Decrease of FET threshold voltage due to boron depletion during thermal oxidation

Solid-Sfufe Ekcrronics

Pergamon Press 197 1, Vol. 14, pp. 467-474.

Printed in Great Britain

DECREASE OF FET THRESHOLD VOLTAGE DUE TO BORON DEPLETION DURING THERMAL OXIDATION GO’ITFRIRD SCHOlTKY IBM Laboratories, D-703 Boeblingen, Germany (Received

6 July 1970; in revisedform

24 August

1970)

Abstract-Oxidation of a boron doped silicon wafer reduces the surface concentration of boron due to segregation into the oxide. This in turn reduces the threshold voltage of an FET fabricated on such a wafer. This effect is calculated for realistic process types including a sequence of several oxidations at different temperatures. The threshold voltage is found to be reduced by about I V (I 000 A oxide) which is quite considerable. The depletion effect on threshold voltage is expressed in terms of two parameters (effective doping and apparent surface charge). The approximations used can be adapted to most processes. Also, the effect of boron depletion on the MOS capacitance-voltage curve is calculated. An apparentflat-bandvoltage shift of only 0.1 V is found (1000 A oxide, 2 ohmcm). Resume-L’oxydation dune lamelle de silicium dopee au boron reduit la concentration de surface du boron due a la segregation dans I’oxyde. Cet effet reduit alors la tension de seuil d’un FET fabrique sur une telle lamelle. Cet effet est calcule pour des types de processus realistes y compris une sequence de plusieurs oxydations a des temperatures differentes. La tension de seuil est trouvee &tre reduite d’environ 1 V (oxyde de 1000 A) ce qui est considerable. L’effet d’abaissement sur la tension de seuil est exprimee en fonction de deux param&tres (doping effectif et charge de surface apparente). Les approximations utilisies peuvent etre adaptees a la plupart des procedes. On calcule Cgalement I’effet de I’abaissement du boron sur la courbe tension-capacite MOS. Un deplacement apparent de la tension de bande plate de 0,1 V seulement est trouvee (oxyde de 1000 A, 2 ohm.cm). Bei Oxidation eines Bor-dotierten Silizium-Pkittchens wird ein Teil des Bors vom Oxid aufgenommen. Das verringert die Oberflachenkonzentration des Bors und damit die Schwellspannung von FETs, die auf dem Plattchen hergestellt werden. Dieser Effekt wird fiir realistische Prozegtypen mit mehreren Oxidationen bei verschiedenen Temperaturen bestimmt. Die Schwellspannung kann urn den erheblichen Betrag von 1 V (1000 A-Oxid) verringert werden. Der Einflug der Bor-Verarmung fal3t sich durch zwei Parameter (effektive Dotierung und scheinbare Oberthichenladung) beschreiben. Die benutzten Naherungsmethoden lassen sich an die meisten Prozesse anpassen. Die Bor-Verarmung beeinfluf3t such die MOS-Kapazitats-Spannungs-Kurve. Der Effekt wird berechnet, es tritt eine geringe scheinbare Verschiebung der Flachband-Spannung urn etwa0.1 V auf (1000 A Oxid, 2 ohmcm). Zusammenfassung-

INTRODUCTION THE THRESHOLD voltage,

V,,

field effect devices depends on the doping level, NA, and the substrate (source-substrate voltage): v,=

?&+Y4=

with V,, for zero tivity of absolute

(e.g. see [ 11). The + and - signs apply to II and p

of surface channel

channel

devices, respectively. Close to the interface the doping level can be different from that in the bulk since various dopants have a tendency to either accumulate (P. As) or deplete (9) in silicon at the interface due to a redistribution between Si and SiO, during the oxidation [2]. The accumulation generally does not exceed 10 per cent, the depletion, however, can be much stronger. This change of the effective NR has a significant effect on VT only if V,, is large.

substrate bias, V,,

EoIEO~24ito~NA~/~PbJ+~)11’z

(I)

= flat-band voltage, v = band bending substrate bias, E,,, esi = relative permitSiOZ and Si, respectively, q, = vacuum dielectric constant, q = elementary charge

467

G. SCHOTTKY

468

For p-channel devices usually V,, = 0, and the square root term in (1) is not larger than the other ones. For n-channel devices @-substrate), however, often a V,, of a few volts is applied to obtain a positive threshold voltage (enhancement device). In this case, the term dependent on N,., in (1) is the dominant one. This means, that for n-channel devices VT depends strongly on NA, and the marked decrease of boron concentration near the interface is expected to result in a noticeable decrease of VT. The segregation of boron into the oxide results in a non-homogeneous concentration. This concentration profile will be determined, and then Poisson’s equation for the space charge region close to the interface will be solved to yield the relation between VT and V,,. BORON

CONCENTRATION

PROFILE

I. Basic theory

The boron concentration profile is the result of the joint action of boron uptake by the growing SiO, (boron diffusion in the oxide can be neglected) and the boron diffusion in the Si. The case of a single oxidation of a fresh Si wafer has been treated by Grove. Leistiko and Sah[2]. Their result for the concentration, C, at a distance x from the Si-SiO, interface is C(x)/NA = 1 -R

erfc

(

;+s

1

.

(2)

Here, d = 2dDt with D the diffusion coefficient of B in Si at the oxidation temperature and t the oxidation time. Further s = cxt,,/d

(3)

is the ratio of silicon thickness consumed during oxidation (toz = oxide thickness, (Y= 0.44 is the thickness or volume ratio of Si and SiO,) and the length characteristic for the diffusion. This ratio is independent of time since (2) is based on a parabolic oxide growth law. (This means that the interface concentration is stationary.) The coefficient, R(s)

= (l/elfc~){l-[I+(~-l)~‘~Zs

exp(?)

erfc s --I II

(4)

depends on s and on the segregation coefficient. m. This is defined to be the ratio of boron concentrations in Si and Si02 at thermodynamic equilibrium at the oxidation temperature. It is expected to depend on temperature, its value will be discussed later. 2. Application to FET processes The FET process includes several oxidations and heat treatments. The essential steps are: (a) lnitial oxidation (b) Diffusion (deposition and drive-in), further oxidation (c) Gate oxidation after etching the thick oxide at gate sites. Step (c) is different for gate sites and thick oxide regions. Therefore, the boron concentration profiles beneath thick oxide and gate oxide will be slightly different. A theoretical treatment of this sequence of oxidations can be done by numerically solving the differential equation of diffusion for a migrating interface for the differential equation and boundary conditions, see [2].). For steps (b) and (c), the initial concentration is nonhomogeneous and the computations are even more complex. A different approach will be followed here. If steps (b) and (c) are short compared to step (a), or more exactly have smaller Dt products than step (a), the final concentration profile will be nearly the same as after step (a)- which is given by equation (2). The overall effects of steps (b) and (c) will be small and even a simple approximation is sufficient. Due to the small Dt product, step (b) affects only a narrow region close to the interface, compare Fig. I. The boron concentration after step (a) in this region can be approximated by a constant value, say KNa. This simplification permits applying the theory expressed in equation (2) also to step (b), replacing N,, by KNA. The resulting boron concentration is a superposition of terms like equation (2) with different concentration factors. This is only the basic idea of the approximation. The details must be adjusted to each particular process and a general expression cannot be given. Only two process types will be presented as examples.

DECREASE

OF FET THRESHOLD

01’ , , , ,

, 1.

Cl

,

, , 2.

VOLTAGE

, , ,

469

, ,

3.

4. x [P]

Fig. 1. Approximate boron concentration profiles near interface (I ) after first oxidation (large Dr) and (2) after second oxidation (smaller Dr). The shifted interface after the second oxidation is indicated. Process example

I

All the oxidations are in dry oxygen (oxidation rates are different in dry oxygen and in steam), step (a) is dominant in Dr and in oxide thickness. The oxidations need not be at the same temperature. Thick oxide

In thick oxide regions, the oxide is not etched off after step (b). All oxidations are. as an approximation, considered as one single process step. The concentration profile is given by an equation similar to equation (2):

depth of steps (a) and (b). This means that the additional boron depletion caused by step (c) is restricted to a narrow range where the concentration profile after step (b) can be approximated by a constant, KNA (compare Fig. I): C(x)/N,=

I-R,erfc

:+sp

i I

>

-KR,erfc

$+s,

( 3

>

(9)

Here, introducing s? = s, + nt,ld,

C(x)/NA = 1 -R,

erfc $+s,

(,

>

(5)

takes care of the shift in x coordinate due to the interface shift during gate reoxidation, t~t:~.with t:, the gate oxide thickness. Further,

(6)

$ = Z(Dt(step c))liz

Here, d, = 2 (XDt) ‘r2

s, = ar,,(thick)/d,

(7)

and

are calculated using the sum of all Dt products and the total thick oxide thickness and R, = R(s,),

(8)

the function R(s) being defined in equation (4). For sl, equation (7) defines an effective value (unless all oxidation temperatures are equal). For this process, this is the only approximation introduced as compared to the theory for a single oxidation of a homogeneously doped crystal. Curve 1 in Fig. I shows the concentration profile after step (b); this is practically identical to the final profile beneath thick oxide, equation (5). Gate oxide

At gate sites, the oxide is etched away after step (b) and a reoxidation, step (c) is applied. The resulting gate oxide is much thinner than the thick oxide and the diffusion depth, 2qDr(c), is much smaller than the diffusion

(10)

s:~= ar,ld,

(I 1)

R:, = R(s,).

(12)

The profile due to step (b) changes slightly by diffusion during step (c). This has been accounted for approximately by using d, of equation (6). which is based on total diffusion. The thickness of the thick oxide changes only negligibly during step (c), therefore, R, from equation (8) can be used also in (9). For the average concentration, KNA. the interface value before gate oxidation is a sufficient approximation: K = 1 -R,

As an alternatice.

erfc (sq)

(13)

a true average has also been used for

K with little difference in predicted threshold voltage. Process example 2

Step (a) is an extended oxidation in dry oxygen (dominant in Dr), step (b) is a much shorter oxidation in steam

470

G. SCHOT’l-KY

(low Dt, but large increase in oxide thickness), step (c) is a dry oxygen oxidation (thin gate oxide, but Dr slightly larger than step(b)). Because of the steam oxidation, step (b) results in a narrow but strong boron depletion. It is not a good approximation to treat steps (a) and (b) as one step. The concentration profile after step (b) can be approximated in the same way as for the two-step simplification in process example I, gate oxide: C(x)/NA = 1--R(s,)

erfc :+s. ( 1

)

-KR(s,)

erfc x+s2 ( d2

)

(14)

where d, refers to the Dr products of steps (a) and (b), d2 only to (b), s1 is the s parameter of step (a) alone, s2 that of step (b) alone. The interface shift is accounted for in ~5= sl+ at,,(b)ld,

(15)

where r,,(b) is the increase in oxide thickness during step (b). Treatment of step (c) is different for gate oxide (oxide etched off before reoxidation) and thick oxide. Thick oxide During gate oxidation the thick oxide growth is negligible. Since the oxide can take up boron only by growth (boron diffusion in the oxide can be neglected), practically no boron penetrates the interface during gate oxidation. The profile of equation (I 4) is subject to diffusion with an impenetrable border at x = 0. A closed solution to this diffusion problem has not been found and the following approximation has been chosen. The last term in (14) has been approximated by a truncated linear function (see Fig. 2) so that the exact term and the straight line agree in interface concentration and in total amount of boron missing (i.e. they have the same integral). For this function, the solution of the diffusion problem is straightforward. In the second term on the right hand side of ( 14) the effect of diffusion is sufficiently accounted for by adjusting dl to the total Dr sum. The final boron concentration profile is C(x)/N,

= I-R(s,)

erfc (d, x+s

5) --KR

x, = 4 erfc(s,) . (d,/d,)A

-I

(19)

.Mx) =2xerfcx-(x+x,)erfc(x+x,)-(x-x,)erfc (x-x,)

- n-“2[2 exp(- x2) - exp(- (x+x,)*) - exp

(20)

e(x-%d*)l. Gate oxide

After step (b) the boron concentration profile looks like the curve in Fig. 2. The diffusion depth, d3, of step (c) is of the same order as the extent of the low concentration part of the profile, and the concentration in this range cannot well be approximated by an average constant as had been done when treating process example I. Generally, the dry oxygen oxidation of step (c) should result in a higher surface concentration than the steam oxidation of step (b) (lower oxidation rate, lower s parameter, lower R in equation (2)). So the profile resulting from step (c) if applied to a homogeneously doped wafer is similar to the low concentration part of the profile after step (b), the main difference being the larger surface concentration. This means that the change of the profile during step (c) involves mainly diffusion of boron to the surface, while boron uptake by the growing oxide is less important. The steep slope of the concentration after step (b) favors this diffusive transport, and it can be concluded that during step (c) the concentration profile will approach the “ideal” form for step (c) (i.e. for homogeneous doping). The effect of step (b) will be overruled by step (c) and the profile can be approximated by the two-step profile, equations (9) through (I 2), with sq = (olld,) (t,,(thick)+

t&gate))

taking care of the total surface shift. The expressions shown are not the only possible approximations and in some cases alternatives have been tested in terms of the resulting threshold voltage. For example, if for the thick oxide growth of process 2 steps (b) and (c) are treated as one step with boron segregation ocurring for an effective (average) oxidation rate, then the threshold voltage turns out lower by about 0.5 V per I Frn oxide thickness (for 2 ohm cm material). This was the largest variation found and is an indication of the uncertainties of the approximations applied.

(~z&Ki(~) (16)

THRESHOLD VOLTAGE AS A FUNCTION OF SUBSTRATE BIAS

where d, = 2(XDt)“2 dz = 26(b) d3 = fv”&(c)

ss = (44) (t,,(a) + Mb)) sz = %,(b)/d, K= 1-R(s,) erfc(s,) with f.,(b) the increase in oxide thickness (b). Further, A =t[erfc(s,)r[W1lZexp

(-szz--sr,erfcs,r

(17)

during step

(IS)

When a substrate bias and a gate voltage are applied to a FET with an inhomogeneous acceptor concentration, Poisson’s equation must be solved to yield the potential distribution and ultimately the relation between substrate bias, Vsb, threshold voltage, VT, and the width w of the space charge region:

DECREASE OF FET THRESHOLD

VOLTAGE

471

Fig. 2. Boron concentration, C/N*, profile after steam drive-in and approximation for this profile as used for solving the diffusion equation.

v,,+vr+-I C(X)dX. 11)

vr=

%.&o

(22)

IJ

The appropriate oxide thickness (gate or thick oxide) has to be chosen for tot. If C(x) = N,, is constant, w can be eliminated to yield equation (I). It is straightforward though tedious to write down the integrals in (21) and (22) for the C(n) expressions derived above. In a large range of substrate bias voltages, however, the relation of V, vs. (v&+*)1’* can be closely approximated by a straight line (least squares fit):

-&N,),

(23)

where the two parameters NM and h are obtained from slope and intercept. This means that to a good approximation the effect of boron depletion can be described by a reduced apparent substrate doping, Ndj, and an apparent increase in oxide charge, qhNA. The apparent oxide charge is mainly due to the boron depletion effect of gate oxidation (and steam drive-in, if applied) close to the interface. The effective doping is related to the depletion of a deeper region. The values of Neff and h depend on the process as well as on the Vaarange for which the least squares fit is done.

band voltage) are known with reasonable accuracy. Little is known about the segregation coefficient, m. This quantity is defined as the ratio of boron volume concentrations in Si and SO, in thermodynamic equilibrium. Grove et al. [2] obtained the concentration profile of a B doped wafer oxidized at 1200°C by diffusing a shallow .+ layer and measuring the voltage-capacitance curve. They report m = O-33. Combining their concentration profile with more recent values of boron diffusivity and oxidation rater31 yields m = 0.25 at 1200°C. Additional information on m can be obtained from threshold voltage measurements if the experimental conditions are chosen so that VT depends strongly on m, that is if the space charge region is confined to the range close to the interface where the boron depletion is most pronounced. Usually this means long oxidation times or high doping. Measurement of the VT vs. Vsb characteristic of FETs on a 0.3 ohm cm substrate* indicated a value of N,,,/N* = 0.59 (experimental); the main processing temperature was 1100°C. From a comparison with this theory a value of m = O-45 at 11OfK is derived. Both values of m are not very accurate. For application to process m = O-4

(24)

SEGREGATION COEFFICIENT

Most of the materials parameters in the above equations (dielectric constants, zero charge flat-

*I would like to thank E. Duh for providing these devices.

G. SCHOTTKY

472

.6

0

2

.C

.6

.6

1.

1.2

1.4

1.6

1.8

2

xPm1 Fig. 3. Calculated final boron concentratton profiles in thick oxide and gate oxide regions (process with dry 0, drive-in). This and following figures are for 0.1 p (gate) and I w (thick) oxide thicknesses, (100) oriented Si of 2 ohmcm.

01

1.6 “sb [“I 1. 1.2 1.L .6 .6 0 .2 .L Fig. 4. Calculated threshold voltage vs. substrate bias curves (gate oxide) for (I) no boron depletion, (2) dry 0, drive-in, (3) steam drive-in.

has been chosen, based on processing temperatures around 1000” or I 100°C. The same value has been used for all process temperatures. RESULTS Concentration profiles and VT vs. vsb curves have been calculated for actual FET process data. Figure 3 shows the boron concentration in thick oxide and gate oxide regions for a process with dry oxygen drive-in. It is seen that the interface concentration can be considerably below the bulk value. Figure 4 shows examples of VT vs. I&, curves

(1000 .& oxide), (I) neglecting boron depletion, (2) for a dry oxygen drive-in, (3) for a steam drive-in. The influence of boron depletion amounts to about I V, with little difference between the two processes. Values of NdN, are not tabulated here since they are process dependent and should be calculated for each individual process. For 2 ohm cm material and substrate bias voltages of a few volts typical values between O-7 and 0.9 have been found, with even lower values for very extended oxidations. The apparent increase in oxide charge,

DECREASE

OF FET THRESHOLD

qhN,, was found to be in the range of (0.5 to 1 .O) x 10” qcm-‘. Generally, a process involving long oxidations (dry 0,) will cause a deeply ranging boron depletion which results in a low N,,,/NA but only small apparent oxide charge. A process with short oxidation treatments (steam oxidation) will result in a shallow region severely depleted of boron. Here, NdN, is closer to 1, the depletion effect being characterized by a larger apparent oxide charge. Threshold voltages derived from theory have been compared to measured data on a statistical basis. Good agreement has been observed, subject to some uncertainty due to the oxide and surface charges. The existence of a boron depletion effect on V, is beyond question from the data, threshold voltages calculated using the actual doping level in equation (I) are too high. MOS CAYACITANCE

Boron depletion also affects MOS vs. voltage curves. In this type of the gate-substrate voltage is measured to the gate-source voltage). In close equations (2 1) and (22) we have

v,:-v,, = 2

IY&)dx+~

capacitance experiment, (in contrast analogy to

EBsE” &)dx. I0

0

(25)

The MOS capacitance, CMOS,can be expressed in terms of the oxide capacitance, C,, (both per unit area), and the space charge layer width, w: cNIOSICOs= [ 1

+

(%x/4i)

(W/fox)]-‘.

(26)

These expressions are based on the assumption of a sharp boundary between the space charge region (completely ionized acceptors) and the neutral semiconductor. This assumption is valid only in the depletion part of the complete MOS curve, not in the accumulation nor flat-band ranges. An example is shown in Fig. 5 (stream drive-in, 1000 h; oxide). In the inversion region a constant minimum capacitance, C,,, has been assumed equal to the value of equation (26) for threshold band bending. The calculated part of the MOS curve is indicated in Fig. 5. In addition, the flat-band value has been estimated from textbook expressions using the surface concentration (concentration profile as derived above averaged over the Debye length pertinent

VOLTAGE

473

OI -.5

0

.5

1

1.5VG-&I

Fig. 5. Depletion part of the MOS capacitance vs. voltage curve, - calculated, 0 flat-band point, --interpolated, -extrapolated.

to this concentration). Commonly either the bulk concentration is used or a concentration derived from Cmin. These three values of flat-band capacitance are indicated in Fig. 5 and also the errors introduced when using the incorrect CFB values. It is seen that the correct VFAis less negative by about 0.1 V than the value determined in the usual way. Similar values have been found for other processes. This error does not affect measurements of flat-bands shifts. However. when comparing MOS and k’, measurements the correct VP,, should be used.

SUMMARY

Oxidation of boron doped silicon wafers decreases the doping level near the oxide-silicon interface. This lowers the threshold voltage of insulated gate field effect transistors fabricated on these wafers. This effect has been calculated approximately. The expressions derived can easily be adapted to a specified process. For processes as commonly used the decrease of VT due to boron depletion may well amount to 1 V ( 1000 A oxide). This fact may be disguised by insufficient knowledge of the actual substrate doping. Also the MOS capacitance vs. voltage curve is affected by the segregation of boron. The change

414

G. SCHOTTKY

in apparent flat-band voltage may amount to about a tenth of a volt. Neglecting this effect may simulate too large an oxide or surface charge. of this work has been done in the IBM Thomas J. Watson Research Center, Yorktown Heights. 1 would like to thank D. Critchlow for his hospitality and encouragement.

Acknowledgment-Most

REFERENCES

1. A. S. Grove and D. J. Fitzgerald, Solid-St. Electron. 9,783 (I 966). In particular, see equation (2 1). 2. A. S. Grove, 0. Leistiko and C. T. Sah, J. uppl. Phys. 352695 (1964). 3. A. S. Grove, Physics and Technology of Semiconductor Devices. Wiley, New York (1967).