IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-24, NO. 6, JUNE 1977 643

Vertical Current Components in lntegr ted Injection Logic

Abstract-Analytic expressions representing a double diffused transistor impurity profile are used to calculate the current com- ponents in IIL structures. The expression for the hole current is given for IIL structures with the epitaxial layer grown on a wide n+ substrate and for buried layer structures. It was found that an equivalent recombination velocity at the n-n+ interface, S,,+, is of order lo2 higher in buried layer structures than in structures with the epitaxial layer grown on a wide n+ substrate for compa- rable doping levels.

Results obtained using the analytic expressions are compared with those obtained using a computer program which includes heavy doping effects and doping level mobility dependence. Both calculated and computed results are also compared with measured currents for a given IIL structure with the epitaxial layer grown on a wide n+ substrate. The calculated and the computed results a r e i n good agreement with the experimental results.

T I. INTRODUCTION

HE IIL device shown in Fig. 1 is an integrated device that consists of an inverted n-p-n transistor

having a multicollector which is merged with a p-n-p transistor. A terminal-oriented model for the IIL devices has been described in 111 using the Ebers-Moll equations. A structure-oriented model that describes the IIL struc- tures from the viewpoint of physical structure and mech- anism is explained in [2].

The purpose of this paper is to provide simple analytic expressions to calculate the vertical electron and hole current components for IIL structures using a simplified model of a double diffused transistor impurity profile. The expression for the hole current in n-p-n vertical IIE structures is given for structures with the epitaxial layer grown on a wide n+ substrate and for TTL compatible structures with n+ buried layers. Using a computer pro- gram [3] based on the variable boundary regional ap- proach, including heavy doping bandgap reduction effects 141 and doping level mobility dependence [5], the electron and hole current components are obtained.

The currents calculated using the derived simple ana- lytic expressions and the computed currents are compared with the currents measured on a given structure with an epitaxial layer grown on a wide n+ substrate.

TI. ANALYSIS

A. Base Regions

A simplified model of the impurity profile in the in- trinsic base region (i.e. under the collector) is shown in Fig.

was supported by a research grant from the National Research Council Manuscript received July 26,1976; revised January 28,1977. This work

of Canada.

Fig. 1. IIL device, example with 3 collectors, the vertical current com- ponents Jni , J,,, and Jpu are shown.

2(a). The major part of the base region and the collector are represented by an exponential distribution of impurity density, while a possible opposing field region near the emitter is considered to be linearly graded; i.e.

where x’ = x - x j l .

For low level injection conditions, and for J i >> Jp , the minority carrier distribution in the intrinsic base region is given by [6]

where m = WzIL, x : = x , - xjl, x: = x, - x j l , x, and x, are neutral-depletion layer boundaries of the base. W is the neutral base width and W2 is the width of the retarding field region. D,,,, is the average diffusion constant in the base region.

The electron current density can be written in the form:

where

The simplified impurity profile in the diffused p ex- trinsic base region is shown in Fig. 2(a). The impurity profile near the collector junction can be represented by an exponential distribution of impurity density. Taking

IEEE TRANSACTIONS ON ELECTRON DEVICES, JUNE 1977 644

NS

( b )

Fig. 2. (a) Simplified model of the base region of double diffused 11: L, impurity profile. (b) Double Gaussian representation of double diffused IIL impurity profile.

*Wepi+

about 2 X 1OI8 for a real doping level of about 5 X 1011' ~ m - ~ . The real impurity profile is rarely known with pre- cision and there exists some uncertainty as to the magnj:. tude of the bandgap reduction effect. The analysis therefore simplified and the impurity profile near thi: surface is assumed to be a uniform doped layer ofNs = :? X l0l8 C M - ~ for 0 I x I W3. There remains, however, a h i

accelerating field region of a width comparable to the ex. trinsic base width, which will further reduce the electroll current. This effect is taken into account by introduciq; a correction factor K in the electron current formula.

For low level injection conditions, the minority carrier concentration distribution in the extrinsic base (p region I

under the metal contact, with the assumption of a plane of high recombination at the ohmic contact, can be written in the form

n ( x ) = - JncK [ w 3 e ( x - W 3 ) / L + L(e(x-Wd/L - I)], qDnav

w3 I x I x,. (7 , )

Similarly the minority carrier distribution under thc oxide-silicon interface region, with the assumption of L L

surface recombination velocity V, at this interface can bo written as

h - COMPUTED -_ CALCULATED

Fig. 3. Minorit carrier distribution in the intrinsic [Z = (xi - x ' ) /W] and extrinsic Z = ( x , - x ) / x , ] base re ion of a structure with Nss = 2.5 X 10'8 cm- e , N D ~ ~ ~ = 1.3 x 10'6 cm- f , NDsub = 1019 6111-3, xjl = 0.71 y, xj2 = 1.5 IL, Wepi = 2y and Xsub,, = 200 w.

where Jnc and J,,o are the recombination currents at the metal contact and the oxide-silicon interface, respectively, and K is a correction factor.

From (7) and (9) and for values of (x, - W3)/L 1 3, the electron currents Jnc and Jn0 can be written in the form

where N A ( x , ) is the doping level at the emitter-base de- pletion layer boundary and Ln is the electron diffusion length in the base region. The recombination current term including L, has been added to take account of the ex- treme case of low Ln.

In writing (10) and (11) we have assumed that the in- jected minority carrier concentration in the base region is decreased considerably in the retarding field region of the extrinsic base ptofile, and most of the injected minority carriers recombine in this region. The validity of this as- sumption can be examined from the minority carrier dis- tribution in the base region. Fig. 3 compares the calculated minority carrier distribution in the base region of the IIL structure with the parameters given in Section I11 (using the simplified model of the impurity profile) with results obtained by computer simulation [3] (using the double Gaussian impurity profile of Fig. 2(b)). The minority carrier distribution in the intrinsic and extrinsic base re- gion are calculated using (2), (3), and (6)-(9), respectively.

ELSAID et d . : VERTICAL CURKENT COMPONENTS IN

0 X e p i XI XZ

( b )

Fig. 4. (a) Substrate region impurity profile of IIL devices with the epitaxial layer grown on a wide n+ substrate. (b) Substrate region impurity profile of IJL device with n+ buried layer.

In Fig. 3 the minority carrier distributions in the extrinsic base region under the metal contact and the oxide-silicon interface coincide. From Fig. 3 we can see that in the re- tarding field region of the extrinsic base (2 = [ X , - x m ] / x , = 0.43), the minority carrier concentration decreases to about two orders of magnitude lower -than its injected value. This shows that the approximation made in writing (10) and (11) is quite reasonable.

B. n and n+ Regions

Consider now the hole current injected into the epitaxial layer and the substrate region. This current can be ex- pressed as

Jpu = Jp(epi ) -i- J p ( s u b ) (12) where Jp(epi) is the recombination current in the epitaxial layer and J p ( s u b ) is the current of the outdiffused region and the substrate (cf. Fig. 4(a) and (b)). On the assumption that the thickness Wepi of the epitaxial layer measured from the p-n junction to the n-n+ junction is less than one diffusion length, we may write J,(epi) as

J p ( e p i ) = q p ( X e r t ) W e p i / r p (13) where x,, is the space-charge layer boundary on the n side of the p-n junction at xj2, p(x , , ) is the injected minority hole concentration, and rp is the hole life time in the n region.

It can be shown that for low level injection in the epi- taxial layer and with J n >> Jp, we can write ( p / n ) J , << J p and the substrate hole current Jp(sub) will take the form

In the outdiffused region we assume an exponential im- purity profile (Fig. 4(a)) and

C. Wide n+ Substrate

In the substrate region of structures with the epitaxial layer grown on a wide n+ substrate ( p / n ) ( d n / d x ) << ( d p l d x ) and we have only a diffusion current. The sub- strate current, with the above assumption and with as- sumed high recombination velocity at the substrate con- tact, can be written as

where Dps is the substrate hole diffusion constant, Dpav is the average diffusion constant in the outdiffused region, Lps is the diffusion length in the substrate region, and x s u b is the characteristic length of the exponential doping of the out diffused region. For IIL structures with the epitaxial layer grown on a wide n+ substrate we can write

&L& << & (17) Dpav Dps

and (16) will take the form

Combining (12), (13), and (18) we have for IIL structures with a wide n+ substrate

In writing (16) we have assumed that the minority carrier concentration p(x , , j is almost uniform under the p region [7]. This is a reasonable approximation for devices with Wepi smaller than the width of the p region stripe and for Wepi << L, which is the case for IIL structures with shallow epitaxial layers.

D. n+ Buried Layer

For 111, structures with n+ buried layers shown in Fig. 4(b), using (14) and assuming a symmetrical exponential impurity profile in the substrate region, with the as- sumption of a reverse biased n+ - p- junction at x = x2,

the substrate hole current can be written in the form

Equation (20) includes the effect of the accelerating and the retarding field regions in the substrate. Combining (la), (13)) and (20), we have for n+ buried layer struc- tures

646 IEEE TRANSACTIONS ON ELECTRON DEVICES, JUNE 1977

E. Recombination Velocity at the rl - n+ Interface

The substrate hole current JP(sub) can be expressed as an equivalent recombination current at the n - n+ inter- face with a recombination velocity s,,+:

J p (sub) = qP ( x e n )snn+* (22)

Combining (18) and (22) we obtain an expression for the recombination velocity Snn+ for the IIL structures with the epitaxial layer grown on a wide n+ substrate,

NDeDi D p s snn+ = (%3)

Similarly for an IIL structure with an n+ buried layx, using (20) and (22) we have

NDsub Lp, '

(24)

A wide range of Snn+ values have been reported in the literature. Values of 103-104 cm/s are given in [8], [9]. A typical value of,Sn,+ I 20 cm/s was reported in [7] for p+-n-n,+ structures for either an n+ buried layer or an I ) +

substrate under an epitaxial layer of doping N D ~ ~ ~ N lC1I5 ~ m - ~ . Also a value of Snn+ I 400 cmls can be deduced frcm the results given in [lo] for moderate biased p+-n-n+ ey)i- taxial diodes. In fact the recombination velocity at the n-11." interface is firstly a structure dependent parameter and secondly a function of the epitaxial layer and substrate dopings. For example, for IIL structures with the epitax: a1 layer grown on a wide n+ substrate with Xsubo 2 100 puli?, (NDepi/NDsub) = D,, = 2.5 cm2/s, Wepi = 2 pm, arid Tp = 3 ps , we have (using (23)) Snn+ 1.0 cm/s << Wepi/,//?. For.IIL structures with n+ buried layers with the same parameters, and Xsub = 0.25 ym (which is equivalent to ;in n+ buried layer of about 4-ym width) and Dpav = 5 crnz1's, we have (using (24)), Snn+ N 100 cm/s > Wepi/rp. From the above we can see that 1) Snn+ (buried layer) is of ordt:r 100 times greater than Sn,+ (n+ substrate) and 2) Sn,,+ (buried layer) is greater than or comparable to ( Wepi/7,?) for IIL structures.

F. Relative Injection Current Densities

For low level injection conditions we can write,

(26)

where ni is the intrinsic carrier concentration, V , is tE e applied voltage on the emitter-base junction, and V, -- k T/q.

Using (41, (5), (101, (11), (19), (21), (25), and (26), and taking ND(x,,) as approximately equal to the epitaxid layer doping level N D ~ ~ ~ , we have

__- Jni - KJIDnavNDepi T p ICp'''1

where S,,+ is given by (23) or (24). Assuming that the surface and the epitaxial layer doping

densities N,, and N D ~ ~ ~ , the junction depths x j l , xj2, and xepi of the double Gaussian impurity profile shown in Fig. 2(b) are known for a given IIL structure, then the param- eters L, No, A, and x , of the intrinsic base impurity profile model can be determined as given in [6]. The parameters x,, xc , W3, and W4 shown in Fig. 2(a) can be determined as follows.

For the forward biased emitter-base junction, the junction can be considered to a fair approximation as lin- early graded with a gradient equal to that of the expo- nential doping profile at x = xj2, which is given by NoePi/L. The space-charge layer width in the base side can then be written as

x , = xjz - we. (31)

On the collector side, the space-charge layer width is

X : = (3V,b~/qA)~/~ (32)

x , = x : + X j l (33)

w4 = L In (NSlNDepi) (34)

and

w, = xj2 - w,. (35)

In the above E is the permitivity and Veb and V c b are the total voltages across the emitter-base and the collector- base junction, respectively.

In the following section we calculate the reIative injec- tion current densities (referred to J,,) from (27)-(29) for a given IIL device with the epitaxial layer grown on a wide n+ substrate. Using a computer program [3] based on the variable boundary regional approach, including heavy doping bandgap reduction effects [4] and doping level mobility dependence [5], the relative injection current densities are obtained. The calculated and the computed results are compared with the experimental results.

111. RESULTS AND DISCUSSION The calculated, the computer simulated, and the mea-

J p u NA(Xe)W(Wepi + TpSnn+) \" I

sured relative injection current densities for two IIL

ELSAID et al.: VERTICAL CURRENT COMPONENTS IN P L 647

Jni Jnc Jno Jpv CALCULATED

CALCULATED

COMPUTED

( a ) 665

COMPUTED

(b)

l3 ;n- 4.2 ,

MEASURED

1‘ MEASURED

Fig. 5. (a) Column graphs of relative injection current densities for a structure with N,, = 2.5 X 10I8 ~ m - ~ , L ’ V D ~ ~ ~ = 1.3 X 10l6 ~ m - ~ , NDsub

Column graphs of relative 1nJectlon current densities (the measured = 1019 ~ m - ~ , xjl = 0.71 y , x p = 1.5 p , We,i = 2 p and = 200 p. (b)

results are results given in ref. [2]) for a structure with N,, = 1019 cmW3,

= 1.E p and = 200 p. ND, i 4 X cm+, NDsuh = 10’9cm-3, Zjl = 0.8 p, = 1.5 p, wepi

structures with the epitaxial layer grown on a wide n+ substrate are shown in Fig. 5(a) and (b). The results shown in Fig. 5(a) are for an IIL structure with a surface doping, epitaxial layer doping, and substrate doping of 2.5 X 1018/cm3, 1.3 X 1016/cm3, and 1019/cm3, respectively. The metallurgical base junction width, the epitaxial layer, and the n+ substrate layer thickness are 0.79 pm, 2 pm, and 200 pm, respectively. Fig. 5(b) shows the calculated and the computed relative injection current densities of an IIL structure with the (incomplete) data given in [2]. Berger’s experimental results for the structure of [2] are also shown in Fig. 5(b) for comparison.

The Calculated and computed injection current densities for both structures are for a hole lifetime in the epitaxial layer rP = 3 ps, electron lifetime in the base region T, = 0.05 ps, and a surface recombination velocity at the oxide-silicon interface Vs = 40 cm/s.l The correction factor introduced in the expressions of the current density J,, and J,o ((10) and (11)) was taken as K = 1.5. D n a v = 12 cm2/s, D,, = 2.5 cm2/s and Dpav = 5 cmz/s are-used to

1 In our devices T~ was deduced entirely from the measured data and is consistent with other published values [7], [lo]. The value of T~ was chosen after a computer run to give a best fit using a value of Vs for thermally oxidized silicon close to values reported in [7], [ l l ] . Note that choosing a different value of Vs will lead to a different value for fitted T, as can be seen from (11).

calculate the vertical current components. The injected vertical hole current density Jpu of the experir3lental re- sults shown in Fig. 5(a) was measured carefully taking into account the lateral and the corner injected hole currents. This was done by making measurements with diffused p regions of different dimensions and solving the corre- sponding algebraic equations involving area, peripheral length, and allowing for excess current at each “corner.” All the results shown in Fig. 5 are for 0.7-V forward biased emitter-base junction and 1-V reverse biased collector- base junction.

From the results shown in Fig. 5(a) and (b) we can see that the calculated ratios using (271429) can provide a good estimate for the relative injected current density of a given IIL structure. The analytic expressions with the assumed simplified model of the double diffused transistor impurity profile thus provide a useful and efficient tool for use in the design of the vertical structure of the IIL de- vices.

ACKNOWLEDGMENT The authors thank SESCOSEM, Thomson-CSF, St.

Egreve, France, for supplying test devices and data. Fruitful discussions with M. Depey at the same laboratory are also gratefully acknowledged. The reviewer’s comments have been most useful in revising this paper.

REFERENCES H. H. Berger and S. K. Wiedmann, “Terminal-oriented model for merged transistor logic (MTL),” IEEE J. Solid-state Circuits, vol.

H. H. Berger, “The injection model-A structure-oriented model for merged transistor logic (MTL),” ZEEE J. Solid-state Circuits,

D. J. Roulston, S. G. Chamberlain, and J. Sehgal, “Simplified computer-aided analysis of double diffused transistor including two-dimensional high level effects,” IEEE Tram. Electron Devices, vol. ED-19, pp. 809-820, June 1972. R. J. Van Overstraeten, H. H. De Man, and R. 1’. Mertens, “Trans- port equations in heavy doped silicon,” IEEE Trans. Electron Deuices, vol. ED-20, pp. 290-298, Mar. 1973. D. M. Caughey and R. Thomas, “Carrier mobilities in silicon em- pirically related to doping and field,” Proc. IEEE (Lett.), vol. 55, pp. 2192-2193, Dec. 1967. M. H. Elsaid, D. J. Roulston, and L. A. K. Watt, “Current and base transit time relations in normal and inverted (TIL) biDolar transis-

SC-9, pp. 211-217, Oct. 1974.

V O ~ . SC-9, pp. 218-227, Oct. 1974.

tors,” this issue, pp. 761-763. S. Chou, “An investigation of lateral transistors-D.C. character-

. . -

istics,” Solid-state Electronics, vol. 14, pp. 811-826, 1971. R. W. Dutton and R. J. Whittier, “Forward current-voltage and switching characteristics of silicon p+-n-n+ epitaxial diodes,” IEEE Trans. Electron Devices, vol. ED-16, pp. 458-467, May 1969. D. L. Scharfetter, “Minority carrier injection and charge storage in epitaxial Schottky barrier diodes,” Solid-State Electronics, vol. 8,

K. Venkateswaran and D. J. Roulston, “Recombination dependent characteristics of silicon p+-n-n+ epitaxial diodes,” Solid-state Electronics, vol. 15, pp. 311-323, 1972. A. S. Grove and D. J. Fitzgerald, “Surf,ace effects on p-n junctions characteristics of surface space-charge regions under nonequilibrium conditions,” Solid-State Electronics, vol. 9, pp. 783-806, Aug. 1966.

pp. 299-311,1965.