determination of si-sio2 interface recombination parameters using a gate-controlled point-junction...

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988 203

Determination of Si-Si02 Interface Recombination Parameters Using a Gate-Controlled Point-Junction

Diode Under Illumination REINHARD B. M. GIRISCH, ROBERT P. MERTENS, MEMBER, IEEE,

AND ROGER F. DE KEERSMAECKER, MEMBER, IEEE

Abstract-A new method is presented to determine Si-SiOz interface recombination parameters. The device employed is constituted by a polysilicon-oxide-semiconductor capacitor with a microscale central junction (a gate-controlled point-junction diode). The excess minority carriers are photo-generated rather than injected, which results in a one-dimensional current flow normal to the Si-SiOz interface. The minority carrier quasi-Fermi level is probed at the Si-SiOz interface by means of the point-junction. The one-dimensionality of the current flow and the exact knowledge of the minority carrier quasi-Fermi level per- mit an accurate measurement of the recombination rate. The method has been applied to characterize p-type { 100 } Si-Si02 interfaces with boron dopant concentrations ranging from 2.5 X 10’’ to 5 X 10” ~ m - ~ . Data analysis has been performed using a numerical scheme to find a quasi-exact solution for the current recombining at the interface. It was found that the interface recombination parameters depend only weakly on trap energy in a wide range around midgap. The cross-section for capturing electrons (u,,) was found to exceed the cross-section for capturing holes ( u p ) by a factor of 10’ to lo3.

I. INTRODUCTION HE INVESTIGATION of the electron-hole recom- T bination process at the Si-Si02 interface and the mea-

surement of this recombination process is of great impor- tance for the understanding and improvement of the performance of a variety of devices. Current develop- ments tend even to increase the impact of interface recombination on device performance. The scaling down of devices (e.g., bipolar and BIMOS devices), resulting in an increasing surface-to-volume ratio, and the general trend to reduce junction depth (e.g., in high-efficiency solar cells) render these devices more sensitive to interface phe- nomena than in the past.

The interface recombination rate U, is generally described by an extended Shockley-Read-Hall formalism [ 11-[3], where recombination of electron-hole pairs occurs after a two-step process via localized states at the Si- Si02 interface. In this model the rate U j depends on a

Manuscript received January 20, 1987; revised September 9 , 1987. R. B. M. Girisch was with the ESAT Laboratory, Katholieke Univer-

siteit Leuven, Kardinaal Mercierlaan 94, 3030 Heverlee, Belgium. He is now with Philips Elcoma, Gerstweg 2 , 6534 AE Nijmegen, The Nether- lands.

R. P. Mertens and R. F. De Keersmaecker were with the ESAT Labo- ratory, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 94, 3030 Heverlee, Belgium. They are now with IMEC, Kapeldreef 75, B-3030 Leu- ven, Belgium.

IEEE Log Number 8717689.

number of interface trap parameters, such as the density of interface traps (Dit), and the cross sections for capturing electrons (a,) and holes (vp). These capture cross sections may depend on trap energy ( E t ) , temperature, and perhaps also on the electric field.

Until now simplified expressions for Ui have commonly been used [2]-[5], where the interface trap density and the capture cross sections were assumed to be uniform. In these treatments the so-called fundamental recombination velocity So = 6 uthkTDi, is the key parameter 141, [5] . First systematic measurements of the fundamental recombination velocity were carried out by Fitzgerald and Grove on gate-controlled diodes [2], [3]. Forward (recombination) as well as reverse (generation) currents were studied as a function of gate voltage. The reliability of the reverse-current method has been questioned by Pierret [6], whose detailed analysis showed that the lateral variation of the minority-carrier quasi-Fermi level tends to yield underestimated So values. Neither has the gated diode been suitable for any easy and reliable So determination at forward bias, due to the lateral injection and resulting two- dimensional current pow. To overcome the problem of two-dimensional current flow, a device structure has recently been employed in which the injecting junction is parallel to the gated Si-Si02 interface and the minority- carrierjow normal to this interface [4], [5] . For this pur- pose, “vertical” gated diodes (the diode being formed by a p-nf epitaxial structure) have been used and, alterna- tively, gated n-p-n transistors in the 12L mode (the collec- tors being essentially redundant). The results obtained with these devices appear much more reliable; in some cases a comparison between independently determined trap parameters and So has been pursued [4]. The method, however, is not applicable at relatively low forward bias because the current is then limited by diffusion rather than by interface recombination. This paper describes a new method to determine Si-Si02 interface recombination parameters; the basic principle and some experimental results have been reported before [7], [8]. The device employed is constituted by a polysilicon-oxide-semiconductor capacitor with a microscale central junction. The current flow is perpendicular to the Si-Si02 interface, the excess minority carriers being photogenerated

0018-9383/88/0200-0203$01 .OO 0 1988 IEEE

204 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35. NO. 2, FEBRUARY 1988

rather than being injected from a forward-biased junction. A second feature of the method is that the minority-carrier quasi-Fermi level is measured at the Si-SiO, interface. Consequently, the recombination current can be studied over a wide range of forward voltages. As regards the analysis, we have not confined ourselves to the quantity So. Starting from general equations, a numerical scheme has been worked out that calculates the interface recombination rate Ui in a quasi-exact manner for any distribution of interface traps and any model for the capture cross sections. Although more complicated, this method has the virtue of needing fewer assumptions, which permits a more detailed analysis and, therefore, more exact modeling of the recombination process.

After presentation of the theoretical background and numerical examples (Section 11) , the characterization method is applied to real devices on p-type silicon. In Section I11 the experimental details are presented. In Sec- tion IV, some selected series of experimental data are presented, showing small deviations from the ideal (theoretical) case; the origins of these deviations will be identified. In Section V, the method is applied to a systematic characterization of p-type { 100 } Si-SiO, interfaces with boron dopant concentrations ranging from 2.5 X l O I 5 to 5 X 1017 ~ m - ~ . Finally, an in-depth discussion of the technique and the results obtained is given (Section VI).

11. THEORY

A. Background of Measurement Principle

The basic configuration of the test device, for the case of a p-type Si substrate, is shown in Fig. 1. The structure is constituted by a large-area polysilicon-oxide-semiconductor capacitor with a microscale central junction. The small n+ area forming this junction (point junction) serves to access or probe the minority-carrier electrons in the silicon surface layer [7]- [9] . The device is illuminated con- tinuously by means of an adjustable light source in order to generate electron-hole pairs in the substrate.

Two modes of operation are distinguished: 1) Open-circuit operation, the n+ region being con-

nected to an ultra-high-impedance volt meter. This allows probing of the electron quasi-Fermi level & ( O ) at the front surface with respect to the hole quasi-Fermi level q&( W ) at the back contact of the device. Due to the incident photons, the electron quasi-Fermi level is shifted from its equilibrium value.

2) Short-circuit operution, the n+ region being connected to a low-impedance ampere meter, while a sufficiently large positive bias V, is applied to the gate such that a highly conducting surface inversion layer is formed (induced junction). The n+ region now serves to drain the photogenerated electrons collected by the induced junction. In this mode the photocurrent at a given photon flux can be measured.

In Appendix A it is shown that the balance of electron

poly-Si gate *\ n+ region ! \

9 I

Fig. 1. Schematic diagram of the test device used in this study.

currents in open-circuit operation can be approximated by

JO( exp ( q ~ o c / k ~ ) - 1 ] - qui ( ~ o c , ~ c ) + ~ s c = 0

( 1 )

where V,, equals the photovoltage in open-circuit operation

V,, = +do) - 4 p ( W (2) J,, equals the photocurrent density as determined in short- circuit operation, Ui (V,,, V,) is the carrier recombination rate at the Si-SiO, interface, and Jo represents the bulk component of the saturation dark current density.

Mathematically, (1) expresses a relation between the open circuit voltage V,,, generated at a given light intensity (i .e. , J,, value), and the applied gate voltage V,. This corresponds, however, to an unequivocal relation between the measurable V,, and the interface recombination rate Ui ( V,,, V,), the latter being a complicated function of V,,, V,, and the interface trap parameters. Clearly the open-circuit voltage V,, and the interface recombination rate Ui (V,,, V,) depend in a complemetary way on the gate voltage V,, as shown schematically in Fig. 2. Curve fitting of experimental V,, versus V, data using (1) and an appropriate (numerical) expression for Vi (V,,, V,) yields the interface recombination parameters that are a function of the density of interface traps and the capture cross sections.

In the derivation of (1) three assumptions are made (Appendix A). First, the presence of the n + area is assumed not to disturb the flatness of the quasi-Fermi levels along the Si-SiO, interface in open-circuit operation (approximation of infinitesimally small nf area). This issue will be addressed in Section IV-B where deviations from the ideal case are explained by the presence of the finite n+ region. Second, the assumption is made that electron- hole recombination in the space-charge layer can be neglected with respect to recombination in the quasi-neutral bulk. This assumption will be justified in Section IV-A by considering J,, versus V,, measurements for various light intensities, where the open-circuit voltage V,, was mea-

GIRISCH er a/ . : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS 205

I I

gate voltage V,

Fig. 2 . Schematic plot of the open-circuit voltage V,, and the interface recombination rate (I, ( Voc, V , ) as a function of gate voltage V,.

sured under strong inversion conditions (cf. (1) neglect- ing the interface recombination term Vi (V,,, V G ) ) . In this way it has been established that the recombination in the space-charge layer is either completely negligible with respect to the bulk diffusion current or at least so small that the J,, versus V,, data could be excellently fitted by a single exponential with an ideality factor equal to 1 over a sufficiently large voltage range.

It is also tacitly assumed that generation of electron- hole pairs via interface traps (this mechanism would generally depend on the surface potential $$) may be neglected. For this assumption an analogy is made with electron-hole generation in bulk material: the two-step generation processes via deep levels are much less favor- able than the one-step phonon-assisted direct generation process.

B. InterJGace Trap Model

Interface traps that contribute to the recombination of electrons and holes at the Si-Si02 interface are described as localized electronic states, each being characterized by a discrete energy level in the forbidden energy gap. Elec- tronic transitions are considered to occur only between delocalized states of the conduction (or valence) band and the localized state of a discrete energy level in the forbidden energy gap, and not between localized states within the forbidden energy gap themselves ( “noninteracting trap model”). We assume that an interface trap is either a donor or an acceptor and that it is either neutral or singly ionized. For the moment we do not consider multivalent traps and the even more complicated amphoteric traps [IO].

For the density of interface traps

( 3 ) where D D ( E ) and D,.j ( E ) are the donor and acceptor trap density, respectively, two energy-dependent distributions [11]-[14] have been considered: 1) a doubly peaked distribution (curve 1 of Fig. 3 ) and 2) a U-shaped distribution approximated by a baseline onto which two half- Gaussian functions have been superimposed (curve 2 of

trap energy

Fig. 3 . Interface trap distributions used for numerical computations: curve 0: a doubly peaked distribution and curve 0: a U-shaped distribution approximated by a baseline upon which two half-Gaussian functions have been superimposed.

Fig. 3); exceptionally the uniform (constant) interface trap distribution has been considered. Below it will be defined which of these traps are acceptor and which are donor traps.

With respect to the capture cross sections, several models can be employed. Let a,,, upA, unD, and upD be the cross sections for electrons and holes for acceptor and donor traps, respectively; these cross sections are taken to be independent of energy and/or electric field. Follow- ing the more conventional model, a cross section a,, for electrons and a cross section up for holes are defined irrespective of the nature of the interface trap, Le. .,

@,A = anD = an (4a)

(4b)

and

apA = apD = u p .

A physically more satisfactory model has been proposed by Panayotatos and Card [lS]. Equal “neutral” capture cross sections ( uN) are assumed for nonionized acceptor traps and nonionized donor traps. Equal “Coulombic” capture cross sections (ac) are assumed for ionized acceptor traps (occupied by an electron/without a hole) and ionized donor traps (without an electron/occupied by a hole), i.e.

= u p 0 = ON ( 5 4

and

apA = OnD = (Tp

Numerical results of both models (4) and ( 5 ) will be presented in Section 11-D.

(5b)

206 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988

C. Calculation Method of the Interface Recombination Current

An exact calculation of the interface recombination current for a given gate-electrode voltage Vc would require simultaneous solution of the continuity equations and the Poisson equation with the boundary conditions dictated by the interfacial properties (charge trapping/detrapping and e-h recombination) and the gate voltage Vc. This, however, would result in excessively lengthy iterative numerical calculations. An excellent quasi-exact solution of the interface recombination current can be achieved using the approximation of flat electron and hole quasi-Fermi levels in the space-charge region. With this approximation, the accuracy of which is always checked for self- consistency at the end of the calculations, the problem to be solved reduces to a set of six equations in six unknowns. The unknown quantities are the quasi-Fermi levels & and 4p, the electrostatic potential at the surface $s

(Fig. 4(b)), the charge induced in the silicon Q,,, the charge in the interface traps Q,,, and the charge induced in the gate electrode Qc (Fig. 4(a)). The set of equations can be represented by

Qsi = HI(II/~, 4 n , 4 p )

Q,r = Hd$sy 4n, 4 p )

( 6 4

(6b)

Qsi + Q u + Q f + QC 0 ( 6 4 0 s E dz + $s = V, ( 6 4 -dox

4 n = 4 p + V , O S z s d ( 6 4

P ( $ , &, 4) = 0, z L d ( 6 f )

where E is the electric field, Qfis the fixed insulator charge density (per unit area) near the Si-Si02 interface, and p is the charge density (per unit volume) in the silicon. De- tails about the set of equations and the technique for solv- ing this set numerically have been included in Appendix B. Once &, &,, and II/, are known for a given value of the (photogenerated) voltage V , the interface recombination current is calculated by integrating the interface recombination rate over the entire energy gap, yielding either

U, = ( p n - n f ) x Vfhunu,

using the first definition for the capture cross sections (4), or

ui = ( p n - n') x v,huNac

w t charge' cm-2 gate electrode [ oxide shcon

I I

v -do, -dtO d x

Fig. 4. Charge distribution (a) and band diagram with definitions of electron energy and potentials (b).

using the second definition for the capture cross sections (5 ) ; nl a n d p , are defined by

nl = nl exp ( ( E - E,) /kT)

PI = n, exp { ( E , - W k T }

( 8 4

(8b)

and

and v , h is the camer mean thermal velocity. These formulas can easily be deduced by analogy with the net bulk recombination rate in stationary state [ 13 when assuming noninteracting interface traps.

Of particular interest is the recombination rate at maximum value

E2

EI U Y = ~ n , u o v f h exp (qV/2kT) x D , , ( E ) dE

(9) where uo denotes the mean capture cross section Ju,,up or Gc depending on the definition of the capture cross sections. The integration interval ( E , , E 2 ) comprises those interface traps that act as effective recombination centers at the particular voltage V. For smoothly varying interface trap densities this interval increases almost linearly with increasing V and can be expressed as

From the maximum Uf""" the quantity E ( AE ) can be determined, being defined as

A E = E 2 - E l = q V + k T I n 4 . (10)

E2

E ( A E ) E uovfhkT D,, ( E ) d E / A E Ei (11)

E U o V t h k T ( D , r ( A E ) ) .

GIRISCH et a/ . : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS 207

For the case of a uniform (i.e., energy-independent) interface trap distribution, the quantity C ( A E ) is a constant and equals the fundamental surface recombination velocity So [4].

Finally, a comment is made on the approximation of flat quasi-Fermi levels in the space-charge region. Pan- ayotatos and Card, who studied the recombination velocity at grain boundaries in n-type polycrystalline silicon [15], found the minority-carrier quasi-Fermi level not to be constant in the space-charge layer adjacent to the grain boundary. This was due to the high grain boundary trap density and the absence of fixed charge, which caused high grain boundary recombination currents. However, in the present study the trap density at the Si-Si02 interface and concomitant recombination current are several orders of magnitude smaller. Flat quasi-Fermi levels, therefore, have been found to be a good approximation.

D. Numerical Examples In this section a set of numerical examples will be pre-

sented from which the impact of several interface trap parameters on the measured open-circuit voltage can be understood, such as the type of interface trap, the capture cross sections, and the distribution across the energy gap. These simulations are also helpful for understanding which interface trap parameters can and which cannot be determined from V,, versus VG measurements.

First, the “neutral” and “Coulombic” capture cross sections are employed (see (5)). Fig. 5 displays the calculated open-circuit voltage as a function of gate voltage VG corrected for the flat-band voltage VFB.’ The interface recombination current density has also been drawn (dashed line). Parameter values used for these computations are listed in Table I. An equal amount of donor and acceptor traps has been chosen. The presence of both donor and acceptor traps causes a double peak in the interface recombination current and consequently a double minimum in the open-circuit voltage. The one on the left is predominantly due to recombination via donor traps ( p = 225 X n ) and the one on the right via acceptor traps ( n = 225 X p ) .

For these computations, the relative distribution of acceptor and donor traps were taken to be such that DA(E - E , ) = DO( E, - E ). Typical examples of such distributions are: 1) both donor and acceptor traps spread equally across the energy gap, and 2) all traps below E, being donor and all traps above Ei being acceptor. All these distributions yield identical V,, versus ( VG - VFB) dependencies. In the case of relative distributions of acceptor and donor traps with DA ( E - E, ) # DD ( E , - E ), the minima in the V,, versus VG curve become different from those of Fig. 5 . For instance, a distribution of interface traps, which were predominantly donors over a

‘Note: the flat-band voltage, required for experimental data analysis, has been determined experimentally from high-frequency capacitance- voltage (HFCV) measurements.

t

‘\ J \ 10.~ 4 ’ - I ’ 1 ’ ; ’ 5

V,-V,, lvolts)

Fig. 5 . Numerical results of the open-circuit voltage and interface recombination current as a function of V , - VFB using the second model for the capture cross sections. An equal amount of donor and acceptor traps has been chosen. Parameter values used are listed in Table I .

TABLE I PARAMETER VALUES USED FOR NUMERICAL V,, VERSUS ( V , - V F B )

CALCULATIONS

(The interface trap parameters refer to interface trap distribution (2) of Fig. 3 . )

dopant concentration (cm-’) 3 x 10’6

oxide thickness do, (nm) 100

“Coulombic“ capture cross-section 0~ (cut’) 0.54 x io-’* 0.24 x 10-16

fixed oxide charge layer thickness df(nm) 2

“neutral“ capture cross-section ON (cm’)

trap density near midgap Dit(Ei) (cm-’.eV-’) 6 X lo9 trap density at valence band edge Dit(Ev) (cm-’.eV-’)

trap density at conduction band edge Dit(4) (cm?.eV-’)

standard deviation s (kT) 3

P - - - - 1.5 x 10”

1.5 X 10”

short circuit current density .Isc (A.cK2) 2 x io-’

open circuit voltage in strong (mv) 560 inversion

wide range across the energy gap and acceptors only toward the conduction (and/or valence) band, would result in a V,, versus ( VG - VFB) curve with a distinct minimum due to recombination via the donor traps, whereas a less pronounced minimum would occur due to recombination via the acceptor traps.

In anticipation of experimental results (Sections IV and V) it is remarked that only singly peaked recombination currents have been observed in this study on high-quality Si-Si02 interfaces. The observation that the experimentally determined currents always reached their maximum at an electron concentration orders of magnitude different from the hole concentration would imply that either donor or acceptor traps are involved. Fig. 6 shows some numerical results of the open-circuit voltage as a function of V , - VFB for exclusively 1) donor traps and 2) acceptor traps. Within the validity of this model, curve fitting of experimental data gives information on the nature of the

208 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35. NO. 2, FEBRUARY 1988

I I I

1 I I I -3 1 1 3 5

v, -vFB (volts1

Fig. 6. Numerical results of the open-circuit voltage as a function of Vc - VFB for exclusively donor traps and acceptor traps using the second model for the capture cross sections. Parameter values used are listed in Table I .

I 1 1 I -3 I 1 3 5

v, - v,, (volts1

Fig. 7 . Numerical results of the open-circuit voltage as a function of V, - VFB for three values of the ratio un/up using the first model for the capture cross sections. The same parameter values have been used as before.

interface traps. One aspect relating to this model requires some additional attention, viz. the total charge in the interface traps at flat-band condition. This charge Qi, ($, = 0) may become quite considerable when only donor traps or only acceptor traps are involved, depending on their distribution across the energy gap. For the calculations displayed in Fig. 6 this charge is about 3.3 X lop9 C cmW2 and -2.4 X lop9 C cmP2 for the donor- and acceptor-type cases, respectively. However, it should be borne in mind that these charge densities may become lower in the case of asymmetrical trap distributions without essential changes in the V,, versus ( Vc - V,,) rela- tionships. In view of the magnitude of this charge and the accuracy of standard electrical characterization techniques it seems, at present, impossible to choose between a model based upon a single type and a model upon two types of interface traps.

Next, the first model concerning capture cross sections is considered: irrespective of the nature of the trap, cross sections u, and a,, are defined for electrons and holes (see (4)). Fig. 7 displays typical V,, versus ( VG - VFB) curves for three values of the ratio .,/up while the mean capture cross section uo equals 0.36 X cm'. Both peak shape and peak position depend on the relative magnitude of the electron and hole capture cross sections, which can be understood from inspection of (7a). The V,, versus ( VG - VFB) curves are, however, completely independent on the relative amounts of donor type and acceptor type traps (the interface trapped charge at flat-band condition, and hence the flat-band voltage V F B , does of course depend on the nature of the interface traps).

Comparing the numerical results of Fig. 6 with those of Fig. 7 and having in mind (4) and (5), it is concluded that curve fitting of experimental V,, versus ( VG - VFB) data can yield the ratio of the electron and hole capture cross sections, at least in the regime of maximum recombination. It should be emphasized that the result for the determined ratio is independent of the model chosen for the capture cross sections.

Until now the computations have been restricted to the case of the U-shaped interface-trap distribution. Fig. 8

562 K

uniform

...... distr 1 1

dstr. # 2

%-3 -2 -1 0 1 2

v, -vFe (vdtsl

Fig. 8. Numerical V,, versus ( V, - VFB) curves using the uniform (constant) (----), the doubly peaked ( . . * ), and the U-shaped distribution for interface traps (-).

displays three numerical V,, versus :Vc - VFB) curves using 1) a uniform interface trap distribution with D,, = 7.5 X 10" cm-2 - eV-', 2) the doubly peaked distribution (curve 1 of Fig. 3) with Di, (Ei) = 4 x lo9 cmP2 eV-', and 3) the U-shaped distribution (curve 2 of Fig. 3) with D,, ( E , ) = 6 X lo9 cm-* - eV-', Dit (E,) = D,, ( E , ) = 3 X 10" cmp2 * eV-' in this case, and s = 3 kT. For the electron and hole capture cross sections a, and up, values of 0.54 X and 0.24 x cm2 were chosen. The shallower in energy the interface-trap distribution, the wider the peak due to interface recombination appears to be. This effect of shallow interface traps can easily be understood from consideration of (7a) and (7b): shallow traps are effective recombination centers only in the accumulation and (strong) inversion regime. The dependence of the peak shape on interface trap distribution suggests that careful curve fitting of experimental V,, versus ( VG - VFB) data may give information

GIRISCH et a/. : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS 209

on the density of shallow interface traps. Our experimental data indicate U-shaped distributions with shallow interface traps to be more likely than the others. However, details on the shallow trap levels are difficult to obtain. Neither can asymmetries in trap distributions be identified.

E. Recapitulation Depending on the method of data analysis the following

model parameters can be determined: 1) If the analysis is confined to the recombination cur-

rent at maximum value, using (9) to (1 l ) , only the product of the mean capture cross-section uo and the interface trap density can be determined.

2) Analysis of the recombination current as a function of gate voltage VG in the regime near maximum recombination, using the set of equations ( 6 ) , yields in addition the average value of the ratio of the electron and hole capture cross sections. The experimentally determined value of this ratio is independent of the assumptions concerning the model of the cross sections and the type of the interface traps.

3) A similar analysis in conjunction with an independent measurement of the interface trap density in a wide range around midgap enables the determination of average values of both minority-carrier and majority-carrier capture cross sections. Some information on the recombination via shallow interface traps can be obtained by extending the analysis toward the regimes of accumulation and strong inversion.

111. EXPERIMENTAL

A. Measurement Circuit The basic configuration of the measurement circuit is

shown in Fig. 9. In open-circuit operation the Keithley 602 B electrometer serves as a high-impedance unity-gain amplifier, whereas in short-circuit operation it is used as a sensitive current-to-voltage convertor. Current measurements were frequently checked with I- V measurements; in this way it has always been ensured that the gate voltage VG chosen was high enough for complete current collection.

The wafer under consideration was fixed on a temperature-controlled block (27 * 0.5"C). This block, as well as several micro-manipulators with probes, was placed in a shielded box. The adjustable light source had been mounted on top of the box.

B. Device Structure and Fabrication Technology Fig. 10 gives the cross sections of the two basic device

structures; field electrodes and n+ region all exhibit axial symmetry. Structure A is a single polysilicon gate-controlled point-junction diode, whereas structure B is a similar device containing double-layer polysilicon electrodes. By means of the inner gate of structure B the surface potential right at the metallurgical junction can be controlled independently of the main gate bias (normal

adjustable light swrce

Keithley 602 B

data acqulsltlar

i V

I h" I I u programmMe

voltage r-l generator

Y T Fig. 9. Measurement setup.

f l

[structure E j

Fig. 10. Cross-sectional views of the two device structures used. Black and shaded areas correspond to aluminum and polysilicon, respectively, in the actual device (p-type substrate).

mode of operation: Vig >> V,,). The outer guard ring in both devices serves to reduce side effects; in device A it consists of a narrow aluminum ring and in device B of a broad polysilicon electrode overlapping the main gate.

Flaps for contacting the field electrodes and n + region are located at the outer part of the gate in structure A and outside the main gate in structure B. Connection to these flaps is performed by aluminum and/or polysilicon contact lines; the widths of these contact lines, where they run across the (main) gate, are 8 and 14 pm, respectively.

For the present experiments we have used two mask sets. Mask set 1 contains three devices of structure A with different sizes of the n+ area (radii R of 8 , 13, and 18 pm), whereas mask set 2 contains one device of structure A (with nf area radius R = 13 pm) and one device of

2 10 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988

structure B. In addition, all mask sets have been provided with a capacitor (polysilicon electrode) with overlapping guard ring and a polysilicon-gate field-effect transistor. The latter devices have been designed for additional characterization of the Si-Si02 interface using various techniques (HFCV, QSCV, charge pumping, etc.) as well as for determination of the oxide thickness (typically - 124 nm).

The processing technology used to fabricate the devices is closely related to NMOS processing schemes. The gate oxides were grown at 1025°C in dry oxygen with 0.2 percent trichloro-ethane.

C. Starting Material

Floating-zone-grown p-type substrates, { 100 } orien- tated, have been utilized with three dopant concentrations ranging from 2.5 x lOI5 to 5.0 x 10’’ crnp3. Table I1 gives the bulk dopant concentrations of the wafers and in addition the dopant concentration values of the surface layer, as determined by means of HFCV measurements and threshold voltage ( VTH) measurements. These values are well below the corresponding bulk values due to boron redistribution during device processing.

In the following sections the different wafers will be referred to by their bulk dopant concentrations, but V,, versus V , data will be analyzed using the experimentally determined values of NA.

D. Data Analysis

A series of V,, versus ( VG - V F B ) data, as acquired at various light intensities, can be analyzed using the analytical approximation (9) to the interface recombination rate or using the quasi-exact numerical scheme (6).

1) Analytical Method of Data Analysis: First, the saturation dark current density J o of (1) is determined by plotting In (.Isc) versus V,, data, acquired at various light intensities under the strong inversion condition.2 The interface recombination current is negligible because of the strong inversion (or accumulation) condition. The resulting straight line corresponds to the diffusion current of electrons injected into the quasi-neutral bulk and yields Jo. This procedure is free from errors due to series resis- tance. Once Jo is known the interface recombination rate at maximum value is determined for the whole series of V,, minima using (1). By means of (9) to (1 1) the value of C ( A E ) is subsequently calculated for all minimum values of the open-circuit voltage.

2) Numerical Method of Data Analysis in the Regime Near Maximum Recombination: V,, versus ( VG - VFB) data are considered for various values of the incident light intensity. Curve fitting of these data in the regime of maximum recombination yields 1) the quantity o0 x ( Di, ( A E ) ) , or equivalently E ( A E ), and 2) the average

’Note: by preference, the corresponding Voc values at strong accumulation have been used (see Sections IV-A and IV-B).

TABLE I1 BULK NA VALUES AND CORRESPONDING EXPERIMENTALLY DETERMINED N ,

VALUES I N THE SURFACE LAYER

NA (cm-’) N A (cm-’) N~ (cm-’)

bulk surf. layer, IlFCV surf. layer , VTH

2.5 x 1015 2.1 x 1015 2.3 x 1015

5.0 x 10” 1.9 x 10” 2.1 x 1017

2.9 X 10” 2.7 x 10l6 4.6 x 1016

value of the ratio of the electron and hole capture cross sections. For relatively low interface trap densities ( D i t ( E i ) 5 1 x 10” cmP2 - eV-‘) the change of the interface trapped charge Qi, with GS varying in the depletion and weak inversion regime can be neglected. There- fore, no precise knowledge of the interface trap density is required for this analysis.

3) Numerical Method of Analysis in Conjunction with Independent Dit Measurements: From combined high- frequency CV (HFCV) and quasi-static CV (QSCV) measurements, and from charge-pumping measurements, the interface trap density Dit ( E ) is determined. Subsequently experimental V,, versus ( VG - VFB) data are fitted with numerical simulations as displayed in Figs. 5 to 8, for various values of the incident light intensity. The capture cross sections are adjusted for an optimum fit of the data in the regime of maximum recombination. The distribution and density of shallow interface traps are adjusted in order to obtain the peak width and shape as observed experimentally.

IV. EXPERIMENTAL RESULTS 1 : DEVIATIONS FROM ONE-DIMENSIONAL THEORY

A. Peripheral Effects

Deviations from one-dimensional theory occur due to recombination in the periphery of the device. Fig. 11 displays the lateral recombination currents that may flow when the silicon under the main gate is inverted. J , represents a diffusion limited current of electrons that recombine either in the peripheral bulk (and back contact) or at the peripheral interface ( a component with ideality factor n = 1) . J2 represents an electron drift current along the inverted silicon surface toward the peripheral interface, where a higher recombination rate may prevail ( a component with 1 < n 2 2 ) . This component is only present when the silicon under the guard electrode is biased into inversion.

These currents cause the electron density under the main gate to be lower than in an ideal device with an infinitely large gate. As long as the electron conductivity under the main gate is small (accumulation-depletion-onset of strong inversion) the reduction in electron density is localized to the outer region under the gate and is not sensed by the nf region. However, the more the conductivity of the inversion layer increases, the more the reduction in

GIRISCH ef a / . : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS

103

10.'

211

:

3 -

7

aluminium (opaque I

J, - peripheral interface recombina-

- _ - - - - - _ _ _ _ _

- - E 625 rF ~ : i p + , ~ ~ i recombination bulk

back contact recombination

621 -6 0 6

't IWbI

Fig. 11. Cross-sectional view of the outer part of the device showing the lateral recombination currents that may flow at V , >> 0. Inset: typical V,, versus V , data showing the decrease of V,, in strong inversion ( NA = 4.6 X I O i 6 ~ m - ~ , device A ) for two values of the guard ring voltage ( - 9 , f 1 8 V ) .

the electron density is spread out toward the n+ area. As a result the measured open-circuit voltage starts to decrease once the main gate voltage exceeds the threshold voltage. The inset of Fig. 11 illustrates this decrease of V,, in strong inversion ( N A = 4.6 X 10I6 cmP3, device A ) for two values of the guard ring voltage ( -9, + 18 V ) .

The J 2 component can be suppressed effectively by biasing the silicon surface under the guard electrode into accumulation. This is shown in Fig. 12(a), where J,, versus V,, data are displayed for both surface conditions under the guard electrode ( N A = 5.0 x 1017 cmP3, device B).

It may be noted in passing that the J,, versus V,, data, acquired with the appropriate surface condition under the guard electrode, perfectly obey a single exponential relation with ideality factor equal to 1 over the whole voltage range under study. This supports our approximation, made in Section 11-A, of negligible electron-hole recombination in the space-charge layer under the gate electrode.

The magnitude of the J1 component depends on device geometry and on minority-carrier diffusion length. In device A of Fig. 10, which has a 10-pm-wide opaque guard ring for only J 2 suppression purposes, the Jl component appeared to be quite significant. Fig. 12(b) gives typical J,, versus V,, data for V, = 1 V, which is close to the onset of strong inversion ( V,,), and V , = 10 V ( N A = 4.6 x 10l6 crnp3). The difference between the two Jo values is about 20 percent. In device B of Fig. 10, which has a large 220-pm-wide semi-transparent guard ring ( Vg < VFB), the Jl component was considerably reduced. Simi- lar J,, versus V,, data acquired using device B of the same wafer virtually coincide, the difference between the two Jo values being about 2 percent or less. In addition, the effect of J1 was found to decrease with decreasing minority-carrier diffusion length L, (the values of L, were calculated from the experimental Jo values and decreased with increasing dopant concentration ).

lo-' - . 0

- . N

E, 9 10-3 - 7*

e . I c

3 " 3 c

- c

0 L

Vguord

Vguord

v, = +

= - 9 Volt laccum I

/ /

Vguord = - 9 Volt laccum I Vguord = 18 Volt ( invers I

open circuit voltage (mV1

(a)

'r. v, = 10.0 volt (strong inv1

31 ' I ' I " ' L35 L70 505 UO

J 515

open circuit voltage ImVI

(b) Fig. 12. (a) J, , versus V,, data for the two surface conditions under the

guard electrode. Solid line: accumulation, and dashed line: inversion (NA = 5.0 X 10'' ~ m - ~ , device B; V , = + I 5 V, VFs = -0.9 V ) ; (b) J,, versus Voc data for two surface conditions under the gate electrode: near threshold and strong inversion, respectively (NA = 4.6 x 10l6 ~ m - ~ , device A; V,,,, = -9 V, V,, = -0.9 V).

B. Effects due to the Finite Size of the n+ Region The finite size of the n' region may disturb the flatness

of the electron quasi-Fermi level in the silicon surface layer. Two effects may contribute.

The first one is related to the current component injected into the n+ region. When the n+ region communi- cates with the photogenerated bulk electrons exclusively by means of the diffusion mechanism (Le., while the silicon is not yet strongly inverted) the electron quasi-Fermi level at z = 0 near the n+ region has a local minimum due to the additional recombination in the diffused region. On the other hand, when the silicon surface is biased in strong inversion, the electron quasi-Fermi level becomes flat all along the silicon surface due to the high lateral electron conductivity. In the latter case the presence of the n+ region has virtually no effect because the total current recombining in the diffused region is very small com- pared to the total current recombining in the bulk under the main gate (the n+ area is less than loP3 of the main

212 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988

gate area). As a consequence the open-circuit voltage measured at accumulation is slightly lower than at the onset of strong inversion. This phenomenon is always observed unless it is outweighed by the effect of peripheral recombination. Typical V,, versus VG data for N A = 4.6 X 10l6 cm-3 are given in Fig. 13 (device B). In the inset the difference in open-circuit voltage AVO, is displayed as a function of the radius R of the n+ region (device A). A simple model, detailed in Appendix C , predicts AVO, to increase linearly with R provided that AVO, << k T / q and R << L,, where L, is the bulk electron diffusion length. For the idealized case of an infinitely thick substrate, AVO, can be approximated by

620

7 E 6,8

3 5 616

t, O“

614

I I I I

-

-

-

-

-

.

-

R R l p m l I I I I

0 5 10 -10 - 5 (12) 612 I kT J,+

AVO,.- - - X - X & X - - 9 Jo Ln

where J,+ and Jo are the one-dimensional dark current components toward the n+ region and toward the bulk, respectively, for the corresponding plane junction. Using this equation the experimental AVO, versus R data of the inset of Fig. 13 have been fitted with an effective diffusion length L, of 370 pm; the Jo and J,’ values were obtained from analysis of (J,,, V,,) data acquired on the gate-controlled diodes and simultaneously processed planar n+-p solar cells [ 161. The value of 370 pm for the electron diffusion length is qualitatively in agreement with the determined Jo value, which indicated L, to exceed the wafer thickneys (285 pm).

The AVO, value as defined in Fig. 13 has been found to increase with increasing dopant concentration. This can be understood qualitatively by appreciating that AV,, var- ies with dopant concentration as N A / D , ( N A ) .

There is a second effect that may disturb the flatness of the electron quasi-Fermi level in the silicon surface layer. The n+ region has been made opaque for incident light (see Fig. 10). Consequently, no electron-hole pairs are generated immediately below the n+ area. It is easy to deduce that this causes a similar AVO, effect to that described above. However, for the devices under study ( R << L n ) , this effect is probably less important.

C. Edge Effects of the n+ Region The diffusion of phosphorus during device processing

may cause diffusion-induced defects and concomitantly an increased interface trap density around the metallurgical junction [17]. In structure A these defects develop below the main gate. Such an increased density of interface traps would cause additional recombination currents and introduce errors into thp, results for the interface recombination parameters. In structure B the n+ region is surrounded by a permanent induced junction by the application of a positive bias to the ring-shaped inner gate ( Vg >> VTH). Therefore, no additional interface recombination currents due to defects close to the metallurgical junction can occur and (more) correct values for the interface recombination parameters are obtained.

With the latter structure possible edge effects have been investigated. Fig. 14 displays experimental V,, versus VG

gate voltage VG IVoltsI

Fig. 13. Typical V,, versus VG data showing the difference in open-circuit voltage AVO< due to the finite size of the n+ region ( N , = 4.6 X 10l6 ~ m - ~ , device B; J,, = 2.12 X A . cm-2). Inset: the difference in open-circuit voltage AV,,, versus radius of the n t region (Jrc = 1.52 X

A . cm-’).

670<

-10 -5 0 5 x) 6501 1 I I I I 1

gate vdtage V, IVolts)

Fig. 14. Experimental V,, versus Vc data for three values of the bias applied to the inner gate: curve 0: V,, = + 18 V (inversion), curve 0: Vt8 = -9 V (accumulation), and curve 0: V,8 = VG (N,, = 5.0 X 10” cm-3, device B; J,, = 2.06 X lo-* A . cm-’).

data for three values of the bias applied to the inner gate: curve @ Vjg = + 18 V (inversion, the normal mode of operation), curve @ Vig = -9 V (accumulation), and curve @ Vjg = V,. The difference between the data sets @ and @ can be explained by the difference in the electron transport mechanism below the inner gate and will not be commented on here. As expected, the minimum V,, values with respect to their reference V,, values (i.e.. the accumulation values) are equal for Vig = + 18 V and Vig = -9 V. On the other hand, the V,, versus VG data with Vig = VG exhibit a lower V,, minimum @, indicating enhanced recombination below the inner gate, which suggests a phosphorus-related edge effect. We believe that the locally inferior interface properties around the n+ re-

GIRISCH e1 u l . : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS 213

gion in device B are due not merely to the lateral phosphorus diffusion itself, but rather to the regrowth of the oxide after the phosphorus diffusion. This idea is based on the experimental results that the E ( A E ) values as determined with structure A were found not to be systematically higher than the C ( A E ) values as determined with structure B (with Vi, >> V T H ) . A close correspondence has always been found, typically better than 5 percent (Section V-B). It is even possible that the inferior interface properties of the regrown oxide are an artifact and have nothing to do with the lateral phosphorus diffusion. HFCV and QSCV measurements have been carried out on large polysilicon-gate capacitors present on the wafer for independent characterization of the Si-Si02 interface under the first-grown and the regrown oxide. In both cases the interface trap density near midgap appeared to be so low that a definite answer could not be given on this point.

V. EXPERIMENTAL RESULTS 2: Si-Si02 INTERFACE RECOMBINATION CHARACTERIZATION FOR { 100

P-TYPE Si WITH VARIOUS DOPANT CONCENTRATIONS

A . Outline This section presents the experimental results on Si-

Si02 interface recombination characterization using { 100 } oriented p-type silicon substrates with dopant concentrations ranging from 2.5 x 10" to 5.0 X lot7 cmP3. The analytical approach is applied for a first characterization in terms of E ( A E ) . Next, the numerical method will enable us to characterize the interface recombination parameters in more detail with particular reference to the capture cross sections for electrons and holes. Additional information concerning the interface trap densities has been obtained from room-temperature HFCV and QSCV measurements, and charge-pumping measurements [ 181.

The electron and hole capture cross sections will be de- noted as u, and up, irrespective of the nature of the interface traps.

B. Analytical Method of Data Analysis The interface recombination rate at maximum value was

determined for a range of incident light intensities. From these ( U v , V ) data, C ( A E ) values were calculated using (9) to ( 1 1 ) . Both A and B devices have been considered. The values at the various light intensities, however, are based on measurements on devices A.3 Re- sults for all dopant concentrations are given in Fig. 15; the C ( AE ) values are essentially independent on device layout.

The E ( AE ) values are almost independent of energy interval AE for the wafers with bulk dopant concentrations of 2.5 x lOI5 and 4.6 x 1OI6 cmP3. This means that the average of oo X D , ( E ) is almost independent of the

'Note: the J , , values of the B devices are 25 to 30 percent higher than those of the A devices, operating at the same light intensity. These appar- ently higher short-circuit currents are due to electrons that are generated below the polysilicon guard ring ( Vzudrd << V F H ) and partly diffuse toward the inversion channel below the main gate.

N, = 50 x 1017 c m 3

w 45

300 400 500 600 700 35

N, = L6 x 1Ol6 cm-'

w 35

300 400 500 600 700

I " ' I " ' I

N,; 2 . 5 ~ 1 0 ' ~ cni3 35 1 , 1 1 1 1

200 300 400 500 600

energy interval AE (meV)

Fig. 15. Experimental C ( A E ) values as a function of the energy interval AE. Solid and open dots refer to device structures A and B, respectively.

energy interval AE. On the other hand, C ( A E ) for the wafers with the highest dopant concentration (5.0 X 1017 ~ m - ~ ) was found to increase somewhat with increasing energy range A E , by about a factor of 1.4. A possible explanation for this increase is the presence of boron-associated interface traps, which arise at substrate dopant concentrations above lOI7 cmP3 [19], under the hypothe- sis that the energy levels induced by these boron com- plexes are lying in a limited energy interval (e.g., toward the valence band) rather than uniformly over the entire bandgap.

C. Ratio of the Capture Cross Sections In order to obtain the ratio between the capture cross

sections a,, and a,, for various A E values, experimental V,, versus ( V , - VFB) data have been fitted with numerical computations in the regime of maximum re~ombination.~ Results of .,/up versus A E are shown in Fig. 16 for all dopant concentrations under study. For the lower concentrations, NA = 2.5 X lOI5 and 4.6 X 10l6 cmP3, the ratio u,,/a, does not exhibit a strong dependence on energy interval AE. For the highest concentration, NA = 5.0 X 1017 ~ m - ~ , the data at low A E values indicate a decrease of a,/o,, with decreasing AE; these data are, however, uncertian due to errors associated with boron redistribution (Section VI-A). Considering the more reliable data, we conclude that the cross section for capturing electrons is higher than the cross section for capturing holes by a factor of lo2 to io3.

D. Numerical Method of Data Analysis in Conjunction with D , Measurements

Several experimental tools have been applied for an independent determination of D j , ( E ) in the central part of the bandgap.

4Note: the necessary VFB values were determined from HFCV measurements.

2 14 IEEE TRANSACTIONS ON ELECTRON DEVICES. VOL. 3.5. NO. 2, FEBRUARY 1988

. + .

+ p lo2:

r

/-/*,?E- _.-• -0

/

L

a

NA.25x10'icmi device B

N,-L6x10'6cm'- device A B - . N A = 5 0 x 1 0 " c m 7 - device A

i

8 . z t 8 / 4

NA.25x10'icmi device B

N,-L6x10'6cm'- device A B . N A = 5 0 x 1 0 " c m 7 - device A

i

MO 30 LW 500 6w 700 m q y intwml AE lmeVl

Fig. 16. Experimental results of the ratio between the electron and hole capture cross sections versus energy interval A E for the different dopant concentrations. Each series has been connected by lines.

1) HFCV and QSCV measurements have been carried out on all wafers using the polysilicon-electrode test capacitor. Standard analysis methods of QSCV data (Le., comparison of QSCV data with the theoretical LFCV curve) did not yield reliable results because of the low Di, values and the presence of boron redistribution under the gate oxide [20]. The difficulty caused by the boron profile is eliminated by the use of an extended analysis method, which relies on the comparison of measured QSCV and HFCV data near the intrinsic situation. This method indicated near midgap D;, values around 1 X 10" cmP2 * eV-' or somewhat less [20].

2) Charge-pumping measurements have been performed on polysilicon-gate field-effect transistors. These measurements have been confined to wafers ( N A = 4.6 X 10I6 cm-3 ) with single-polysilicon gate devices, using a slightly different processing scheme. The C ( A E ) values determined on these wafers were typically 0.7 cm * SKI,

which is somewhat higher than the values shown in Fig. 15. The charge-pumping measurements yielded a value of 9 x lo9 cmP2 eV-' , being an average over the central 0.8 eV of the bandgap.

In view of these results, we have concluded that the interface trap density in a certain energy range around midgap is somewhat below 1 x 10" cmK2 eV-', but an accurate determination could not be made. For the numerical calculations presented below we have used a value of 6 X lo9 cmP2 eV-l for D;, ( E , ) , being the baseline density of distribution @ in Fig. 3 . The capture cross sections (for which we chose the conventional definition) and the density of shallow interface traps were adjusted to obtain optimum fit curves of the experimental V,, versus V, data.

Fig. 17 displays four series of experimental V,, versus V , data (solid lines) as acquired on a wafer with N A = 4.6 x 10l6 ~ m - ~ , together with numerical results (dotted lines); the four light intensities employed correspond to photon fluxes in the 3 X l O I 3 to 3 x lOI7 cm-2 * s-' range. At each light intensity the measured .I,, value is given. as well as the values of 0.. and (T- used for the nu-

622 - V

J,,= 2 M x 1 0 2 Acm' , I ,

-7 -5 -3 -1 1 3 5

gnte wltage V, (Wtsl

LlO

gate voltage V, IVOlts)

Fig. 17. Experimental V,,, versus Vc data (solid lines) for N , = 4.6 X 10l6 cm-' (device B), together with numerical results; VFB = -0.9 V. At each of the four light intensities the measured I,, value is given, as well as the values for un and u,, used for the numerical calculations.

merical calculations. The arrow on the V , axis indicates the position of the V,, minimum when equal cross sections for electrons and holes are assumed. For the shallow interface traps we chose Di,(Ev) = Dil(Ec) = 1.5 x 10" cmP2 * eV-' and s = 3 kT (U-shaped distribution).

In all cases the numerical simulations fit the experimental data fairly well, with the exception of the data near the onset of strong; inversion: the experimental V,,,

GIRISCH ef al. : DETERMINATION OF Si-SiO? INTERFACE PARAMETERS 215

data were found to increase systematically less steeply with gate bias than the numerical curves. No satisfactory explanation has been found for this discrepancy. For the electron capture cross section un average values were deduced ranging from 3 .8 x lop" to 5.9 x IO-15 cm'. For the hole capture cross section up the average value was about 1.5 x cm2; no dependence on energy interval A E was observed, indicating that up depends only weakly on trap energy in a wide range around midgap. Similar results for the capture cross sections have been obtained on wafers with dopant concentration NA = 2 . 5 X 10" ~ m - ~ .

Another result obtained from the complete analysis of the experimental V,, versus V, data is that the quantity uo X Dit( E ) probably increases monotonically toward the conduction and/or valence band edge(s) (cf. Section II- D).

VI. DISCUSSION

A . Origin of Possible Errors I ) Surface Potential Fluctuations: Until now it has

been assumed that the fixed insulator charge and the charge into interface traps were uniformly distributed in the plane of the interface. However, experimental data acquired by Nicollian and Goetzberger using the MOS conductance technique indicate a random distribution of charges near (or at) the Si-Si02 interface [ 121. As a consequence the surface potential lc/,y is subject to statistical fluctuations. In order to study the impact of these fluctuations on the interface recombination current, we closely followed their treatment and divided the plane of the interface into a number of squares with equal area. The characteristic area a is the largest area within which the surface potential is uniform (Appendix D). The interface recombination current in the presence of surface potential fluctuations due to the nonuniform charge distribution has been calculated by integrating the current contribution from each characteristic area over all characteristic areas. A series of V,, versus ( V , - V F B ) calculations, using the parameter set of Fig. 17 (lowest light intensity) and using values up to 2 X 10" charges per square centimeter for the mean density Q,,/q, have shown potential fluctuations to have only a minor impact on the interface recombination current. Therefore, these fluctuations will hardly af- fect the experimental results for the interface recombination parameters such as C ( A E ) , at least for these high- quality Si-Si02 interfaces.

Additional consideration of these numerical simulations has also confirmed that surface potential fluctuations have no effect on the experimentally determined ratio between the capture cross sections.

2) Boron Redistribution Under the Si-Si02 Inter- face: For all numerical calculations a uniform boron distribution in the space-charge layer was tacitly assumed. Nevertheless, considerable redistribution of boron occurs during device processing, particularly during the first ox- idation. Fig. 18 shows the normalized boron concentra-

depth (pm)

Fig. 18. Normalized boron concentration as calculated with SUPREM I1 [21] for the double-polysilicon device B. The arrows, marked ( I ) , (2), and (3), indicate the maximum equilibrium depletion layer widths corresponding to the experimentally determined concentrations ( N A . $ ) in the surface layer.

tion calculated with the process simulator program SU- PREM I1 [21] for the double-polysilicon device; the default value for the boron segregation coefficient has been used. The boron redistribution was also manifest from the dopant concentration values in the surface layer, as determined by means of HFCV measurements and threshold voltage measurements, which were well below the corresponding bulk values (Table 11, Section 111-C). Inspec- tion of Fig. 18 shows that these values merely represent an average value at maximum equilibrium space-charge layer width.

In order to estimate the impact of errors in the dopant concentration on the ratio between the capture cross sections, the value of ( V , - V F B ) at the maximum interface recombination rate has been calculated as a function of dopant concentration, using two values of the cross section ratio; two light intensities have been considered (Fig. 19). At high light intensity, an error in N A appears not to have much effect on the determined cross section ratio, even for the highest dopant concentration under study. On the other hand, at low light intensity and high dopant concentration a small error (e.g. , 15 percent) in NA may cause a large error in the cross section ratio (a factor of ten!). This error will be cancelled out to some extent due to the concurrent error in the VFB determination.

The error caused by the use of a uniform rather than a space-dependent boron distribution is not easily ascertain- able. In view of the latter calculations we believe that this will not be severe for the majority of cases investigated. For the highest dopant concentration ( N A = 5.0 X IOI7 cmP3) at low illumination levels, an appreciable uncer- tainty exists.

B. Interface Trap Model Interface traps have been described as localized elec-

tronic states, each being characterized by a single discrete energy level in the forbidden energy gap. They were assumed to be either of the donor type or of the acceptor type, to be monovalent and noninteracting (Section 11-B). Furthermore, neither (spin) degeneracy nor the occur- rence of excited states was included. These assumed properties need further discussion.

216

' conduc&& 'band

IEEE 'TRANSACTIONS ON ELECTRON DEVICES. VOL. 35, NO. 2. FEBRUARY 1988

15 , . . . . , . . . , . . . . . I . high light intensidy - J,, = 2 0 x 10' Acm2 1 0

05

OD

-

-

05 -

-10 ' ' ' ' ' . , . I ' ' ' ' I * . . ' ' 10'~ 10l6 lon

J,=20w106 Acm2

30 -

20 -

dopant concentration N, ( ~ 1 - 6 ~ 1

Fig. 19. Dependence of VG - V,, on dopant concentration N , at the maximum interface recombination rate. Two values of the ratio between u,, and up and two light intensities (.I,' values) have been considered.

1) The nature of intevface traps has not been conclu- sively established until now. Besides monovalent donor type and acceptor type, multivalent and especially amphoteric traps are possible candidates for Si-Si02 interfaces. Fig. 20 displays schematically the electronic spectrum and the charge diagram for an amphoteric trap (cf. Blakemore [lo]). Several authors call the amphoteric character a fundamental property of interface traps [22], [23]. Theoretical models also exist that point out the multivalent amphoteric character [24], [25]. Amphoteric traps with the neutral Fermi level near midgap (Fig. 20) are predominantly donor-like when p > n and acceptor-like whenp < n. Referring to the calculations of Section II- D (Fig. 5), we recognize that such traps would result in two maxima of the interface recombination rate as a function of V,. This would conflict with all our experimental data, which always showed one single maximum at p > > n (i .e. , u, >> u p ) . Therefore, it seems quite unlikely that amphoteric traps with neutral Fermi level near midgap are present at the Si-Si02 interfaces under investigation.

2) Spin Degeneracy: If degeneracy were accounted for, this would, first, result in slightly different values of the interface trapped charge Q j , because the spin degeneracy weighting factors are usually smaller (larger) than unity for donor (acceptor) type traps [ 101. However, this effect is so small that it can be completely neglected for low trap density Si-SiO, interfaces. Second, degeneracy factors would introduce a slight asymmetry (with respect to n andp) in the formulas for the interface recombination rate ((7a) and (7b)). The neglect of degeneracy may, therefore, introduce small errors in the experimentally determined ratio between the capture cross sections. Few experimental data have been reported on the values of the

w charge per center

Fig. 20. Left: Electronic spectrum of an amphoteric trap. For three loca- tions of the Fermi energy level the possible state configurations have been drawn. Note that two electronic states (with binding energies E , - E , and .Ec - E 2 . respectively) are only present when the Fermi level is somewhere near mid-gap position (the so-called neutral Fermi level). Right: Charge diagram of the amphoteric trap showing how the charge on the center depends on the Fermi energy at low temperature.

degeneracy factors (g-factors) for traps at the Si-Si02 interface. For dry and HCI-grown oxides the g-factors have been found to be close to unity for { loo} oriented silicon [26]. Therefore, the assumption of g = 1 seems to be reasonable and has not caused significant errors in the determined interface recombination parameters.

3) Noninteracting Interface Traps: Electronic transitions were considered to occur only between delocalized states of the conduction (valence) band and localized states with a discrete energy level in the forbidden energy gap, and not between localized states within the forbidden energy gap themselves. It is not clear a priori whether this assumption is justified. Due to the multitude of states at the Si-Si02 interface, having an almost continuous energy spectrum, one might expect quantum mechanically large probabilities for electronic transitions between the localized states. We shall, however, show that a trapped electron (hole) is unlikely to "see" other neighboring trap centers.

Donor-type interface traps are considered; such Cou- lombic centers can form bound states with electrons available in the silicon half-space near the interface. The energy eigenvalues of the bound states can be written in the form [27], [281

where eOX and tS are the dielectric constants of SiO, and Si, respectively, m* is the appropriate effective mass, mo is the free-electron mass, and En,H are the energy eigenvalues of the hydrogen atom

The corresponding effective Bohr radius reads

"A _. " a , = ~ - 2 m*"

GIRISCH et al. : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS 217

where aH is the Bohr radius for the hydrogen atom. This so-called ''effective mass approximation" model has been discussed by several authors in an attempt to calculate the energy levels for donor- and acceptor-type interface traps, but no agreement exists concerning the proper choice of the effective mass and the eigenstates allowed [29], [30]. Nevertheless, we believe that this model may give a correct idea of the extension of the charge cloud of an electron trapped at an energy Et. Using the density-of-states effectiye mass for electrons, an effective Bohr radius of 12.6' A is calculated and a binding energy of 0.073 eV. The states of the deeper level^,^ those which are relevant for electron-hole recombination, are probably even more localized in space. On the contrary, the density of interface traps with deep levels lying in an energy interval of a few kT is certainly less than 10'' cm-2 for the Si-SiO;? interfaces investigated. Consequently? the average dis- tance between such traps exceeds lo3 A, which is already two orders of magnitude larger than the effective Bohr radius of the shallow donor traps. It is, therefore, unlikely that direct transitions between localized states with deep energy levels would play an important role. Of course, this issue should be treated quantum mechanically, taking into account excited states, in order to get a more quan- titative answer.

C. Results on the Electron and Hole Capture Cross Sections

From our data, obtained on samples with NA 5 5 x 10l6 cmp3, it was deduced that 1) the electron capture cross section exceeds the hole capture cross section by a factor of lo2 to lo3 for interface traps near midgap, and 2 ) the average values of a,, and u are in the range of 10p'5-10-'4 cm2 and 10p'7-10-p6 cm2, respectively. These results compare well with reported conductance data for dry-grown SiOz films. The conductance technique yielded capture cross section values being larger for electrons than for holes, at least for low interface trap densities [13], [31]-[33].

We have also made a preliminary comparison with pub- lished DLTS data. From the many data available only those that had been obtained on { loo} oriented wafers, oxidized in dry oxygen, using advanced DLTS techniques (energy-resolved DLTS [34] and small-signal DLTS [35], [36]) were considered. For interface traps near midgap some evidence exists that u, exceeds up [34]-[36], thereby supporting our results.

However, a controversy seems to exist as regards the energy-dependence of the capture cross sections. Gener- ally, a weak energy dependence of a,, and up has been found in the depletion and weak inversion regime with the conductance technique [ 121, [ 131, [3 11, whereas a strong dependence has always been observed with DLTS [34]- [36]. In the present study the recombination parameters C ( A E ) and .,,/up were found to depend only weakly on

5Note: the weakness of the model is that for deeper levels the value of the effective mass is not directly related to the density-of-states effective mass.

energy range A E . Inherent in the method, energy dependencies are somewhat obscured because average values are determined for the parameters under study. Although some evidence was found for a weak energy dependence of the hole capture cross section, no definite answer could be obtained.

VII. SUMMARY AND CONCLUSIONS

A new method has been presented to evaluate Si-Si02 interface recombination parameters. Some of its features are: 1) external currents are absent; therefore, a completely one-dimensional treatment is applicable at any gate-electrode bias. 2) The bulk minority-carrier quasi- Fermi level is probed right at the surface where recombination occurs; consequently, the recombination parameters can also be determined at relatively low voltages. 3) A very simple device is suitable for the determination of the key recombination parameters, viz. a gate-controlled point-junction diode (structure A of Fig. 10).

Besides the conventional analytical approximation of the interface recombination current, we have worked out a numerical scheme to find a quasi-exact expression for this current; in this numerical scheme much less simpli- fying assumptions are involved than in conventional methods of solution. By means of numerical examples it was shown how the interface recombination current is af- fected by 1) the nature of the interface traps (donodac- ceptor type; multivalent, amphoteric traps have also been discussed), 2 ) the relative magnitude of electron and hole capture cross sections, and 3 ) the distribution of the interface traps.

From numerical simulations we have decided which parameters can and which cannot be determined from curve fitting of experimental data. Parameters that can be determined are: 1) the average value of the product D j , ( E ) x uo, and 2) the ratio of the electron and hole capture cross sections (u,,/u,). It has been shown that these quantities can be determined irrespective of the model chosen for the capture cross sections and the nature of the interface traps. Asymmetries of D,, ( E ) X uo with respect to midgap cannot be resolved.

Experimentally p-type { 100 } Si-Si02 interfaces have been investigated with boron dopant concentrations ranging from 2.5 X l O I 5 to 5 X lOI7 cmp3. The main conclusions based on our experimental data are as follows: 1) The average values of the quantity Dit ( E ) x uo and the ratio u,,/up are only weakly dependent on energy interval AE in a wide energy range around E;. 2) Near the conduction and/or the valence band edge the quantity Dit ( E ) X uo probably increases monotonically toward the band edge(s). 3) The electron capture cross section u,, was found to exceed the hole capture cross section up, greatly (by a factor of lo2 to lo3) for interface traps lying in a broad energy band around midgap ( cm2 5 a, 5 lopi4 cm2 and cm2 up 5 l o p i 6 cm2). This outcome is in agreement with many conductance data reported in the literature [ 131, [3 11-[33]. 4) The parameters under study

218 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35 , NO. 2, FEBRUARY 1988 I

were found to depend weakly on dopant concentration in the investigated range, in agreement with earlier results [3], [5], [19]. 5 ) No evidence was found for the presence of amphoteric traps with neutral Fermi level near midgap.

Finally, possible sources of errors have been discussed: 1) boron redistribution may influence the results for CT,/CT,

(for high NA and low voltages), and 2) surface potential fluctuations due to charge randomness have little effect.

APPENDIX A PROOF OF (1)

In open-circuit operation the electron and hole quasi- Fermi levels are flat along the Si-Si02 interface ( z = 0) in the idealized case of an infinitesimally small n+ area. In short-circuit operation the drop in the electron quasi- Fermi level can be made negligibly small by choosing a suitably large gate voltage V,. Therefore, the real device structure can be replaced by a one-dimensional structure (Fig. 2 1) having the following (hypothetical) interface properties ( z = 0):

1) electrons and holes recombine at the interface at a rate of Ui ( V , V,), where V is the quasi-Fermi level separation at z = 0 and

2) electrons can be drained through the interface at z = 0, giving rise to the external current Jext.

For this system, the semiconductor basic equations

1

4 1 -V,J, - R + G = 0 4

- V z J p + R - G = O (Ala)

(Alb)

(fw 0 ; q + p/t, = 0

have to be solved with the boundary conditions: a t z = 0

- JP I r = O = qUi(V3 vG)

v Z + I 2=0 = -8, ( + n ( O ) > 6 p ( o ) j vG)

( A 2 4

( A2b )

( A ~ c )

P = NA ( A 3 4

n = npo (A3b)

* = kq. (A3c 1

Jn l z = 0 = Jext + q u i ( V , v G >

a n d a t z = W

As long as the bulk remains in low injection-a condition that has always been met experimentally-the electrical potential J. equals the value in thermodynamic equilibrium lc/,q, and only the continuity equation for electrons has to be solved in the quasi-neutral bulk wherep = NA.

Here the assumption is made that electron-hole recombination in the space-charge region (Fig. 21) can be neglected with respect to the recombination in the quasi-

space chorge regon field free bulk

/ - J

0 2 W

Fig. 21. Band diagram of the one-dimensional representation of the device structure.

neutral bulk. Owing to the low injection condition and the latter approximation, only the continuity equation (A 1 b) for electrons in a field-free semiconductor has to be solved

with the boundary conditions

~n l z z 0 = Jext + qUi(V7 vG), at^ = 0 ( ~ 5 )

and

a t z = W. (A6)

According to the well-known superposition principle [37], [38], the current density at z = 0 can be written in the form

n = npo,

Jn l z = o = Jo(exP ( q V / W - 1) + Jsc (A71

where Jo is the bulk component of the saturation dark current density

and J,, is defined as the short-circuit density at a given generation rate.

Substitution of (A7) into (A5) yields

Jo{exp (W/W - 13 + J,, = J~~~ + qu i (V , vG>. (A9)

The proof is completed by considering two special cases: 1) open-circuit operation (Jext = 0)

Jo{ exp ( q V / k T ) - 1 } - qui ( V , VG) + J,, = 0

( AlOa)

2) short-circuit operation ( V = 0)

Jx = Jext. (AlOb)

GIRISCH er ul. : DETERMINATION OF Si-SiO, INTERFACE PARAMETERS 219

APPENDIX B METHOD OF SOLUTION OF THE SET OF EQUATIONS (6) The problem to be solved consists of a set of six equa-

tions in six unknowns. The unknown quantities are the quasi-Fermi levels 4, and &, the electrostatic potential at the surface +s (Fig. 4(b)), the charge induced at the silicon Qsi, the charge in the interface traps Q,, and the charge induced in the gate electrode Q , (Fig. 4(a)). The set of equations can be represented by

Qsi = HI(+^, 4n, 4 p ) (Bla)

I n* I;,,+++ 1 +

+ * + + + I '

~

I I p -si p - S I

circular diode hemispherical diode semi-infinitely thick bose semi-infinitely thick base

R ' . R I ~

Fig. 22. Cross sections of the circular diode of a real device (left) and the hypothetical hemispherical diode replacing the former (right).

4n = + V , 0 z d (Ble) (B4b)

z s d

A. Qsi-The Charge Induced in the Silicon In the flat quasi-Fermi level approximation, an analyt-

ical integration of the one-dimensional Poisson equation yields the relation between the electric field strength 8 (2) and the potential +(z). By Gauss's law the total charge induced in the silicon is then found as a function of +, [2]

( B l f ) where the first model for capture cross sections (4) has been used; the expressions using the second cross section model ( 5 ) are similar. The conventional definitions for n , and P i have been used [I].

The cdculations of Qio using (B3) with the appropriate occupancy functions, were carried out numerically by re- Placement Of the integration Over the bandgap by a sum- mation ( lo-mev-wide energy intervals).

44, +n, 4,) = 0,

Qsi = - 2 q n , A D { F ( + s , +p, d'n))"' (B2a) C. Faraday's b w where From Faraday's law of induction we derive

where VG denotes the bias applied to the gate electrode. From (B5) the charge induced in the electrode Qc is de- d ~ e d

F ( + , 4,, +,J = exp P(+, - +) - exp (P&,> + exp p ( + - 4n) - exp ( -64,)

Note: work function differences between the polysilicon electrode and the substrate have not been implemented explicitly. This is, however, irrelevant because all experimental data were analyzed with reference to the flat-band voltage V,,, measured on the polysilicon electrode capacitor.

D. Charge Neutrality Charge neutrality in the bulk (Blf) also implies charge

neutrality at the edge of the space-charge layer, from which we directly deduce

with /3 = q/kT.

B. Qi,-The Charge in the Interface Traps The charge in the interface traps can be written as

j" D A ( E ) & ( E ) dE Q . = -q Ev

Ec

Ev ( ~ 3 ) + 4 'j D D ( E ) ~ D ( E ) ~ E

- 0 where DA( E ) and Do( E ) are the acceptor and donor trap exp P(4p - +) - exp b(+ - 4n) + ND ~ - NA - densities respectively, fA ( E ) is the electron-occupancy ni

037) function of acceptor traps, and fo( E ) is the hole-occupancy function of donor traps. In stationary state the net rate of capture (Le., capture minus emission) must be zero for any interface trap [ l ] . This leads to the following

where + is the equilibrium potential in the bulk (i.e., numerically zero).

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL 35, NO. 2, FEBRUARY 1988 220

E. Scheme to Solve the Set of Equations ( B l )

calculation of 4, and 4p using (Ble) and (B7)

t I estimation of +, I

correction Ilol,/ Calculation of: QG using (B6) Qsi using (B2) Q , using (B3)

I t

t YES

APPENDIX C

OF A CIRCULAR DIODE We consider a circular junction with radius R much

smaller than the bulk electron diffusion length L,. The base is assumed to be infinitely thick. The n+ area is surrounded by an accumulated surface. Recombination at the accumulated surface is negligible; consequently, the current flow at the interface is tangential.

In order to achieve a simple analytical solution to the diffusion current injected into the base the circular junction is replaced by a hemispherical one with the same junction area (Fig. 22). This replacement is suggested by the approximately hemispherical diffusion pattern at large distances from the junction.

APPROXIMATED FORMULAS OF THE INJECTION CURRENTS

The radius R’ of the latter junction is equal to

R‘ = R/&. (c1)

For the spherical junction in an infinitely thick base, the density of the dark current injected from the curved junction reads [39]

J,(R’) = Jo(1 + L, /R’) ( c 2 ) where Jo is the density of the dark current injected from the corresponding plane junction

nTD, JO = 4.,..

I y A L n

Let J,+ be the density of the dark current injected from the base toward the n+ region. Then the lowering of the open-circuit voltage due to recombination in the n + region is equal to

4

For small values of AVoc and under the condition R’ << L, this expression can be written as

after substitution of (C2) and (C 1). Remark: an accurate analytical solution for the two-di-

mensional minority-carrier current spreading from a shallow circular p-n junction has been presented recently [40]. Our computations for the ratio of the two-dimensional current to the one-dimensional current ((Cl), (C2)) correspond within 20 percent to their results over the investigated range for R / L ( R / L 2 0.2) .

APPENDIX D SURFACE POTENTIAL FLUCTUATIONS

The surface potential is subject to statistical fluctuations arising predominantly from a random distribution of charges near (or at) the Si-SiO, interface. Under the conditions of weak depletion and low electron-hole generation the minority electron concentration is dilute every- where in the space-charge layer. In that case the statistical model by Nicollian and Goetzberger can be applied [12]. They have derived the following expression for the Gaus- sian approximation of the Poisson charge distribution

p ( Q ) = (2*aQo/q)-”* ( U / q )

~ X P { - a ( Q - Qo)2/2qQo} (D1)

where Qo is the mean of the density Q of built-in and trapped charges. The characteristic area CY is the largest area within which the surface potential is uniform. The value of CY depends on the space-charge layer width W or equivalently on the surface potential G,. By fitting of experimental MOS conductance ( G p / w versus w ) data, they

GIRISCH et a/. : DETERMINATION OF SI-SIO, INTERFACE PARAMETERS 22 1

found an almost linear relation between the square root of a and W [12, Fig. 221. This relation is independent of dopant concentration and can be expressed as

all2 = 1.63 X W.

The space-charge layer width W is calculated from the surface potential $s using the abrupt depletion approximation (low disturbance from thermodynamic equilibrium)

W = ( ~ E , $ , / ~ N A ) ” ~ .

Under medium and high electron-hole generation rates the expressions (D2) and (D3) cannot simply be applied because of the space charge associated with the minority carrier electrons.

ACKNOWLEDGMENT

The authors would like to thank Dr. M. Heyns for his accurate measurements of the interface trap densities. R. B. M . Girisch is also grateful to him for numerous valu- able discussions.

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171 R. Girisch, R. P. Mertens, and R. Van Overstraeten, “Limitations of the open circuit voltage of induced junction silicon solar cells due to surface recombination,” in Proc. 4th EC Photovoltaic Solar En- ergy Conf., pp. 643-647, 1982; also, in Proc. 16th IEEE Photovol- taic Specialists Conf., pp. 1231-1236, 1982.

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1131 H. Deuling, E. Klausmann, and A. Goetzberger, “Interface states in Si-SiO, interfaces,” Solid-Stare Electron., vol. 15, pp. 559-571, 1972.

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H. Sakaki, K. Hoh, and T. Sugano, “Determination of interface-state density and mobility ratio in silicon surface inversion layers,” IEEE Trans. Electron Devices, vol. ED-17, pp. 892-896, 1970. P. Panayotatos and H. C. Card, “Recombination velocity at grain boundaries in polycrystalline Si under optical illumination,” IEEE Electron Device Lett . , vol. EDL-1, no. 12, pp. 263-266, 1980. R. Girisch, unpublished results. M. Nishida, “Distribution of surface state density related to diffusion-induced dislocations near the junction formed by diffusion of phosphorus in silicon,” Japan. J . Appl. Phys . , vol. 11, no. 5, pp. 673-677, 1972. A. B. M. Elliot, “The use of charge pumping currents to measure surface state densities in MOS transistors,” Solid-State Electron., vol. 19, pp. 241-247, 1976. J. Snel, “The doped Si/SiO, interface,” Solid-state Electron., vol. 24, pp. 135-139, 1981. M. Heyns, private communication. D. A. Antoniadis and R. W. Dutton, “Models for computer simula- tion of complete IC fabrication process,” IEEE Trans. Electron De- vices, vol. ED-26, no. 4, pp. 490-500, 1979. C. T. Sah, “Origin of interface states and oxide charges generated by ionizing radiation,” IEEE Trans. Nuclear Sr i . , vol. NS-23, no. 6, pp. 1563-1568, 1976. Y. C. Cheng, “Electronic states at the silicon-silicon dioxide interface,” Progress in Surface Sci. , vol. 8, pp. 181-218, 1977. Y. C. Cheng, “A model for interface states in silicon/silicon dioxide structure,” Surface Sc i . , vol. 23, pp. 432-436, 1970. K. L. Nagi and C. T. White, “A model of interface states and charges at the Si-SiO, interface: Its predictions and comparisons with experiments,” J . Appl. Phys . , vol. 52, no. 1 , pp. 320-337, 1981. W. D. Eades and R. M. Swanson, “Determination of the capture cross sections and degeneracy factor of Si-SiO, interface states,” Appl. Phys. Le t t . , vol. 44, no. IO, pp. 988-990, 1984. I . H . Jeans, The Mathematical Theory of Electriciry and Magnetism. London: Cambridge, 1958. W. Kohn, “Shallow impurity states in silicon and germanium,” Solid State Phys . , vol. 5, pp. 257-320, 1975. A. Goetzberger, V. Heine, and E. H. Nicollian, “Surface states in silicon from charges in the oxide coating,” Appl. Phys. Lett., vol. 12, no. 3, pp. 95-97, 1968. I . D. Levine. “Nodal hvdrogenic wave functions of donors on semi-

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[33] A. K. Aganval and M. H. White, “On the nonequilibrium statistics and small signal admittance of Si-Si02 interface traps in the deep- depleted gated-diode structure,” J . Appl. Phys . , vol. 55, no. 10, pp. 3682-3694, 1984.

1341 T. J. Tredwell and C. R. Viswanathan, “Determination of interface- state parameters in a MOS capacitor by DLTS,” Solid-state Elec- t ron. , vol. 23, pp. 1171-1178, 1980.

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222 IEEE THANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 2, FEBRUARY 1988

Reinhard B. M. Girisch was born in Leeuwar- den, The Netherlands, in 1949. He received the B.Sc degree in physics (great distinction) from the Groningen State University, The Netherlands, in 1979 and expects to have received the Ph.D. degree in January 1988 from the University of Leuven, Leuven, Belgium. His B.Sc. research concerned a technique to measure minority-carrier lifetime in silcon.

From 1979 to 1983, he was a Research Assis- tant at the ESAT Laboratory of the University of

Leuven, where he worked on solar cell device development and modeling, and on techniques to determine interface recombination parameters. His interest also included heavy doping effects in induced junction devices These subjects consitituted his Ph.D dissertation Since 1984, his activi- ties have been within the semiconductor industry (Philips-Elcoma, The Netherlands), where he is involved with the characterization of insulating films on silicon and with the research and development of backside getter- ing techniques in single-crystal silicon wafers.

*

From 1973 to 1974, he versity of Florida, Gal

Robert P. Mertens (M’80) was born on March 9, 1946, in Antwerp, Belgium. He received a degree in electrical engineering (great distinction) in 1969 and a doctorate degree in applied sciences (great- est distinction) in 1972, both from the University of Leuven, Heverlee, Belgium.

From 1969 to 1973, he was a Research Assis- tant at the Electronics, Systems, Automation and Technology (ESAT) laboratory of the University of Leuven. In the summer of 1973, he was a Re- search Associate at Tektronix, Beaverton, OR.

was a Post-Doctoral Research Associate at the Uni- inesville. After his return to Belgium in 1974, he

became a Fellow of the National Belgian Science Foundation. Since 1978, he has also been lecturing at the University of Leuven on a part-time basis. In the summer of 1979, he was a Visiting Scientist at the Solar Energy Research Institute, Golden, CO. Since 1983, he has been a part-time professor at the University of Leuven, and in 1984 he joined the Inter Uni- versity Microelectronics Laboratory (IMEC) as a Vice President respon- sible for research on materials and packaging.

Roger F. De Keersmaecker (S’71-M’80) was born in Tienen, Belgium, on September 18, 1948. He received the M.S. degree in electncal engineering in 1971 and the Ph.D. degree in 1977, both from the Katholieke Universiteit Leuven, Leuven, Belgium.

From 1971 to 1977, he was a Research Assis- tant in the Laboratory for Physics and Electronics of Semiconductors of the Katholieke Universiteit Leuven working on integrated-circuit technology In 1977, he was granted an IBM World Trade Post

Doctoral Fellowship, and worked from 1977 to 1979 at the IBM Thomas J Watson Research Center, Yorktown Heights, NY, on SiO, and Si-SiO, interface properties. In 1979, he returned to the ESAT Laboratory of the Katholieke Universiteit Leuven where he was appointed Research Associ- ate and in 1984 Senior Research Associate of the National Fund for Sci- entific Research (NFWO) and also a Lecturer at the University In January 1986, he joined the Interuniversity Microelectronics Laboratory (IMEC) as group leader for VLSI Materials and Technologies in the Advanced Semi- conductor Processing Division. He has also served since October 1986 as a Professor at the University. His interests are in materials sciences and in the physics and technology of semiconductor devices.

determination of si-sio2 interface recombination parameters using a gate-controlled point-junction...

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