Effect of structure on the quantum efficiency and R0A product of lead-tin chalcogenide photodiodes

Infrared

Phys.

Printed

in

Vol.

22. pp.

199 10 208.

1982

00204891/82/040199-1OSO3.00/0

Great Britain

PergamonPressLtd

EFFECT OF STRUCTURE ON THE QUANTUM EFFICIENCY AND RoA PRODUCT OF LEAD-TIN CHALCOGENIDE PHOTODIODES A. ROGALSKIand J. RUTKOWSKI Military Technical Academy. Warsaw. Poland (Receiued 1 September 1981)

Abahnct--The conditions are determined under which the quantum efficiency of lead-tin chalcogenide photodiodes achieves its maximum. The effect of the structure of photodiodes on their quantum efficiency and on the R,-,A product has been analysed. It has been shown that at a surface recombination velocity of 0 C sI Q 104m/sec and depth of the junction not less than O.ZI_. (where L is the minority carrier diffusion length) the product R,A differs from (R,,A), for diodes with thick regions on both sides of the junction by a factor of 0.3-2.

INTRODUCTION

The detectivity depends on the quantum efficiency and the zero bias junction resistance are product RoA. Previous theoretical estimates of the RoA product for lead-tin chalcogenide diodes considered photodiodes with thick regions on both sides of the junction.“-‘) However, photodiodes with such a geometry are not realized in practice, since their quantum efficiency would then be zero. Hitherto the effect of structure of photodiodes on their quantum efficiency and R,A product has not been analysed in detail. Mention of that subject is made in Refs (2) and (9). In the present work the conditions under which the quantum efficiency of lead-tin chalcogenide photodiodes attains its maximum and the effect of structure of photodiodes of this type on the RoA product are determined; besides, it is checked for what real photodiode structure is the RoA product (calculated for photodiodes with thick regions on both sides of the junction) correct.

QUANTUM

EFFICIENCY

Three regions contribute to the photodiode quantum efficiency: two neutral regions of different types of conductivity and the spatial charge one. Thus:“O’ rl

aLh

+

71 -

=

tl,

+

VDR

(Y2

-

VP

e-““~?lch,/Lh)

?lsh(xn/Lh)

rl _ P-

+

+

(1)

+ s&h/Lh)]

aLhe_ %

(2)

ch(xn/Lh)

(1 - r)aLe

,-l&+tq

a2L2 e -

1

aL,)e -qf+d-xn-w’- sh[(t -t- d-x, - w)/L,] -y2ch[(t + d-x, ch[(r + d -x, - M/L,1 + wW + d - x, - W&l ~~~ = (1 - r) [e--n

199

_ e-qxn+“‘1

- w)/L,]

+ aL, (4)

A. ROGALSKIand J. RUTKOWSKI

200

where: r is the illuminated junction surface reflection coefficient; a is the absorption coefficient; YI = s,L,lD,, 72 = s,Ll&; L, and L,, is the electron and hole diffusion length, respectively;

D, and Dh is the electron and hole diffusion coefficient, respectively;

s1 and s2 is the surface. recombination velocity photodiode surface, respectively.

at the illuminated

and back

The above formulae derived for a low carrier injection level are true for the onedimensional photodiode model with an abrupt junction where the spatial charge of width w surrounds the metallographic junction boundary x = t. and two quasineutral regions (0. x,) and (x, + w. t + d) are homogeneously doped (see Fig. 1). In the following we shall consider the internal quantum efficiency neglecting the losses due reflection of the radiation from the illuminated photodiode surface. Obtaining high photodiode quantum efficiency requires that the illuminated region of the junction be sufficiently thin so that the generated carriers may reach the junction potential barrier by diffusion. We shall first estimate the thickness of that region for the Pbo.,sSno.22Te photodiode at 77K assuming that the region of opposite conduction-type is thick. Let us consider two cases: the surface recombination velocity is zero (sl = 0) and the surface recombination velocity is high (sl = lo4 m/set). The calculation will be based on formulae (l-4) for the typical absorption coefficient of 5.10’ m-l at wavelengths close to the intrinsic absorption edge in lead and tin chalcogenides. (I ‘-13) Let us further assume symmetrical doping of both sides of the junction, N,, Nd = 1O23me3. We are justified to assume such concentration values since they are close to the optimal ones at which highest RoA values are obtained.‘1*3*4, 6*7*14) We also assumed that the electron and hole mobilities in Ph,,,8Sn0.22Te at 77K are equal and amount to p = 3m’/Vse~,“~) and the life times, as determined in terms of the interband radiation and Auger recombinations, are ,re=‘5*= lo-* set (‘816) Using the Einstein relation D = (kT/q)p, true for nondegenerate semiconductors, we get the diffusion length L, = L,, = (Dr)“’ = 14 pm. The width of the abrupt junction spatial charge w = { [2 es/q] [(IV, + Nd)/NsNd] Vbi} 1’2 at E, = 500 and V,, = E,/q is 0.33 pm. In Fig. 2 the relationship is presented between the components of the Pb0.78Sn,,22Te photodiode quantum efficiency and the normalized thickness of the junction illuminated region t/L* at infinite thickness of the p-type region. The contribution of the illuminated region to the quantum efficiency initially increases with thickness to a maximum and then decreases to zero when t + L,,. In contrast, qp rapidly decreases to zero as the junction depth increases, and for very small values of t qp > q.. The quantum efficiency of the depletion layer gradually decreases with increasing t, but it is small and plays no major role. The contribution of 9 oR to the total quantum efficiency may be significant or even ciucial if the depth of the junction is small and the values of

-

nv

GYPn 1

L

I

1

I

’

I

1

VP P

I

d

Fig. 1. The one-dimensional

photodiode model.

Lead and tin chalcogenide photodiodes

0.4

0.8

201

1.2

t/L,

Fig. 2. The dependence of the quantum efficiency on the normalized thickness of the junction illuminated region at s, = 0 (yr = 0) and s, = 104m/sec (y, = 7). In the calculations it was = 5.lOsm_‘. assumed: d = CC,N, = N, = 10” m-‘, L, = L* = 141(m, w = 0.33manda

L, and L,, are much smaller than those considered in the present work. From Fig. 2 we see that the total quantum efficiency attains its maximum at f z 0.2 L,, for sr = 0. That maximum is shifted towards smaller I values as the surface recombination velocity s1 increases. The position of the total quantum efficiency maximum depends also on the absorption coefficient. That is seen in Fig. 3, where the variation of 17 with t/L,, at s1 = 0 for z = 5. 104, 2. lo’, 5.10’ and 2. IO6 m-l is shown. For Pb0.7eSn,,12Te with a carrier concentration of 1O23me3 and at 77K the above absorption coefficient values correspond

Fig. 3. The dependence of the quantum efficiency on the normalized thickness of the junction illuminated region at s, = 0 (y, = 0) for absorption coefficient values 5.10’. 2.10’. 5.105 and 2.10 m-r.

202

A. RCGAUKI

to the wavelengths relation :(’2,

and J. RUTKOWSKI

12.05, 11.1, 9.0 and 2.6 pm, respectively,

a(z) = :IC* ,

(22 - 1)“2(1 + 22& 3J2 z2

in accordance

with the

_f,) ’

a_

(5)

where: K, = 6.5.10’(eVcm)-‘, z = hv/E,, n, is the refractive index, /” and fC are Fermi functions for holes and electrons, respectively. Formula (5) accounts for the non-parabolicity of the bands according to the Kane model. The position of the Fermi level, necessary for calculating fY and f,, was found in terms of the Kane model. (l’) Figure 3 shows that the depth of the junction at which the total efficiency attains maximum is smaller, the higher the absorption coefficient. Let us now consider more closely the effect of the surface recombination velocity s1 on the quantum efficiency. In Fig. 4 the variation is shown of the quantum efficiency with the absorption coefficient for sI = 0 and s1 = lo4 m/set at r/L,, = 0.2. We see that the surface recombination velocity affects significantly q in the range of high absorption coefficient values (small wavelengths) so the depth of radiation penetration l/a is very small. In turn, Fig. 5 shows the variation of quantum efficiency with s1 for chosen a values. The character of the curves in this figure is similar. The quantum efficiency is constant for all values of the absorption coefficient when the surface recombination velocity is much smaller than a certain characteristic value s0 and then decreases to a smaller but also constant value in the range s1 % so. In Ref. (18), it was found that the value so can be determined from the formula:

Dhcth 3 Lh Lh

so = -

and it is independent of the absorption coefficient. At constant Dh and Lh, so depends only on the depth of the junction, and so for x,/L, = 0. I, 0.2, 0.5 it amounts to 1.6. 104, 7.5. lo3 and 3.1 * lo3 m/set, respectively, at D, and Lh as given above.

10" a,

m-l

Fig. 4. The dependence of the photodiode quantum efficiency on the absorption coefficient for s, = 0 (y, = 0) and s, = lo* m/set (vl = 7). In the calculations it was assumed: d = Q), r/L, = 0.2. N. = N, = 10’) m-‘. I.., = f_., = 14 pm and w = 0.33 pm.

Lead and tin chalcogenide photodiodes

ld

ld sl*

203

10' m/su

Fig. 5. The dependence of the photodiode quantum efficiency on the surface recombination velocity for absorption coefficient values 5.10.. 2.10’. 5.10’ and 2. lo6 m-l. In the calculations it was assumed: d = 00, t/L, = 0.2, N, = N, = 10z3 m--‘, L, = LI = 14pm and w = 0.33pm.

All the above considerations relate to a classical photodiode with a thick p-type region (d = co). However, in lead-tin chalcogenide photodiode technology structures of types (n)Pb I _ ,Sn,Te+p)Pb, _XSn,Te---@+)Pb, _ .Sn,Te” ‘) and (n)PbTe(p)Pb, -,Sn,Te-(p+)Pb, _XSnXTe(2G22)are used where the p-type region decisive for the junction properties has a thickness of the order of 1Opm. Structures of that type will be considered in the next section. The m-p-p+ structure can be obtained when the metal constituting the back contact diffuses in a p-type semiconductor as acceptor impurity and when the transition from the metal to the semiconductor is abrupt enough to permit formation of a space-charge layer between the p-type and p+-type regions In this section we shall still consider the effect of p-type region thickness on the photodiode quantum efficiency. According to formula (3) qp depends on the junction depth by a factor exp[ -a(~, + w)]. Let us consider a case when the depth of the junction is very small, i.e. x, = 0. Implanted junctions and field induced junctions in CCD structures present a good approximation. In Fig. 6 the variation of quantum efficiencywithd/L,for three recombination velocities:s, = CO,s2 = De/L, = 1.4. IO3 m/set and s2 = 0 with a = 5.10’ m- ‘. If the back contact is ohmic (s2 = CO),the maximum quantum efficiency is obtained for a thicker region, i.e. d/L, % 1. When the recombination velocity decreases, q increases more rapidly with increasing d. In the case of a blocking contact (s2 = 0) a distinct quantum efficiency maximum is observed for d/L, = 0.7. For a wide p-type region (d 9 L) the quantum efficiency is independent of the carrier recombination conditions in the x = d + t plane. THE RoA AND qRoA PRODUCTS It can be shown that for a diode the R,J product determined current is: DiiPn Y~ch(x,fL,)

R

by the diffusion

+ sh(xnlL,)

0 Lh

+

rlsh(xnl4

+

Den,y2cW + d L,

y2sh[(t

Ck/Lh)

x, - w)/LeJ + sh[(t + d - x, - w)/L,J

+ d - x, - w)/LJ

+ ch[(t + d - x, - w)/L,J

-’ (7)

A.

204

R~GALSKI

and J.

RUTKOWSKI

Fig. 6. The dependence of the quantum efficiency of a photodiode with field induced junction on the normalized thickness of the p-type region at the surface recombination velocities s1 = co (y2 = w), 1.4.10’ m/set (y2 = 1) and 0 (yl = 0). In the calculations it was assumed: x, = 0, N.=10’3m-‘,L,=14~manda=5~105m-‘.

where p. and nP are the concentrations of minority carriers on both sides of the junction. For lead-tin chalcogenide photodiodes with symmetric junctions we can assume that L, = L, = L, D, = Dh = D and nP = pm.Then for a junction with thick quasineutral regions (x, B L,,, t + d - x, - w % L,) expression (7) assumes the form: kTL (ROA), = %ZDn,

(8)

and in accordance with (7):

-=RoA (Ro40

2

YlChkILh) + s&,/L,) Y1s&,/L,)

+

c&blLh)

+ y2ch[(c + d - x, - w)/L,] + sh[(t + d - x, - w)/L,]

y&[(r

+ d - x, - w)/L,] + ch[(t + d - x, - w)/L,]

-’

(9)

From formula (9) we see that if yr = y2 = 1, then the RoA product is the same as in the case of a diode with thick regions on both sides of the junction. The basic parameters of photodiodes such as voltage sensitivity and detectivity depend on qRoA and q(R,,A) ‘I2. It is interesting therefore to consider also the ratio VoAI(Ro&. Figures 7, 8, 9 and 10 show the variations of rf, RoA/(RoA)o and qRoA/(RoA)o with normalized depth of the junction for p-type region thicknesses of d = 0.1 L,, d = 0.4 L, and d = 00, and for different surface recombination velocities s1 and s2. In the case of zero carrier recombination velocities sr = s2 = 0, we observe an increase of RoA product with decreasing junction depth and p-type region thickness (Fig. 7). That increase is particularly pronounced in the range of t/L, and d/L, values smaller than 0.1. The use of structures with a thin p-type region is disadvantageous when the back contact is ohmic, i.e. when s2 = co. If s2 = 00, then the highest values of R. A and qRoA/(RoA)o are obtained for a junction of small depth and thick p-type region when d/L, $ 1 (see Fig. 8).

205

Lead and tin chalcogenide photodiodes

Fig. 7. The dependence of q. RoA/(RoAh, and qR,A/(R,,A),, on the normalized depth of the junction for p-type region thicknesses of d = 0.1 L, (I), 0.4 Le (2) and 00 (3) and surface recombination velocities s1 = s2 = 0 (y, = y1 = 0). In the calculations it was assumed: N, = N, = 10” m-l, L, = LI = 14 pm. w = 0.33 pm and o1= 5. IO5 m-‘.

The recombination of carriers on the illuminated junction surface not only decreases the quantum efficiency but also the RoA product. This is shown in Fig. 9 for si = lo4 m/set (Yr = 7). The shapes of the curves in that figure differ greatly from those shown in Fig. 7 for which si = 0 (yi = 0). If s2 = 0, then RoA decreases with increasing thickness d. On the other hand, the greater the depth of the junction, the greater is the R. A product and the smaller the quantum efficiency. Thus, qR oA/(R, A), and hence the voltage sensitivity and detectivity reach maximum at a certain depth I of the junction.

2

-

~A/u?,AI,,

-----

T)%A/V+,A),

Fig. 8. The dependof q, RoA/(RoA)o and qR,A/(Ro& on the normalized depth of the junction for p-type region thickneasu of d = 0.1 L, (I), 0.4 & (2) and 00, (3) and surface recombination vetocities s, = 0 (yt = 0) and s2 = CO (yz = 00). In the calculations it was nssumed: N, = N, = 102’m-3, f_, = L* = 14 pm, w = 0.33pmanda = 5*10’m-‘.

A. R~CALXI LO

F ..T

’

o-

Fig. 9. The dependence of junction for p-type region recombination velocities s, assumed: N. = N, =

2

-.-,-

2\i

and J. RUTKOWSKI

-

r) R,A/V$A,,

----

r)ROA/bQOA),

I

I

043

I

I

I

I

1.2

0.8

1, R,A/(R,& thicknesses of = 10’ m/set (y, 1O23m-‘, I_, =

,

0

and qRoA/(Ro.4),, on the normalized depth of the d = 0.1 L, (1). 0.4 L. (2) and a~ (3) and surface = 7) and s1 = 0 (y2 = 0). In the calculations it was 4 = 14 pm, w = 0.33 pm and (II = 5. lo5 m-l.

That maximum is shifted from t = 0.2 Lh for d = 00 to t = 0.4 Lk for d = 0.1 L,,. The greater the surface recombination velocity sr, the lower the voltage sensitivity, and the sensitivity maximum is shifted towards greater junction depths (see Fig. 10). For n--p+-type junctions the relation analogous to (9) has the form:

RoA ___

(Ro40

=

YlC&lL) Yl s&,/L,)

+ s~(x,lL,) +

c&l~,)

(10)

In Fig. 11 the dependence is presented of RoA/(RoA)o on the n-p+(n+-p) junction depth at various yr values. For y1 < 1 (blocking contactt23’) we get RoA > (R,A),, the increase of RoA being particularly high for small values of y1 and x,/Lb+ 0. For non-blocking contacts (1 -z y1 < ~0) RoA < (R,A),.

CONCLUSIONS

Analysis of the effect of structure of a classical Pbo.,t,Sno.22Te photodiode (of thick p-type region) on its quantum efficiency and R. A product at 77K has shown that: (i) The optimum junction depth at which greatest photodiode sensitivity is obtained depends on the surface recombination velocity, and so at sI = 0 the depth of the junction must be very small (t + 0). When st increases, the optimum junction depth also increases and reaches values of, e.g. cu. 0.1 Lh for 1.4. lo3 m/set and ca. 0.2 L,, for s1 = lo4 m/set (see Figs 8, 9 and 10). (ii) The product RoA for junction depths 0 G t < 0.2 &, and surface recombination velocities 0 < s1 G lo4 m/set differs from product (R,A), for a photodiode with thick regions on both sides of the junction by a factor of 0.3-2. This shows that the product RoA calculated for photodiodes with thick p-type and n-type regions is a good approximation of that for photodiodes of optimum construction (see Figs 8, 9 and 10).

Lead and tin chalcogenide photodiodes

0

I

I 0.4

1

1 0.8 r/L,

I

I 1.2

I

207

0

Fig. IO. The influence of the surface recombination velocity at the illuminated photodiode surface and qRoAMR~Ah: s, = 0 (1). 1.4~103m/sec (2) and 03 (3). In the w=0.33pm and calculations it was assumed: N. = N, = 102’ m-‘, L,=LI=14pm, CI= 5.105 m-l.

on V. RoAl(R~&

The most disadvantageous structure is that of the photodiode with a thin p-type region and high recombination velocity s 2. One should aim at designing photodiodes with a thin p-type region and a very small recombination velocity s2. Then a significant growth of RoA can be achieved for t < 0.1 L, (by more than one order of magnitude). Fabrication of such structures may encounter great technological difficulties connected with the need to fulfil the condition s2 z 0. In that case it is advantageous to use n-p-p+ structures, since the potential barrier between the p- and p+-type regions limits the flow of minority carriers to the region with more impurities. Lead and tin chalcogenides show similar physical properties so the considerations given above and the conclusions made apply to photodiodes based on a large group of A’“B”’ compounds. The results and conclusions relating to product R,A are true for every photodiode (irrespective of the semiconductor and temperature) since dimensionless quantities have only been used. It remains to be considered if the above conclusions relating to symmetric junctions with thick quasineutral p-type region hold for non-symmetric p+--n(n+-p) type junctions for which greater RoA values can be obtained. It can be seen that they hold indeed. In p+-+I+-p) structures the concentrations of impurities on the p’(n’) type side are high (> 10” m-‘). This proves that on illumination of the p’--n(n’-p) junction from the p’(n’) side, the thickness of the illuminated junction region must be small to eliminate absorption of radiation by the free carriers. In n-p+(p-n+) structures illuminated from the @)-type side the major contribution to the quantum efficiency comes from the region with less impurities of n(p)-type. That is why the thickness of that region, and hence the depth of the junction, should be greater, i.e. 0.2 L,, < t < 0.4 Lh (see Fig. 2). On the other hand, at lower t values and 0 < y, < 1 we can obtain a significant increase of the product R,A (see Fig. 11). It follows therefrom that the optimum depth of the junction is shifted towards smaller t values. In conclusion it should be noted that the influence of structure on the RoA product is determined by the diffusion component of current density. In the case when the RoA product is determined by another mechanism (generation-recombination in the depletion layer, tunneling or leakage current), the above considerations are not justifiable. The considerations concerning the quantum efficiency still remain valid. WT. 2214-s

208

A. ROGALSKI and

J. RUTKOWSKI

Fig. 11. The dependence of R,,A/(R,,A), on the normalized depth of the junction at different surface recombination velocities st = 0 (y, = 0). 7.lO’m/sec 1.4.10” (y, = l), 2.8.10s (y, = 2) and m (y, = co).

n-p’(n’-p) (7, = 0.5X

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