The generation lifetime in high resistivity silicon

Nuclear Instruments and Methods m Physics Research A260 (1987) 201-209 North-Holland, Amsterdam

201

THE GENERATION LIFETIME IN HIGH RESISTIVITY SILICON K.J . RAWLINGS

Instrumentation and Applied Physics Division, Harwell Laboratory, Oxfordshire, England

Received 16 March 1987 The dark current at 295 K m some large area n + p diodes with gold base contacts has been analysed to show the quality of the high resistivity wafers was generally very good . Estimates of the generation lifetime in the processed wafers ranged from 5 to 30 ms . The diffusion current injected at the base contact was often larger than the generation component and both were spatially variable . The behaviour of the diffusion component implied a base contact interface generation velocity falling to values near 10 ° mm/s or lower m places 1. Introductory discussion We wish to know the generation lifetime Tg and minority carrier lifetime Tn (for p-type silicon) for wafers of silicon 0.5 mm thick with a nominal resistivity of 30 k,f2 mm . Ideally we should also like to know Tg and T before as well as after making n + p diodes so as to have a measure of how the high temperature processing affected the quality of the starting material . At the very least an estimate of the final rg is required to assess the integrity of the processing applied to silicon wafers that are anticipated to have an initial T value of 1 ms or more [1]. Large area n +p diodes operated under reverse bias have been used for a number of years as alpha particle detectors in plutonium in air monitoring equipment at many UK nuclear installations. To quantify the performance of the n + p diode as a radiation detector one needs to know the equivalent circuit for the diode and the nature and magnitude of the dark current. The equivalent circuit is now reasonably well understood [2,3]. Some special diodes were made in order to study the dark current and an attempt is made in the present work to separate the surface and volume contributions to the dark current. The dark current in n +p diodes made from high resistivity p silicon is very sensitive to the chemical state of the surface near the function edge . If the surface properties are not adequately controlled, reverse biased diodes can have lateral surface currents that are orders of magnitude higher than the volume ones and the diodes can also exhibit excessive low frequency noise [4-9]. These aspects are under study and will not be pursued in this paper. The generation lifetime Tg is an important parameter describing the quality of a semiconductor that has been 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)

depleted of majority carriers . It is therefore particularly relevant to the space charge layer in reverse biased diodes . It has been shown that to the best case [10,11] this parameter Tg determines the reverse dark current for diodes with a high base resistivity. In practice one has to work backwards since Tg cannot be measured directly. An assumption that is frequently made is 7g = 2T. (for p-type material) where T is the minority carrier lifetime . However, there is no guaranteed relationship between Tg and T., it being possible for Tg to be either larger or smaller than Tn [12-14]. If there were several active defect levels it would be likely that Tg would be greater than Tn since crystal defects having energy levels more than a few kT away from the middle of the semiconductor band gap may contribute effectively to Tn whereas they will more likely have a negligible effect on rg ; the equality Tg = 2 T applies only to the special case of a single defect level at midgap for which the capture cross sections for electrons and holes are the same [14]. Before using the dark current in a reverse biased diode to determine Tg one must be sure that all other contributions are negligible compared with the generation current in the space charge layer. Since a,lunction is required to deplete the silicon, it seems that Tg cannot be measured in a piece of unprocessed semiconductor such as a wafer of 30 k52 mm p-type silicon. It is also difficult, though not impossible (e.g . refs . [15,16]), to measure the minority carrier lifetime in high lifetime (T. > 1 ms) silicon since the diffusion length Dj (D = diffusion constant for electrons [17]) is of the order of 2 mm or more, making it hard to separate the wanted volume effect from the unwanted surface ones . For example, if one processes a p silicon wafer of 0.5 mm thickness to make an n +p diode of nominal base width d = 0.5 mm, standard lifetime methods such as reverse recovery or photocur-

202

K.J. Rawlings / Generation lifetime m high resistivity silicon

rent decay [18] fail to give a measure of carrier lifetime because the surface effect swamps the volume one . Since d < DnTn the minority carriers are swept out of the base by diffusion before they have time recombine appreciably. In summary, it is concluded that Tg cannot be measured before our silicon wafers are processed ; it is considered that Tn cannot readily be measured before or after processing our high lifetime material since the minority carrier diffusion length exceeds the wafer thickness; the dark current in the n+p diodes will be analysed to estimate the final value of Tg . 2. Experimental detail and results The experiments were performed on modified forms of the SRD25 detector . This is made from 30 U mm p silicon of 30 mm diameter and 0.5 mm thickness. It is described in detail in ref. [2] but the sketches in fig. 2 of the present text show the modified diodes in both plan and cross-sectional views. The junction edge occurs on the back face, adjacent to the gold contact, since the n+ diffusion wraps round the edge of the wafer, see fig. 2. The gold back contact has been separated into five segments in one of two ways . To measure the current going to each segment the circuit illustrated in fig. 1 was used . This is a bridge arrangement in which the potential across four of the segments in parallel is adjusted to be the same as that of the fifth segment. Since the do impedance between one segment and the other four was about 1 kQ the bridge had to be balanced to within 1 IN for the current measurement to have better than 1

nA resolution . This was achieved in practice since the sum of the five segment currents differed from the total dark current by less than 5 nA . However, considerable care was needed to obtain this accuracy owing to drift in the dark current of the unpassivated diodes. Two designs of segmented gold contact were used and these are shown in the lower part of fig. 2. The first design (left hand sketch) gave good protection of the central segment against lateral surface contributions to the dark current; the second design gave more information about the uniformity of the volume current whilst providing extra protection against lateral surface currents for the two smaller area edge protected segments (inner 2 and inner 3) . EBIC (electron beam induced conductivity) studies [19] in a scanning electron microscope showed that the less protected segment, inner I in fig. 2, was free from lateral surface effects for reverse biases up to about 50 V; beyond this there was evidence of surface inversion extending into the gap between the two edge gold electrodes . Eight diodes of each back contact design have been investigated at a fixed temperature and reverse bias ; five diodes from the first set (left hand sketch in fig. 2) have been analysed at constant temperature for reverse biases up to 100 V. The first set of dark current data are presented in fig. 2 . The reverse bias was 15 V which is the value used for alpha detection purposes . The segment dark currents have been normalised to their associated function area before plotting in fig. 2 but the actual dark currents can be retrieved since the junction area is indicated below each column . The current data in the three right hand columns is organised to preserve the identify of each diode, e.g . the fifth line in each column belongs to the

Variable d c supply

Fig. 1. Circuit for measuring the dark current in each segment of the segmented back contact SRD diode.

20 3

KJ. Rawlings / Generation lifetime in high resistivity silicon 15V Reverse T= 295 K

bias

Measurement uncertainty

30mm diameter N

E E w

150

a

a

,~

c a,

100

Calculated maximum diffusion current, JZ (injection)

cw U

50

Assoc Jn Area (mm 2 )

Centre 140

Inner I

240

1

Inner 110

2

Inner 3 110

I

D iode design and back contact detail

Fig. 2. Dark current

in

segmented back contact SRD diodes (sample size =16 diodes). The current to a segment has been divided by thejunction area associated with it .

same diode. Fig. 2 shows that the volume dark current is not only variable from diode to diode but also within each diode. Taken as a group of current measurements, the data in fig. 2 indicate an average current density of 90 pA/mmz with a standard deviation of 30 pA/mmz . The dashed line near 70 pA/mmz in fig. 2 will be discussed later. It was mentioned above that the central diode segments in each series of segmented back contact experiments were anticipated to have a negligible dark current contribution originating from the p silicon surface adjacent to the gold contact. To check this further the diodes were exposed to either ammonia or iodine vapour which made the exposed p silicon surface either more nor more p-type [4,5]. The total diode dark current could be increased by two orders of magnitude in this way whereas the current in the central segments changed by less than 10%. It is therefore concluded that surface current can be ignored in the analysis of the edge protected segments.

3. Interpretation of results On the assumption that there is a negligible contribution to the currents in fig. 2 from gross localised defects such as extended dislocations in the space charge layer, the major contributors to the volume current are likely to be the diffusion and generation currents in the lightly doped base of the n+ p diodes [8]. However, some mention should be made (for completeness) of the current expected from the heavily doped emitter before pursuing the above. Our asymmetric pn junction is of the type discussed by Redfield [20] and the emitter contribution to the volume current has been investigated in the context of large area pn junction solar cells (e .g. refs . [20-24]) . From works such as these, the emitter current density in our diodes is expected to be of the order 10 -2 pA/mmz , i.e . negligible in comparison with the currents in fig. 2. Consequently, an interpretation of fig. 2 will be sought in terms of just two components : diffusion and generation of mobile carriers in the base .

20 4

K.J. Rawlings / Generation lifetime in high resistiviti, silicon

In diodes with a long minority carrier lifetime or with a thin base width the diffusion current Jd can be important [25] . For an n +p diode it is given by _ ón Jd -qDn óx w

where q is the electron charge, n(x) is the electron concentration in the p silicon and W is the x-coordinate specifying the edge of the space charge layer. To evaluate eq . (1) one must solve the continuity equation to obtain n(x) . The diffusion current consists in general of two components J and J, . The first one comes from thermal generation of electrons in the quasineutral base and J, comes from the interface generation or infection from the base contact. The second component only contributes to the diffusion current when the electron diffusion length L is comparable with the quasineutral base width (d - W) . The diffusion current for V » kT/q (k is the Boltzmann constant) can be written as [251 Jd =

gn2,S NA

cosh(a) + (D n/S L n ) sinh(a) cosh(a) + (SL  /D ) sinh(a) '

where n, is the intrinsic carrier concentration, S is the effective generation velocity at the base contact, NA is the net acceptor concentration in the p silicon base, a = (d - W )/L n where d is the thickness of the base and the diffusion length is defined as L = D 7 . As mentioned in sect . 1, we expected L  > 2 mm provided that the subsequent processing does not degrade the lifetime . Since d = 0 .5 mm for the present diodes it seems best to consider the following two simplifications to eq . (2) : Jd=gDn

n; NA (d_ W)

,

[d-W«L, S»D/(d-W) ],

and

2

Jd= q n, (d-W), NAT

[d-W«L  ; S«D/(d-W) ] .

(4)

Eqs. (3) and (4) give the diffusion current for a short base diode (d - W < L ); eq . (3) corresponds to infection of carriers from the base contact and predicts (see later) a current of 50 pA/mm2 or more in the present diodes ; eq . (4) predicts (see later) a current of 4 pA/mm2 or less in the same diodes and corresponds to carriers diffusing from the quasi neutral p silicon, the contribution from the base contact being negligible . Eqs. (3) and (4) therefore define the upper and lower linuts respectively for the diffusion current in the present diodes . Should the diffusion component of the total diode current be suspected of falling between the two limits defined by eqs. (3) and (4), the general solution eq . (2) ought be be used . However, thus requires a knowledge of

both L  and S, neither of which are known with sufficient accuracy . Consequently eq. (2) will not be used in what follows and the use of eqs. (3) and (4) will be pursued with caution, appropriate comments being made where necessary regarding the reliability of the ensuing analysis . For the present diodes and voltages up to 100 V we can say D/(d - W) _ 10 4 mm/s . Consequently, if S » 10 4 mm/s for the gold-p silicon base contact, eq . (3) would be the appropriate expression for the diffusion current. Shockley's definition of an ohmic contact is S = cc which implies that the electron concentration at the base contact remains at the thermal equilibrium value of n,/NA under all conditions . Hence Jd as given by eq. (3) approaches infinity as the quasineutral base width (d- W) shrinks to zero . This is unrealistic since it implies no limit to the carrier velocity . In silicon near 300 K the maximum carrier velocity is ca. 10" mm/s [26a] and this should be the upper limit on the value of S for a metal-silicon contact. The gold-p silicon contact is in theory a low barrier height Schottky barrier. Thermionic emission-diffusion theory [26b] suggests a thermal velocity of ca . 3 x 10 7 mm/s for holes approaching such a barrier at 300 K and this is therefore taken to be the upper limit on S for the present diodes . The quality of a contact is defined in terms of its specific contact resistance p, [27] and for the ideal gold-p silicon contact one expects pc -- 1 S2 mm2 [26c,27] . Real contacts usually exhibit larger, variable values of p c which reflect the quality of the metal-semiconductor interface. For the present process pc was in the range (2800 ± 1500) S2 mm2 [3] EBIC studies [28] also showed a patchy response of the gold-p silicon interface, indicating a nonuniform contact. Assuming an approximately inverse relation between S and p, the above discussion implies a value S -- 10 4 mm/s for the gold back contact; values in the range 10 3-10 5 mm/s may occur m practice . This casts some doubt over the validity of eq . (3) serving as a model for the diffusion current and will be returned to later on . Fig. 3 shows as a dashed line the diffusion current calculated from eq . (3) with n, = 1 .5 X 10 7 mm -3 , NA =4 x 10 9 mm -3 and W= 17 V+0.7 pin [2]. It is noted that n, is not known to better than about a factor of 2 (e .g ., ref. [29]) and that the above value is the commonly quoted one at 300 K [26] . The diffusion current as shown in fig. 3 has a slight voltage dependence, its value increasing from 50 to 90 pA/mm2 to the interval 1 to 100 V. It is of interest to compare this with a prediction from eq . (4) which would hold m the event of S « 10 4 mm/s. With T = 1 ms, eq . (4) gives a maximum value of Jd = 4 pA/mm2. In practice Jd might fall between these two limiting behaviours for some diodes, as discussed before. The generation current in the space charge layer is

205

KJ . Rawlings / Generation lifetime to high resistioity silicon given by Jg = - q

( W(V) U(x) dx, J0

(5)

where U(x) is the generation rate of electron-hole pairs per unit volume . Detailed analysis of MOS structures [30-33], Schottky barriers [34,35[ and pn junctions [36-39] have shown that generation is significant in a width of the space charge layer that is considerably smaller than the width W(V), given by the depletion approximation [2,26d]. For reverse biases exceeding about 1 V it can be shown that (see the appendix) Jg=

qn~

Tg [ W(V)

_

WO(V)

_

Will

to a good approximation, where W0 a 1/(V+ Vb,) i/2 and Wi = constant are defined in eqs. (27) and (23) in the appendix . Eq . (6) has been plotted as solid curves in fig. 3 for Tg = 2 ms and 7g = 20 ms with Wi = 7 lim which corresponds to an active defect close to midgap . Fig. 3 shows that at 15 V reverse bias and a temperature near 300 K the diffusion current predicted in eq . (3) is expected to dominate over the generation current for Tg = 20 ms and that Jd and Jg should be comparable for Tg = 2 ms . The measured reverse I(V) data from the central segment of five diodes from the left hand column in fig. 2 are shown as symbols in fig. 4 and the measurement uncertainty is indicated by the vertical line through the symbols. The solid lines in fig. 4 are simulation curves generated from eqs. (3) and (6). These show quite an encouraging fit to the experimental data from four of the five diodes over the range 1 to 100 V reverse bias . However, given (a) the uncertainty over the validity of eq . (3), (b) the uncertainty over the precise value of n, and (c) the assumption of midgap defect levels for eq . (6), one should not place too much faith in the genera-

N

E E

i

200 Generation current, ('r9= 2msec)

áa N

c

tion lifetimes derived from such an analysis . Although fig. 3 suggests that most of the current below 1 V comes from the diffusion component, more detailed calculations show that for active defect levels away from midgap the generation current also exhibits a large dump near zero bias (see fig. 4 in ref. [39]). The last comment should be tempered by remembering eq . (6) and noting that the generation lifetime Tg increases exponentially as 4E/kT where AE is the energy difference between the active defect level and the midbandgap energy (i .e . Tg is likely to be dominated by states near midgap, if they exist) . Not all of the data in the present figs . 2 and 4 can be explained with recourse to eqs. (3) and (6). The lowest currents m fig. 2 and especially those for diode no . 3 in fig. 4 suggest a diffusion current intermediate to those given by eqs. (3) and (4). The dashed horizontal line in fig. 2 indicates the maximum diffusion current, according to eq . (3). A smaller diffusion current in turn implies that S was not significantly greater than 10 ° mm/s for the central gold back contact in some of the diodes . The above observation implies that variations in the diffusion current infected at the base contact account for at least some of the variation in the total volume dark current evident in fig. 2. The finding via fig. 4 of different values of rg , albeit in different silicon wafers (from the same batch), renders it unlikely that the variation in the dark current in fig . 2 is due entirely to changes in the diffusion component. There is good reason to believe that the generation current from the space charge layer might contribute to the variation in the dark current within a single diode. Firstly, this might occur via local variations in the resistivity [40-42] which in turn will give rise to local variations in the space charge layer width W. Secondly, since defect concentrations as low as 10 7 trim -3 can determine the

Diffusion current

100

--__-_-_-__

cm

Generation current (T9=20msec)

V

20

40 60 Reverse bias (V)

80

100

Fig. 3. Calculated diffusion and generation currents in 30 U mm base planar n' p diodes at 300 K.

20 6

K.J Rawlings / Generation lifetime 1n high resistivity silicon

a c

c

É

9

d

c û

Syrn bo I Diode No t

0

1 2 3 4 5

0 X

c v

0

v

U

Reverse Bias (V)

80

90

100

Fig 4. Measurement and simulation of the dark current to the central segment of the segmented back contact SRD diode. The solid curves correspond to I =Id (V)+ Ig (V, Tg ) where eqs. (3) and (6) were used .

value of Tg , there might well occur local variations in the silicon interstitial defect density [40] that could give rise to significant variations in rg across a wafer. It is concluded from figs . 2-4 that in more than half the diodes the diffusion current injected at the gold p-silicon base contact exceeded the generation current from the space charge layer at 15 V reverse bias . The model in the appendix indicates a space charge layer width W of about 70 lim for 15 V bias and an active generation width 10% less than W. 4. Conclusions The volume current m some large area n + p diodes has been isolated from the total reverse dark current. It was found to vary from diode to diode and also within a single diode. The volume current was modelled satisfactorily by assuming dust two components : a generation current from the space charge layer in the lightly doped base ; a diffusion current in the quasineutral base arising almost entirely from carrier infection at the base metal-semiconductor contact . The volume diffusion current was variable and this was attributed to spatial variation in the quality of the base contact manifesting itself through a variable value of the generation velocity at the gold-p-silicon interface in the base contact. The volume generation current was also variable though it was smaller in magnitude than the diffusion component in most cases for a reverse bias of 15 V and room temperature (295 K) operation. Estimates of the generation lifetime ranged from 5 to 30 ms, indicating not only that the processing was clean but also suggesting that the high temperature step did not degrade the lifetime .

Acknowledgements I wish to thank Prof. S.C. Jain for discussions on surface generation, Miss N .G . Blamires for many conversations about the EBIC studies, Mr. M.L . Awcock for providing the diodes and Dr . J.W . Leake for criticising the manuscript . Work described in this report was undertaken as part of the Underlying Research Programme of the UKAEA. Appendix The depletion width and the generation width

Although the depletion width W(V) and the electron-hole generation width Wg(V) are defined by different criteria, the original text [14] implied that they were the same to a good approximation. This is now known not to be the case [30-39] and the particular case of a reverse biased n+ p diode with a lightly doped base is treated in this section. The depletion or space charge region width W(V) is derived from an application of Poisson's equation m one dimension to the abrupt n +p function subject to the so-called depletion approximation [26d]. Defining the n +p boundary to occur at x = 0 as in fig. 5 and noting that the potential drop in the n+ region cannot exceed kT/q [43,44], one finds

w( v) -

1/2

~ qNA ~

(V + Vb

)1/2,

K.J. Rawlings / Generation lifetime in high resistivity silicon

20 7

From eq ; (10), - U(x) has a maximum value of - Umaz = n2,/ ( n i Tp + P,Ta )

= n,/2 ,ro cosh(d + 8),

To =

(TnTP)i/2>

8=

1/2

(14) ( 15 )

ln(TP/Tn ) .

(16)

It follows from eqs. (9) and (14) that the generation lifetime is given by Tg

=

2TO

cosh(d + 8) .

(17)

The boundaries which define Wg (V) are given from eq. (9) by [39]

Distance, x

Fig. 5. Band diagram (upper) for a reverse-biased n + p junction with a defect level at E, and the corresponding carrier generation rate (lower) via this defect in the space charge layer.

by ignoring the thermal voltage kT/q . ,ß(x) is the potential and W(V) corresponds to the region in which the majority carrier concentration p(x) is small in comparison with NA. Alternatively W(V) refers to the region where a significant electric field exists, the boundaries corresponding to the points where band bending effectively ceases, see fig. 5 (upper). The generation width Wg (V) is defined via eq . (5) in the main text such that Jg (V) _ -q

fn W(V) U(x) dx

= -gU_a~Wg(V)

The quantity - U(x) has been sketched in figure 5 (lower) and is given by [14]

U(X) ri l

- Tp[n(x)+n, ] +r, [ p(x)

=n,

exp(d),

pi =n, exp(-J), J = (E, - E, )/kT .

+p,]

n(x,)=(Tg/ )ni,

(18)

P( X 2)

(19)

= ( TB/Tn)nil

and these are shown schematically in fig. 5 (lower) for the case of a defect level Et lying between E, and the Fermi level EFp in the p silicon, fig. 5 (upper). Eq. (18) gives xi = W,(V) and eq . (19) gives x 2 = W(V) - Wl as shown in fig. 5. The purpose of the remainder of this section is to give a simple picture of how to determine the boundaries xi and x 2 to a reasonable approximation and to derive a corresponding formula for the generation width Wg(V)

= x2 -

xi

= W(V) - WO (V) - Wi .

(20)

It should be noted from fig. 5 (upper) that both boundaries xi and x 2 occur in the p silicon. Consequently T and TP in eq . (10) both refer to the p silicon. If the products of the cross section o and thermal velocity v, are similar for holes and electrons and the defect concentration Nt is constant then we can say Tn - TP (since T= 1/Ntavth) . If follows from eqs. (15)-(17) that for E, = E, one has T, - Tn or TP ; for (E, - E,) = 3kT one has Tg - IOT or 10Tp . These examples are given with eqs. (18) and (19) in mind since we wish to know xi and x 2 . It is evident from eq . (19) that p(x 2 ) exceeds n, for the above examples . If Tn - TP one can deduce from eq . (10) that x 2 corresponds to p(x 2 ) -pi since n (x) and ni are smaller than p i for d < 0, eq . (13) . Consequently x 2 is given by the intersection of the level Et with the hole quasi Fermi level - gOP (x), see fig . 5 (upper) . The latter is a convenient mathematical contrivance for showing carrier concentration information in energy band diagrams . Op(x) is defined as [26d]

(10)

OP(x) = (kT/q) ln(p(x)/n,),

(11)

with respect to midbandgap . The quasi Fermi level - gO (x) in fig. 5 has been drawn as horizontal until P beyond its intersection with E, . This is not strictly correct [14] but seems to be a good approximation

(12)

(13)

(21)

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K.J.

208

.

according to because whereas of can potential -

-(

.

. .

gives 4 =

Eq. present V . below should

.

=

(22)

which W1=W(V)-x2 = LD-

(23)

D EkT

Eq. should EFp mm interest extrinsic about From sponds level " E, E, eqs. corresponds of respect and

(24) . 

. .

..

.

.

.

.

.

.

.

.

(EFn =  -Et-2kT4)lq =1G  which

(25)

'P(-x,)="P,-(V+VbJ = Eq. W.

ZNA

=W(V)[ =

W(V)d`Pi 2(V+Vb,)'

.

. .

(26)

qN

2q(V+

 .

.

) . ~/2

(27)

.

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