Solid-Slate Electronics Vol. 25. No 4. pp. 313-315. 1982 0038-I 101/82/@lO31343$03.00/0 Printed in Great Britain Pergamon Press Ltd

DEPENDENCE OF MOSFET NOISE PARAMETERS IN N-CHANNEL MOSFETs ON OXIDE THICKNESSt

H. S. PARKS and A. VAN DER ZIEL Electrical Engineering Department, University of Minnesota Minneapolis, MN 55455, U.S.A.

(Received 30 h/y 1981; in revised form 3 October 1981)

Abstract-The expression for the I/f noise resistance R, of a MOSFET at low drain bias contains the factor Ii/[g,( V, - VT)]*, which is unity in the elementary MOSFET theory but can be considerably larger than unity in practical units. The number fluctuation model characterizes R. further by the parameter [NT(E,)l.rr/r and the mobility flucuation model introduces Hooge’s parameter a. Measurements show that [Nr(E,)]eff/~ varies as l-*, a as t-’ and the mobility p varies as t, where t is the oxide thickness. The dependence of R, upon T is chiefly determined by the t-dependence of the factor I&,( V,- VT)12. Since the drain noise spectrum S,&fi is practically independent of f, it is a very useful parameter for characterizing the noise. All data are now mutually consistent.

1. INTRODUCTION

In the theory of flicker noise in MOSFETs at low drain bias, one usually transformed from the output current noise 81, into the equivalent gate noise emf SV,,, [ 1,2]. Van der Ziel et al. [3] have shown, however, that this leads to a significant error when the elementary MOS- FET theory is applied to this transformation, because the transconductance g,,, at low bias is smaller than this theory predicts.

The reason is simple. At low drain bias V,, and strong inversion the drain current Id may be written as

Id = (q/.LN/L? v, = (P~C,,/L)( v, - VT) v, (1)

where N is the number of carriers, V, - VT the effective gate voltage, k the mobility, w the device width and L the device length, so that

g,,, = tZ,/( V, - V,)Hl -d V,/d V, + [( V, - VT)/PI dpuld VJ (2)

where d VJd V, > 0 and dp/d V, < 0. In the elementary theory both derivatives are taken to be zero and hence Z,ltg,( v, - VT)1 = 1.

It is now seen that when one transforms from SZ, to fiV,,o, a factor Z,/[g,( V, - VT)] enters in, since

sv.,o = SZJg, = {Z&LI( v, - VT)114 V, - VT)SZCflZ, (3)

independent of what mechanism causes SZ,. In the number fluctuation model [4],

srd(fl/zd’ = &(f)/N2 = (wL/N’fl [N,(E,)l.a/r (4)

tsupported by AR0 contract. $Now at IBM. Burlington. Vermont.

where $.,(fl is the spectrum of the number of carriers, [NT(Ef)leff the effective trap density at the Fermi level and E, = 10’ cm-‘, a tunneling parameter. After some manipulations we obtain for the spectrum of SV,,,

S,,,(f) = {Ykd V, - V,)Y q’[N~(E,)l,~I(~fc~xwL). (5)

According to the mobility fluctuation model [5],

.Sd(n/Z: = a/W (6)

where (Y is Hooge’s parameter. After some manipulations we have

S”,,&f) = 1Z&L( V, - VT)lY W( V, - VT)/(fC0,WU (7)

Klaassen [l] has the same formula but interprets a as a number fluctuation parameter and puts Z,z/[g,( V, - V,)]’ = 1.

If one measures S,,,(f) and determines all the parameters involved, one can evaluate [NT(Ef)leff/~ and a from the noise data. By measuring how Zd2/[g,,,( V, - VT)‘, [NT(Ef)].J~ and a depend on the oxide thickness t, one can explain how S,,,(f) depends on t.

One cannot discriminate between the two noise models, for the snme measurement is interpreted in two ways. Rather, eqns (5) and (7) define two parameters [NT(E,)]JE and a; they are formally related as

[NT(E,)I,,T/~ = a&( V, - Vr)/q. (8)

Since C,, is inversely proportional to the oxide thickness t, either [NT(E,)]Je or a or both must depend on t.

Since the parameter Zd*/[g,,,( V, - VT)]’ is awkward to carry along, we eliminate it by substituting

(9)

313

314 H. S. PARK and A. VAN DER ZIEI

f I09

CT ‘E u

Y F c w

E loe

IO7

106

o BT- 5(6@ 130X( 10’6)

I BP-5(6/L) 5158(10’6 )

a BP-3(6/o 5l5X(lO’51

Fig. I. [NT(E,)J,~/c versus gate voltage V, for0BT5(8p), 1= 13Ok Nd = 10’%m3, for BPS@m), t = 515 A, Nd = 10%m3 and for BP3(8p), I = 515 A, Nd = 10”/cm3; [N,(E,)],,/e varies roughly as t?.

where I_, is the equivalent saturated diode current of &. We then obtain instead of (5),

a s,cn/ v,’ = (4’~2/fL3)[NT(E,)l,~/~ (10)

I : and instead of (7) -4 IO -

(11)

0 ET-5(8p) 130i(10’6)

A BP-5 (qu) 515 i (10’6)

0 BP-3(tlp3 515 i (lo’sl

from which the two parameters are easily determined.

2. MEASUREMENTS

Figure 1 shows [NT(Ef)le,Je vs V, for two normal (not ion implanted) MOSFETs having an oxide thickness t of 515 A and acceptor concentrations N, of 10’6/cm’ and 10’5/cm3, respectively, and a device with an oxide thickness t = 13OA and N, = 10’6/cm3. We see that [NT(E,)]Je depends little on N, but varies ap- proximately as f-*. Substituting this into (5) shows that the dependence of S,,,(f) upon t corresponds ap- proximately to the dependence of I,*/[g,,,( V, - VT)]’ upon t.

0 2 4 6 6 IO 12

- “9 Fig. 2. (I vs gate voltage V, for BTS, BP5 and BP3; u varies

roughly as t -‘.

BP-5.0.1 v 0 BT-S(8p) 1300i(10’6)

BP-3. 0.2 v a BP-slap) 515 iclo’6,

p BT-5 .-OOZV 0 tiP-3teP)stnitrd5)

Figure 2 shows Q vs V, for the same devices. There is again little dependence on N,, but (Y varies ap- proximately as t-‘. Substituting this into (7) shows again that the dependence of Sv,,&) upon t corresponds to the dependence of Zd*/[g,( V, - VT)]’ upon t. The dependence of a upon t corresponds to what is expected from (8).

0 2 4 6 8 K) I2

- “9 Figure 3 shows p vs V, for the same devices. The

130 A device had a much smaller p than the 515 A Fig. 3. Mobility p versus gate voltage V, for BTS, BP5 and BP3;

p varies roughly as t.

Dependence of MOSFET noise parameters 315

*w 10-3 1

-4 IO I a BP-5&)5lS Aild6, 0 BP-3mp)515~ (10’5)

Fig. 4. Equivalent saturated diode current Icq vs gate voltage V,

Ii5

for BTS, BP5 and BP3. Note that I,, is practically independent of

0 2

1. f = 1000 Hz, I,, in Amperes.

4 6 8 IO 12

BV 0

devices; p varied approximately as t. There was little dependence of /L upon N,.

We note that the turn-on voltage V, differs somewhat for the three units; apparently the quality of the oxide of these devices was not quite identical.

If one substitutes into (10) the dependence of p and [NT(E,)]Je upon t, one finds that S,(j) at a given V, is

approximately independent of the oxide thickness t. Figure 4 shows this is indeed the case. Neither is there a significant dependence on N., as expected from the previous data. This indicates that S,V, is a very useful parameter for characterizing MOSFET l/f noise.

Earlier discussions on l/f noise in MOSFETs [l, 6-81 set Zdz/[g,,,(V, - VT)]’ equal to unity. This led to conflicting results that have now been removed.

Acknowledgements-The authors are indebted to Dr. S. M. Sze, Bell Laboratories, Murray Hill, New Jersey, for providing sam- ples, and to an anonymous reviewer, whose constructive criti- cism led to considerable improvements in the manuscript.

REFERENCES

3. A. van der Ziel, H. S. Park and S. T. Liu, Appl. Phys. Leflers 35, 942, (1972).

I. F. M. Klaassen, IEEE Trans. ED-U, 887 (1971). 2. H. Katto, M. Aoki and E. Yamada, 1. Appl. Phys. 48, 5135

(1977).

4. A. van der Ziel, Flicker noise in electronic devices, in Ad- vances in Hectronics and Electron Physics (Edited by L. Marton), Vol. 49. Academic Press, New York (1979).

5. F. N. Hooge, Physica 60, 130 (1972); Physica 83B, 14 (1976). 6. N. R. Mantena and R. C. Lucas, Electron Letl. 5, 605 (1969). 7. S. T. Hsu, Solid-St. Electron. 13, 1451 (1970). 8. S. Christenseen, I. Lundstrom and C. Svenson, Solid-St.

Electron. 11,797, (1%8).