. A comparison of Fig. 2(a) and Fig. 2(b) shows that the rate of increase of tE with WEM is larger for an RCA cleaned device than for an HF cleaned device, when parameter values for both the devices are taken to be identical except for the presence of the oxide layer. So far as the variation of tE is concerned, since the contribution of tEP which decreases with WEM is absent in the RCA cleaned device, it follows that the rate of increase of tE with WEM would be larger for the RCA cleaned device than the HF cleaned device.

Fig. 3. Dependence of transit time on polysilicon thickness, WEP, (with WEM = 50 nm and WB = 100 nm), continuous lines for HF device and dotted for RCA device, respectively. Dashed lines represent Suzuki's plot [1].

S. Basu et al. / Solid-State Electronics 43 (1999) 189±197

195

Fig. 4. Dependence of transit time on the fraction of oxide covered interfacial area, rox, (with WEM = 50 nm, WEP = 300 nm, WB = 100 nm) for uniform emitter doping concentration.

Base transit time tB which is given by W2B/2Dn, for uniform doping concentration in the base region is also shown in Fig. 2(a) and (b) for WB = 100 nm. It is seen that for values of WEM smaller than about 100 nm, tB is much greater than tE for RCA cleaned device and is somewhat greater for HF cleaned device. Thus the contribution of tE to the forward transit time tF is smaller in the RCA cleaned device than in the HF cleaned device. As such, tF may be lowered appreciably by decreasing WEM in a HF cleaned device while such a reduction in WEM would have no appreciable e€ect on tF in an RCA cleaned device. 3.2. Dependence of transit time on polysilicon thickness (WEP) of emitter region having uniform doping concentration For HF devices, tEM increases with WEP for small values of WEP as may be seen from Fig. 3 (continuous line). Ultimately, tEM becomes constant when WEP exceeds LpP. So far as tEP is concerned for HF devices,

it is found that tEP increases with WEP. Its rate of increase decreases beyond WEP = LpP. For RCA cleaned device, tEM is independent of WEP (dotted line in Fig. 3), consequently, tE is also independent of WEP. As stated before, tB is entirely independent of WEP and is shown as such in Fig. 3. It is clearly seen that tB is larger than tE for both HF and RCA cleaned devices. While the relative contributions of tB and tE to tF remain unchanged for an RCA cleaned device, the contribution of tE towards tF increases slowly as WEP is increased. A reference to Fig. 2(a) and (b) and Fig. (3) shows that there is very little di€erence between our plots and those of Suzuki [1] (shown by dashed lines). It is to be noted, however, that in our calculation we have used the value of Dn as appears to have been used by Suzuki, namely Dn = 7.7 cm2/s. This value is higher than which is reported in literature [8±9]. If this latter value is used for Dn, the values of transit time as calcu-

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S. Basu et al. / Solid-State Electronics 43 (1999) 189±197

Fig. 5. Dependence of transit time on the fraction of oxide covered interfacial area for exponential emitter doping concentration (with peak emitter doping concentration ND(WEM) = 1020/cm3, WEM = 50 nm, WEP = 300 nm and WB = 100 nm).

lated from our expressions will come out to be somewhat higher than the values given by Suzuki. 3.3. Dependence of transit time on base width (WB) Since GB is directly proportional to WB, tE is also directly proportional to WB. Again, since tB is proportional to W2B, for smaller values of WB, tB may be smaller than tE. However, the rate of increase of tB with WB is much faster than that of tE and as such, for large values of WB, tF is mainly determined by tB. 3.4. Dependence of transit time on the fraction (rox) of interfacial oxide covered area for uniform doping concentration in the mono-emitter region From Eqs. (12) and (18), tEM and tEP are calculated and plotted in Fig. 4 as functions of rox. It is seen from the ®gure that tEM increases very slightly with rox whereas, tEP decreases with rox almost linearly. Physically this can be explained in terms of injected

hole charge storage in the mono and poly regions. The charge stored in the mono region does not depend on the poly/mono interfacial oxide layer break-up and tEM remains almost independent of rox. As the oxide covered interfacial area increases, the injected charge stored in the poly region decreases which in turn reduces tEP. The net e€ect is the reduction of tE with increase in rox. Since rox = 0 and rox = 1 correspond to HF and RCA cleaned devices respectively, all the other parameters remaining the same, tEvRCA is less than tEvHF. The variation of tE with rox is shown in Fig. 4 for two di€erent values of emitter doping concentration: ND = 1019/cm3 (continuous line) and ND = 1020/cm3 (dashed line). tE decreases with increase in doping concentration. Since the product of electron and hole concentration is constant in any region of the emitter in the steady state, for a given value of junction voltage, with increase in ND, the injected hole concentration decreases which results in the decrease in the injected hole charge storage. Consequently, tE decreases.

S. Basu et al. / Solid-State Electronics 43 (1999) 189±197

Using Eqs. (12) and (18), the di€erence DtE of tE values for rox = 0 and rox = 1 can be approximately given by   GB W 2 DpP DtE ˆ LpP ÿ EM : NDeff 2DpM LpP For ND = 1020/cm3, DtE comes out to be 3 ps as is also found from the graph corresponding to ND = 1020/cm3. The above expression also shows that with increase in doping concentration, slope of the tE± rox curve decreases. It can therefore be concluded that tE of a PET with lightly doped mono-emitter region is more sensitive to oxide layer break-up than tE of a PET with heavily doped mono region. 3.5. Dependence of transit time on the fraction (rox) of interfacial oxide covered area for exponential doping distribution in the mono-emitter region For exponential distribution in the mono-emitter region, tEM and tEP are calculated from Eqs. (13) and (18) and plotted in Fig. 5 as a function of rox. It is seen that tEM remains almost independent of rox and tEP decreases with rox as in the case of uniform doping distribution. As a result, tE decreases with the increase in rox. For a given value of monosilicon thickness and peak doping concentration, as the ratio ND(WEM)/ND(0) increases, tEM increases since the built-in ®eld opposing the hole movement increases as shown in Fig. 5. tEP does not depend much on the mono-emitter pro®le. As a result, tE increases as the slope of the exponential distribution curve ln[ND(WEM)/ND(0)] increases. tE as a function of rox is shown in Fig. 5 for three di€erent values of ln[ND(WEM)/ND(0)]. Rate of change of tE with rox does not depend much on the doping distribution and remains almost the same as long as peak doping concentration ND(WEM) remains constant. 3.6. Dependence of relative contribution of tEM and tEP towards tE, on tunneling probability ( ph) From Eqs. (12) and (18) the ratio of tEM and tEP can be written as   tEM WEM GE ˆ ‡ 1 for rox tEP ph LpP tanh…WEP =2LpP † 2…Gp ‡ Ge † ˆ 1, tEM WEM ˆ tEP LpP tanh…WEP =2LpP †



 GE ‡ 1 for rox ˆ 0: 2Gp

This shows that tEM/tEP varies approximately as 1/ph

197

for RCA cleaned device. As ph decreases, the ratio increases and tEM becomes dominant for small values of ph. Since ph depends on the thickness of the oxide layer, this indicates that tEP becomes negligible as oxide thickness increases. If WEM is smaller than LpP and WEP is much greater than LpP, then for HF cleaned device the ratio is less than unity, showing that contribution from mono region is less than that from poly region.

4. Conclusion Expressions for transit time in the mono and polysilicon regions of the emitter of a PET have been derived. It is found that for RCA cleaned devices, the contribution of tEP is negligible compared to tEM, whereas for HF cleaned devices, both the contributions are appreciable and tEP increases with increase in the thickness of the polysilicon layer. For small values of base width (WB), both tE and the base transit time tB contribute towards forward transit time tF. With increase in WB, tB increases sharply and dominates. tE decreases with the increase in the fraction of oxide covered interfacial area. tE of a PET with lightly doped mono-emitter region is more sensitive to oxide layer break-up than tE of a PET with heavily doped mono region. With the increase in interfacial oxide layer thickness, tEP/tEM which is approximately proportional to ph decreases. Instead of uniform doping, if an exponential doping distribution is considered in the mono region with peak doping concentration equal to the uniform doping case, values of tE are enhanced for both HF and RCA cleaned devices.

References [1] Suzuki K. IEEE Trans Elect Dev 1991;38:2512. [2] Basu S, Pal DK, Daw AN. Int J Electron 1994;77:441. [3] Overtraeten RJV, Demon HJ, Mertens RP. IEEE Trans Elect Dev 1973;20:290. [4] Roulston DJ. Bipolar semiconductor devices. McGrawHill, 1990:11. [5] Lindmayer, Wrigley. Fundamental of semiconductor devices. Aliated East±West Press, 1971:124. [6] Ning TH, Issac RD. IEEE Trans Elect Dev 1981;27:2051. [7] Slotboom JW, de Gra€ HC. Solid-St Electr 1977;20:279. [8] Sze SM. Physics of semiconductor devices. 2nd ed. Wiley, 1981:29. [9] Colclaser RA. Microelectronics: processing and device design. Wiley, 1980:119.