Ionization coefficient measurement in GaAs by using multiplication noise characteristics

Solid.State Electronics, Vol. 24, pp. 629-634, 1981

0038.-I101/$I/070629-06502.00/0 Copyright© 1981PergamonPress Ltd.

Printed in Great Britain. All rishts reserved.

IONIZATION COEFFICIENT MEASUREMENT IN GaAs BY USING MULTIPLICATION NOISE CHARACTERISTICS H. ANDOand H. KANBE Musashino Electrical Communication Laboratory, Nippon Telegraph and Telephone Public Corporation, 9-11, Midori-cho3, Musashino-shi,Tokyo, 180 Japan

(Received 18 June 1980; in revisedform 15 October 1980) Al~tract--Multiplicationnoise measurementsfor p+n type (100) GaAs avalanchephotodiodeswith various n-layer dopings rangingfrom 6 x l0ns to 9 x 1016cm-a confirmedthat the ionizationcoefficientof electrons a is about two times larger than that of holes fl in the electric field range from 2.4 x IOs to 5.6 x l0s V/cm. When pure electrons were injected into the avalanche region, the multiplicationnoise power was proportionalto the 2.7th power of the multiplicationfactor and the ionizationcoefficientratio k = ~/a was constant, where k = 0.5 in the above electric field range. The result was consistent with the multiplicationfactor dependence on light wavelength. Using the constant ionizationcoefficientratio k and the multiplicationfactor dependenceon applied bias voltage,ionization coefficientsa and j8 for electrons and holes were estimated.

I. INTRODUCTION

III-V compound semiconductors have been investigated in order to realize low dark current and low multiplication noise avalanche photodiodes for 1.0-1.7/zm wavelength region optical communications[l-7]. In this wavelength region, InGaAs[l-3] and InGaAsP [4, 5] are foreseen as materials for avalanche photodiodes. The noise property of an avalanche photodiode is determined by the impact ionization coefficients of electrons and holes, and by the kind of carriers injected into the avalanche region. Much effort has already been expended, to measure the ionization coefficients for GaAs [812], InAs[13], InP[14, 15] and InGaAs[16]. Evaluation of the ionization coefficients for the binary semiconductors is important to aid in estimating fine values for the ternary and quaternary semiconductors. The ionization coefficients also are known to affect the performance of IMPATT diodes using avalanche multiplication as a gain mechanism. For GaAs, since StiUman et al. first reported the unequal ionization coefficients of electrons and holes[8], the orientation dependence[10], the temperature effect[ll] and the carrier density dependence[9] have been reported. These measured ionization coefficients, however, seem to contradict each other in their magnitude, and which of the ionization coefficients is larger than the other has not yet been made clear. The ionization coefficients previously reported were evaluated by measurement of multiplied photocurrent as a function of applied bias voltage when only electrons or only holes were injected into the avalanche region. The ionization coefficient ratio can also be estimated by comparing the measured multiplication noise with McIntyre's equation[17]. Multiplication noise is considered as another measure to evaluate relative magnitude of ionization coefficients of electrons and holes. This paper delineates experimental results on ionization coefficients of electrons and holes in GaAs,

evaluated by measuring multiplication noise and multiplication factor. The multiplication noise for diodes with various n-layer carrier densities ND from 6 x 1015cm -3 to 9 x 1016cm -3 was proportional to the 2.7th power of the multiplicationfactor when only electrons were injected into the avalanche region. These results show that for ionization coefficient for electrons is two times larger than that for holes in the electric field range of 2.4 x l0s_ 5.6 x 105 V/cm for the (I00) direction. The result was confirmed by measuring multiplication factor and multiplication noise dependences on incident light wavelength. 2. DIODE STRUCTURE AND FABRICATION

GaAs avalanche photodiodes used in the experiment were p+-n mesa type, as shown in Fig. 1, with various n-layer carrier densities ND in 6 x 1015-9 x 1016cm -3 range. The diodes met the following conditions necessary to evaluate ionization coefficients precisely: (1) Uniform avalanche multiplication could be obtained over the whole junction area; (2) The electric field in the depletion layer could be calculated exactly and (3) Pure electron injection into the avalanche region was realized when multiplication noise and multiplication factor are measured. The junction was formed in the (I00) plane and an electric field was applied along the (100) direction. The n-layer was grown by vapor phase epitaxy. Zinc was 175tJm

j iO n

(1 )

n ( No = 2xldacm-3) J~',,Au-Ge-N i

Fig. 1. Structure of p+n type GaAs avalanchephotodiodeused in the experiments.

629

H. ANDO and H. KANBE

630

diffused to form the p+-n junction by vapor phase diffusion in an evacuated fused silica ampoule, using ZnAs2 as the source[18] to prevent arsenic decomposition from GaAs. The junction was formed about 0.7#m deep from the surface after a 6.3hr diffusion at 550°C. Ohmic contacts for the n + substrates were formed with Au--Ge-Ni alloy. After the Zn diffusion, a mesa was formed by chemical etching with H202:H2SO4:H20 etchant. The junction diameter was 175 #m. Aluminium pressure contacts were applied as the p+ electrode. Diodes with n-layer carrier densities No of 0.6 x 106, 1.2 x 1016, 2 × 1016, 3.5 × 1016 and 9 x 1016cm-3 were fabricated to evaluated multiplication characteristics and ionization coefficients. C-V characteristic measurement showed that these diodes have onesided abrupt junctions and that n-layer carrier densities are uniform. The n-layers are thick enough so that the depletion layers do not punch-through to the n + substrates. Electric field strengths in the depletion layer decrease linearly with distance from the junctions and their magnitudes can be calculated exactly. Figure 2 shows the dark current dependences on applied bias voltage for the fabricated diodes with various n-layer carrier densities. These diodes show so called hard breakdown characteristics. Breakdown voltages for these diodes are summarized in Table 1, together with the range of maximum electric field applied in ionization coefficient measurements. Dark currents of the diodes are lower than 10 -7 A at the 1/2 Ve bias voltage.

measured by scanning focused 0.633 #m He-Ne laser beam over the whole sensitive areas. Figures 3(a) and 3(b) show, as an example, photoresponse uniformity of a diode with n-layer carrier density ND of !.2 × 1016cm -3. The quantum efficiency and multiplication factor are uniform, except for the bonding area. The same photoresponse profiles for diodes with various ND values were confirmed to be uniform by the measurement. Multiplication factors were measured at two different carrier injection conditions in magnitude. One light source was a He-Ne laser with 0.633 #m wavelength for pure electron injection into the avalanche region. The other was A1GaAs LED with 0.81 #m for simultaneous electron and hole injection. Quantum effÉciency for individual samples with different ND values was independent of the applied bias voltage sufficiently lower than its breakdown voltage. Photocurrent increase at a deep bias voltage is caused by avalanche multiplication, and not by depletion

IOOpm

f

3. MULTIPLICATION FACTORS

Uniform sensitivity and multiplication in the sensitive area are important in precise measurement of ionization coefficients. Photoresponses of all the samples used were x

(a)

10 -4

lOOpm 10 -'=!9.0=

10"6: .

10-7=

o

20

40 60 80 APPLIED VOLTAGE( V )

100

Fig. 2. Dark current dependences on applied bias voltage for diodes with various n-layer carrier densities.

(b) Fig. 3. Photoresponse distribution in the sensitive area. Wavelength is 0.633#m. (a) Bias voltage is 5V and multiplication factor is 1 and (b) Bias voltage is 48 V and multiplication factor is 10.

Table i. Breakdown voltages Vs and applied electric field ranges Emx for diodes with various n-layer carrier densities No ND(cm-~) VB(V) Em,~(10s V/era)

6.0 × 1015 85 2.4--3.1

1.2 × 1016 49 2.6-3.8

2.0 x 1016 35 2.8-4.2

3.5 x 1016 24 3.0-4.5

9.0 × 1016 13 3.7-5.6

Ionization coefficientsin GaAs layer stretching. The multiplication factor is defined unambiguously as the ratio of photocurrent at a voltage near breakdown to that at 10% of breakdown voltage. Figure 4 shows the multiplication factor dependence on light wavelength in a diode with No = 6 x 10~scm-3 carrier density. In the experiments, a 0,633 #m He-Ne laser and a 0.81/~m LED were focused on a photosensitive area with less than 20#m dia., and initial photocurrent levels were fixed at 1/zA. At a constant voltage, the multiplication factor at 0.633 pm is larger than that at 0.81~m. The same dependences on wavelength were obtained for diodes with various ND. Figure 5 shows the calculated optical absorption rate by the following equation; = K exp (-

p

Kx),

(1)

where K and x are optical absorption coefficient and distance from the diode surface, respectively. Optical absorption coefficients are assumed to he 1 x 104 cm-t and 4 x 104 cm-~ at 0.81/~m and 0.633/zm wavelengths, respectively[19, 20]. The absorption coefficient at 0.633/zm is large enough for the light to be absorbed in the 0.7 ~m thick p÷ layer. If internal quantum efficiency is unity and electron excitation rate is equal to the absorption rate p, the ratio of electrons injected into the avalanche region from the p+ layer amounts to 94% of the total injected carriers. In contrast, the light at 0.81/zm penetrates into the n-layer and almost equal amounts of electrons and holes are injected into the avalanche region. As mentioned before, the multiI00

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0.633pm 0.81 pm •

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-

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4. MULTIPLICATIONNOISE

The multiplication noise for the diodes was measured to evaluate the ionization coefficient ratio. As shown in Fig. 6, the multiplication noise was measured by using a lock-in detection system, which consisted of a noise signal channel and a reference signal channel. In the noise signal channel, light illuminates the diode through a chopper with 225 Hz frequency. The noise power from the diode was applied through a bias tee to the receiver, where the noise component with 1 MHz bandwidth at 30 MHz was detected. In the reference signal channel, a 30 MHz RF signal was chopped by the modulator, which was synchronized with light chopper frequency, and applied to the receiver through a calibrated attenuator. By comparing the noise power and the reference RF power, the absolute noise power level was measured. Noise measurement precision depends mainly on the attenuator performance. Noise lower than - 130 dBm can be measured within less than 0.5 dB error. The system has been used in the precise noise measurement for several kinds of diodes[21, 22]. Figure 7 shows the excess noise factor F at 0.633/~m wavelength as a function of multiplication factor M. The multiplication noise power is approximately proportional to the 2.7th power of M. The broken lines in Fig. 7 show the calculated excess noise factor F given by McIntyre's equation[17]

i

80

(2)

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I

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I00

Fig. 4. Dependence of multiplication factor on light wavelength of functions of bias voltage.

v

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plication factor at 0.633 p.m is larger than that at 0.81/zm in each diode with No =0.6x 10~6-9x 10~6cm-3. The results indicate that the ionization coefficient of electrons c~ is larger than that of holes//.

F=M[1-(1-k)~],

APPLIED VOLTAGE (V)

z

631

0.5 1 1.5 DISTANCE FROM SURFACE X (.urn)

Fig. 5. Optical absorption calculated for 0.633/zm and 0.81 jzm wavelengths.

where k is defined as ionization coefficient ratio for pure electron injection. The measured excess noise is evaluated by effective ionization coefficient ratio k=a, which corresponds to the ratio k in eqn (2), and is obtained by comparing the measured and calculated excess noise factors. From the results in Fig. 7, the effective ionization coefficient ratio k=a at 0.633 ~m is estimated to be between 0.4 and 0.6. Measured k=~ value for the diodes with different Nz, values are shown in Fig. 8. The tail of the optical absorption p beyond the junction at 0.633/zm wavelength causes the increase of multiplication noise. However, the estimated increase of the noise is less than 0.3dB, since more than 90% electron injection into the avalanche region is realized. Therefore, k¢~ for pure electron injection lies in the range 0.4-0.6. These results lead to the following: 1. When a pure electron injection condition is satisfied, k d is nearly equal to 0.5 for diodes with ND values ranging from 6 × l0 ts to 9 x 10t6 cm-3. 2. k~a is constant within the 2.4 x 10s-5.6 x 10s V/cm electric field range, which corresponds to the maximum electric fields for different No values. 3. From koa = 0.5 in a wide doping range, the ion-

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Fig. 6. Block diagram of the noise measurement system.

5.IONIZATIONCOEFFICIENTEVALUATION

20 B. re

ND= 6 x 1131Scrn "3

o

Ionization coefficients for electrons and holes can be calculated by using the applied bias-voltage dependence of the multiplication factor at 0.633 p,m, assuming that the ratio k is constant according to the results obtained in Fig. 8. Since the electric field profile in the depletion layer is triangular for uniform n-layer carrier density, the ionization coefficients are obtained as functions of maximum electric field Em,x in the avalanche region, using the following equation [23],

/ : 0.8

::i," : 0.6

5" 0.,

c.}

w z

.,j~"~ ~'e" ~.e~'- •

ILl

0

* 0 633pm x 081pm

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Fig. 7. Excess noise factors for 0.633/~m and 0.81p,m wavelengths as functions of multiplication factor, n-layer carrier density No = 6 × 10~5cm-3. , i , , r,[

I

_+ ....

I

where Me and Mh are multiplication factors for pure electron and pure hole injection conditions into the avalanche region, respectively, and w is the width of the depletion layer. The relation between Me and Mh is expressed by [17]

,k .....

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CARRIER DENSITY N D

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= I + k(M~ -

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(cm -3)

Fig. 8. Measured effective ionization coefficient ratio ken vs n-layer carrier density Nt} ization coefficient ratio is nearly constant, independent of electric field strength. Figure 8 also shows k,n at 0.81 tzm. At 0.81 ~m, higher multiplication noise was observed and ko~ is 0.7-0.9. This multiplication noise dependence on light wavelength, also confirms that electron ionization coefficient is larger than that of holes, ken for a diode with N o = 9 x 10'6 cm -3 is smaller than k~ values for others, since the n-layer of the diode is thinner than 1 ~m and the hole contribution to multiplication noise is less effective than in other diodes.

The relation between a and Me can be obtained from eqns (3)--(5).

1

dM,

~(Emax) = Me[| + k ( M , - 1)] dw"

(6)

Figure 9 shows the ionization coefficients of electrons and holes determined by eqn (6), assuming k is a constant 0.5. The ionization coefficient a, estimated for the diodes with various No values, is an exponential function of liE. The ionization coefficients a and ~ are independent of the n-layer carrier density, and are ap-

Ionization coefficientsin GaAs '

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Fig. 9. Ionization coefficients a and/~ vs I/E.

proximately expressed by the following equations: a = 1.1 x 10Texp (- 2.2 x 10+/E)[cm-'], =

(7)

0.5 =,

(8)

where the dimensions of E are V/cm. According to Baraff's theory[25], the ionization coefficient a is represented as a function of electric field strength E by exp ( - C / E " ) ,

a =

where n = I for low electric field in the avalanche region, and n = 2 for higher electric field. In the present work a is shown to have exp (-C/E) dependence on electric field, similar to that for Silicon[26] and Germanium [27]. In the higher electric field region, a is thought to have an exp ( - C / E 2) dependence on E. The k values estimated from multiplication noise are in the 0.4--0.6 range. The accuracy of the ionization coefficients a and /3 is affected by this measurement error by as much as + 10%. Ionization coefficients of GaAs in the (100) direction, obtained by the present work are compared with those reported previously [8-12] in Fig. 10 as a function of 1/E. i0 =

'

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I

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",

<~

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at.

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Fig. 11. Dependence of ionization coefficient ratio on n-layer carrier density Nz>Data points a, b and c reported by Pearsall et a/.[10] are due to electric field strengths of 4.5 × 10s, 4x 105 and 3.3 × 105V/cm.

I , ,~, ~ t ,

2

o"

"

0.1 ........ ' ........ ' 1015 1016 101~ CARRIER DENSITY NO (crn -3)

9

¢,..

. .. ~ - - - X .......

e : P R E S E N T DATA O: PEARSALL ¢ t a l X : CAW I t al.

'< N

'E

A .X/"

4

Fig. 10. Comparison of ionization coefficients a and/3, thick and thin lines show a and ~, respectively.

Figure 11 shows the ionization coefficient ratios k = B/a measured for various n-layer carrier densities Nz> Law et aL [9] reported that the electron ionization coefficient for an applied electric field decreases with increasing ND and is larger than that of holes when the n-layer is highly doped. The present data for electron ionization coefficient are nearly equal to those reported by Law et aL in the low electric field region, i.e. for low doping of the n-layer. However, an increase of k at high doping level was not observed in the present measurement. Pearsall et aL measured the ionization coefficients for diodes with a p÷n junction fabricated by liquid phase epitaxy[10]. The ionization coefficient ratio k depends strongly on the electric field, and k is larger than unity in an electric field lower than 4.2 x I05 V/cm. The present data seem to disagree with Pearsall's data in regard to ionization coefficient value as well as in regard to the value of k obtained. Ito et aL determined ionization coefficients by using a mesa type GaAs p+n avalanche photodiode made by Zn diffusion[12]. The n-layer carrier density was 1.2 x 1017cm-3 and ionization coefficients were measured in the electric field region above 4 x lO~V/cm, Although the magnitude of their hole ionization coefficient agrees with the present data, their k value is larger than unity, which disagrees with the present work. These ionization coefficient data have been evaluated by measuring multiplication factor dependences on bias voltage for pure electron and pure hole injections. However, there is still confusion and uncertainty among the data. In these experiments, precise measurement performance, such as pure hole and pure hole injection into the same avalanche multiplying region and multiplication factor correction for depletion layer stretching, as well as uniform avalanche multiplication in the photosensitive area, are required to be achieved. The discrepancies among the data are thought to be caused by these measurement errors to some degree, In the present work, a new approach to the ionization coefficient estimation was made. The major difference of this work from previous ones lies in that our ionization coefficient ratio was estimated from the multiplication noise measurement, which is free from the experimental errors in the previous measurements. The result that the electron ionization coefficient is larger than that of

634

H. ANDOand H. KANBE

holes was obtained independently by measuring the multiplication factor dependence on light wavelength and multiplication noise measurement. Electron ionization coefficients, evaluated independently for the diodes with different No values in different electric field regions, agree with each other as a function of I/E, as is shown in Fig. 9. Breakdown voltage, calculated by using the ionization coefficients, shows good agreement with that measured by several authors[9, 11], as shown in Fig. 12. The solid line in Fig. 12 is the breakdown voltage dependence on carrier density No calculated from the ionization integral, assuming eqns (7) and (8) as a and/L respectively, while several symbols show measured values. From the above considerations, the result that the electron ionization coefficient is about" two times larger than that of holes is considered to he valid.

coefficient than the other. Recently, the result that the hole ionization coefficient ratio is larger than that of electrons in InP has been observed from our multiplication noise measurement[24]. It is concluded that pure electron injection into the avalanche region is preferable to minimize multiplication noise in GaAs avalanche photodiodes. The multiplication noise, however, is essentially higher than that of Si, because the ionization coefficient ratio k in GaAs is about 0.5, independent of carrier density and electric field strength.

6. CONCLUSION Ionization coefficients for electrons and holes in GaAs in the (100) direction were estimated by using p+-n type avalanche photodiodes with various n-layer carrier densities No from 6 × 1015 to 9 × 1016cm-3. Multiplication noise measured for the diodes was proportional to the 2.7th power of the multiplication factor, when pure electrons were injected into the avalanche region. The corresponding ionization coefficient ratio k =/3/a is about 0.5 in 2.4 × 105-5.6 × 105 V/cm electric field range. These observations are consistent with the dependence of multiplication factor on optical wavelength, that is, the multiplication factor decreasing with increasing optical wavelength. Ionization coefficients a and ~ were estimated from the applied voltage dependence of the multiplication factor for pure electron injection into the avalanche region, assuming that the ionization coefficient ratio k is constant, and is independent of the electric field. The ionization coefficients are exponential functions of l/E, and are independent of the n-layer carrier density. The method adopted in the experiment is useful in determining which type of carrier has a larger ionization

I. T. P. Pearsall and M. Papuchon, Appl. Phys. Left. 33, 640 (1978). 2. Y. Matsushima, K. Sakai, S. Akiba and T. Yamamoto, AppL Phys. Left. 35, 466 (1979). 3. N. Susa, Y. Yamauchi and H. Kanbe, IEEE J. Quantum Electron. QE-16, 542 (1980). 4. Y. Takanashi and Y. Horikoshi, Japan, J. AppL Phys. 17, 2065 (1978). 5. H. D. Law, L. R. Tomasetta and K. Nakano, Appl. Phys. Lett. 33, 920 (1978). 6. T. Kagawa and G. Motosugi, Japan. J. Appl. Phys. lg, 1001 (1979). 7. H. D. Law, L. R. Tomasetta, K. Nakano and T. S. Harris, Appl. Phys. Lett. 33, 416 0978). 8. G. E. Stillman, C. M. Wolfe, J. A. Rossi and A. G. Foyt, Appl. Phys. Lett. 24, 471 (1974). 9. H. D. Law and C. A, Lee, Solid-St. Electron. 21,331 (1978). 10. T. P. Pearsall, R. E. Nahory and I. R. Chelikowsky, Phys. Rev. Lett. 39, 295 (1977). 11. F. Capasso, R. E. Nahory, M. A. Pollack and T. P. Pearsall, Phys. Rev. Lett. 19, 723 (1977). 12. M. Ito, S. Kagawa, T. Kaneda and T. Yamaoka, J. Appl. Phys. 49, 4607 (1978). 13. M. P. Mikhailova, N. N. Smirnova and S. V. Slobodchikov, Soy. Phys. Semicond. 10, 509 (1976). 14. O. Hildebrand, W. Kuebart, R. Deufel, K. W. Benz, I. Strottner and M. H. Pilkuhn, 37th Ann. Device Research Conf., TP-C13 (1979). 15. C. A. Armiento, S. H. Groves and C. E. Hurwitz, AppL Phys. Lett. 35, 333 (1979). 16. T. P. Pearsall, Phys. Lett. 3, 218 (1980). 17. R. J. Mclntyre, IEEE J. Quantum Electron. ED-13, 164 (1966). 18. Y. Yamamoto and H. Kanbe, Japan, J. Appl. Phys. 19, 121

Acknowledgement--Theauthors wish to thank Drs T. Kimura, O. Mikami and N. Susa for their useful discussion, and Dr. Y. Yamamotofor zinc diffusion.

REFERENCES

(1980).

~ 100

i

. CALCULATED

z O

II PRESENT DATA o : C A P A S S O e t at X : L A W e*~ aL

uJ n-

i

,

i ll,,it

1015

",,,w.

i

1016 CARRIER

DENSITY

i

I i ,,.,I

,

,~,

1017 NO ( c m -3)

Fig. 12. Breakdown voltage V~ vs n-layer carder density N~. Solid line shows calculated Vs by using eqns (7) and (8).

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