Semiconductor ultraviolet detectors - Antoni Rogalski

42 Pages·1996·0.62 MB·English

APPLIED PHYSICS REVIEWS
Semiconductor ultraviolet detectors
M. Razeghia) and A. Rogalskib)
CenterforQuantumDevices,DepartmentofElectricalEngineeringandComputerScience,
NorthwesternUniversity,Evanston,Illinois60201
(cid:126)Received 7 September 1995; accepted for publication 12 January 1996(cid:33)
In this review article a comprehensive analysis of the developments in ultraviolet (cid:126)UV(cid:33) detector
technology is described. At the beginning, the classification of UV detectors and general
requirements imposed on these detectors are presented. Further considerations are restricted to
modern semiconductor UV detectors, so the basic theory of photoconductive and photovoltaic
detectorsispresentedinauniformwayconvenientforvariousdetectormaterials.Next,thecurrent
state of the art of different types of semiconductor UV detectors is presented. Hitherto, the
semiconductorUVdetectorshavebeenmainlyfabricatedusingSi.Industriessuchastheaerospace,
automotive,petroleum,andothershavecontinuouslyprovidedtheimpetuspushingthedevelopment
of fringe technologies which are tolerant of increasingly high temperatures and hostile
environments. As a result, the main efforts are currently directed to a new generation of UV
detectorsfabricatedfromwideband-gapsemiconductorsthemostpromisingofwhicharediamond
and AlGaN. The latest progress in development of AlGaN UV detectors is finally described in
detail. © 1996 American Institute of Physics. (cid:64)S0021-8979(cid:126)96(cid:33)06110-7(cid:35)
TABLE OF CONTENTS V. Schottky barrier ultraviolet detectors............ 7458
VI. SiC ultraviolet detectors..................... 7459
A. p-n junction photodiodes................... 7459
I. Introduction................................. 7434
B. Schottky barrier photodiodes................ 7461
II. Classification of ultraviolet detectors............ 7435
VII. III–V nitrides as a materials for ultraviolet
III. Ultraviolet photodetectors.................... 7437
detectors................................. 7462
A. General theory of photodetectors............. 7437
A. Physical properties........................ 7463
B. Photoconductive detectors.................. 7439
B. Ohmic contacts to GaN.................... 7465
1. Current and voltage responsivity.......... 7439
C. Etching of III–V nitrides................... 7466
2. Sweep-out effects...................... 7440
D. AlGaN ultraviolet detectors................. 7467
3. Noise mechanisms in photoconductors..... 7441
1. Photoconductive detectors............... 7467
4. Quantum efficiency.................... 7441
2. Photovoltaic detectors.................. 7468
5. Influence of surface recombination........ 7442
VIII. Other materials for ultraviolet detectors........ 7470
C. p-n junction photodiodes................... 7442
IX. Conclusions............................... 7470
1. Ideal diffusion-limited p-n junctions...... 7443
2. Other current mechanisms............... 7445
3. Response time......................... 7449 GLOSSARY OF FREQUENTLY USED SYMBOLS
D. Schottky barrier photodiodes................ 7450 a lattice constant
1. Schottky–Mott theory and its A detector area
modifications.......................... 7450 b electron to hole mobility ratio
2. Current transport processes.............. 7451 c speed of light
3. R A product and responsivity............ 7451 D,D ,D ,D diffusion coefficient, ambipolar, of elec-
0 a e h
E. Comparisonofdifferenttypesofsemiconductor trons, of holes
photodetectors............................ 7452 D*, D* detectivity, background limited
BLIP
F. Semiconductor materials used for ultraviolet E ,E ,E energy gap, Fermi energy, trap level en-
g F t
detectors................................ 7452 ergy
IV. Si ultraviolet detectors....................... 7454 (cid:68)f bandwidth
A. Diffused photodiodes...................... 7454 G recombination rate
B. Si photodiodes for vacuum ultraviolet g optical gain
applications.............................. 7457 h,(cid:92) Planck’s constant h/2(cid:112)
I,I ,I ,I current,ofelectrons,ofholes,photocurrent
e h ph
I ,I ,I ,I diffusion, generation–recombination, tun-
a(cid:33)Electronicmail:[email protected] D GR T n
b(cid:33)Present address: Institute of Technical Physics, Military University of neling, and noise current
Technology,01-489Warsaw,Kaliskiego2,Poland. I ,I dark, saturation current
d s
J.Appl.Phys.79(10),15May1996 0021-8979/96/79(10)/7433/41/$10.00 ©1996AmericanInstituteofPhysics 7433
J,J ,J ,J currentdensity,ofelectrons,ofholes,pho- vacuum ultraviolet VUV 200–10 nm
e h ph
tocurrent density deep ultraviolet DUV 350–190 nm
ultraviolet-A UV-A 400–320 nm
k Boltzmann’s constant
ultraviolet-B UV-B 320–280 nm
l length
L,L ,L diffusion length, of electrons, of holes Again, it must be emphasized that these appear to be the
e h
m free electron mass most common names and wavelength limits, but others will
m*, m*, m* effective mass, of electrons, of holes be found.
c n
n,n electron and intrinsic carrier concentration Ultraviolet research began in the latter half of the 19th
i
n ,n ,n ,(cid:68)n equilibrium electron concentration, major- century, when the invisible radiation beyond the blue end of
0 n p
ityandminorityelectronconcentration,ex- the visible spectrum began to receive attention. It was soon
cess free electrons realized that the Earth’s atmosphere set limitations on ultra-
N ,N concentration of acceptors, of donors violet research. For solar and celestial observations, strato-
a d
NEP noise equivalent power spheric ozone limited the wavelengths reaching the surface
p,p ,p ,p ,(cid:68)p hole concentration, equilibrium, majority oftheEarthtoabout300nm.Spectrographscarriedtohigher
0 p n
and minority hole concentration, excess altitudes on mountains gave intriguing evidence that solar
free holes and stellar emissions continued to shorter wavelengths. In
q electron charge laboratory spectrographs, atmospheric molecular oxygen ab-
r surface reflectance sorption limited the useful lower wavelengths to about 200
R,R ,R resistance, load, series nm, unless the spectrograph could be placed in a vacuum
L s
R0 zero bias detector resistance chamber.Thewavelengthsshorterthan200nmthuscameto
Ri,Rv current and voltage responsivity becalledthevacuumultraviolet.Becauseofthelackofgood
s surface recombination vacuum pumps and associated technology, research was dif-
t thickness ficult and not widely done. In addition to atmospheric limi-
T temperature tations, optical methods used in the visible failed in the ul-
v,vd,va,vth velocity, drift, ambipolar, saturation, and traviolet because of the lack of materials having good
thermal carrier transmissivityandreflectivity.Inthebeginningofthe1880s,
V,Vb,Vbi,Vn electrical voltage, bias, built-in and noise Rowlandandco-workersdevelopedconcavediffractiongrat-
w width ings and discovered the Rowland circle mount for vacuum
x alloy composition, distance variable spectrographs. This was a great step forward, since only
(cid:97) absorption coefficient single reflection and no transmission were needed to obtain
(cid:98) coefficient of I–V diode characteristic spectra on a photographic plate. Vacuum ultraviolet spec-
(cid:171)0 permittivity of space trography was pioneered by Schumann, Lyman, and others
(cid:171),(cid:171)0,(cid:171)(cid:96) dielectriccoefficient,relativestaticandop- in the early decades of this century. The lack of suitable
tical windows, filters, gratings, calibration standards, light
(cid:104) quantum efficiency
sources,andvacuumpumpsresultedindifficultiesinexperi-
(cid:108),(cid:108) ,(cid:108) wavelength, peak wavelength, cutoff
p c mentation.ThenextlargestimulusoccurredafterWorldWar
wavelength
II, when it was possible to use first sounding rockets and
(cid:110) frequency
then satellites to investigate the Earth’s upper atmosphere
(cid:109),(cid:109) ,(cid:109) mobility of carriers, of electrons, of holes
e h and to make solar and astronomical observations without in-
(cid:116),(cid:116) ,(cid:116) ,(cid:116) carrier lifetime, of electrons, of holes and
e h ef terference by the atmosphere. These applications areas
effective lifetime
openeduptheneedforbetterinstrumentation,includingbet-
(cid:116) ,(cid:116) ,(cid:116) response time limited by RC, diffusion,
RC d s ter windows, gratings, filters, detectors, and light sources as
and transit time
well as improved spectroscopy of the atoms, molecules, and
(cid:116) carrierlifetimeindepletionjunctionregion
0 ions of planetary and stellar atmospheres and reliable stan-
(cid:70) ,(cid:70) background, signal photon flux
B s dards for calibrations.
(cid:102) work function
The major constituents of the terrestrial atmosphere are
(cid:67) barrier potential
strong absorbers of radiation at wavelengths below 300 nm.
(cid:118) angular frequency Radiation of mid ultraviolet (cid:126)MUV(cid:33) wavelengths between
200 and 300 nm is absorbed primarily by ozone while mo-
I. INTRODUCTION lecularoxygenisthemajorabsorberatfarultraviolet(cid:126)FUV(cid:33)
The ultraviolet (cid:126)UV(cid:33) region is commonly divided into between 110 and 250 nm. Consequently, at wavelengths be-
thefollowingsubdivisions.Thesenamesarewidelyusedand low about 200 nm, the use of evacuated instrumentation is
are recommended: mandatory. At extreme ultraviolet (cid:126)EUV(cid:33) wavelengths of
near ultraviolet NUV 400–300 nm 110 nm, atomic and molecular gases become strong absorb-
mid ultraviolet MUV 300–200 nm ers.
far ultraviolet FUV 200–100 nm
Several books from the mid 1960s describe the ultravio-
extreme ultraviolet EUV 100–10 nm
let technology of this time. These books are on vacuum ul-
In addition to the above names, the following names for traviolet spectroscopic techniques,1 the middle ultraviolet
wavelength regions may be encountered: (cid:64)near ultraviolet (cid:126)NUV(cid:33) and MUV, generally(cid:35),2 ultraviolet
7434 J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski
FIG.1. Classificationofultravioletphotondetectors.
light sources,3 and spectroscopy.4 The historical develop- II. CLASSIFICATION OF ULTRAVIOLET DETECTORS
ment of spectroscopy is traced in the introductory chapter in
Samson’sbook,1alsothechapterinGreen’sbookbyHennes Ingeneral,UVdetectorsfallintotwocategories:photon
and Dunkleman,5 entitled Ultraviolet Technology, is an detectors(cid:126)alsonamedphotodetectors(cid:33)andthermaldetectors.
available source for the development of experimental tech- Inphotondetectorstheincidentphotonsareabsorbedwithin
niques of that time. Recently, Huffman has published two thematerialbyinteractionwithelectrons.Theobservedelec-
booksabouttheultravioletspectralregions.6,7Thesecondof trical signal results from the changed electronic energy dis-
them7 supplements previously published books, since this tribution.Thephotondetectorsmeasuretherateofarrivalof
volume is a collection of reprints that present the milestone quanta and show a selective wavelength dependence of the
articles in ultraviolet optics and technology. response per unit incident radiation power. In thermal detec-
The issue of UV detectors is treated in several mono- tors, the incident radiation is absorbed and raises the tem-
graphs and reviews. An extensive examination of various perature of the material. The output signal is observed as a
detector systems for both imaging and nonimaging applica- change in some temperature-dependent property of the ma-
tions is presented by Carruthers.8 Timothy and Madden9 terial. In pyroelectric detectors a change in the internal elec-
have restricted their review to photon detectors that are cur-
tricalpolarizationismeasured,whereasinthecaseofbolom-
rently available for use at ultraviolet and x-ray wavelengths.
eters a change in the electrical resistance is measured. The
More information about the history of the development of
thermal effects are generally wavelength independent since
UV detectors and their current status in astronomy can be
the radiation can be absorbed in a ‘‘black’’ surface coating.
found in an excellent book entitled Low light level detectors
Because of greater sensitivity, photon detectors are more
in astronomy by Eccles, Sim, and Tritton.10 Another of
commonly utilized at UV wavelengths. Thermal detectors,
Timothy’s review articles is devoted mainly to detectors for
however, are sometimes employed at UV wavelengths as
optical wavelengths,11 and a comparison of charge coupled
absolute radiometric standards.
devices (cid:126)CCDs(cid:33) to other optical detectors is given by Jan-
UVphotondetectors(cid:126)seeFig.1(cid:33)havetraditionallybeen
esick etal.12 The reviews of the present and future techno-
devoted into two distinct classes, namely, photographic and
logical concepts currently being considered in astrophysics
photoelectric.Photographicemulsionhasthegreatadvantage
and astronomy are given by Welsh and Kaplan,13 Joseph,14
of an image-storing capability and can thus record a large
and by Ulmer etal.15 However, the UV detectors have also
amount of data in a single exposure. However, photographic
found terrestrial applications. They can detect UV emissions
from flames in the presence of hot backgrounds (cid:126)such as emulsion has a number of limitations: sensitivity is consid-
infrared emission from the hot bricks in a furnace(cid:33). This erably lower than that of a photoelectric detector, the dy-
namic range is limited, the response is not a linear function
provides an excellent flame on/off determination system for
of the incident photon flux at a specific wavelength, and
controlling the gas supply to large furnaces and boiler sys-
emulsion is sensitive to a very wide energy range (cid:126)accord-
tems. Flame safeguard and fire control areas are just two of
ingly the elimination of background fog levels induced by
the various possible applications for the UV detectors.
scattered light and by high-energy charged particles is ex-
In this article we will first present the classification of
UVdetectorsandgeneralrequirementsimposedonthesede- tremely difficult(cid:33).
tectors. Further consideration will be restricted to modern Photoelectricdetectors,ontheotherhand,aremoresen-
semiconductor UV detectors, so the basic theory of photo- sitive, have a greater stability of response and provide better
conductive and photovoltaic detectors will be presented in a linearity characteristics. In the last decade considerable
uniformwayconvenientforvariousdetectormaterials.Next, progressintheimage-recordingcapabilityofphotoelectronic
thecurrentstateoftheartofdifferenttypesofsemiconductor devices has been observed. Recently developed photovoltaic
UV detectors will be presented. The main effort will be es- arraydetectors(cid:64)suchasthechargecoupleddevices(cid:35)andpho-
pecially directed to a new generation of UV detectors. This toemissive array detectors (cid:64)such as the microchannel array
generation of detectors is the product of five years of mate- plates (cid:126)MCPs(cid:33)(cid:35) for the first time combine the sensitivity and
rials and device research, which resulted in the development radiometric stability of a photomultiplier with a high-
of high quality GaN layers. resolution imaging capability.
J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski 7435
Thereareanumberofimportantdifferencesbetweenthe
two classes of detectors. In the photoemissive detectors, the
primary photoelectron produced by the photocathode can be
multipliedbytheprocessofsecondaryemissiontoproducea
large cloud of electrons. The degree of multiplication is
called the gain of the detector. If the gain is sufficiently
large, the electron cloud generated by a single photoelectron
canbedetecteddirectlywithconventionalelectroniccircuits.
Alternatively, the electron cloud can be accelerated to high
energyandallowedtoimpactaphosphorscreen.Theresult-
FIG.2. Principleoperationofphotoemissive(cid:126)a(cid:33)andsemiconductordetec-
tors(cid:126)b(cid:33). ing pulse of visible-light photons emitted from the phosphor
can be viewed directly or can be detected and recorded by
additional photosensitive systems. Detectors operated in this
pulse-countingmodecanprovidetheultimatelevelofsensi-
In the most commonly employed photoemissive UV de-
tivity at very low signal level. That form of intensification
tectors, the photon is allowed to impact a solid surface real-
izing a photoelectron into the vacuum environment (cid:64)Fig. implies, however, high voltages and the inherent associated
2(cid:126)a(cid:33)(cid:35). Applying a voltage between the photocathode surface difficulties. Moreover, it is not possible in this mode of op-
eration to store the detected events within the detector, and
and a positively biased anode causes a photoelectron current
thedetectedsignalmustbeintegratedinaseparaterecording
toflowinproportiontotheintensityoftheincidentradiation.
system. Table I compares these two types of UV detectors.
Since these detectors make use of the external photoelectric
The importance of UV semiconductor detectors has re-
effect, the wavelength range of sensitivity is defined prima-
sultedintherecentmeteoricexpansionofthesemiconductor
rily by the work function of the surface material.
industry, and second, the continuing emphasis on the devel-
Inthesemiconductordetectors,thephotonsareabsorbed
opment of low-light-level imaging systems for military and
in the bulk of the semiconductor material producing
civilian surveillance applications. These detectors should:
electron-holepairswhichareseparatedbyanelectricalfield.
These detectors make use of the internal photoelectric effect (cid:126)1(cid:33) not be sensitive to light at optical wavelengths (cid:126)com-
where the energy of the photons is large enough to raise the monly referred to as being solar blind(cid:33),
electronsintotheconductionbandofthesemiconductorma- (cid:126)2(cid:33) have high quantum efficiency,
terial.Inthecaseofphotovoltaicdetectors,theelectron-hole (cid:126)3(cid:33) have a high dynamic range of operation,
pairs are separated by the electrical field of p-n junctions, (cid:126)4(cid:33) havelowbackgroundssincenoisearisingfromtheback-
Schottkybarrier,ormetal-insulator-semiconductor(cid:126)MIS(cid:33)ca-
ground often dominates in faint UV observations.
pacitors, which leads to an external photocurrent propor-
tional to the number of detected photons (cid:64)Fig. 2(cid:126)b(cid:33)(cid:35). Apply- Multiplying the number of primary charge carriers is
ing a voltage across the absorbing region causes a current to generally not possible in semiconductor detectors (cid:126)although
flow in proportion to the intensity of the incident radiation. thisdeficiencymaybeoffsetbytheveryhighinternalquan-
In the photoemissive detectors, the primary photoelec- tum efficiency of the semiconductor material(cid:33). These detec-
tron can be multiplied by the process of secondary emission torsarethuslesssensitiveatthelowestsignallevelsthanthe
to produce a large cloud of electrons. The occurrence of a photoemissive detectors operating in pulse-counting mode.
single photoelectron event then can be detected either di- However, the semiconductor detectors have the ability to
rectlywithconventionalelectroniccircuitsorbyaccelerating store charge and integrate the detected signal for significant
theelectroncloudtohighenergyandallowingittoimpacta periodsoftime.Recently,therehasbeenmuchdevelopment
phosphor screen. The emitted pulse of visible-light photons ofCCDdetectorsforuseintheUVspectralranges.7,8,12,16–18
can then be viewed directly, or detected and recorded by On the contrary, for visible spectral range devices the use of
additional photosensitive systems. Detectors operated in this SiCCDsintheUVregionisnotyetwellestablishedbecause
pulse-countingmodecanprovidetheultimatelevelofsensi- of the many problems connected with the interaction of UV
tivity set by the quantum efficiency of the photocathode. radiationwiththematerialstypicallyusedinsilicontechnol-
TABLEI. ComparisonofphotoemissiveandsemiconductorUVdetectors.
Type Advantages Disadvantages
Photoemissivedetectors Easytooperate Lowquantumefficiency
Highsensitivity Strongspectraldependenceofresponsivity
Solarblind Sensitivenesstosurfacecontaminations
Semiconductordetectors Broadspectralresponsivity Inducedagingeffects
Excellentlinearity
Highquantumefficiency
Highdynamicrangeofoperation
Large-formatimagearrays
7436 J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski
tect the photoelectron released from a photocathode. The
photoelectron is accelerated to very high energy by an elec-
trostatic field and allowed to bombard the semiconductor
material.Ifsufficientenergyisreleasedwithintheabsorbing
region, enough electron-hole pairs can be produced to pro-
videameasurablesignalfromasinglephotoelectronimpact.
Figure 3 shows the current status of the quantum effi-
ciencyofcommondetectors.ThetopplotinFig.3showsthe
quantum efficiencies that can be obtained with various con-
figurations of thinned, back-illuminated CCDs. Future anti-
reflection coatings, depicted as a dot-dash line, may extend
the range well into the UV range. Figure 3(cid:126)b(cid:33) shows the
solar-blind efficiencies obtained for various UV detectors.
III. ULTRAVIOLET PHOTODETECTORS
Ultraviolet semiconductor photodetectors work in three
fundamental modes:
(cid:126)1(cid:33) photoconductive detectors,
(cid:126)2(cid:33) photodiode p-n junctions, and
(cid:126)3(cid:33) Schottky barrier detectors.
Below,afterdescribingthegeneraltheoryofphotodetectors,
the basic theories of photoconductors, p-n junctions, and
Schottky barriers are presented. In the last part of this sec-
tion,ashortpresentationofsemiconductormaterialsusedfor
the fabrication of UV detectors is included.
FIG.3. QuantumefficiencyofthinnedbacksideilluminatedCCDs(cid:126)a(cid:33)and A. General theory of photodetectors
solar-blindefficienciesofvariousUVdetectors(cid:126)b(cid:33).Thedetectivequantum
The photodetector is a slab of homogeneous semicon-
efficiency(cid:126)DQE(cid:33)ofacompletedetectorsystemtakesintoaccountanyloss
ofdetectedphotonsandthequantumefficiencyofeachstageofthesystem. ductorwiththeactual‘‘electrical’’areaAe whichiscoupled
TheDQEcanbeexpressedintermsofthesignal-to-noisecharacteristicsof to a beam of infrared radiation by its optical area A . Usu-
o
theinputandoutputsignalsastheratioDQE(cid:53)(cid:126)S/Nout(cid:33)2/(cid:126)S/Nin(cid:33)2(cid:126)afterRef. ally, the optical and electrical areas of the device are the
14(cid:33).
same or close. The use of optical concentrators can increase
the A /A ratio.
o e
ogy. For example, the relatively thin gate oxide layer (cid:126)500– The current responsivity of the photodetector is deter-
1200 Å(cid:33) on the CCD front face is strongly absorbing of UV mined by the quantum efficiency (cid:104)and by the photoelectric
gaing.Thequantumefficiencyvaluedescribeshowwellthe
radiation, so that it is not possible to use front-illuminated
detector is coupled to the radiation to be detected. It is usu-
CCDsfordirectdetectionofthisradiation.Theelectron-hole
ally defined as the number of electron-hole pairs generated
pairs created in this layer are not separated by an internal
perincidentphoton.Theideaofphotoconductivegaing was
field and will therefore not contribute to the photocurrent.
put forth by Rose22 as a simplifying concept for the under-
Thinned, back-illuminated CCDs also have some problems.
standing of photoconductive phenomena and is now widely
In fact, after the device is thinned, a native back-oxide layer
used in the field. The photoelectric gain is the number of
formsnaturally,andevenifitisverythin,typicallylessthan
carriers passing contacts per one generated pair. This value
50 Å, this dramatically influences overall sensor perfor-
showshowwellthegeneratedelectron-holepairsareusedto
mance.Anumberofsolutionshavebeentried,rangingfrom
the deposition of a scintillator, such as coronene19 or generatethecurrentresponseofaphotodetector.Bothvalues
lumigen,20tothebacksideilluminationofthinneddevices,so are assumed here as constant over the volume of the device.
The spectral current responsivity is equal to
to avoid the absorption of radiation by the thick polysilicon
(cid:108)(cid:104)
gatestructure.Somemethodshavebeendevelopedtoreduce R (cid:53) qg, (cid:126)1(cid:33)
the surface state problems using ‘‘back-accumulation’’ i hc
techniques.21 They are based on the hypothesis that the back where (cid:108) is the wavelength, h is Planck’s constant, c is the
surfacepotentialcanbepinnedbyheavilypopulatingitwith
light velocity, q is the electron charge, and g is the photo-
holes which create an electric field that directs the photoge-
electric current gain. Assuming that the current gains for
nerated charges away from the back surface. They can be
photocurrent and noise current are the same, the current
divided into three categories: backside charging, flash gate noise due to generation and recombination processes is22
techniques, and ion implantation.8,21
A semiconductor array can also be used to directly de- In2(cid:53)2(cid:126)G(cid:49)R(cid:33)Aet(cid:68)fq2g2, (cid:126)2(cid:33)
J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski 7437
where G and R are the generation and recombination rates,
(cid:68)f is the frequency band, and t is the thickness of the de-
tector.
DetectivityD*isthemainparametercharacterizingnor-
malized signal-to-noise performance of detectors and can be
defined as
R (cid:126)A (cid:68)f (cid:33)1/2
D*(cid:53) i o . (cid:126)3(cid:33)
I
n
According to Eqs. (cid:126)1(cid:33)–(cid:126)3(cid:33)23
(cid:83) (cid:68)
(cid:108) A 1/2
D*(cid:53) o (cid:104)(cid:64)2(cid:126)G(cid:49)R(cid:33)t(cid:35)(cid:50)1/2. (cid:126)4(cid:33)
hc A
e
For a given wavelength and operating temperature, the
highest performance can be obtained by maximizing
(cid:104)/[t(G(cid:49)R)]1/2 which corresponds to the condition of the
highestratioofthesheetopticalgenerationtothesquareroot
of sheet thermal generation–recombination.
Theeffectsofafluctuatingrecombinationcanfrequently
be avoided by arranging for the recombination process to
take place in a region of the device where it has little effect
duetolowphotoelectricgain:forexample,atthecontactsin
sweep-out photoconductors or in the neutral regions of di-
odes.Inthiscase,thenoisecanbereducedbyafactorof2.5
and detectivity increased by the same factor. The generation FIG.4. Minimumdetectablemonochromaticpowerasafunctionofwave-
process with its associated fluctuation, however, cannot be length for composite of SFL and BLIP limit for two detector areas and
avoided by any means. electrical bandwidths. Background temperature is 290 K and FOV is 2(cid:112)
steradiants. Detector long wavelength limit is equal to source wavelength
At equilibrium the generation and recombination rates (cid:126)afterRef.25(cid:33).
are equal, and assuming that A (cid:53)A we have
o e
(cid:108) (cid:104)
D*(cid:53) G(cid:50)1/2. (cid:126)5(cid:33)
2hc t1/2 it is rarely achieved with solid-state devices, which are nor-
mally detector-noise or electronic-noise limited. The (cid:126)NEP(cid:33)
The total generation rate is a sum of the optical and and detectivity of detectors operating in this limit have been
thermal generation derived by a number of authors (cid:126)see, e.g., Kruse etal.24,25(cid:33).
G(cid:53)G (cid:49)G . (cid:126)6(cid:33) The NEP in the SFL is given by
th op
2hc(cid:68)f
The optical generation may be due to the signal or ther- NEP(cid:53) (cid:126)8(cid:33)
(cid:104)(cid:108)
mal background radiation. For infrared detectors, usually
thermal background radiation is higher compared to the sig- when Poisson statistics are applicable. This threshold value
nal radiation. If the thermal generation is reduced much be- impliesalownumberofphotonsperobservationinterval.A
low the background level, the performance of the device is more meaningful parameter is the probability that a photon
determined by the background radiation (cid:64)conditions for willbedetectedduringanobservationperiod.Kruse25shows
background limited infrared photodetector (cid:126)BLIP(cid:33)(cid:35). The that the minimum signal power to achieve 99% probability
noiseequivalentpower(cid:126)NEP(cid:33)inthisapproximationisgiven that a photon will be detected in an observation period t is
o
by24,25 (cid:83) (cid:68) 9.22hc(cid:68)f
NEP(cid:53)(cid:126)A(cid:68)f (cid:33)1/2(cid:53)h(cid:103) 2A(cid:70)B(cid:68)f 1/2, (cid:126)7(cid:33) NEPmin(cid:53) (cid:104)(cid:108) , (cid:126)9(cid:33)
D* (cid:104)
where(cid:68)f isassumedtobe1/2t .Notethatthedetectorarea
o
where (cid:70) is the total background photon flux density reach- does not enter into the expression and that NEP depends
B min
ing the detector, and (cid:68)f is the electrical bandwidth of the linearly upon the bandwidth, which differs from the case in
receiver.Thebackgroundphotonfluxdensityreceivedbythe which the detection limit is set by internal or background
detector depends on its angular view of the background and noise.
on its ability to respond to the wavelengths contained in this Seib and Aukerman26 also have derived an expression
source. fortheSFLidenticaltoEq.(cid:126)9(cid:33)exceptthatthemultiplicative
When photodetectors are operated in conditions where constant is not 9.22 but 23/2 for an ideal photoemissive or
the background flux is less than the optical (cid:126)signal(cid:33) flux, the photovoltaicdetectorand25/2foraphotoconductor.Thisdif-
ultimateperformanceofdetectorsisdeterminedbythesignal ference in the constant arises from the differing assumptions
fluctuationlimit(cid:126)SFL(cid:33).Itisachievedinpracticewithphoto- as to the manner in which the detector is employed and the
multipliersoperatinginthevisibleandultravioletregion,but minimum detectable signal-to-noise ratio.
7438 J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski
It is interesting to determine the composite signal fluc-
tuationandbackgroundfluctuationlimits.Figure4illustrates
the spectral NEP over the wavelength range from 0.1 to 20
(cid:109)m assuming a background temperature of 290 K detector
areasof1cm2and1mm2(cid:126)applicableonlytothebackground
fluctuation limit(cid:33), a 2(cid:112)steradian field of view (cid:126)FOV(cid:33) (cid:64)appli-
cable only to the background fluctuation limit(cid:35), and band-
widths of 1 and 104 Hz. These additional values of param-
etersarespecifiedbecauseofdifferentdependenciesofNEP
(cid:126)upon area and bandwidth(cid:33) for signal fluctuation and back-
ground fluctuation limits. Note that the intersections of three
pairs of curves, for which the bandwidths of the signal and
background fluctuation limits are equal, lie between 1.0 and
1.5 (cid:109)m. To illustrate the composite, a detector with an area FIG.5. Geometryandbiasofaphotoconductor.
of1cm2(cid:126)applicabletothebackgroundfluctuationlimit(cid:33)and
abandwidthof1Hzhasbeenscored.Forthispair,atwave-
lengths below 1.2 (cid:109)m the SFL dominates; the converse is nisms: Shockley–Read, radiative, and Auger mechanisms.
trueabove1.2(cid:109)m.Theminimumdetectablemonochromatic TheShockley–Readmechanismoccursvialatticedefectand
radiant power at 1.2 (cid:109)m is 1.5(cid:51)10(cid:50)18 W in a 1 Hz band- impurity energy levels within the forbidden energy gap and
width. Below 1.2 (cid:109)m the wavelength dependence is small. is the dominant mechanism in wide band-gap materials.
Above1.2(cid:109)mitisverylarge,duetosteepdependenceupon
wavelength of the short wavelength end of the 290 K back-
B. Photoconductive detectors
ground spectral distribution.
The basic equations for dc analysis of detector perfor- The photoconductive detector (cid:126)also named as the photo-
mance are well known: two current-density equations for conductor(cid:33) is essentially a radiation-sensitive resistor. The
electrons I and holes J two continuity equations for elec- operation of a photoconductor is shown in Fig. 5. A photon
e b
trons and holes, and Poisson’s equation which are collec- of energy h(cid:110) greater than the band-gap energy E is ab-
g
tively referred to as the Van Roosbroeck model27 sorbedtoproduceanelectron-holepair,therebychangingthe
electrical conductivity of the semiconductor.
dn d(cid:67)
J (cid:53)qD (cid:50)q(cid:109)n current density for electrons, In almost all cases the change in conductivity is mea-
e e dx e dx suredbymeansofelectrodesattachedtothesample.Forlow
(cid:126)10(cid:33)
resistancematerial,thephotoconductorisusuallyoperatedin
dp d(cid:67) a constant current circuit as shown in Fig. 5. The series load
J (cid:53)qD (cid:50)q(cid:109)p current density for holes, (cid:126)11(cid:33) resistanceislargecomparedtothesampleresistance,andthe
h h dx h dx
signalisdetectedasachangeinvoltagedevelopedacrossthe
1 dJ sample.Forhighresistancephotoconductors,aconstantvolt-
e(cid:49)(cid:126)G(cid:50)R(cid:33)(cid:53)0 continuity equation for electrons, agecircuitispreferredandthesignalisdetectedasachange
q dx
(cid:126)12(cid:33) in current in the bias circuit.
1 dJh(cid:50)(cid:126)G(cid:50)R(cid:33)(cid:53)0 continuity equation for holes, (cid:126)13(cid:33) 1.Currentandvoltageresponsivity
q dx We assume that the signal photon flux density (cid:70) (cid:126)(cid:108)(cid:33) is
s
d2(cid:67) q incident on the detector area A(cid:53)wl and that the detector is
(cid:53)(cid:50) (cid:126)N (cid:50)N (cid:49)p(cid:50)n(cid:33), Poisson’s equation, operated under constant current conditions, i.e., R (cid:64)R. We
dx2 (cid:171) (cid:171) d a L
0 r suppose further that the illumination and the bias field are
(cid:126)14(cid:33)
weak, and the excess carrier lifetime, (cid:116), is the same for ma-
where(cid:67)istheelectrostaticpotential,N istheconcentration jorityandminoritycarriers.Toderiveanexpressionforvolt-
d
of donors, N is the concentration of acceptors, D and D age responsivity, we take a one-dimensional approach for
a e h
are the electron and hole diffusion coefficients, n and p are simplicity. This is justified for a detector thickness, t, that is
the electron and hole densities, and (cid:171) (cid:171) is the permittivity small with respect to the minority carrier diffusion length.
0 r
of the semiconductor. A self-consistent iterative procedure We also neglect the effect of recombination at frontal and
for the solution of this mathematical model is well docu- rear surfaces.
mented in the literature.28 The method reformulates the The basic expression describing photoconductivity in
model in terms of integral equations which incorporate the semiconductors under equilibrium excitation (cid:126)i.e., steady
boundaryconditionsandeliminate J andJ asintermediate state(cid:33) is
e h
variables. This allows the carrier densities to be computed
I (cid:53)q(cid:104)A(cid:70) g, (cid:126)15(cid:33)
from the potential distribution. ph s
The generation–recombination term (G(cid:49)R) is associ- where I is the short circuit photocurrent at zero frequency
ph
atedwiththepredominantrecombinationmechanisms.There (cid:126)dc(cid:33), i.e., the increase in current above the dark current ac-
are three important generation and recombination mecha- companying irradiation. The photoconductive gain is deter-
J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski 7439
minedbythepropertiesofthedetector,i.e.,bywhichdetec- V (cid:104) (cid:108)(cid:116)V
tion effect is used and the material and configuration of the Rv(cid:53)P(cid:108)s(cid:53)Iwt hc n0b, (cid:126)24(cid:33)
detector.
In general, photoconductivity is a two-carrier phenom- where the absorbed monochromatic power P(cid:108)(cid:53)(cid:70)sAh(cid:110).
enon and the total photocurrent of electrons and holes is Thisexpressionshowsclearlythebasicrequirementsfor
high photoconductive responsivity at a given wavelength (cid:108):
I (cid:53)wtq(cid:126)(cid:68)n(cid:109)e(cid:49)(cid:68)p(cid:109)h(cid:33)Vb, (cid:126)16(cid:33) one must have high quantum efficiency (cid:104), long excess car-
ph l rier lifetime (cid:116), the smallest possible piece of crystal, low
where(cid:109) istheelectronmobility,(cid:109) istheholemobility,V thermal equilibrium carrier concentrations n0, and the high-
e h b
est possible bias voltage V .
is the bias voltage and b
Thefrequencydependentresponsivitycanbedetermined
n(cid:53)n (cid:49)(cid:68)n, p(cid:53)p (cid:49)(cid:68)p. (cid:126)17(cid:33)
0 0 by the equation
The terms n and p are the average thermal equilibrium
0 0 (cid:104) (cid:108)(cid:116) V l
carrier densities, and (cid:68)n and (cid:68)p are the excess carrier con- R (cid:53) ef b , (cid:126)25(cid:33)
centrations. v lwt hc n0 (cid:126)l(cid:49)(cid:118)2(cid:116)e2f(cid:33)1/2
Takingtheconductivitytobedominatedbyelectrons(cid:126)in where(cid:116) istheeffectivecarrierlifetime.Usually,thephoto-
el
all known high sensitivity photoconductors this is found to
conductive detectors fabricated from wide band-gap materi-
be the case(cid:33) and assuming uniform and complete absorption
als reveal strongly sub-linear responses and excitation-
of the light in the detector, the rate equation for the excess
dependent response time is observed even at relatively low
electron concentration in the sample is29
excitation levels. This can be attributed to the redistribution
d(cid:68)n (cid:70) (cid:104) (cid:68)n of the charge carriers with increased excitation level.
(cid:53) s (cid:50) , (cid:126)18(cid:33)
dt t (cid:116) The above simple model takes no account of additional
limitations related to the practical conditions of photocon-
where(cid:116)istheexcesscarrierlifetime.Inthesteadycondition,
ductoroperationsuchassweep-outeffectsorsurfacerecom-
the excess carrier lifetime is given by the equation
bination. These are specified below.
(cid:68)nt
(cid:116)(cid:53) . (cid:126)19(cid:33)
(cid:104)(cid:70) 2.Sweep-outeffects
s
Equating (cid:126)15(cid:33) to (cid:126)16(cid:33) gives Equation (cid:126)25(cid:33) shows that voltage responsivity increases
monotonically with the increase of bias voltage. However,
g(cid:53)tVh(cid:109)e(cid:68)n (cid:126)20(cid:33) therearetwolimitsonappliedbiasvoltage,namely:thermal
l(cid:104)(cid:70) conditions (cid:126)joule heating of the detector element(cid:33) and sweep
s
out of minority carriers. The thermal conductance of the de-
and invoking Eq. (cid:126)19(cid:33) we get for the photoconductive gain
tector depends on the device fabrication procedure. If the
(cid:116)(cid:109)V (cid:116)
g(cid:53) e b(cid:53) . (cid:126)21(cid:33) excess carrier lifetime is long, we cannot ignore the effects
l2 l2/(cid:109)eVb of contacts and of drift and diffusion on the device perfor-
mance. Present-day material technology is such that at mod-
So, the photoconductive gain can be defined as
erate bias fields minority carriers can drift to the ohmic con-
(cid:116)
g(cid:53) , (cid:126)22(cid:33) tacts in a short time compared to the recombination time in
t
t the material. Removal of carriers at an ohmic contact in this
where t is the transit time of electrons between ohmic con- way is referred to as ‘‘sweep out.’’30,31 Minority carrier
t
tacts. This means that the photoconductive gain is given by sweep out limits the maximum applied voltage of Vb. The
theratiooffreecarrierlifetime,(cid:116),totransittime,t between effective carrier lifetime can be reduced considerably in de-
t
the sample electrodes. The photoconductive gain can be less tectors where the minority carrier diffusion length exceeds
than or greater than unity depending upon whether the drift the detector length (cid:126)even at very low bias voltages(cid:33). At low
length, L (cid:53)v (cid:116), is less than or greater than interelectrode bias the average drift length of the minority carriers is very
d d
spacing, 1. The value of L (cid:46)1 implies that a free charge muchlessthanthedetectorlength,I,andtheminoritycarrier
d
carriersweptoutatoneelectrodeisimmediatelyreplacedby lifetime is determined by the bulk recombination modified
injection of an equivalent free charge carrier at the opposite bydiffusiontosurfaceandcontacts.Thecarrierdensitiesare
electrode. Thus, a free charge carrier will continue to circu- uniformalongthelengthofthedetector.Athighervaluesof
late until recombination takes place. the applied field, the drift length of the minority carriers is
WhenR (cid:64)R,asignalvoltageacrosstheloadresistoris comparabletoorgreaterthan1.Someoftheexcessminority
L
essentially the open circuit voltage carriersarelostatanelectrode,andtomaintainspace-charge
equilibrium, a drop in excess majority carrier density is nec-
l
V (cid:53)I R (cid:53)I , (cid:126)23(cid:33) essary. This way the majority carrier lifetime is reduced. It
s ph d ph qwtn(cid:109)
e shouldbepointedoutthatthelossofthemajoritycarriersat
where R is the detector resistance. Assuming that the one ohmic contact is replenished by injection at the other,
d
changeinconductivityuponirradiationissmallcomparedto but the minority carriers are not replaced. At high bias the
the dark conductivity, the voltage responsivity is expressed excess carrier density is nonuniformly distributed along the
as length of the sample.
7440 J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski
To achieve high photoelectric gain, low resistance and time.Thisleadstoconductivitychangesthatwillbereflected
low surface recombination velocity contacts are required. as fluctuations in current flow through the crystal. Many
The metallic contacts are usually far from expectation. The forms of g–r noise expression exist, depending upon the in-
contactsarecharacterizedbyarecombinationvelocitywhich ternal properties of the semiconductors.
can be varied from infinity (cid:126)ohmic contacts(cid:33) to zero (cid:126)per- Thermsg–rnoisecurrentforanextrinsicn-typephoto-
fectly blocking contacts(cid:33). In the latter case, a more intensely conductor with carrier lifetime (cid:116)can be written32
doped region at the contact (cid:126)e.g., n(cid:49) for n-type devices or
heterojunction contact(cid:33) causes a built-in electric field that 4I2(cid:68)N2(cid:116)(cid:68)f
I2 (cid:53) , (cid:126)27(cid:33)
repelsminoritycarriers,therebyreducingrecombinationand g–r N2(cid:126)1(cid:49)(cid:118)2(cid:116)2(cid:33)
increasing the effective lifetime and the responsivity. Practi-
cal realization of the device would require double epitaxial whereN isthenumberofcarriersinthedetector.Usually,in
growth and the subsequent removal of the heavy doped ma- an extrinsic semiconductor there will be some counterdop-
terial from the active area of the device. ing,i.e.,electronstrappedatdeeplyinglevels.Ifthenumber
of deep traps is small compared to the number of electrons
3.Noisemechanismsinphotoconductors (cid:126)electronsbeingthemajoritycarriers(cid:33),thenthevariance(cid:68)N2
isequaltoN32.ThecurrentflowinginthedeviceisI(cid:53)Nqg/
All detectors are limited in the minimum radiant power
(cid:116), hence
which they can detect by some form of noise which may
ariseinthedetectoritself,intheradiantenergytowhichthe
4qIg(cid:68)f
detector responds, or in the electronic system following the I2 (cid:53) . (cid:126)28(cid:33)
detector. Careful electronic design, including low noise am- g–r 1(cid:49)(cid:118)2(cid:116)2
plification, can reduce the system noise below that in the
output of the detector. This topic will not be treated here. Generation–recombinationnoiseusuallydominatesthenoise
We can distinguish two groups of noise; the radiation spectrum of photoconductors at intermediate frequencies.
noise and the noise internal to the detector. The radiation An additional type of noise, referred to as 1/f noise,
noise includes signal fluctuation noise and background fluc- because it exhibits an approximately 1/f power law spec-
tuation noise. Under most operating conditions the signal trum,isalwaysobserved.Itislessunderstoodthanthemore
fluctuationlimitisoperativeforultravioletandvisibledetec- fundamental noise sources and is not generally amenable to
tors. mathematical analysis. The general expression for the 1/f
The random processes occurring in semiconductors give noise current is
(cid:83) (cid:68)
rise to internal noise in detectors even in the absence of
KI(cid:97)(cid:68)f 1/2
illumination. There are two fundamental processes respon- I (cid:53) b , (cid:126)29(cid:33)
sible for the noise: fluctuations in the velocities of free car- 1/f f(cid:98)
riersduetotheirrandomthermalmotion,andfluctuationsin
thedensitiesoffreecarriersduetorandomnessintheratesof whereK isaproportionalityfactor,I isthebiascurrent,(cid:97)is
b
thermal generation and recombination.32 aconstantwhosevalueisabout2,and(cid:98)isaconstantwhose
Johnson–Nyquist noise is associated with the finite re- value is about unity.
sistance R of the device. This type of noise is due to the In general, 1/f noise appears to be associated with the
random thermal motion of charge carriers in the crystal and presenceofpotentialbarriersatthecontacts,surfacetrapping
not due to fluctuations in the total number of these charge phenomena, and surface leakage currents. Reduction of 1/f
carriers. It occurs in the absence of external bias as a fluctu- noise to an acceptable level is an art which depends greatly
ating voltage or current depending upon the method of mea- ontheprocessesemployedinpreparingthecontactsandsur-
surement. Small changes in the voltage or current at the ter- faces. Up until now, no fully satisfactory general theory has
minals of the device are due to the random arrival of charge beenformulated.Thetwomostcurrentmodelsfortheexpla-
at the terminals. The root mean square of the Johnson– nationof1/f noisewereconsidered:Hooge’smodel,33which
Nyquist noise voltage in the bandwidth (cid:68)f is given by assumes fluctuations in the mobility of free charge carriers,
and McWhortel’s model,32 based on the idea that the free
V (cid:53)(cid:126)4kTR(cid:68)f (cid:33)1/2, (cid:126)26(cid:33)
j carrier density fluctuates.
where k is the Boltzmann constant and T is the temperature. The UV semiconductor detectors usually exhibit 1/f
This type of noise has a ‘‘white’’ frequency distribution. noise at low frequency. At higher frequencies the amplitude
At finite bias currents, the carrier density fluctuations drops below that of one of the other types of noise.
cause resistance variations, which are observed as noise ex-
ceedingJohnson–Nyquistnoise.Thistypeofexcessnoisein
photoconductive detectors is referred to as generation–
4.Quantumefficiency
recombination (cid:126)g–r(cid:33) noise. G–r noise is due to the random
generation of free charge carriers by the crystal vibrations In most photoconductor materials the internal quantum
and their subsequent random recombination. Because of the efficiency (cid:104) is nearly unity; that is, almost all photons ab-
0
randomness of the generation and recombination processes, sorbedcontributetothephotoconductivephenomenon.Fora
it is unlikely that there will be exactly the same number of detector, as a slab of material, shown in Fig. 5, with surface
charge carriers in the free state at succeeding instances of reflection coefficients r and r (cid:126)on the top and bottom sur-
1 2
J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski 7441
faces,respectively(cid:33),andabsorptioncoefficient(cid:97),theinternal (cid:104)(cid:39)(cid:104)(cid:126)1(cid:50)r(cid:33)(cid:39)1(cid:50)r. (cid:126)33(cid:33)
0
photogenerated charge profile in the y direction is34
(cid:104)(cid:126)1(cid:50)r (cid:33)(cid:97) By anti-reflection coating the front surface of the detector,
S(cid:126)y(cid:33)(cid:53) 0 1 (cid:64)exp(cid:126)(cid:50)(cid:97)y(cid:33)
1(cid:50)r r exp(cid:126)(cid:50)2(cid:97)t(cid:33) this quantity can be made greater than 0.9.
1 2
(cid:49)r exp(cid:126)(cid:50)2(cid:97)t(cid:33)exp(cid:126)(cid:50)(cid:97)y(cid:33)(cid:35). (cid:126)30(cid:33)
2
Theexternalquantumefficiencyissimplytheintegralofthis
function over the detector thickness
(cid:69) 5.Influenceofsurfacerecombination
t
(cid:104)(cid:53) S(cid:126)y(cid:33)dy
0 The photoconductive lifetime in general provides a
lower limit to the bulk lifetime, due to the possibility of
(cid:104)(cid:126)1(cid:50)r (cid:33)(cid:64)1(cid:49)r exp(cid:126)(cid:50)(cid:97)t(cid:33)(cid:35)(cid:64)1(cid:50)exp(cid:126)(cid:97)t(cid:33)(cid:35)
(cid:53) 0 1 2 . (cid:126)31(cid:33) enhanced recombination at the surface. Surface recombina-
1(cid:50)r1r2 exp(cid:126)(cid:50)2(cid:97)t(cid:33) tion reduces the total number of steady-state excess carriers
When r and r (cid:53)r, the quantum efficiency is reduced to by reducing the recombination time. It can be shown that (cid:116)ef
1 2 is related to the bulk lifetime by the expression35
(cid:104)(cid:126)1(cid:50)r(cid:33)(cid:64)1(cid:50)exp(cid:126)(cid:97)t(cid:33)(cid:35)
(cid:104)(cid:53) 0 . (cid:126)32(cid:33)
1(cid:50)r exp(cid:126)(cid:50)(cid:97)t(cid:33) (cid:116) A
ef(cid:53) 1 , (cid:126)34(cid:33)
Intrinsicdetectormaterialstendtobehighlyabsorptive;soin (cid:116) (cid:97)2L2(cid:50)1
D
apracticalwell-designeddetectorassemblyonlythetopsur-
face reflection term is significant, and then where
(cid:70)
(cid:126)(cid:97)D (cid:49)s (cid:33)(cid:36)s (cid:64)ch(cid:126)t/L (cid:33)(cid:50)1(cid:35)(cid:49)(cid:126)D /L (cid:33)sh(cid:126)t/L (cid:33)(cid:37)
A (cid:53)L (cid:97) D 1 2 D D D D
1 D (cid:126)D /L (cid:33)(cid:126)s (cid:49)s (cid:33)ch(cid:126)t/L (cid:33)(cid:49)(cid:126)D2/L2(cid:49)s s (cid:33)sh(cid:126)t/L (cid:33)
D D 1 2 D D D 1 2 D
(cid:71)
(cid:126)(cid:97)D (cid:50)s (cid:33)(cid:36)s (cid:64)ch(cid:126)t/L (cid:33)(cid:50)1(cid:35)(cid:49)(cid:126)D /L (cid:33)sh(cid:126)t/L (cid:33)(cid:37)e(cid:97)t
(cid:51) D 2 1 D D D D (cid:50)(cid:126)1(cid:50)e(cid:50)(cid:97)t(cid:33)
(cid:126)D /L (cid:33)(cid:126)s (cid:49)s (cid:33)ch(cid:126)t/L (cid:33)(cid:49)(cid:126)D2/L2(cid:49)s s (cid:33)sh(cid:126)t/L (cid:33)
D D 1 2 D D D 1 2 D
and
D p (cid:109)(cid:49)D n (cid:109)
D (cid:53) e 0 h h 0 e
D n (cid:109)(cid:49)p (cid:109)
0 e 0 h
is the ambipolar diffusion coefficient, s and s are the surface recombination velocities at the front and back surfaces of the
1 2
photoconductor, and L (cid:53)(D (cid:116))1/2. Other marks have their usual meanings, D (cid:53)(kT/q)(cid:109) are the respective carrier
D D e,h e,h
diffusion coefficients for electrons and holes.
If the absorption coefficient (cid:97)is large e(cid:50)(cid:97)t(cid:39)0 and s (cid:33)(cid:97)D , Eq. (cid:126)34(cid:33) is simplified to the well-known expression30
1 D
(cid:116) D s (cid:64)ch(cid:126)t/L (cid:33)(cid:50)1(cid:35)(cid:49)(cid:126)D /L (cid:33)sh(cid:126)t/L (cid:33)
ef(cid:53) D 2 D D D D . (cid:126)35(cid:33)
(cid:116) L L (cid:126)D /L (cid:33)(cid:126)s (cid:49)s (cid:33)ch(cid:126)t/L (cid:33)(cid:49)(cid:126)D2/L2(cid:49)s (cid:49)s (cid:33)sh(cid:126)t/L (cid:33)
D D D D 1 2 D D D 1 2 D
Further simplification for s (cid:53)s (cid:53)s leads to insulator-semiconductor (cid:126)MIS(cid:33) photocapacitors. Each of
1 2
these different types of devices has certain advantages for
1 1 2s
(cid:53) (cid:49) . (cid:126)36(cid:33) UV detection, depending on the particular applications.
(cid:116) (cid:116) t
ef Themostcommonexampleofaphotovoltaicdetectoris
the abrupt p-n junction prepared in the semiconductor,
C.p-njunction photodiodes which is often referred to simply as a photodiode. The op-
Photoeffects which occur in structures with built-in po- erationofthep-n junctionphotodiodeisillustratedinFig.6.
tential barriers are essentially photovoltaic and result when Photonswithenergygreaterthantheenergygap,incidenton
excesscarriersareinjectedopticallyintothevicinityofsuch the front surface of the device, create electron-hole pairs in
barriers. The role of the built-in electric field is to cause the the material on both sides of the junction. By diffusion, the
charge carriers of opposite sign to move in opposite direc- electrons and holes generated within a diffusion length from
tions depending upon the external circuit. Several structures the junction reach the space-charge region. Then electron-
arepossibletoobservethephotovoltaiceffect.Theseinclude hole pairs are separated by the strong electric field; minority
p-n junctions, heterojunctions, Schottky barriers, and metal- carriers are readily accelerated to become majority carriers
7442 J.Appl.Phys.,Vol.79,No.10,15May1996 Appl.Phys.Rev.: M.RazeghiandA.Rogalski