Measurements on the depletion layer properties of planar diodes

Solid-State Electronics

Pergamon Press 1969. Vol. 12, pp. 539-547.

MEASUREMENTS

Printed in Great Britain

ON THE DEPLETION OF P L A N A R

LAYER PROPERTIES

DIODES

P. R. W I L S O N A.E.I. Semiconductors Ltd., Carholme Road, Lincoln, England (Received 6 January 1969) A b s t r a c t - - E x p e r i m e n t a l results are reported for the capacitance-voltage (C-V)relationships of square, circular and P I N planar diodes and for plane diodes. These results show the predicted influence of the curved regions of the junctions. Experimental values of the built in voltage also agree with theoretical values for diffused junctions. A sectioned planar diode was also examined using a scanning electron microscope to determine the movement of the depletion region under conditions of reverse bias. T h e results are in reasonable agreement with theoretical values. R 6 s u m 6 - - L e s rdsultats expdrimentaux sont report6s pour les relations capacit6-tension des diodes carr6es, circulaires et P I N planes et pour des diodes planes. Ces rdsultats montrent l'influence pr6dite des r6gions courb6es des jonctions. Les valuers exp~rimentales de la tension induite s'accordent aux valeurs th6oriques des jonctions diffus6es. Une diode plane sectionn6e a aussi 6t6 examinee en employant u n microscope ~tbalayage 61ectronique pour d6terminer le mouvement de la r6gion d'6puisement sous des conditions de polarisation inverse. Ces r6sultats sont en bon accord avec les valeurs th6oriques. Z u s a m m e n f a s s u n g - - E x p e r i m e n t e l l e Ergebnisse fiber die Kapazit~its-Spannungscharakteristik yon quadratischen u n d kreisf6rmigen PIN-Planar-Dioden sowie yon ebenen Dioden werden berichtet. Die Ergebnisse zeigen den vorhergesagten Einfluss der gekrfimmten Bereiche der pnObergiinge. Die experimentellen Werte ffir die Diffusionsspannung stimmt mit theoretischen Werten ffir diffundierte Dioden fiberein. Eine aufgeschnittene Diode wttrde mit einem AbtastElektronenmikroskop untersucht, u m die Verschiebung der Verarmungszone bei Belastung in Sperrichtung zu studieren. Auch diese Ergebnisse sind in vernfinftiger l~bereinstimmung mit theoretischen Werten. INTRODUCTION A TYPICAL p l a n a r j u n c t i o n h a s a flat c e n t r a l r e g i o n s u r r o u n d e d b y a c u r v e d r e g i o n as s h o w n i n Fig. 1. The curved regions of the junction can have an a p p r e c i a b l e effect o n t h e electrical c h a r a c t e r i s t i c s o f t h e j u n c t i o n t h a t d e p e n d o n t h e d e p l e t i o n layer width. Recently theoretical results have been

\

1

P

I

-/

FIG. h. Cross section through a planar junction.

539

reported for the capacitance of planar junetions. ¢1'2) The curved regions can be considered to be circular with a radius of curvature equal to the junction depth. The capacitance of a reverse biased planar p-n junction then consists of a parallel combination of plane, cylindrical and spherical capacitors, the actual combination depending on the diode masking geometry. WILSON (1) reported on the capacitance of gaussian diffused junctions and LEE and SZE(2) reported on linear graded and abrupt junctions. In this paper experimental results are reported for the capacitance voltage characteristics of planar junctions and are compared with theoretical characteristics calculated from Refs. 1 and 2. In addition some direct observations of the variation of depletion layer width with applied

540

P. R. W I L S O N

voltage, o b t a i n e d u s i n g a s c a n n i n g e l e c t r o n m i c r o scope, are r e p o r t e d . CAPACITANCE-VOLTAGE

CHARACTERISTICS

Experimental Four different diode geometries were used s h o w n i n Fig. 2 w h i c h will b e r e f e r r e d to as

Square

Circular

Plone

Pin

FIG. 2. Geometrics of square, circular, plane and PIN diodes. s q u a r e , circular, P I N a n d p l a n e , t h e first t h r e e all being of planar type. The square diode had a s q u a r e m a s k o p e n i n g o f side l e n g t h 2 × 1 0 - 2 c m a n d t h e c i r c u l a r d i o d e h a d a m a s k o p e n i n g of 1 . 1 2 5 × 10 -9. c m r a d i u s i.e. b o t h d e v i c e s h a d a m a s k o p e n i n g area o f 4 x 1 0 - ~ c m . The PIN diode had a circular geometry with a mask opening o f 3 - 0 × 10 - s c m r a d i u s ( a n area o f 2 " 8 2 × 10 - 5

c m 2). A range of diodes were produced with different d o p i n g levels a n d j u n c t i o n d e p t h s . T h e plane,

c i r c u l a r a n d s q u a r e d i o d e s w e r e all d i f f u s e d o n t h e s a m e slice to e l i m i n a t e all d i f f e r e n c e s b e t w e e n t h e d i o d e s e x c e p t for t h e i r g e o m e t r y . N - t y p e silicon was u s e d as t h e s t a r t i n g m a t e r i a l a n d t h e j u n c t i o n s w e r e f o r m e d b y d i f f u s i n g b o r o n diffusion i n a n o p e n t u b e s y s t e m . A s h a l l o w layer o f p h o s p h o r u s was d i f f u s e d i n t o t h e b a c k of t h e slices to p r o v i d e a n N + c o n t a c t , a n d e v a p o r a t e d gold was u s e d as t h e c o n t a c t m e t a l . T h e d i o d e s were t h e n s e p a r a t e d b y s c r i b i n g . T h e pellets to b e u s e d for the plane diodes were etched in 4 : 1HNO s : HF u n t i l t h e y w e r e t h e c o r r e c t area, t h e gold o n t h e t o p a n d b o t t o m of t h e p e l l e t p r o t e c t i n g t h e s e f r o m the etch. Special areas w e r e p r o v i d e d o n e a c h slice for t h e m e a s u r e m e n t of s u r f a c e c o n c e n t r a t i o n a n d j u n c tion depth. Junction depths were measured by bevelling and staining, and surface concentrations w e r e calculated, u s i n g IRVIN'S (3) curves, f r o m four point probe measurements and junction depths. Capacitance measurements were made with a B o o n t o n C a p a c i t a n c e B r i d g e m o d e l 7 5 B - $ 8 at a

Table 1. Diode parameters for square, circular and plane diodes Diode Background _-No. concentration, cm - 3 1 2 3 4 5

2"1X101~ 2 ' 1 x 1 0 ~4 2'lx1014 2"1Xl014 2 " 1 × 1 0 I4

Surface concentration, cm

Junction depth, cm

1"4x1019 1"3×101° 1 " 4 x 1 0 l° 1"6X10 *° 1"5×10 l°

5"10X10 -a 1"98 x l 0 - s l'01xl0 -s 4 " 9 × 1 0 -~ 2 ' 0 × 1 0 -4

Table 2. Diode parameters for P I N diodes Diode No.

Background concentration, cm - 3

Surface concentration, cm - s

Junction depth, cm

I Region, cm 4"6 X 10 - s 1 "3 X 10 - 2

1 2

1"2 XlO 12 1 "2 X 10 ~2

1"3 XlO ~9 1 "3 X 10 ~9

5'03 XlO -a 5'03 X 10 - s

3

1 "2 X 1 0 *2

1 "3 X 1 0 *~

5'03 X 10 - s

2"5 x 1 0 - 2

4 5 6

1"2 X 10 ~2 1 . 2 × 1 0 ~2 1"2>(10 *2

1"1 XlO ~9 1"I ×10 ~9 1"1 x l O .9

5"1 XlO -4 5.1 x l O -4 5"1 x l O -4

4"8 Z 10 - s 1"3 x l O -2 2"4 x I0 -2

DEPLETION

LAYER

PROPERTIES

OF

PLANAR

DIODES

I c

I

× ' ' ~ ' x ~ x ~ × ~ × ~ × -0 5

-025

0

0.25

05

0.75

Applied

voltoge

i0

125

I5

r I

I

I

175

(a)

10--

¢ a-

IO

ct u

O

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~

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Io

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Ioo

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IOOO

Applied voff-oge

(b) FIG. 3. C a p a c i t a n c e - v o l t a g e [] A +

rj=5.1×I0-3cm, r~ = 1 . 9 × 1 0 - 3 c m r~ = 2 × 1 0 - 4 c m

c u r v e s for square d i o d e s (a) 1 / C ~ v s . V (b) C vs. V. × (3 (b)

rj=l.98×10-3cm rj = 4 " 9 X 1 0 - 4 c m theoretical Ref. 1.

541

542

P.R.

WILSON

o

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Applied voltage

(a)

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Applied voltage

(b) FIG. 4. Capacitance-voltage curves for circular diodes (a) 1/C" vs. V (b) C vs. V. T h e d o t t e d lines i n d i c a t e a va l a nc he b r e a k d o w n . [] a +

rj=5-1xl0-3cm rj = l ' 0 1 × 1 0 - S c m r~ = 2"0 X 1 0 - 4 c m

x O (b)

rj = l ' 9 8 x 1 0 - S c m rj = 4 " 9 x 1 0 - 4 c m - - t h e o r e t i c a l Ref. 1.

DEPLETION

LAYER

PROPERTIES

OF

PLANAR

--

DIODES

cl

__

I:I

X

X

--0 5

-025

I

0

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025

0'5

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0 75

J

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r

125

I

I

I5

175

Applied voltage

(a)

IC--

ta_ o-

d

I l0

I

100

I I 1000

Applied volfage

(h) FIG. 5. C a p a c i t a n c e - v o l t a g e curves for p l a n e di ode s (a) I / C n vs. l/" (b) C vs. V. [] A +

rj=5"l×10-acm rj = 1 . 0 1 × 1 0 - ~ c m rj = 2"0 × 10 - 4 c m

× © (b)

rj=l.98×10-3cm rj = 4 " 9 × 1 0 - 4 c m t h e o r e t i c a l Ref. I.

543

544

P. R. W I L S O N

frequency of 1 M H z , voltage measurements being made with a Solartron D V M model LM.1420-2.

corresponding to abrupt or graded junctions approximations, in order to obtain the best straight line plot. T h e built in voltage was taken as the intercept on the voltage axis. Table 3 gives the measured value of the built in voltage for each diode, the value of n used in obtaining this, and also the value for the built in voltage calculated from Ref. 4. T h e r e is close agreement between the measured and calculated values for the built in voltage except for circular diode no. 5. T h e measured values of the built in voltage were later

Results

T h e results given below are for one range of diodes b u t are typical of all the diodes made. Tables 1 and 2 give the diode parameters. Figures 3a, 4a, 5a and 6a show plots of 1/c ~ vs. applied voltage for the four types of diode. These were used to determine the built in voltage of the diodes. T h e value of n was taken to be either 2 or 3

9-5 -0-25

0

0"25

05

0'75

lq9

125

l'5

I'75

20

Applied voltage

(a)

I

°j il r=5xlO -~ + ~ ~' ~ ~-..._ 5.1xl0-4

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o, - ~ + . . . . _ _ -

~+.~.+ ~ +

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-+~x--~-.x

I

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n

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~,~-~

- ~ 2 5 x 1 0

-z

~ ~4.8x10-s

I I

I00

I

1

I I [

I000

Applied voltage

(h)

FIO. 6. Capacitance-voltage curves for P I N (b) C vs. V. q- r~ = 5 " 0 3 X 1 0 - a c m (b) ~ theoretical Ref. I.

0

diodes (a) 1/C n vs. V

rj ~ 5 " l × 1 0 - 4 c r n

545

DEPLETION LAYER PROPERTIES OF PLANAR DIODES

Table 3. A comparison of the measured and calculated built-in voltage Built-in voltage

Built-in voltage Diode no.

n

Diode no. Measured

Plane 1 2 3 4 5

n Measured

Calculated

2 2 2 2 2

0"48 0.51 0.52 0.56 0.33

0.49 0-52 0"535 0"555 0"58

2

0.30 0.35

0.295 0.355

Calculated

3 3 3 3 2

0.48 0.525 0.54 0.55 0-57

0.49 0.52 0-535 0.555 0-58

1

3

0-49

0.49

2 3 4 5

3 3 3 2

0 "51 0.53 0-56 0.59

0'52 0.535 0.555 0.58

Square

used for calculation of capacitance voltage curves except in the case of the circular diode no. 5 where the calculated voltage was used. Figures 3b, 4b, 5b and 6b show the measured and calculated C-V curves for the four types of diodes. The theoretical curves were calculated from Ref. 1 using equation (17) for the square diode and equation (24) for the P I N diode. It can be seen that there is very close correlation between experimental and calculated values. Although the square, circular and plane diodes all have nominally the same area, the curved edges of the planar junctions have a noticeable effect on the C-V characteristics, the effect increasing with increasing applied voltage and with increasing junction depth. The effect is greater in the square diode than in the circular diode due to the larger perimeter of the square diode. It is also interesting to note that in the plane diode the capacitance decreases with increasing junction depth but in the planar diodes the capacitance increases with increasing junction depth. The curves for the P I N diode shown in Fig. 6b also show the effects of the curved region of the planar junction as the capacitance continues to decrease after the I region under the flat portion of the junction has become fully depleted. Figure 7 shows curves calculated from Ref. 2 for square diodes. Capacitance values for the flat region of the junctions were taken from Ref. 1

Circular I 2 3 4 5

PIN 1-3 4-6

2

and the cylindrical and spherical capacitances were taken from Ref. 2. Included for comparison are curves calculated from Ref. 1. It will be seen that neither the linear graded nor the abrupt curves are as close a fit to the experimental data as are the Gaussian curves. At large junction depths the linear curve gives a closer fit than the abrupt curve but at shallow junction depths the linear curve cannot be calculated because of depletion layer breakthrough to the surface. SEM OBSERVATIONS

The scanning electron microscope (SEM) is being increasingly used as a diagnostic tool in the study of semiconductor devices. THORNTONet al. ~5) have pointed out the use of the SEM in the photoconductive mode for determining depletion layer widths o f p - n junctions. In this work planar diodes were sectioned and examined in the photoconductive mode of the SEM.

Experimental Circular planar diodes 2.54 x 10-2 cm dia. were manufactured in n-type material with a background doping of 2 × 1 0 1 ~ c m - S and with a nominal junetion depth of 45/~. The high resistivity and deep junction were chosen in order to allow adequate spreading of the depletion layer. The diodes were encapsulated in DO7 style packages and then sectioned perpendicular to the plane of

546

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¢3

×10-3

-

0~

~ + ~

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[

1 I P I0

f

I

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pO0

i×10 ~ !

r

I ~ I

iO00

Applied voltoge

FIO. 7. Capacitance-voltage curves f o r square diodes.

rj = 5 . 1 x l 0 - 3 c m rj = 2 . 0 × 1 0 - 4 c m

rj = l ' 0 I × 1 0 - 3 c m Theoretical (linear) Ref. 2. Theoretical (abrupt) Ref. 2. Theoretical Ref. 1.

The theoretical curves are terminated either at avalanche breakdown or when the depletion layer meets the surface.

the junction. V - I characteristics of the diodes were measured before and after sectioning to ensure that no serious degradation of the leakage currents had occurred, over the observed range of reverse biases. A n A . E . I . S E M 2 Scanning Electron Probe Micro-Analyser was used to make the electron b e a m measurements. Observations were made using both the emissive and photoconductive modes b u t most of the results reported were obtained from the photoconductive mode. All observations were made with a b e a m voltage of 5 kV, which gives a penetration d e p t h of 0.5/z in silicon. (6) Figure 8 is an emissive micrograph of a diode operating at a reverse bias of 50 V, and Fig. 9 gives an explanation of the micrograph. Figures 10-14 are conductive micrographs of the same diode operating with reverse bias between zero and 80 V. T h e faulty region towards the left side of the

Sp6nqc o n ~ O~,icie

,

J

Bock confacf

FIG. 9. Sketch of Fig. 8.

DEPLETION

LAYER PROPERTIES

diode is probably due to surface damage caused during sectioning. T h e measurements were terminated at 80 V because at higher reverse voltages the diode started to become leaky.

OF PLANAR DIODES

547

0"(

~1~ °' RESULTS As the diode was not sectioned across a diameter there is some magnification of the depletion layer width round the curved regions of the junction. T h e sectioning plane was 6 - 0 5 × 1 0 - 3 c m off a diameter leading to a magnification of 1.135. T h e centre line of the depletion layer for the diode under zero bias, Fig. 10, was taken to be the position of the p - n junction. T h i s is shown plotted in Fig. 15, corrected for the magnification, together

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Oxide

ii o, 0"~

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20

30

40

50

60

70

SO

90

I00

Appied

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Fro. 16. Depletion layer width as a function of reverse bias taken from Figs. 10-14. 0 plane region of junction + curved region of junction calculated from Ref. 1. circular they may be treated as such for the purposes of calculation.

0( I.C

,zL -=z

'

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-os

I

-os

f

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-o2 o Spread Junction depi'h

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oo

CONCLUSIONS T h e results presented in this paper for the built in voltage, the capacitance and depletion layer widths of planar p - n junctions adequately confirm the theoretical results in Refs. 1, 4 and 7.

FIG. 15. Measured junction shape taken from Fig. 10, corrected for magnification, due to position of the sectioning plane. 0 measured calculated from Ref. 7.

Acknowledgements--This work was performed as part of a PhD thesis for Nottingham University in cooperation with A.E.I. Semiconductors Limited. Thanks are due to Mr. I. K. OPENSHAWand Mr. R. W. CmLVERS for the SEM micrographs.

with the theoretical position of the junction. (7) T h e agreement between the two curves is close, thus confirming the observations of MACDONALD and EVERHART.(s) Figure 16 shows the measured depletion layer widths, from Figs. 10-14, for the plane and curved parts of the junction together with theoretical values taken from Ref. 1. T h e agreement is reasonably good. T h i s justifies the usual assumption that although the curved regions of a planar junction are not

I. P. R. WILSON,Solid-St. Electron. 11, (1968). 2. T. P. LEE and S. M. SzE. Solid-St. Electron. 10, 1105 (1967). 3. J. C. IRVlN, Bell Syst. tech. J. 41, 387 (1962). 4. P. R. WILSON--to be published. 5. P. R. THORNTON, K. A. HUCHES, D. V. SULWAYand R. C. WAYTE,Microelectron ~ Reliab. 5, 291 (1966). 6. T. E. EVERHART, O. C. WELLS and R. K. MATTA, Prec. IEEE, 52, 1642 (1964). 7. D. P. K~NEDY and R. R. O'BRIEN, I B M 3"l Res. Dev. 9, 179 (1965). 8. N . C . M A C D O N A L D and T. E. EVERHART, J. appl. Phys. 38, 3685 (1967).

REFERENCES