Sensitive high speed photodetectors for the demodulation of visible and near infrared light

Journal ot Luminescence 7 (1973) 390 414. North-Holland Publishing Company

SENSITIVE HIGH SPEED PHOTODETECTORS FOR THE DEMODULATION OF VISIBLE AND NEAR INFRARED LIGHT H. MELCHIOR Bell laboratories, Murray Hill, NJ. 07974, USA.

Photomultipliers. solid state photodiodes and avalanche photodiodes are the preferred detectors for the demodulation of light intensity variations at visible and near infrared wavelengths. The principles of operation of these detectors will be described together with their basic construction and operational characteristics. Photomiltipliers with the recently developed high efficiency photocathodes for visible and near infrared wavelengths and the high gain dynode arrangements with fast speed of response will be mentioned. The various types of silicon and germanium photodiodes with and without internal current gain will be discussed. Tradeoffs involved in the optimization of quantum efficiency, speed of response, internal current gain and sensitivity to weak light signals will be treated in detail for silicon photodiodes operating at wavelengths either in the visible or at the GaAs (—P0.7 0.9 Mm) or YAG (1.06 Mm) infrared laser emission lines. The capabilities of germanium avalanche photodiodes for the detection of infrared light at wavelengths up to about 1.6 ~.smwill be mentioned.

1. Introduction The invention of the laser and its promise as a communications source has greatly stimulated the entire field of photodetection [1 4]. New detection techniques became practical, such as optical mixing or heterodyne detection at longer wavelengths in the infrared. Novel types of photodetectors emerged. A pressing need arose for the development and the perfection of photodetectors with high sensitivity to weak lights signals and response to light intensity modulations at frequencies extending into the microwave region. Great progress has been made, both in the technology of detector materials and in the understanding of their basic device physics. It is now possible to design photodetectors and entire optical receivers with highly optimized performance for various light wavelengths and speed of response combinations. This paper gives a review and discussion of high speed photodetectors and optical receivers with good sensitivity to weak light signals in the visible and infrared wavelength range between 0.4 and 1.6 ~.tm.After an enumeration of the performance criteria for photodetectors and optical receivers high speed photodetectors will be discussed with particular emphasis on the influence of materials technology and device design on detector performance. Photomultipliers with the new high sensitivity, 111-V semiconductor photocathodes and high gain dynodes will be described. 390

H. Meichior, Sensitive high speed photodetectors

391

The optimization of silicon and germanium photodiodes for various wavelength and speed of response combinations will be described and the use of internal current gain in avalanche photodiodes will be advocated as a means to increase the sensitivity to weak light signals in solid state optical receivers with large signal bandwidths and high speed of response.

2. Performance criteria Any photodetector with some response at a particular wavelength might be useful for some applications. A well designed optical receiver which consists usually of a photodetector with an amplifier at its output requires however a carefully chosen photodetector and proper optimization of both the photodetector and amplifier [1 8]. The major requirements for a photodetector and optical receiver with high performance include: (1) large response at the wavelength of the incident optical signal; (2) sufficient electrical bandwidth, i.e., speed of response, to accommodate the information bandwidth of the incoming signal; (3) minimum excess noise introduced by the detection and amplification process. Large response requires a photodetector with a high quantum efficiency at the wavelength of operation and negligible internal shunt conductance for the electrical output signal, (1) opt

and gives the number of photocarriers (‘~h/~) collected per unit time in response to the number of photons (P0~Jhv)incident per unit time with energy hu. Resolution of optical signals with large information bandwidth or short duration requires optical receivers with wide electrical bandwidth and high speed of response. The electrical bandwidth or speed of response of an optical receiver is limited either by carrier transport or multiplication processes within the photodetector or by RC time constants within the photodetector and output amplifier [1 4]. Minimization of both the photodetector (C1) and amplifier input capacitance (CA) is mandatory if the photosignal is to develop a high output voltage across the largest possible load or amplifier input resistance. Realization of the risetime T,. or information bandwidth B of an optical signal limits the resistance RA of the photodetector load or amplifier input to a value lower than RA

Tr 1 ~<2.3(CI+CA) or RA ~<2~(CJ+CA)B~

(2)

While high speed of response and adequate quantum efficiency is all that is required for the detection of fast optical signals as long as their intensity is relatively

392

H. Meichior, Sensitive high speed photodetectors

high, the demodulation of weak optical signals requires in addition minimization of the parasitic current and noise sources within the photodetector and output amplifier [1 8]. But even in an ideal optical receiver with unity quantum efficiency and no extraneous noise sources, the sensitivity to weak light signals is limited, by fluctuations in the photoexcitation of carriers [9 Il]. Since the number of photocarriers released within a period of time fluctuates statistically, usually in accordance with a Poisson distribution [9 12], there is a mean square noise current

=

(3)

2q’~,h~.”

(with ôf= electric bandwidth and q = unit electronic charge) associated with the average photocurrent ‘ph [1 4]. Assuming an ideal optical receiver and a threshold that counts even single carriers, the average number of photons in an optical pulse has to be at least o

=

2.3 log \error1 ratej

(4)

if its presence is to he detected subject to a given error rate [121 Practical receivers hardly ever reach this so called quantum noise limited sensitivity [1 4]. Especially in receivers with large electrical bandwidth and photodetectors without internal current gain, the sensitivity is much lower and usually limited by the noise of the load or output amplifier [1 4]. A significant improvement in sensitivity is possible if the photocurrent is amplified within the photodetector before it reaches the large noise sources at the output [1 4]. Practically useful current gain mechanisms with relatively low excess noise and high speed of response capability include carrier multiplication in photomultipliers and avalanche photodiodes. Phototransistors and photoconductors too [1 4] exhibit large current gains with low excess noise at somewhat slower speed of response. Detection of the weakest possible optical signals requires optimization of the photodetector and optical receiver subject to the constraints that either the signal bandwidth and a given signal to noise ratio be maintained or that the presence or absence of the signals which arrive at a given rate be determined with a certain error rate. The power signal to noise ratio at the output of an optical receiver which contains a photodetector with internal current gain and a noisy amplifier is given by [1 9] i 2M21A(W)12 ph

IYJ+YAI2

N~j2~2~2~ 2

(5)

H. Meichior, Sensitive high speed photodetectors

PHOTODETECTOR

393

AMPLIFIER

Fig. 1. Equivalent circuit of generalized optical receiver shows the principal signal and noise sources of a photodetector with internal current gain and a noisy output amplifier.

and includes the signal and noise sources of the generalized equivalent circuit of fig. 1. The multiplied signal zPh2M2 of the photodetector with internal current gain M has to override the noise sources of the photodetector and amplifier. The noise sources of the photodetector include the mean square value i~ = 2q(J~ ~‘B +ID)M2F(M)6f of the multiplied shot noise which is due to the average photocurrent (‘ph)’ the background radiation induced photocurrent (1B) and the part of the dark current (ID) that is multiplied within the photodetector. The factor F(M) accounts for the increase in that noise induced by the current gain process within the photodetector. For high gain photomultipliers this noise factor is quite low; F 1.5 3 [1 4]. In avalanche photodiodes the noise factorF(M) increases with carrier multiplication as will be pointed out in more detail later. For well designed phototransistors and photoconductors this noise factor can be as low asF = 2 [2 4]. Possible noise due to the non-multiplied dark current and any shunt and load conductance at the output of the photodetector is accounted for by the noise source i 2. The internal admittance of a well designed photodetector Y 1 1 is mainiy capacitive (C1). The output amplifier is represented in fig. I by a noise-free amplifier with input admittance ~A = GA +jWCA and voltage gain A(w) and a set of noise sources which give a complete representation of the noise of the amplifier [13]. In this particular case the amplifier noise is in accordance with Rothe and Dahlke [13] represented by a noise voltage source in series with its input, an uncorrelated noise i~jin to parallel withvoltage the input and v~by a noisethe current 2thatcurrent is fullysource correlated the noise source comsource v3~ Y~,I admittance Y~ ReYc +jImYc. plex correlation High sensitivity and a large signal to noise ratio requires low background and dark currents within the photodetector and an output amplifier with the lowest possible noise. Reduction of the influence of the major amplifier noise source v~, i.e. keeping

394

H. Meichior, Sensitive high speed photodetectors

j(~3)YJ+YCI2df(~+~÷~df

(6)

is possible by using a first amplifier stage with large transconductance and a much higher input resistance RA than compatible with eq. (2) [6 81. The full signal bandwidth and pulse shape can be restored by differentiation of the amplified signal at a later stage in the amplifier provided the amplifier is sufficiently fast to follow the voltage rise at the input [7]. As can be seen from eq. (6) minimization of the major noise contribution of the amplifier is greatly aided by low photodetec tor (Y1) and cross-correlation admittances (~c)~ Current gain within the photodetector helps raising the signal level above the amplifier noise in cases where the amplifier is designed in accordance with eq. (2) to pass the full signal bandwidth at its input and in wide bandwidth cases where the amplifier is designed to keep noise extremely small. The highest sensitivity is reached, when the current gain M reaches (or exceeds) an optimal value determined from = 0, i.e., when as much current gain is used such that the multiplied shot noise of the photodetector reaches (or exceeds) a level comparable to the amplifier noise [1 4].

3. Photomultipliers As indicated schematically in fig. 2 photomultipliers consist in essence of a photocathode which emits electrons in response to incident optical radiation, a chain of secondary electron emission dynodes for the multiplication of the photo-excited electrons and an anode to couple the multiplied electron current to the output circuit. Major advances in the technology and a better understanding of the operation of photoemitters and secondary electron emission dynodes have lead to the development of new photomultipliers with greatly improved performance. The introduction of a new type of photocathode, the cesiated GaAs photoernitter by Scheer and Van Laar [14] has led to an entire family of new Ill-V compound photocathodes [15, 16] with substantially improved sensitivities, especially at longer wavelengths in the near infrared. Similarly constructed GaP/Cs dynodes [17] with high secondary electron emission gain made possible photomultipliers with lower excess noise and a smaller number of dynode stages. Special dynode arrangements, which minimize the time of flight differences of the electrons resulted in photomultipliers with electrical bandwidths extending into the GHz region [18, 1 3]. Electrostatically focused photomultipliers are now available with speeds of response as short as 300 ps [19]. These conventional photomultipliers are compact in size, use small high sensitivity photocathodes and have dynodes whose configurations have been chosen with the help of a computer to minimize the time broadening effects on the electron cloud.

H. Meichior, Sensitive high speed photodetectors

395

INCIDENT LIGHT

PHOTOCATHODE DY NODE

ANODE ELECTRICAL OUTPUT

Fig. 2. Schematic view of a photomultiplier with photocathode, conventional electrostatically focused dynode chain and coaxial anode output.

The new Ill-V compound photocathodes and dynodes basically consist of a heavily doped p-type semiconductor whose surface is either coated with a thin monolayer of cesium or with a somewhat thicker Cs20 layer as indicated in fIg. 3. Bandbending near the surface of the semiconductor occurs due to the adsorption of positively charged cesium ions [14—16,20,211 or due to the formation of a heterojunction between the Ill-V semiconductor and the Cs20 layer [16, 22, 231 and leads to a lowering of the work function and to an effectively negative electron affinity. An effectively negative electron affinity (combined with a sufficiently low interfacial barrier at the heterojunction [231)allows electrons thermalized at the bottom of the conduction band to escape into the vacuum. The escape depth for electrons is quite large (of order 1 jim) because electrons which diffuse to the bandbending region have sufficient energy for emission into the vacuum. Negative electron affinity photocathodes with low interfacial barriers should thus have a high quantum efficiency for all photon energies a few tenths of an electron volt larger than the bandgap [16]. Narrowing of the bandgap of the photoemitter extends the photoresponse to longer wavelengths in the infrared. As an indication of the present state of the art, fig. 4 and table 1 compare the spectral response, quantum efficiency and dark current densities of these new 111-V semiconductor photoemitters with some of the best conventional photocathodes.

396

H. Meichior, Sensitive high speed photodetectors

BAND BENDING REGI ON

CONDUCTION BAND

-‘

NEGATIVE EFFECTIVE ELECTRON AFFINITY VACUUM LEVEL BAND

)_S~’

GAP

WORK FUNCTION FERMI LEVEL

+ VALENCE BAND

P TYPE SEMICONDUCTOR

CESIATED SURFAcE

/

INTERFACIAL

IONIZED DONORS

+ BAND GAP

~

P TYPE SEMICONDUCTOR

COMPOSITE WORK FUNCTION

Cs

2O

Fig. 3. Idealized energy-band diagrams for cesium (top) and Cs20 (bottom) covered Ill-V corn pound p-type semiconductor photocathodes.

The negative electron affinity photocathodes show a higher quantum efficiency, both in the visible and in the infrared. At the GaAs laser wavelength of 0.87 pm the 18% quantum efficiency of a GaAs (Cs) photocathode [20] compares favorably with the 2% efficiency of an extended red sensitive multialkali (ERMA) cathode [24]. At the 1.06 pm YAG laser wavelength, the highest reported quantum efficiencies of 2 3% of the developmental Ga1 ~In~As(Cs) [20] and InAs1 ~P~(Cs) [21] photocathodes are more than 10 times larger than for the best S-I infrared photocathodes.

H. Meichior, Sensitive high speed photodetectors

397

GaAs /C5

20

100

~I-

InA504P06/Cs20

_—

0.1

0.6

0.8

—

—

—

.0

1.2

WAVELENGTH, MICRONS

Fig. 4. Responsitivity spectrum and quantum efficiencies of highly developed commercial photocathodes (S-i, S-20, ERMA, GaAs/Cs20) and developmental infrared sensitive photoemitters (lnAs1 ~1~/~’ Cs20, Ga1 xInxAs/ Cs20).

4. Photodiodes Solid-state photodiodes, phototransistors [4, 28 30] and avalanche photodiodes contain as an essential element a depleted semiconductor region with a high electric field that serves to separate photoexcited electron-hole pairs. As discussed also by Moss in the preceding paper, these junction photodetectors usually operate in the wavelength range where absorbed photons excite electron-hole pairs through band to band excitation. High speed photodiodes are usually connected to relatively low impedances so as to allow the photoexcited carriers to induce a photocurrent in the load circuit while they are moving through the high field region. Photodiodes for the visible and near infrared range are commonly operated at relatively large reverse bias voltages, since this helps reduce the carrier drift time and lowers the diode capacitance without introducing excessively large dark currents. Operation in the photovoltaic mode, with open circuited terminals is possible, but not suitable for the

398

H Meichior, Sensitive high speed photodetectors Table 1 High-efficiency photocathodes

Cathode material Ag 0 Cs Si opaque or semitransparent

Quantum efficiency (%) 0.87gm 0.63 pm

1.06 pm

Dark current density (A/cm2)

Reference

0.07

< 10

12

[15]

< 10

‘~

[151

0.3

0.7

2KSb Cs S-20 semitransparent

6

0.2

Extended-redsensitive-multi alkali (ERMA) semitransparent

12

2

10

‘~

[241

GaAs/Cs20 25 opaque [semitransparent]

18

10

14

1141 25] [161 1201

Na

261 lnAs013P087/Cs20 opaque

16

9

3

Ga1 XlnXA~~/(’s2O x’—0.i4 0.31

12

8

2

[21] [27] [23] [25]

1161 120]

demodulation of high speed signals. A charge integration mode [28] by which a photodiode or phototransistor is preset by a reverse bias voltage and then open circuited to allow integration of the signal and dark current is often useful, especially in detector arrays [29]. The operation of a reverse biased p-i-n [31] photodiode with a load resistance RL is illustrated in fig. 5. Incident light which is not reflected at the surface penetrates some distance into the photodiode material before it is absorbed and generates~photocarriersas indicated by the light absorption or pair generation characteristic of fig. 5. Electrons and holes generated within the high field region (W) of the junction and minority which diffuse from the p and n bulk regions to the junction before recombination are collected across the high field region and contribute to the photocurrent at the output. Carriers generated in the bulk regions, on the average within a diffusion length L~or L~respectively from the junction edges can diffuse to the high field region and will be collected.

H. Meichior, Sensitive high speed photodetectors

399

VREVERSE DEPLETION LAYER p

ELECTRIC FIELD

~

Iph

CON~~T ION

C-)

hi’

hi’

BAND VALENCE

ELECTRON DIFFUSIOP~1

DRIFT SPACE

~-~--‘

DIFFUSION

BAND

~I~Rle~

iia EABSORPTION OR PAIR GENERATION CHARACTERISTIC

Fig. 5. Operation of solid state photodiode. Cross-sectional view of p-i-n diode and energy-band diagram under reverse bias conditions is shown together with optical absorption or pair generation characteristic.

High quantum efficiency requires minimization of the light reflection off the diode surface and placement of the junction in such a way that most of the photoexcited carriers are collected across the junction region. Low reflectivities (R) are usually achieved by means of antireflection coatings as indicated for various diodes

ANTIREFLECTION COAT INS ,-METAL (CONTACT

___

~

\J_1~I 0+

ID)

p—n DIODE

ANTIREFLECTION COATING 11025 ASOsI

+~~ETION LATER

~TM

________________ I ________________

Ib)

_______________

NTIREFLECTION ~

~ II33~m

Id p i-n DIODE (SI OPTIMIZED FOR O.63~m1

Fig. 6.

METAL (CONTACT II’

hi~~TING

(I fl+J REFLECTION COATING

--.~AL FOR CONTACT \MET AND LIGHT REFLECTION

P-I-N DIODE PARALLEL WITH (dl DIODE METAL—SEMICONDUCTOR ILLUMINATION TO JUNCTION

Construction of high speed

photodiodes.

400

H. Meichior, Sensitive high speed photodetectors

in fig. 6. Most photodiodes are designed for light incidence normal to the junction plane. A large carrier collection efficiency then requires the carrier collection width Wco~ L~+ W + or W~+ W + W,~,whichever is smaller, to be comparable to or larger than the average penetration depth (1/n) of the light. Specifically, for a W~011~ 1.5 a collection efficiency of 78% or more is achievable. —

Unfortunately, minority carrier 2/2.4 diffusion relatively process.or Ithole takes Dn, isp a(with Dn, pslow = electron difcarriersconstant, a time [32] TDfff = (Wn, fusion respectively) to p) diffuse through a region of thickness Wn, p. Carrier diffusion then limits the frequency response of the photocurrent to f3db ~

l/21TTD

1I.f [32]. As an example, electron diffusion through a 5 pm thick p-type silicon layer takes 3 ns and leads to a frequency limit of 50 MHz (hole diffusion takes 3 times longer). Although carrier diffusion within the quasi-neutral bulk regions can be speeded up (by factors of 2 6) with fields associated to doping gradients [33], diffusion regions have to be kept narrow in high speed photodetectors. Fast photodiodes are generally so designed, that carriers are mainly excited within the high field region of the junction [31, 34] or so close to it, that diffusion times are shorter or at least comparable to the carrier drift times. At sufficiently high reverse bias voltages, carriers are then collected at scattering limited velocities v~across the high field region (W) of the junction. Carrier transit times2.7SI2~Ttr can be as short as Ttrfields = W/Vsat and of the2frequency response as highlimited as.t3dbvelocities = [34]. For in excess X ~ V/cm, wherelimit scattering of order 5 )< 106 1 0~cm/sec are reached in silicon and germanium, carrier transit times through thin, 1 pm thick depletion regions can be as short as 10 ~ sec. More detailed quantum efficiency and pulse and frequency response calculations for particular diode structures various light penetration depths and different surface boundary conditions can be found in References [31 34] and [36 40]. The actual quantum efficiency and speed of response of photodiodes depends strongly on the wavelength of operation and on the diode material and design. The choice of a particular detector material is primarily determined by the wavelength of operation. Light absorption coefficients for a variety of photodetector materials for the 0.4 1.6 pm region are shown in fig. 7(4, 411. Because of their highly developed technology, silicon photodiodes are preferably used in the near ultraviolet, visible and in the infrared up to about 1 pm. With germanium diodes the response can be extended beyond 1.5 pm. Other materials like GaAs, CdTe, CdSe and CdS are only considered for special applications. As can be seen from fig. 7, the light absorption coefficient of silicon, which is an indirect gap material, changes gradually as a function of wavelength. As a consequence of the strongly varying light penetration depth, silicon photodiodes, as well as phototransistors and avalanche photodiodes, have to be optimized for particular wavelength and speed of response combinations. The simplest planar ptn photodiodes of the type shown in fig. 6a, with space charge layer widths between about 1 and 3 pm, are optimal for light absorption coefficients between 5 X iO~cm 1 and 2 X 106 cm 1~For Si this correponds to

H. Meichior, Sensitive high speed photodetectors

401

IO~

iO~

3—

zIO 2

1-100

I\\I

I—

I

I -

I

(I)

tI~

I

-

.

__~~‘SI

~ 4

~

~ z

77~K-~.~j I~ O

0 2_

-CdS

14/

-J

I

IICdSe

\\

-J

300°K

-

I

-

I0~ 0.4

10 2~ 0

~

\

77K

I 0.6

0.8

IO~ 1.0

1.2

1.4

1.6

WAVELENGTH [p.m] Fig. 7. Light absorption coefficients of photodetector materials for the visible and infrared range between 0.4 and 1.6 pm (Si and Ge data from [41], for other materials see refs. in [41).

a wavelength range from 0.45 to 0.6 pm and for Ge to a range between 0.95 and 1.5 pm. Fast response in the i0Ops region is possible for small area junctions of this type, as can be seen from table 2. The quantum efficiency of such a Ge n+ ~p diode is 40 to 50% as shown in fig. 8 but could be higher if proper antireflection coatings were used. At short wavelengths (< 0.5 jim for Si) light is absorbed very close to the semiconductor surface. Recombination of photon-excited carriers at the surface and in the shallow highly doped bulk n~or p~layer then results in a low quantum efficiency [36, 39] even if the built-in fields do not hamper [39], but help [33] carriers to reach the junction. At short wavelengths, metal-semiconductor junctions with properly antireflection coated semitransparent metal layers are more useful [42, 43]. Extremely high speeds of response and good quantum efficiencies are possible if the depletion regions are small and thin, comparable to the light penetration depth. Towards longer wavelengths, where light penetrates deeper into the semiconductor material, various front illuminated p~-i-n~ and metal-semiconductor structures

0.5

0.4

0.38

Sip-in with antireflection coating

Sip i-n with antireflection coating

Au i-n Si

10

60

2.5 )< It)

2

10 ~ at 77°K 10 ~ at 300°K

3

0.6

Ge pin with side illumination

1.65

0.8 at 16V

10 ~

2 x 10 8 at 1OV and 300°K X

50

0.6

Gentp (uncoated) avalanche photodiode

2

1.8 at 300 V

10 V

4 at

4S V

10 nA at 1110 V

10

10 V

3 at

45 V

S V

90 at 1 pm

10

5 X 10 at 45 V

1

3 at

at

<

(pF)

Capacitance

Sip-n with side illumination

2

5 x 10 8 at 45 V

< 10 ~ at 40 V

Dark current (A)

at

1.65

X

10

x 2

10 ~

x

2 X 10

2

70 at 1.06 pm

> 70

2

2

Light sensitive area 2) (cm

90 at 0 9 pm

>90 at 0.6328 pm

Peak quantum efficiency (%)

Schottky barrier with antireflection coating

0.8

1.1

—0.7

Wavelength range (JJm)

Diode

Table 2 High speed photodiodes

2Sns at 500 V

120 ps for lOV and 50 ohm load

< 500 ps

Sns for 10 V and 50 ohm load

2Ons for 200 V and 50 ohm load

3ns for 45 V and 50 ohm load

100 Ps with 50 ohm load

Pulse response time

[7]

[48]

[47]

ogy

United Detector Technol-

RCA Montreal

[441

References

‘5

-‘5

‘5

-~

‘5

H. Meichior, Sensitive high speed photodetectors

403

100 c-METAL _~ \IAu—i~n~ -

\

\,_Si p—i—fl. ANTIREFLECTION COATING FOR 0.6328/tm. W 1 .3.3/tm

/

\

\

\

\

N.

Si a—I—fl WITH WIDE DEPLETION REGION W, ANTIREFLECTION COATING FOR 0.9/tm ANTIREFLECTION COATING FOR 1.06/tm UNCOATED

80 -

N -\

rae

W -0.1mm ~W1-O.7mm~ W1-3.2mm

SIDE ILLUMINATED p-I-fl

~

~

~6O~

X

-

\

-

‘~

I

~—

TOO mAtW

.~

~\

I

N

~4O-

~8OO~A/W ..-...

N

/

“

~

\

N

\/

-~--

~

600 mA/W

°°..

I

‘~—

N

~5OOmA/w

—..

~-.

N.

2

~4O0n’A/W

—~

.~ ~

0

-

I..-

....

—

~

300 mA/W

I 20

..~

~~20On,A/W

-~

IOOmA/W_

-

UNCOATED

I 003

I 0.5

I

I 0.7

—

RESPONSiv~TY

I

I

I

I

0.9 1.1 WAVELENGTH, MICRONS

I

I .3

— —

I

I 1.5

—

I

I .7

Fig. 8. Quantum efficiency and spectral responsivity of several optimized high speed photodiodes.

with wide depletion regions can be used. Fig. 6b shows such a Si p~ j ~ structure [44] that has been optimized for 0.6328 pm. These diodes have quantum efficiencies exceeding 90% (see fig. 8) and, if mounted in a coaxial header [2, 37, 42], they can resolve optical pulses with 100 ps rise time. Front illuminated Si p-i-n diodes [45, 46] with high quantum efficiencies (>70%) at the GaAs (0.85 0.92 pm) and YAG (1.06 pm) wavelengths require depletion layer widths of 20 50 and 500 pm, respectively. With such wide depletion regions, the carrier drift transit times become relatively long, as can be seen from table 3. At wavelengths close to the band edge, a better compromise between quantum efficiency and speed of response can be achieved if light is allowed to penetrate from the side, parallel to the junction, as indicated in fig. 6c. A silicon photodiode of this type has been built [471 and is listed in table 2. Side illuminated Ge p-i-n diodes with higher quantum efficiency at wavelengths close to the band edge than front illuminated Ge nt-p [48] and Ge p-i-n [31] diodes have been built [7] and are listed in table 2 and fig. 8. A different design approach, which stresses highest possible quantum efficiency over an extended wavelength range at the expense of speed of response (especially

~

Si ~

p

88

Pt GaAsO.4 Schottky barrier

1.1

1.1

1.1

1 65

0.6

0.6

0.5

Ge ti~p 0.8

Sip-n side illu minated

-i

~in

-f

0.4

Si n~-p

0.8

Wavelength range (pm)

Diode

x 10

>100

2 X 10

2 X 10

2

Light sensitive 2) area (cm

200

200 at 300°K 10~at 80K

200

10

i04

low

V

X

X

1

0.3

0.5

Maximum current gain Noise factor F ~ Mx

>50

60

30

Not very high

100

60

16.3

200

200

200

23

230

500

2000

Current gainpro- voltage Breakdown bandwidth (V) duct (GHz)

Table 3 Avalanche photodiodes

~at

10 8 at 100 V

boy

10

5 X 10 ~ atI0V

1701

[68]

[69]

[52]

Ref.

71]

0.08 at is V 10 ~ at [48] 10 V.300 K 7 X 10 10at ID V 250°K

1 at 200 V

2 at 200 V

0.8 at 23 V

Capacitance Dark (pF) current (A)

0-

0

H. Meichior, Sensitive high speed photodetectors

405

at short wavelengths) has resulted in metal-semiconductor diodes (Gold-silicon) with wide depletion regions as shown in figs. Sd, 8 and table 2. As can be seen from fig. 8 and table 2, a number of Si and Ge photodiodes are available with high quantum efficiencies and high speed of response. These photodiodes, as well as other solid state detectors are relatively small in size. Typical diameters of the light sensitive areas are between 20 and 500 pm. Small size helps keep the diode capacitance and dark currents low. Dark currents, which limit the sensitivity to weak light signals, originate either from the bulk or from the surface. Surface leakage currents are a problem especially in high resistivity Si devices and in planar, oxide covered Ge diodes. Special surface treatments and various guard ring structures and surface contours are employed to reduce these surface leakage currents. Bulk leakage currents in Si are mainly due to carrier generation within the space charge layer. For carefully processed silicon diodes generation currents as low as 10 6 10 8 A per mm3 of depleted volume have been reached [39, 45, 46]. In germanium diodes the bulk leakage current is mainly due to minority carrier diffusion to the junction.

5. Avalanche photodiodes

Avalanche photodiodes are specially constructed photodiodes which combine the detection of optical signals with internal amplification of the photocurrent. Internal current gain takes place in an avalanche photodiode when carriers gain sufficient energy by moving through the high field region of a highly reverse biasedjunction to release new electron-hole pairs through impact ionization [49]. High current gains are possible by this process [50], event at microwave frequencies [51, 52, 48]. The typical operation of an avalanche photodiode is illustrated in fig. 9, where the voltage dependence of the dark current of a germanium avalanche photodiode as well as the response to puhes from a phase locked 0.6328 pm He Ne laser are shown. At low reverse bias voltages, where no carrier multiplication takes place, the diode operates as a regular photodiode. As the reverse bias voltage is increased, carrier multiplication sets in. as indicated by an increase in the current pulse. The highest amplitude of the photocurrent pulse is reached, when the diode is biased to the breakdown voltage. At higher voltages above the breakdownvohage,a self-sustained avalanche current flows which makes the diode less and less sensitive to photon-excited carriers. The highest gain for the photocurrent is limited either by premature breakdown spots, by spatial inhomogeneities within the avalanche region or more fundamentally by current induced saturation effects [48, 53] and by a current gain bandwidth product [1, 48, 54, 55]. The current gain is influenced by the magnitude of the avalanche current because carriers that emerge from the multiplication region reduce the electric field within the junction and lead to voltage drops across the series and load resistance of the diode. At high light intensities these voltage drops cause the

406

H. Meichior, Sensitive high speed photodeteetors

GERMANIUM PHOTOD ODE HENE LASER

X

6328A Tp~.6flS

~-L0WER MULTIPLICATION

OF PHOTOCURRENT

HIGHEST MULTIPLICATION OF PHOTOCURRENT

-

—

I—

z

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.Sns

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2

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-~

AMPLITUDE OF MULTIPLIED

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I

PHOTOCURRENT I

6

8

10

12

VOLTAGE[V]

14

4 0

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1 ig. 9. Current voltage characteristics and pulse response of germanium avalanche photodiode.

multiplied current to increase on1y as the square root of the photocurrent [48, 53] instead of being proportional to the photocurrent. For low light intensities, the dark current can set a limit on the highest average carrier multiplication that can be

reached at low frequencies. The highest carrier multiplications of 200 in germanium avalanche diodes at room temperature are e.g. limited by dark current [481. For short optical pulses the current gain of silicon and germanium avalanche photodiodes is limited by a current gain bandwidth product, which is inversely proportional to the width of the carrier multiplication region and depends on the ratio between the electron hole ionization coefficients and on the type of carriers that initiates the avalanche [3, 4, 55]. Current gain bandwidth products between 20 100 GHz have been reported for various silicon and germanium avalanche photodiodes as can be seen from table 3.

The temporal build-up and decay of the multiplied current flowing through the short circuited output of an avalanche photodiode in response to excitation with a

short optical pulse is shown schematically in fig. 10. As indicated the optical pulse generates electron-hole pairs throughout the entire width of the junction. Due to the

electric field the electron-hole pairs become separated. The electrons move towards the multiplication region where they free new electron hole-pairs through impact ionization. Since both the secondary electrons and holes give rise to ionizations in

H. Melchior, Sensitive high speed photodetectors

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4PHOTOCURRENT ?hv

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I

TIME~

—~

~.__.l_Teft.

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multi-

silicon and germanium [4, 49], an avalanche of carriers is initiated, that gives rise to a multiplied photocurrent which persists much longer than the initial excitation. The avalanche of carriers decays at the end of an optical pulse because avalanche photodiodes are usually operated at voltages below the self sustained breakdown region. For short optical pulses, the multiplied photocurrent reaches its peak value AA

‘‘ph

Tff

(7)

at the end of the optical pulse T~.The effective multiplication time constant Teff, i.e., the mean time of flight of carriers before a new ionization, depends on the width of the carrier multiplication region, on the magnitude of the electric field, on the ratio of the electron and hole ionization coefficients and on the type of carrier excitation [3, 4, 55]. The effective multiplication time constant is related to the current gain bandwidth product by [1, 4, 55] GB=2~.,

.

(8)

As an illustration for the high current gains, that can be reached even for very short optical pulses, fig. 11 shows the pulse response of an n~-pgermanium avalanche photodiode to 80 ps pulses from a 1.06 pm YAG laser. The lower trace of fig. 11 represents the peak photocurrent as a function of the relative optical pulse power for 1ow reverse bias voltages where no carrier multiplication takes place. The upper

408

H. Meichior, Sensitive high speed photodetectors

GERMANIUM PHOTODIODE Te~f~ 2.7ps 10 YALG:ND 3V LASER n.3 PULSES R—150fl X.I.06/im VB.I.

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0

Fig. 11. Pulse response of ntp germaium mesa avalanche photodiode as a function of the relative power of short optical pulses from a phase locked YAG laser.

tiace shows the maximum pulse amplitudes reached at the breakdown voltage. At moderate light intensities a maximum current gain of 30 is observed for the 80 ps pulses, consistent with a current gain bandwidth product of 60 GHz for these Ge diodes (see table 3). At high light intensities the multiplied photocurrent increases only as the square root of the primary photocurrent due to the current induced

saturation effects. The current gain of an avalanche photodiode fluctuates due to the statistical nature of the carrier multiplication process. Even for spatially uniform avalanche regions the statistical gain variations give rise to excess noise [54, 56] and to a degradation of the Poissonian distribution in the number of photo-generated carriers [57 110]. Measured noise factorsF(M) = i~/2qI~~rrf for various avalanche photodiodes with highly uniform carrier multiplication are shown in fig. 12 and found to be in close agreement with McIntyre’s [56] predicted increase of the mean square noise current with average current gain. For the injection of electrons only, the noise factor of a uniformly multiplying avalanche photodiode with an electron to hole ionization rate ratio of ai/j3 = 1/k increases as F(M)=M

(1 k)

‘M

M l\2

(9)

with carrier multiplication M [56]. In silicon avalanche photodiodes with a high a/is ratio electron injection which occurs for long wavelength excitation in an n~p diode leads to a low noise factor [54, 56, 60, 61]. For germanium avalanche photodiodes

H. Meichior, Sensitive high speed photodetectors

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bc

/

HOLE INJECTION

~

/

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/

a/f3~0.5 ELECT RON

~IO~

4 I~’

I

Si

I lO

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I

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100

bOO

AVALANCHE MULTIPLICATION FACTOR

Fig. 12. Measured noise factor F(M) as a function of carrier multiplication silicon [54, 60 631 and germanium [481avalanche photodiodes.

for highly uniform

with almost equal ionization rates for electrons and holes, the noise factor increases

proportional to the carrier multiplication, irrespective of the wavelength and type of carrier excitation [48]. If a silicon avalanche photodiode is excited with the wrong type of carriers, i.e., with holes in an n~-p diode at short wavelengths, the noise factor increases much steeper with carrier multiplication [61]. The design of avalanche photodiodes requires special precautions to assure spatial uniformity of the carrier multiplication over the entire light sensitive area of the diode [50].Microplasmas, i.e., small areas with lower breakdown voltages than the remainder of the junction and excessive leakage currents along the junction edges can be eliminated by various guard ring structures and other types ofjunction contouring as can be seen from fig. 13. Defect-free semiconductor material and cleanliness in processing helps in the fabrication of microplasma free junctions. Highly uniform carrier multiplications in excess of 106 have been reached in silicon [50, 52] and in cooled germanium avalanche photodiodes. In large area diodes, that are free of microplasmas, the spatial uniformity of the carrier multiplication is usually limited either by doping inhomogeneities of the starting material or by variations in the doping profile. The construction and performance characteristics of typical avalanche photo diodes are presented in fig. 13 and table 3. The simplest silicon avalanche photodiodes consist of an n~-pjunction with an n-type guard ring [52] as shown in fig. 13a. The breakdown voltage of these diodes [64, 65] is typically between 20 and 200 V and space charge layer thicknesses between 1.5 and 10pm render them especially useful for the detection of light in the 0.4 0.8 pm range. Since the diameters of the

(,

410

H. Meichior, Sensitive high speed photodetectors

hi’

hi’ METAL ~

___

a) Si GUARD RING STRUCTURE

~/~SIO2

b) Ge MESA STRUCTURE WITH

GUARD RING

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SIDE ILLUMINATED

STRUCTURE WITH

Si

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STRUCTURE

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Fig. 13. Construction of avalanche photodiodes.

light sensitive areas are typically very small, between 40 and 200 pm, these diodes have small capacitances at most a few pF. Similarly constructed germanium avalanche photodiodes [48] require mesa etching of the guard ring in order to reduce leakage currents. These ntp germanium avalanche photodiodes are the fastest photodetectors with internal current gain in the 0.9 1.6 pm wavelength region. A reduction in diode capacitance and elimination of the guard ring [66] is possible in diodes with a burned n~-pjunction that is surrounded by ann rmg as shown in fig. 13c [66].

H. Meichior, Sensitive high speed photodetectors

411

Extension of the response of high speed silicon avalanche photodiodes towards longer wavelengths around 1 pm has been achieved through the use of n+.p~ir~n [67, 68] (fig. l3d) or p-i-n [69] (fig. 13e) structures and for side illuminated p-n diodes (fig. 13) [70]. In the n~-p-ir-nstructure of fig. l3d, the multiplication is constrained to the narrow n+~pregion. The wide ir region acts mainly as a collection region for the photoexcited electrons. Since the avalanche is initiated with electrons, these photodiodes exhibit high current gain bandwidth products and low excess noise [60, 68]. Silicon avalanche photodiodes with high current gain and low excess noise are thus available for the wavelength range between 0.4 and 0.9 pm. Germanium avalanche photodiodes extend this wavelength range to about 1.6 pm. Despite the excess noise associated with the carrier multiplication process these avalanche photodiodes provide useful gain and significant increase in sensitivity in high speed optical receivers that are otherwise limited by noise of the output amplifier [1,4,48, 64]. The highest sensitivity for the detection of weak light signals is reached, when the current gain is adjusted to an optimal value at which the amplified shot noise of the photodiode becomes about equal to the noise of the amplifier [1,48, 54].

6. Conclusions It is a fundamental goal of the photodetector design and receiver optimization to reach quantum noise limited operation which results in the highest sensitivities for the detection of weak light signals with a given signal bandwidth or repetition rate. Towards this end, photomultipliers with their large internal current gain have long been established as the best, most sensitive detectors for the ultraviolet, visible and near infrared region to about 0.8 pm. With the appearance of new photomultipliers of much smaller size with more efficient photocathodes (quantum efficiency > 20%) and better designed dynode chains even higher sensitivities are possible throughout the visible and especially in the infrared, at present to about 0.9 pm, combined with speeds of response as short as a few hundred pico-seconds. Solid state photodetec-

tors, including photodiodes with and without internal current gain, and to some extent phototransistors and photoconductors have found an ever increasing numbei of applications throughout the visible and infrared region. Silicon and germanium photodiodes with their highly developed technology can be optimized for various wavelengths (in the 0.4 1.6 pm range) and speed of response combinations. They are the simplest, most rugged, cheapest detectors available for the demodulation of optical signals whose intensities are relatively high. Despite their excess noise and relatively large dark currents (at room temperature) silicon avalanche photodiodes start to rival the sensitivity of photomultipliers throughout the visible range and exceed it already in the infrared around 0.9 and 1.06 pm. Germanium photodiodes, which operate in the 0.8 1.6 pm range have (as yet) no counterpart in photomultipliers towards the longer wavelengths.

412

H. Meichior, Sensitive high speed photodeteetors

Undoubtedly, as materials technology progresses and device designs are refined, further improvements in quantum efficiency, speed of response, sensitivity and reduction in dark currents and capacitances can be expected. Photocathodes with practically useful quantum efficiencies (at present 3.5%) at 1.06 pm might become available. GaAs photodiodes with internal current gain [71] might outperform silicon devices in the 0.8 0.89 pm range. And last, but not least, new devices, like avalanche photodiodes which multiply only one type of carriers might appear with greatly improved speed of response and noise performance.

References 11] L.K Anderson and B.J. McMurtry, Proc. 111FF 54 (1966) 1335. [2] L.K. Anderson, M. DiDomenico and MB. Fisher, in: Advances in Microwaves, vol. 5, LcI. L. Young (Academic Press, New York, 1970) 131 11. Melchior, MB. Fischer and F. Arains, Proc. LELE 58 (1970) 1466. [4] H. Melchior, in: laser Handbook, Eds F.1. Arecchi and ED. Schulz DuBois (Elsevier/ North Holland PubI. Co., Amsterdam, 1972) 629. 151 G. Lucovsky and RB. Immons, AppI. Opt. 4 (1965) 697 [6] B.N. Edwards, Appl. Opt. 5 (1966) 1423. [7] D.P. Mathur, R.J. McIntyre and PP. Webb, App). Opt. 9 (1970) 1842. 18] Rh. Ilamstra and P. Wendland, AppI. Opt. 11(1972)1539. 19] L. Mandel, in: Progress in Optics, vol. 2, Ed. L. Wolf (lnterscieuce Publishers, New York,

19b3) I~3. 1101 B.M. Oliver, Proc. IFFF 53(1965)436. [II]H. Hodara, Proc. IEEE 53 (1965) 696. 112] T. Curran and M. Ross, Proc. IEEE 53 (1965) 1770. [13] II. Rothe and W. Dahike, Proc. IRE 44 (1956) 811. [141J.J. Scheer and J. Van Laar, Solid State Commun. 3 (1965) 189. [15]A.11. Sommer, Photoemissive Materials (Wiley, New York, 1968). [16]R.L. Bell and WE. Spicer, Proc. IEEE 58 (1970) 1788. [17] RE. Simon, A.H. Sommer, J.J. Tietjen and B.F. Williams, Appl. Phys. Letters 13 (1968) 355. [18]R.C. Miller and NC. Wittwer, IEEE J. Quantum Electron. QE 1(1965)49. [19] HR. KralI and DL. Persyk, IEEE Trans. Nuclear Science NS 19 (1972) 45. [20] D.G. Fisher, Rh. Engstrom and BE. Williams, AppI. Phys. Letters 18 (1Q71) 371. [211H. Sonnenberg, Appl. Phys. Letters 19(1971)431. [22]II. Sonnenberg, AppI. Phys. Letters 14 (1969) 289. [23]R.L. Bell, LW. James, GA. Antypas, J. Fdgecumbe and R.L. Moon, AppI. P1~ys. Letters

19 (1971) 513. [24] Ph. Persyk, Laser Journal, November-December 1969, 21.

[25]B.F. Williams, Appi. Phys. Letters 14 (1969) 273. [26]Y.Z. Liu, J.L. Moll and WE. Spicer, AppI. Phys. Letters 17 (1970) 60. [27]LW. James, GA. Antypas, J.J. Uebbing, TO. Yep and R.L. Bell, J. Appl. Phys. 42(1971) 580. [28] G.P. Weckler, IEIL J. Solid State Circuits SC’ 2 (1967) 65. [29] IEEE Trans. Electron Devices, Special Issue on Solid-State Imaging, ED-15, April 1968. [30] F.H. Dc La Moneda, ER. Chenette and A. van der Ziel, IEEE Trans. on Electron Devices,

ED-18 (1971) 340.

H. Melchior, Sensitive high speed photodetectors

413

[31] R.P. Riesz, Rev. Sci. Instr. 33 (1962) 994. (32] D.E. Sawyer and R.H. Rediker, Proc. IRE 46 (1958) 1122. [33] A.G. Jordan and AG. Milnes, IRE Trans. on Electron Devices, ED-7 (1960) 242. [341 W.W. Gaertner, Phys. Rev. 116 (1959) 84. [351 For refs. see S. Sze, Physics of SemiconductorDevices (Wiley-Interscience, New York, 1969) 59. [361 J.J. Lofersky and J.U. Wysocki, RCA Review 22 (1961) 35. [371 L.K. Anderson, in: Proc. Symp. on Optical Masers (Polytechnic Institute of Brooklyn, April 1963) 549. [38] 0. Krumpholz and S. Maslowski, Telefunkenzeitung 39 (1966) 373. [39] TM. Buck, H.C. Casey, J.V. Dalton and M. Yamin, Bell Syst. Tech. J. 47 (1968) 1827. [401 R.L. Williams, J. AppI. Phys. 52 (1962) 1237. [41] W.C. Dash and R. Newman, Phys. Rev. 99 (1955) 1151. [42] M.V. Schneider, Bell System Techn. J. 45 (1966) 1611. [431 A.J. Tuzzolino, EL. Hubbard, M.A. Perkins and C.Y. Fan, J. Appl. Pys. 33 (1962) 148. [44] E. Labate, unpublished. [45] R.J. McIntyre and H.C. Sprigings, paper presented at Conference on Preparation and Control of Electronics Materials, Boston, Mass., August 1966. [46] H.C. Sprigings and R.J. McIntyre, paper presented at the International Electron Devices Meeting, Washington, D.C., October 1968. [471 0. Krumpholz and S. Maslowski, Zeitschr. angew. Phys. 25 (1968) 156. [48] H. Melchior and W.T. Lynch, IEEE Trans. on Electron Devices ED-13 (1966) 829. [49] K.G. McKay and K.B. McAfee, Phys. Rev. 91(1953)1079. [50] R.L. Batdorf, AG. Chynoweth, G.C. Dacey and P.W. Foy, J. AppI. Phys. 31(1960)1153. [51] KM. Johnson, IEEE Trans. on Electron Devices ED-12 (1965) 55. [52] 1 K Andersnn. PG McMulhin, I A. D’Acarn and A Gnetrherger, Appi. Pliyc I etters 6 (1965) 62. [53]K. Nishida, Jap. J. Appl. Phys. 9 (1970) 481. [54] H. Melchior and L.K. Anderson, paper presented at the International Electron Devices Meeting, Washington D.C., October 1965. [55] RB. Emmons, J. Appl. Phys. 38 (1967) 3705. [56] R.J. McIntyre, IEEE Trans. Electron Devices ED-13 (1966) 164. [57] R.J. McIntyre, IEEE Trans. Electron Devices ED-19 (1972) 703. [581S.D. Personick, Bell Syst. Techn. J. 50 (1971) 167. [591 S.D. Personick, Bell Syst. Techn. J. 50 (1971) 3015. [60]J. Conradi, IEEE Trans. Electron Devices ED-19 (1972) 713. [611 R.D. Baertsch, IEEE Trans. Electron Devices ED-13 (1966) 987. [621 l.M. Naqvi, C.A. Lee and G.C. Dalman, Proc. IEEE 56 (1968) 2051. [63] T. Igo and K. Sato, Jap. J. Appl. Phys. 8 (1969) 1481. [64] JR. Biard and W.N. Shaunfield, IEEE Trans. on Electron Devices ED-14 (1967) 233. [65]K. Nishida, Y. Nannichi, T. Uchida and I. Kitano, Proc. IEEE, Correspondence 58 (1970) 790. [661W.T. Lynch, IEEE Trans. on Electron Devices ED-iS (1968) 735. [67J I-I. Ruegg, IEEE Trans. on Electron Devices ED-14 (1967) 239. [68] P. Webb and R.J. McIntyre, in: Proc. Electro-optical Systems Design Conf 1971, east, 51 [69] R.J. Locker and G.C. Huth, AppI. Phys. Letters 9 (1966) 227. [70] 0. Krumpholz and S. Maslowski, Wiss. Ber. AEG-Telefunken 44 (1971) 73. [71]W.T. Lindley, R.J. Phelan, C.M. Wolfe and A.G. Foyt, App). Phys. Letters 14 (1969) 197.

414

H. Meichior, Sensitive high speed photodetectors

Discussion H. Kressel: How would you compare the state of the art avalanche diodes and photomulti pliers for 1.06 pm radiation detection? Reply: A comparison of state of the art detectors for 1.06 pm depends on the criteriaused. Highest speed of response (120 ps) combined with good quantum efficiency (> 50~)is found in germanium avalanche photodiodes. For best sensitivity to weak light signals with risetime not shorter than a few ns one might use silicon avalanche photodiodes which are operated at room temperature or cooled if the dark current influences the sensitivity. However, photomultipliers with a few percent quantum efficiency reach comparable sensitivities essentially due to their inherently much lower excess noise. I. Melngailis: The evidence for single carrier (electron) multiplication in CaAs Schottkl barrier avalanche photodiodes is an increase in noise as the square of the multiplication. The Ill-V alloy compounds, such as InGaAs should have significant advantages over Si and Ge for avalanche photodiodes at 1.06 pm and 1.54 pm because the high absorption constant at these wavelengths should permit the simultaneous achievement of high efficiency and high speed res ponse. Rep/v. It avalanche photodiodes with low dark current and unitorm gain can be fabricated from III V alloy compounds, such as InGaAs, they would indeed offer advantages, especially if the excess noise of the carrier multiplication process is losv. U. Heim: For single photon timing techniques like the method of delayed coincidence it is important to know something about the statistics of single photon emission from the cathode of a PM. Do you know how big the timing error due to such statistics will be for the new semiconductor photocathodes? Is it possible that this error is larger than the timespread of the dec tron flight tinies in the fast new dynode chains you have talked about? Reply. The statistical time delay between an incident photon and the pulse at the output 01 a photomultiplier depends not only on the enussion statistics of the photocathode, but on the emission Statistics of the secondary emission dynodes and on the time of flight differences of the emitted electrons between the cathode and dynodes as well. While electron path length differences are minimized and initial velocity distributions of emitted electrons quite narrow, there exists the possibility that diffusion of electrons to the surface of these new negative electron affinity emitters leads to statistically varying time delays. Detailed investigations are lacking, but Krall et al. 119] quoted estimated diffusion times to be of order 30 ps and report (FIR. Krall, F.A. 1-lelvy and D.E. Persyk, IEEE Trans. Nuc. Sci. NS-l7 (1970) 71) improvements in single photon timing resolution from 1.5 ns to 0.9 ns with a GaP (Cs) first dynode photonsultiplier substituted for an otherwise similar BeO-first-dynode tube.