151 Photocondu7. Photoconductivity in Materials Research c Stephen Reynolds, Monica Brinza, Mohammed L. Benkhedir, Guy J. Adriaenssens

7.1 Steady-State Photoconductivity (SSPC) . 153 Photoconductivity is the incremental change in 7.1.1 Definitions and Overview ...... 153 the electrical conductivity of a semiconductor or 7.1.2 Example Applications insulator upon illumination. The behavior of pho- in Materials Research ...... 154 toconductivity with photon energy, light intensity and temperature, and its time evolution and fre- 7.2 Constant Photocurrent Method (CPM) quency dependence, can reveal a great deal about and Related Techniques ...... 157 carrier generation, transport and recombination 7.2.1 CPM ...... 157 processes. Many of these processes now have 7.2.2 Dual Beam Photoconductivity (DBP)...... 158 a sound theoretical basis and so it is possible, 7.2.3 Fourier-Transform Photocurrent with due caution, to use photoconductivity as Spectroscopy (FTPS) ...... 159 a diagnostic tool in the study of new electronic 7.3 Steady-State Photocarrier Grating materials and devices. This chapter describes the Method (SSPG)...... 160 main steady-state and transient photoconduc- 7.4 Modulated Photocurrent Spectroscopy tivity techniques applied in the investigation of (MPC) ...... 161 semiconductors whose performance is limited by 7.4.1 MPC Background and Experiment ...... 161 the presence of localized electronic states. These 7.4.2 MPC Density of States Analysis...... 162 materials tend to be disordered, and possess low 7.4.3 MPC Applications ...... 163 carrier mobilities and short free-carrier lifetimes in comparison with crystalline silicon. They are 7.5 Switch-on and Switch-off Transients .. 164 often prepared as thin films, and are of interest 7.5.1 Switch-on Transient...... 164 for large-area applications, for example in solar 7.5.2 Switch-off Transient...... 165 cells, display backplane transistors, photoemis- 7.6 Transient Photocurrent Spectroscopy sive devices such as organic light-emitting diodes (TPC) ...... 166 (OLEDs) and medical imagers. However, examples 7.6.1 TPC Principles ...... 166

of where these techniques have been useful in the 7.6.2 TPC Experiment...... 166 7 | A Part study of defective crystalline semiconductors are 7.6.3 TPC Density-of-States Analysis ...... 167 also given. The approach followed here is by way 7.6.4 TPC Applications...... 168 of an introduction to the techniques, the physics 7.7 Time-of-Flight (TOF) supporting them, and their applications, it being and Related Techniques ...... 168 understood that readers requiring more detailed 7.7.1 TOF Mobility and DOS Measurements..... 168 information will consult the references provided. 7.7.2 Interrupted Field TOF (IFTOF)...... 170 7.8 Other Photoconductivity-Related Techniques ...... 171 7.8.1 Surface Photovoltage (SPV)...... 171 7.8.2 Spin-Dependent Recombination ...... 171 7.8.3 Time-Resolved Microwave Conductivity (TRMC)...... 171 References...... 172

© Springer International Publishing AG 2017 S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_7 crystalline silicon. benchmark in this way that confirmation of closing the loop Finally, mention should be made of the use of com- Optical absorption coefficient Quantum efficiency Carrier mobility Carrier lifetime Mobility-lifetime products Minority carrier diffusion length Density of localized electronic statesture and and emission their properties cap- Charge state and energetic location andations in spatial transport vari- properties. The information obtained need not be specific to This chapter focuses on the main photoconductivity the validity and limitations ofels proposed or physical data mod- analysisa schemes broader context, can simulations bestin are the be development now achieved. of used solar In cells routinely and other devices. Research has been stimulated by theircommercial highly application successful for overphy, solar 70 energy, large-area displays and years, medical imag- ining. xerogra- Photocopiers are a goodof example thin-film of photoconductors, the beginning evolution withceptor drums photore- coated with selenium, through amorphous silicon, to organic semiconductors. Each ofrials has these been mate- intensively researched withcharge regard generation to and their retention properties, using photo- conductivity methods. puter simulations in photoconductivity studies. This has been an active complementary field of50 research years, for over andderstanding its of value the inelectronic physics developing transport a of in general, coherent photoconductivity, isperiments and un- considerable. The described ex- hereinintegrated furnish into, or datacomputer compared simulations that of physical with processes, can and the itten is be of- predictions by of, the method, andof will the depend measurements.via Recombination on photocurrent can decay the from beintensity wider the and studied context steady temperature state,photoconductivity dependence can but also of be the steady-state used torecombination identify mechanisms, different while details of theof density states in theferred bandgap both of from a the semiconductor spectral candependence response be and of in- temperature the steady-statea photoconductivity detailed analysis and of transient photoconductivity. techniques applied in the investigationtors of whose semiconduc- performance islocalized electronic limited states. by Many theas are presence deposited thin of rapidly films,possess are low structurally carrier disorderedlifetimes and mobilities compared tend and to to short free-carrier         include: in / =.Vs or less in 2 / cm 4 =.Vs 2 cm 6  talline Si and GaAs where Given the complexity of these processes, use of A variety of experimental techniques based on pho- Photoconductivity, defined as thetivity increase of in conduc- aoptical material photons, resulting hasrole from traditionally in played the materials a research, absorptioncovalently most significant bonded of notably semiconductors in and the insulators. studybasic The of processes that governtocurrent the are magnitude the of generation the ofthrough pho- free the electrons absorption and of holes incidentport photons, through their the trans- material under the influencetric of field, an elec- and theirthose recombination. aspects The as study a of functionand any of field of illumination, strength, and temperature their development overoffer time, will insights into theties structure of and the material electronic under proper- investigation.that However, given several processes may be involved in theof production a specific photocurrent, a sufficientlydataset comprehensive is needed to differentiate betweenterpretations. alternative For in- instance, a lowthe photocurrent result may of be agiven low photon optical energy, absorption but coefficientnate it at recombination of may the the photogenerated also electron–hole bepairs, or due it to may reflect gemi- thegenerated formation of charge excitons. needs Photo- to beto transported realize in a athe material current, effective a carrier mobility.ten process orders This of which magnitude; can from depends vary around 10 upon by up to semiconductors such as crys band transport dominates, to 10 disordered inorganic and organic semiconductors where transport is via low-mobility extendedmediated state by conduction carrier traps, or by carrierlocalized hopping between states, or by adepending on combination temperature of and such excitation regimes. processes a range of photoconductivityvisable, experiments as is is the often combination of ad- photoconductivity with complementary techniques such asphotoluminescence, optical dark current absorption, activation, charge col- lection, electron paramagnetic resonancepump-probe experiments. and A various robust modelto should satisfy seek allFrom observations, a slightly as different rationallytasks perspective, of one as the electronic of possible. materials the scientistcorrelate major is material to attempt (and to device)and preparation micro/nanostructure conditions withfollows electronic properties. that It tools structural such as electron information, and scanning probex-ray microscopies, from and electron analytical diffraction andis Raman also spectroscopy, of key importance. toconductivity have evolved. The informationbe that obtained relates can to the mechanisms ofrecombination generation and of carriersand and diffusion. The their physical transport parameters to by be drift extracted Fundamental Properties Part A

152 Part A | 7 Photoconductivity in Materials Research 7.1 Steady-State Photoconductivity (SSPC) 153

This book contains several chapters that strongly provided in references [7.5–7]. Background and proce- support this work, and are referred to below. Compre- dures for computer modeling of solar cells, which has hensive accounts of the principles of photoconductiv- strong relevance to the techniques presented here, is ity may be found in the monographs by Bube [7.1, given in [7.8]. Readers wishing to try out their own sim- 2], Ryvkin [7.3]andRose [7.4]. Detailed information ulations are encouraged to download SC-Simul [7.9], on computer simulation of steady-state and transient a suite of linked software applicable to both steady-state photoconductivity, and comparison with experiment, is and transient photoconductivity studies.

7.1 Steady-State Photoconductivity (SSPC)

7.1.1 Definitions and Overview effect of trapping is reflected in values for n and p that are lower than the theoretical free-carrier or band The simplest photoconductivity experiment uses a con- stant monochromatic light source to generate equal a) Light excess densities of free electrons and holes, n = p, that lead to a change in the conductivity (Chap. 2)by A n = n0 + Δn  D ph D q.nn C pp/; (7.1) p = p0 + Δn where q is the electronic charge and n and p are the L  electron and hole mobilities respectively. ph is termed Ld + Iph + – the steady-state photoconductivity, or SSPC. The ba- sic experimental arrangement is illustrated in Fig. 7.1a, V where L and A are the length and the cross-sectional b) Light area of the sample. When a potential difference V is Thin film applied, a photocurrent Iph is recorded. The correspond- ing photoconductivity ph D Iph=.AF/,whereF D V=L is the applied electric field. The end surfaces of the V sample are normally contacted by metallic electrodes. Substrate L + I However, for thin films rather than bulk samples, copla- d ph nar electrodes in the form of contact pads are typically c) prepared by evaporation through a shadow mask onto

G 7.1 | A Part the film surface, or deposited firstly onto the substrate, which is then coated with the photoconductor. Interdig- Illumination itated electrodes of the type shown in Fig. 7.1bmaybe used to increase the photocurrent if required. The con- tacts to this type of sample are chosen to be ohmic. Δn The current measured in this way is termed a sec- ondary photocurrent, since it arises from replenishment of photogenerated carriers exiting the sample in order τG to maintain charge neutrality. Note that the rate of flow of carriers around the circuit may be many times larger 0 toff Time t than the rate of flow of photons, by a factor ideally equal to the ratio of the carrier lifetime to its transit time Fig. 7.1 (a) Arrangement for photoconductivity measure- across the sample, =.L2=.V//. This is to be distin- ment. V is the applied voltage, L the sample length and A guished from the primary photocurrent exiting a solar the cross-sectional area. Id, n0 and p0 are the current and cell for example, where both flows are ideally equal. the carrier densities in the dark, and Iph, n, p are the A significant fraction of photogenerated carriers incremental values generated by the illumination. (b) Ex- may become immobilized by trapping at localized ample of interdigitated electrode configuration for a thin states in the semiconductor (band tails and/or defects) film sample. (c) Schematic time development of the excess such that not every part of n and p contributes carrier concentration n in response to a period of illumi- equally to the photoconductivity in (7.1)(Chap.9). The nation , /  re- also ph (7.5) (7.4) ,the  is ev-  G lead to G 0 ) can then p values may , which play 0 7.3   p n bimolecular  : and and / / 0 .Thevalueof p n n / 1    is a recombination con- . Equation ( G G C C is small with respect to the . is not the only factor that b 0 0  d =˛ p p ; intermediate  . .  / with the photoconductivity in- b b (at low excess carrier density), are the equilibrium and excess ) are governed by recombination   D 0 D p  p 7.2 n condition, but they may equally well  ,where  monomolecular /˛ : / / 0  G ], as discussed below. In addition, the p R p correspond to variations in the flux ph 4 ,in( 1. It can also be shown from the above n   p and  D .However,  ) indicates that a linear relationship G   1 Ä  n 0 C n . The resulting linear and quadratic regimes p 0  7.5  2  p and = . . Ä 1 / n b in Materials Research  5 G Š ph D  / G The free-carrier lifetimes of excess electrons and 1 holds for  ph n equilibrium free-carrier densities be simplified to depends on  a role in recombination, depend on temperaturethe through Fermi–Dirac distribution function, thuscombination making a re- temperature-dependent process. be a result oftion an centers [7. energetic distribution of recombina- G are referred to as and therefore combination. For a given lightvariations source and in temperature, optical absorption depth 1 when the sample thickness 7.1.2 Example Applications In photoconductors,states recombination in the bandgap. is The presence of mediated discrete, or a by nar- Equation ( Under these conditions theabsorbed, incident and light is so uniformly (neglecting surface effects) erywhere constant rather thanSSPC an is average frequently value. Since nonlinearly dependent on uniformly absorbed conditionferred, is especially in often quantitativeare strongly instances work. where nonuniform However pre- absorption may there beful, use- for example to probe surface effects. holes, with carriers of opposite sign. Assuming, forthe simplicity, frequently encountered casedominated of by photoconductivity thebe majority electrons), the carrier recombination rate (assumed can here be written to as dex 0: that the response time while higher excitation levels with stant, and minority carrier densitiesthat respectively. the It SSPC then may be follows expressed as determines the value of indicate a n p n R ,    n  (7.3) (7.2) , is the )may  n G  7.1 the optical ˛ is defined by ) turns out to be G ,where p ; 7.1 p n   ; p G is illustrated schemat- . A quantum efficiency /  d ocurrent in chalcogenide ph G ˛ the sample thickness. For ntly, monochromatic illu- E =  e mobility-lifetime products d decays gradually to zero. In . 0 /; I and d p n  n p D exp      C 1 / is the average lifetime of the excess n c. When the light is turned on, incident on the sample per unit area  R p or the product n is the reflection coefficient,  ; 7.1 n  h R n  . 1 . For many materials of interest, either the D  0 n , the mobility is a material parameter that, in qG  ph p  . is the quantum efficiency of the generation pro- is the photon flux, the number of photons of E D depend, in general, on the wavelength of the   1 will hold over a significant energy range, i. e., D p  ph ˛ 1 signifies that not every photon absorbed generates  can be written as the product In many measurements on thin films, the condition  G The average carrier generation rate  and photon flux is n d 0 energy cess, a free electron and hole that contributesrent, to due the photocur- to geminate recombinationexciton of formation. the The carriers, values or of the parameters < and mination from aobtain tunable energy-resolved light information source aboutwhile can the illumination with be sample, white light used willaverage. provide to a global ˛ illuminating light. Conseque where which explicitly displays th frequently used to characterizerelationship between photoconductors. The mobility product and rate of generation ofvolume, free electrons and and holes per unit electrons or holes. Substituting into ( per unit time, much larger (the majorityminority carrier) carrier), than because themobilities. of other For strongly instance, (the the unequal electron carrier intrinsic term silicon, dominates while the in phot glasses is carried by holes. In those instances, ( often be reduced to a one-carrier equation. In general, will depend onacteristics, temperature and while sample the char- excess carrier densities monochromatic light, the relation between theI intensity absorption coefficient and are determined by a combinationnal of parameters. material Phenomenologically, the and excess exter- density  increases gradually with time,the steady-state and value we eventually address reaches the in this light section. is When turned off, the steady state, the generationare and equal recombination and rates constant; in thenot. transient regions, Time-dependent they aspects are ofaddressed photoconductivity in are later sections of this chapter. ically in Fig. Fundamental Properties Part A

154 Part A | 7.1 Photoconductivity in Materials Research 7.1 Steady-State Photoconductivity (SSPC) 155 row energy range, of trapping levels leads to thermally a) b) activated photocurrents, with the activation energy in- I (A) I (A) dicating the energetic positions of the traps. Main and –8 Owen [7.10]andSimmons and Taylor [7.11]showed 10 that the positive photocurrent activation energy in the monomolecular recombination regime corresponds to the energy above the Fermi level of a donor-like cen- ∆E = 0.30 eV ter, while a negative activation energy value in the 10–9 b bimolecular region corresponds to the energy above the valence band edge of an acceptor-like center. Fig- ure 7.2 illustrates this photocurrent behavior for amor- phous As Se [7.12]. This is characteristic of chalco- 2 3 –10 genide glasses, where the intrinsic charged defects 10 Id act as recombination centers [7.13]. SSPC measure- ∆Em = 0.17 eV ments of this type can thus determine the recombina- Eo = 0.88 eV tion mechanism and the energetic position of discrete defects. 2.6 2.8 3.0 3.2 3.4 2.6 2.8 3.0 3.2 3.4 3/T –1 3/T –1 The temperature dependence of the SSPC in amor- 10 (K ) 10 (K ) phous silicon (a-Si:H) does not exhibit a definite acti- Fig. 7.2a,b Temperature dependence of the steady-state dark and vation energy, due to the presence of a more distributed photocurrents in an a-As2Se3 sample, (a) illuminated at 1:55 eV and complex set of traps including band tails and with intensities of 0:84, 3:5, 9:8, 38 and 120 1012 cm2s1,and charged and neutral defects (Chaps. 9 and 24). A sim- (b) illuminated at 1:85 eV with intensities of 0:56, 1:7, 4:6, 27 12 2 1 plified electronic density of states (DOS) is shown and 77 10 cm s . Em and Eb represent the photocurrent schematically in Fig. 7.3a. activation energies in the monomolecular and bimolecular recom- Whenever the DOS in the bandgap of a photocon- bination regimes respectively, and E is the activation energy of the ductor consists of a distribution of traps, quasi-Fermi dark current Id.(After[7.12]) levels (QFLs) can usefully be defined. In thermal equi- librium, the QFLs and the Fermi level coincide. Under a) n N b) n + ∆n illumination the QFLs split from the equilibrium Fermi E 0 C E 0 level such that they define the occupancy of states sepa- C C CB tail ∆E EFn rately for electrons and for holes. The QFL for electrons C may be written EG EF Defects EF  à hv > EG n VB tail ∆EV EFp EFn D EF C kBT ln 1 C (7.6) n0 EV EV 7.1 | A Part p0 NV p0 + ∆p with an equivalent expression for holes. In the case of the majority carrier, EF may be determined from Fig. 7.3 (a) Model density of states (DOS) in a disordered the activation energy of the dark conductivity d and semiconductor at thermal equilibrium, electron and hole n=n0 D ph=d. To a first approximation (see [7.11] densities n0 and p0 respectively, depicting localized con- for detailed considerations), the QFLs correspond to de- duction and valence band tail states and defects distributed marcation energies dividing the DOS into a shallower in midgap. (b) Illumination results in splitting of quasi- part, where carriers may be trapped and subsequently Fermi levels EFn and EFp. Localized states between EFn emitted, and a deeper part where traps have become re- and EFp act as recombination centers, those between EFn combination centers. This is illustrated in Fig. 7.3b. It and EFp and the respective band edges act as carrier traps is clear that as the QFLs depend on the carrier den- from which charge is subsequently released sity, varying the light intensity and temperature will influence the role of a given set of localized states in tool. One example is provided by Brüggemann [7.14] generation and recombination processes. In addition to who studied SSPC in microcrystalline silicon thin films. the variation with energy of the DOS in the bandgap, He applied a result first proposed by Rose [7.4]and the capture and recombination constants for the various elaborated by Bube [7.2], that the intensity dependence centers may also be quite different. of the SSPC in an intrinsic semiconductor in which Much progress has been made in understanding electrons are the majority carriers is controlled by lo- photoconductivity in materials with broad distributions cal changes in the DOS at EFn. By adjusting EFn over of localized states, and in applying SSPC as a diagnostic a wide range by varying I0 and T, and measuring  from V E 0.0 0.6 0.4 0.2 5eV : .This = 1 C E  Fritzsche 7.4 EQE (%), EQE  ) to deter- 7.4 Absorption (a.u.) ]) 16 ]. in this model are predicted to 19  5 eV corresponds to the optical Energy (eV) [7. 1.5 2.0 2.5 3.0 ], is illustrated in Fig. Wavelength (nm) 15 1 have been observed in a-Si:H, again 1000 700 500 Bube at low generation rates, and > V is steeper than the valence band tail slope ]and E et al. [7. C 5 eV signal the presence of defect distributions Combination of spectrally-resolved photoconduc- E 18 : = 3 P3HT Absorption PL EQE  T , limiting values of B  0.5 1.0 From a materials characterization point of view, V k E 1.0 Photoluminescence (a.u.) (PL) 1.5 0.0 0.5 2.0 shows the spectrally resolved photocurrent for diamond films prepared by chemical vapor deposition. The risephotocurrent in around 5: bandgap of diamond, while the shoulders at and SSPC offers the possibility of using ( mine the absorptionciency coefficient as and/or a quantumphotons, effi- function and thus of to explore the theductor. bandgap When of energy a materials of semicon- energy with the levels sufficiently are incoming studied, well-defined localto maxima specific corresponding optical transitionstoconductivity may spectra. be An seen example, in fromNesladek the the pho- work of tivity, optical absorption and photoluminescencements measure- used tosemiconductor quantify P3HT. exciton (After [7. formation in the organic be Fig. 7.5 slope at high generationout rates. experimentally Both assuming realistic predictions(25 tail meV are and slope 45 values borne meV),dance and over furthermore the detailed full experimental accor- rangemeans was of achieved computer by modeling. Finally it shouldthat be values noted of in conflict with theing Rose offered model, by a with number explanations ofet be- workers al. including [7.  C 6 ı per- ), it is  0 I Magnitude of as low as 0.4 ) -Oxidized 3 b  ( S Photon energy (eV) Photon energy (eV) a, but in which re- )versuslog( -Oxidized -Hydrogenated 2 7.3 2 ph S S  -Hydrogenated -As grown -Oxidized 2 2 2 S S S . If the conduction band tail Phase shift. ]) ) a ( 15 -As grown 2 ). S 3 ]. They carried out photoconductiv- 17 12345 123456 C(S involved as charge reservoirs required to ı Room temperature AC photocurrent spectra, Photocurrent (A) Phase shift (°) et al. [7. 0 0 0 –8 –4 –6 –10 90 60 30 –12 –14 indirectly Changing the position of the equilibrium Fermi ) and 820 120 10 10 10 2 10 10 10 a) b) sisted even when the photocurrentof was over magnitude two below orders theresults dark is current. predicted Neither of byHowever, these the they Rose model were outlined ablethe above. observations to in terms account ofstates consistently a such typical for as model that density shown of in Fig. maintain charge neutrality combination takes place solely viacase defect band states. tails In do this notare act as recombination centers, but could be observed, and (ii) these low values of ity measurements overtemperature, a and wide range notedture of that ranges, intensity (i) around and over 200 K, certain values tempera- of possible to reconstruct the DOS inbandgap the as upper a half series of of the segments. level by doping also modifies photoconductivity behav- ior. The effect of n-typehas doping on been the studied SSPCMain of by a-Si:H a number of workers, including measured at 7 Hz, afterpor various deposition (CVD) treatments diamond of layers chemicalva- deposited at 920 Fig. 7.4a,b the local slope in a plot of log ( photocurrent. (After [7. (S Fundamental Properties Part A

156 Part A | 7.1 Photoconductivity in Materials Research 7.2 Constant Photocurrent Method (CPM) and Related Techniques 157 in the bandgap. The data were measured using low-fre- commences at 2:6 eV, compared with a value of 1:9eV quency chopped light and a lock-in amplifier. It can be for strong optical absorption in the same sample. The seen that changes in the phase shift between the pho- former energy is that required to generate free carriers, tocurrent and the chopped light may also reveal specific whereas the latter is that required to generate an exciton, features in the DOS. This topic is addressed in de- a bound electron-hole pair (Chap. 3). The difference of tail later, in Sect. 7.4 on modulated photoconductivity 0:7 eV corresponds to the energy required to dissociate (MPC). the exciton. Photoluminescence (Chap. 38) and pho- A further example of the use of spectrally resolved toelectron spectroscopy measurements enable further photocurrent, this time to probe organic semiconduc- details of the interactions to be deduced. This example tors of interest in solar cell development, is shown in illustrates the benefits of combining a range of measure- Fig. 7.5. Deibel et al. [7.16] have measured the quan- ments to provide linked information on semiconductor tum efficiency of charge generation in the conjugated properties, which leads in turn to a comprehensive and polymer P3HT. The onset of strong photogeneration consistent model.

7.2 Constant Photocurrent Method (CPM) and Related Techniques

7.2.1 CPM interference fringes [7.22] and to calibrate the system using the Ritter–Weiser formula [7.23]. The experimen- The constant photocurrent method (CPM) is a simple tal arrangement used in absolute CPM measurements but important development of the basic single-beam is shown schematically in Fig. 7.6. Depending on re- measurement described in Sect. 7.1. It was introduced quirements, the sample may be mounted in a cryostat to by Vaneˇ ˇ cek et al. [7.20, 21] to determine the optical ab- enable operation over a wide temperature range. The sorption coefficient ˛.Eph/ of thin-film semiconductors choice of monochromator system is important, since over a very wide range (typically 0:1105 cm1)as at long wavelengths second-order output can easily a function of photon energy Eph. In CPM, the photocur- dominate the sample photocurrent to give erroneous rent is kept constant by continually adjusting the light readings. A double monochromator plus order filters intensity I0 while Eph is scanned across the spectrum. are recommended to maintain second- and higher-order A constant photocurrent implies that the quasi-Fermi output and scattered light below one part in 105. levels have fixed positions, and thus that the free-carrier The CPM experiment may be operated with either lifetime  remains constant. DC or AC illumination, but as discussed later, the ab- From (7.2)and(7.4), the photoconductivity of a thin sorption spectra obtained need not be identical. Most re- film under uniformly absorbed light (˛d  1) is searchers use low-frequency AC illumination (chopped light, < 10 Hz) to measure the sample photocurrent and atA|7.2 | A Part ph D q.1  R/˛ : (7.7) detector outputs, since values may be small (nA to pA) and thus prone to electrical noise and interference The product ˛ will thus remain constant, and rela- tive values of ˛ can be determined from it, provided Mono Beam Sample that energy dependencies of the parameters , R and  Lamp chromator splitter of (7.7) are negligible. The value at which the photocur- D2 rent is fixed may be chosen freely, but will in practice be dictated by the low-absorption region of the sam- ple. However, since even low-level photocurrents can Chopper still be measured with high precision, the CPM method is especially useful at low values of optical absorption D1 where standard optical transmission measurements lose Electronic their accuracy. circuits It follows from (7.7) that under the above condi- tions a plot of 1= versus Eph will reveal relative values Fig. 7.6 Schematic diagram of an absolute CPM setup. Photode- of ˛. In an improved variant of the CPM technique, tector D1 is used to measure the intensity of light incident on the termed absolute CPM (ACPM) [7.21], optical trans- sample, while detector D2 measures the transmitted light. These mission through the film is measured at the same time signals plus the sample photocurrent are recorded by electronics, as the photocurrent, and the data from the two mea- the latter being maintained constant by control of the lamp current. surements are combined in order to remove optical Details of operation are given in the text. (After [7.21]) ], ˛ at 25 ˛ ]. The 24 Bacioglu 0, is that [7. D F ] investigated E T 29 thermal emission ) could be probed and F v E E et al. [7. ] have demonstrated the itions from filled localized onal disorder of additional 30 between ]. DBP achieves constant life- ), followed by ph Sharma F 31 E ] extended the CPM experiment ] studied the organic semiconduc- E d et al. [7. 26 28 ˛= d H with varying oxygen concentration K W x D depends on the values of the interaction ma- ] determined the Urbach tail slope and es- et al. [7. / et al. [7. Ishihara K 27 ph E  An increasingly wide range of thin-film semi- Main c E 2 eV by a factor of 50 over the same range. This : . usefulness of CPMinvestigating as a transport probe propertiesGa-Zn-O of and deep (IGZO) stability defects thin ofThis when films information In- for enabled useto them to reduce in modify the oxide preparationthreshold defect TFTs. voltage density, stability. which in turn improved nanocrystalline CdSe films using CPMsoaking following light- and thermal annealing,systematic and changes report in abandgap. Urbach series of tail energy and optical tors MEH-PPV and PCBM usingand CPM, in both blended separately form fortion application in solar bulk cells. heterojunc- They observedspectra, differences consistent between with the chargeponents transfer in the between blend. com- timated the deepoxide defect density a-SiO in amorphous silicon by comparing the AC and DC CPM limiting values. conductors haveet been al. [7. studied by CPM. 7.2.2 Dual Beam Photoconductivity (DBP) Like the constant photocurrent method discussed above, the dual-beam photoconductivityused (DBP) to technique determine the is subbandgap opticala absorption in photoconductor [7. [O], calibrated fromBoth parameters the show a Si-O-Si strongear IR dependence, with increase a stretching lin- in peak. increases tail slope from from 0 55 to to 120 meV 50% as and [O] an increase in 1 suggests that the compositi oxygen in thealso structure results in broadens a theWillekens greater number band of tail, Si dangling and bonds. trix element and the DOSMore at the elaborate conduction band and edge. dures potentially assume a more parabolic conduction accurate band DOS proce- [7. constant analysis (on a-Si:H) to includeexcitation the from possibility the of valence optical banddefect into states unoccupied deep (above though generally only trans states to electron transport states are considered. into the conduction band.at These high frequencies transitions but areand significant DC. weak at Thus low DCthan CPM frequencies AC will CPM. tend Thesethe to density workers return of also a empty demonstrated larger states (above that a constant conduction band DOS and g to be ]was / 20 E for a ma- . most com- g / ]. h 21 ˛. , et al. [7. 20 cek 2 eV, that is consid- is a result of all per- eˇ below the Urbach tail / is implicitly involved in ator wavelength is then ˛ ph Van ˇ / E E . figures of merit ˛. g 100 measurement points may  ). If a particular set of transitions 3 . This turns out to be quite straightfor- ˛ , it seems reasonable to suppose that there ˛ .ThetwoCPM / ph E While it is of course useful to know As the electronic DOS ˛. directed at anCPM emerged investigation as of an importantassessing thin-film technique material of silicon, choice quality for and asrate, a substrate function temperature, oflight process exposure deposition and gas subsequent composition,other degradation, factors. and Essentially, many terial per se, forsolar example cell, when a designingextracted. wealth a The of initial thin-film work additional by information may be take several hours to collect sincelong. settling For times may a be detailedculations exposition required of to calibration generatespectrum, and the the cal- reader final is referred absolute to CPM [7. whose effects are minimizedCPM by lock-in measurement detection. process The lamp proceeds current as is adjusted follows.equals until The the the set-point value sample and photocurrent remainsare steady. Readings taken from the calibrated detectors D1to (proportional the intensity of themitted incident beam) beam). and The D2 monochrom (thedecremented, trans- and thephotocurrent lamp once current more adjusted equalsD2 until the are the set-point, read, and D1the so and wavelength on scan until isis the reached. carried desired Normally out end the inalgorithm point process a running of closed on loop, asired by means precision, PC. of the Depending a 30 upon control the de- monly quoted for intrinsic a-Si:H into the (i) literature the relate Urbach tailthe slope, exponential the rise characteristic in energymany of optical disordered absorption materials, observedgree and in of structural a or compositional measure disorder,defect and of (ii) shoulder the the (or de- bump) in typically at a photonered energy a of measure 1: ofcases, the transitions dangling from bondlevel) density. filled to In empty states both states (below closeband to edge the or predominate Fermi (but above see thetron below), conduction since is the the elec- majorityenergy in carrier. a-Si:H It revealed follows byof that CPM the is the valence largely band Urbach a tail slope. measure mitted electronic transitionsintegral representing in this a is referredsity given to of as states sample. the (Chap. joint The den- is dominant, this will be evidencedof in the local behavior determining should be an inverse process that enables ward, provided transitions are limited to thoseabove, indicated and current isrier. carried The by simplest a expression, single obtained mobile by car- assuming obtained from Fundamental Properties Part A

158 Part A | 7.2 Photoconductivity in Materials Research 7.2 Constant Photocurrent Method (CPM) and Related Techniques 159 time conditions by directing an additional constant, is placed between the light output from the interfer- uniformly absorbed, bias beam of approximately the ometer and a broadband detector, and the interfero- bandgap energy at the sample. This beam must be set gram is recorded as the detector output versus optical to maintain a generation rate larger than that from the path difference. The interferogram is then Fourier- monochromator probe beam, throughout the scan. DBP transformed and normalized to a background spectrum, eliminates the need for slow and tedious adjustments of yielding a conventional IR spectrum of absorbtance ver- the probe beam required to maintain constant photocur- sus wavelength. The FT technique effectively scans all rent conditions in CPM. The probe beam photon energy wavelengths in parallel and thus has an inherent speed range may thus be scanned more rapidly than for CPM, advantage over conventional sequential dispersive spec- using a simpler control and measurement system. DBP troscopies. The optical throughput is much higher, so requires a very similar experimental setup to CPM, with there are considerable benefits in terms of noise cancel- the addition of a bias light. This may be in the form of lation. Overall this makes for a faster, lower noise and a laser beam, directed at the sample obliquely so that potentially higher-resolution approach. the detectors do not become overloaded by it. The probe These advantages were recognized as being appli- beam is optically chopped, enabling the resulting sam- cable to the measurement of photoconductive electronic ple photocurrent to be separated from the DC bias beam materials at low absorbtance levels [7.36, 37], since the current by lock-in detection and amplification. Simi- detector in the FTIR system may also play a dual role larly, any stray light from the bias beam reaching the as the sample. Many commercial FTIR setups possess optical detectors will be rejected. an external detector input. In FTPS therefore, the in- A feature of the DBP measurement is that the terferogram is recorded by a detector consisting of the sample QFLs are more widely split, since the con- photoconductor of interest. The photocurrent is am- stant DC bias current must be larger than a typical plified and presented to the external input. The scan constant photocurrent value in CPM. The resulting is carried out, Fourier-transformed, and normalized to differences in occupancy of deep states mean that a background spectrum previously recorded using a cal- ˛.Ep/ values recorded by the two techniques may not ibrated broadband detector, to yield the absorbtance agree. However the difference(s) can also be used to spectrum of the photoconductor. advantage; the occupancy can be varied predictably by measuring the DC photocurrent, and DBP spec- tra recorded at different bias beam intensities may be Norm. FTPS, CPM (a.u.) 104 interpreted to yield additional information on defect μc-Si:H thin film densities [7.32]. Defect capture properties and charge 3 state, and the presence of surface states, may also be 10 inferred in some cases. An example may be found in 2 Günes et al. [7.33], who studied differences in spectra 10 from annealed and light-soaked hydrogenated amor- 7.2 | A Part 1 phous silicon samples in the deep defect region. Remes 10 et al. [7.34] have reported that residual nitrogen con- 0 tamination in nanocrystalline diamond can be identified 10 using this technique. 10 –1

7.2.3 Fourier-Transform Photocurrent –2 Spectroscopy (FTPS) 10

–3 The use of a FT spectrometer to record spectrally re- 10 solved photocurrent in thin films was first reported –4 (S)-CPM by Inushima et al. [7.36], and developed as a quan- 10 Normalized FTPS titative technique (FTPS) by Vaneˇ ˇ cek et al. [7.37]. 0.4 0.8 1.2 1.6 2.0 The concept is a development based around a stan- Photon energy (eV) dard technique used in analytical chemistry for many years, the Fourier-transform infrared (FTIR) spectrom- Fig. 7.7 Normalized FTPS spectrum (full line) compared eter. This technique consists of recording and Fourier- with the standard CPM spectrum (circles), measured on transforming interferograms produced by a Michelson the same microcrystalline silicon sample. Note good corre- setup illuminated by an appropriate broadband light spondence between the spectra, and greatly extended range source. In absorption mode, the sample of interest of sensitivity available from FTPS. (After [7.35]) b ı 7.8 (7.8) .Thein- 2 ]. It seems M Formation 40 ) . The reflected b S ( ]. The increased 39 . The spatial period 2 M SSPG experimental ]) ) and a 42 ( between the two beams to be 1 ]. Recently, FTPS has been

M 38 on to the sample relative to the probe beam, and 1 [7. ı : M Fig. 7.8 arrangement; optical elements aredescribed as in the text. of interference fringes at(After [7. sample. Á 2 

 Holovsky 2sin D It may be concluded that FTPS has several advan-  used to extend thesurements range on of a-Si:H quantum solar efficiency cells mea- [7. signal-to-noise ratio over CPMresolution was found of to the improve FTPS deep to DOS study deep in defectscell this in has a case. helped PbS quantify The nanocrystal aging solar use effects of [7. kept constant in FTPS, as thecovers interferogram a necessarily wide intensitya range. constant carrier However, lifetime as may with bea imposed uniformly DBP, by absorbed applying DC optical bias beam. tages over CPMtime and and DBP, increased specifically sensitivity,A and reduced review few of scan disadvantages. thevided technique by and its applications is pro- likely that FTPS willof enjoy photoconductors greater and usageyears, in photodevices as the in its study potential theresolved advantages photocurrent coming techniques over become other moreknown. spectrally widely varied by adjustment of tensity of the probe beamthe is main reduced beam, to ensuring that aroundremains the 10% modulation of small. amplitude The samplestage, enabling is the angle mounted on a movable of the sinusoidal intensity variation, shown in Fig. is given by by the plane mirror A half-wave retardingplaced plate in the H path ofto may the the main plane be beam, of at polarization. selectedat an This angle and rotates the of the sample 45 main beam by 90 beam (probe beam) is likewise reflected by the two beams superpose incoherently. An optical chop- per is placed inlock-in the detection path of of the the sample probe beam, secondary enabling photocur- Air , ], 41 Substrate ). The 2 billion Photoconductor Λ P of a semi- ]. The tech- et al. [7. L 35 Ritter b) ]. The FTPS method et al. [7. 23 2 cek P 1 ]. As with standard CPM, eˇ , optically identical to the P BS 35 uding amorphous silicon, mi- Van ˇ nce of a coplanar sample illu- filter C [7. ]. 42 ), and to adjust the intensity of the formula [7. 7.7 1 2 1 [7. P M M H θ a. Two polarizers are used, to define the plane 7.8 Ritter–Weiser The applicability of the FTPS method to a wide A basic experimental arrangement is shown in S Brüggemann a) nique is highlyused sensitive, and to extend inthe the some parts measurement cases per of may million limit absorptance be of from CPM, to parts per as shown in Fig. has been used diagnosticallycells. Unlike on CPM, both the sample films photocurrent and cannot solar be range of materials,crocrystalline incl silicon, diamond layers,diamond and nanocrystalline very thin organicin films, a was later demonstrated publication by interference fringes may appear on antrum as-recorded of spec- a thin film.transmission There is measurement no used directapproach equivalent in of to the the remove absolutedo the CPM so fringes, but if it an is auxiliary possible to sample, is available. Thewithout two filter, measurements, can with be and interference-free processed to absorbtance obtain the spectrum,the thin-film by means of beam emerging from the laser (by rotation of beam splitter (BS) provides the requisitebeams. two interfering The transmitted beam (main beam) is reflected 7.3 Steady-State Photocarrier Grating MethodThe SSPG (SSPG) method, first described by enables the ambipolar diffusion length Fig. conductor thin filmticularly to important be parameter determined. inuse This materials as is targeted for absorber afundamental par- layers studies. The in methoding solar consists the cells, in photoconducta measur- asminated well by as aare two-beam in coherent and system formthe when interference electrodes, (i) fringes and parallel thesuperpose (ii) to beams as the beams atailed are spatially review incoherent uniform of and illumination.basis, interpretation the A and applications de- SSPG has beenby provided technique, its theoretical of polarization ( Fundamental Properties Part A

160 Part A | 7.3 Photoconductivity in Materials Research 7.4 Modulated Photocurrent Spectroscopy (MPC) 161 rent under a small external voltage bias. The lock-in a range of thin-film silicon based semiconductors, in- amplifier readings UC and UI, under coherent and inco- cluding hydrogenated amorphous silicon and silicon- herent illumination conditions respectively are recorded germanium [7.43], polymorphous silicon [7.44]and for a series of values of , yielding the parameter microcrystalline silicon [7.45]. It has also been applied to thin-film solar cell materials such as GaN [7.46], UC ˇ./ D : (7.9) CuGaSe2 [7.47] and polymer blends [7.48]. Semicom- UI mercial automated systems have been developed [7.49]. DOS spectroscopies based on SSPG and moving grat- In turn, ˇ is related to L by ing techniques have also been demonstrated [7.50, 51]. 2Z The usefulness of the SSPG method in optimization ˇ./ D 1  h i ; (7.10)   2 of thin film semiconductor properties is dependent on 2 L 2 1 C a number of factors: where Z is a constant between 0 and 1, related to var- 1. The position of the Fermi level in a semiconduc- ious material and system parameters. Low values of Z tor changes in response to variations in preparation can indicate poor definition of the grating due to surface conditions, doping and degradation effects. This light scattering or other inhomogeneities. may alter the recombination kinetics and, as a con- 2 Equation (7.10) may be linearized by plotting 1= sequence, the diffusion length. Thus it is possible, Œ =. ˇ/1=2 versus 2 1 , yieldingp a straight line y D axb, for example, for L to increase without there being 2 2 from which L D 1=2 b and Z D a =b are obtained. a corresponding improvement in material quality. Often the majority carrier  product is signifi- 2. As the method relies upon a uniform photocar- cantly larger than the minority carrier value, in which rier grating being established, surface roughness or case the ambipolar quantity L is determined primar- interior structure may scatter light and reduce its ily by the minority carrier. The corresponding majority uniformity, resulting in inconsistencies and/or inac- carrier product  may be determined from the steady- curacies in the results. state photoconductivity at the same generation rate, 3. Photocurrents in the SSPG experiment may be yielding two important figures of merit small compared with the dark current and this may  à restrict measurements, especially on doped materi-  kT ph als and intrinsic materials at room temperature and ./ D L2;./ D : (7.11) min 2q maj qG above.

The SSPG method has been used to investigate dif- These factors are discussed in detail by Brügge- fusion lengths and minority-carrier  products in mann [7.42] and references therein. atA|7.4 | A Part

7.4 Modulated Photocurrent Spectroscopy (MPC)

7.4.1 MPC Background and Experiment light, though there are instances where a genuine phase lead may occur. MPC is a density-of-states spectroscopy, introduced by Both amplitude and phase are sensitive to the trans- Oheda [7.52] in 1981, used to probe the energetic dis- port processes taking place, and both are of use when tribution of unoccupied trap states in the energy gap calculating the DOS versus electron energy. It is im- of a photoconductor. MPC involves the illumination of portant to note that the states probed directly by this a coplanar photoconductor sample as shown in Fig. 7.9 experiment are empty trap states that capture majority with a quasimonochromatic above-gap light source, carriers. This is unlike CPM, where majority carri- which is amplitude modulated, typically within the fre- ers are ejected from filled trap states by absorption of quency range 0:1 Hz–100 kHz. An LED is a highly a subgap photon. Thus the two techniques are comple- suitable source, though chopped light from a monochro- mentary; in the case of amorphous silicon for example, mator may also be used. A voltage bias is applied to MPC supplies information about the DOS above EF, the sample, and the amplitude and phase of the pho- and CPM about the DOS below EF (but see [7.26]). tocurrent relative to the excitation is measured versus Some means of accurately calibrating the amplitude modulation frequency using a phase sensitive detector and phase of the light at the sample is essential, as (lock-in amplifier). Generally, the photocurrent lags the phase shifts introduced by the measurement electron- . i F n

E E / C ,by ! ]. (7.13) (7.14) (7.12) n Fn ! are ob- 53 n by 100. E ,and . closer to I 1 //,where ! Fn of traps of Fn  T sin s ! E i B Ä . This thresh- at 300 K. The 12 / Fn 1 / ). For intrinsic =.k et al. [7. ! i  ! E ;  . 7.1.2

!>! / qAFG . qAFG ! Kleider exp 04 rad s . for each set of traps. n : Ã  ! 0 : Ã n n ei n . (Sect. I n n Á C  ! D D . Assuming low-level illumi- n C  c ! ei  cos // D E Fn 12 eV, and increase !

T Ä ÃÂ ti : ! B is often taken as 10 ÃÂ 0 T ! is ln ! d  T B d 2 c T 1 D k =.k B E B k !

Fn k ] Â  E Â , yields . The emission frequency into transport  100/ F ti  55 c D . D . , 8eVbelow E closely spaced in energy and centered at N E / / ln n n n ti 54  C exp D T ! ! N B n E  Fn E k D . . ! E ti  N N HF MPC In the HF regime, the measured AC photocurrent E The frequency separating the HF from the LF by ! is the attempt-to-escape frequency. The capture prop- Fn c  erties are governed by the trapproperties density, by and the the emission trap energyance depth. considerations, From detailed bal- We consider thea single single species carrier of case trap whose (electrons), capture coefficient with is old depends on the DC generationture. rate For and example, the increasing tempera- theat illumination constant temperature intensity (300 K) so thatequals the 100 photocurrent times the dark current will move tained [7. is furnished predominantly byfrequency matches states the modulation whose frequency. By emission ing solv- the rate equations,cally two approximate, relationships useful, linking the though DOS mathemati- amplitude to and the phase of the photocurrent at amorphous silicon, E ! density The electron capture frequency into a set where is around 0: and is regime is related torecombination the energy centers, at the which traps quasi-Fermi become level HF regime lies above this,quency of i. the e., applied where modulation the angular fre- states just above nation such that the photocurrent is equal torent, the dark cur- are a number ofare approaches two that limiting differ cases inand termed detail, the the there low high frequency frequencycerns (LF) (HF) the regimes. emission The of former carriersrecombination con- from of carriers. traps, A the review latterof of the these the techniques development is given by t up- ph ) I V of the electric field from the Photocurrent 0 lower frames t feed-forward Photoconductor Finally, the sample amplitude is normalized to the Emitter ), and phase relationship between the exciting light Schematic diagram of an MPC measurement system ( modulation drive electronics canplifier leak by into capacitive the coupling. pream- a This clear manifests phase-leading itself signalbogus as trend. signals Another entering sourceground the of loops. system Generally it is is beneficiallate the to the optically phase presence iso- reference, of or toon disable the the coaxial ground cable. shield Athe further dark obstacle current. is AC presented coupling by duce of a instruments parasitic will phase intro- lead, especiallyThus when at measuring low small frequency. photocurrents below 10in Hz DC mode, it mayDC offset be current at necessary the to input introducecel to a the the preamplifier dark stable to current, can- and thus avoid signal overload. calibration amplitude, and theby sample subtracting the phase calibration corrected phase,To at probe each a frequency. suitablyat wide sample energy temperatures range,350 several K typically are scans carried between out. 120 K and 7.4.2 MPC Density of States Analysis It is possible to extractand phase the data DOS by application from of straightforward MPClae. formu- amplitude The degree of successof depends features upon to be the resolved sharpness inaration, and the the DOS, method their of energy analysis sep- chosen. While there ics must be eliminated to obtainresults. accurate This and may consistent be achievedphotodiode by to connecting the a input fast ofaddition pin the to current pre-amplifier, the in out, sample. with the A light source calibrationthe incident on scan sample the blocked is pin diode tonected carried and to light, the but pre-amplifier. Then, stillis the performed MPC electrically by blocking experiment the con- pin diodelight and at directing the the sample. Complicationsquency, can since arise at high fre- Fundamental Properties Sinusoidal driver Light intensity 0 Part A per frames intensity and the photocurrent ( Fig. 7.9

162 Part A | 7.4 Photoconductivity in Materials Research 7.4 Modulated Photocurrent Spectroscopy (MPC) 163

G! is the AC generation rate. From detailed balance –3 –1 considerations, n D CnNc where Nc is the effective DOS (cm eV ) density of states in the conduction band. Typical values 20 3 8 3 1 LF-MPC are Nc  10 cm and Cn  10 cm s . HF-MPC Performing the HF MPC experiment over a range of 1018 temperatures provides several DOS sections, together covering a wide energy range. These sections should overlap provided the data lie within the HF regime and 1017 the above parameters are correctly matched. This is more convincing if there is a visible bump or shoulder Donors Acceptors in the DOS. As the DOS is temperature-independent, CB tail 1016 any feature should remain fixed at a specific energy for all sections, pinned by a correct choice of . A range of capture properties is possible, depending on the type 15 of trap. It might therefore be argued that without addi- 10 tional information HF MPC cannot deliver the absolute 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 DOS, but only the product NtCn. E–EV (eV) An equivalent set of equations for holes may be derived, and in general both electrons and holes will Fig. 7.10 Comparison of HF and LF MPC techniques. The contribute to the photocurrent and thus to the appar- model DOS shown was used to computer generate MPC ent DOS. There is no means of distinguishing between I.!/ data over the range 100350 K in 50 K steps, inter- these contributions. However, given the ratio =C ap- preted using (7.12)and(7.15) to yield the DOS points pears as a scaling factor in (7.12)and(7.13)theHF shown (gray circle and brown circle). The range of validity DOS technique will tend to probe either the upper or the of HF MPC is illustrated by a rapid fall in the apparent HF lower half of the bandgap, controlled by trapped elec- DOS close to the QFL at each temperature. (After [7.57]) trons or trapped holes. Of the two expressions, (7.12) is capable of resolv- The effectiveness of the LF technique in compar- ing features in the DOS of the order of kBT apart in ison to the HF technique has been investigated in energy, whereas (7.13) has an improved resolution, of detail [7.56], and a comparison based on data gener- order kBT=2. The price to pay is a poorer signal-to- ated by a computer model is shown in Fig. 7.10.The noise ratio in the latter case, since a derivative of the primary advantages of the LF technique are (i) since LF experimental data must be taken. Their relative merits MPC is performed at higher generation rates, the signal- have been compared in detail using computer simula- to-noise ratio of the recovered signal is improved; and tions and by experiments on amorphous silicon, which (ii) the relationship does not involve the attempt to es- we return to later. cape frequency. From (ii) it follows that the intersection 7.4 | A Part of the two techniques may therefore be used as a cal- LF MPC ibration to deduce the trap parameters. This and other The LF MPC technique is based on the relationship developments in interpretation are explored by Schmidt between the recombination lifetime and the DOS at et al. [7.57]. One apparent disadvantage of LF MPC in the quasi-Fermi level for trapped carriers. Koropecki comparison to HF MPC is that the improved resolution et al. [7.56] showed that for the LF MPC experiment offered by (7.13) is not available. the DOS at a probe energy Epr is given by 7.4.3 MPC Applications RGDC N.Epr/ D ; (7.15) kBT ln.2/ Following the initial demonstration of MPC by Oheda where [7.52] in 1981, development was focused on pro- totype disordered semiconductors such as amorphous tan./ 4 As2Se3 [7.58, 59], a-Si:H [7.55, 60] and alloys such as  D and E D E C k T ln.2/: R ! pr Fn 3 B a-Si:Ge:H [7.61]. An example of the use of MPC in the (7.16) study of light-induced defect creation and subsequent thermal annealing in polymorphous silicon [7.62]is R is obtained from the slope of a plot of tan ()versus shown in Fig. 7.11. Application has extended to a wider !,andEFn from the ratio of the photocurrent to the dark range of materials, including the following examples: current (Sect. 7.1.2). Gorgolis et al. [7.63] have studied the DOS in thin films ], ,as 65 3 .The (7.17) / Te 0 2 E Krysztopa ], relatively = et al. [7. E 68 ,  . ] observed a lin- ] mapped a wide 67 71 66 Luckas exp directly proportional 0 [7. N ph  D / Main et al. [7. E : . / g R films similar to those used in 0 , with of charge, in quasi-thermal equi-  ˛ 2  Erslev t t 7.12a. Assuming deep trapping and 1 Á / L. t ph I d /  t d . F were investigated by

 ph 5 reservoir q  ]. They identified five distinct defect species, Te 5 64 D Sb eff 2 , which was confirmed experimentally for a-Si:H.  Some ten years earlier, G early part of the switch-onto characteristic follow was predicted correlated with Cu-rich andsured Ga-rich their phases, capture and properties.with mea- Results junction were capacitance measurements consistent onels. The defect hole lev- conductor a-GeTe anda-Ge phase-change alloy chalcopyrite solar cells have beenet studied al. by [7. of the oligomericthin-film semiconductor transistor pentacene, applications.localized used states They in in this conclude materialdistributed that comprise exponentially band tails duedistribution to of disorder, metastable plus deepimpurities. a defects Gaussian that CuGaSe arise from reproduced in Fig. recombination to be negligible, heprogressive attributed filling this of to a the discrete(linear set, or or Gaussian) a tail,maintain rapidly of falling a shallow traps. These traps librium with the band,charge with remaining the constant ratio over of theear free duration rise of to in the trapped current. lin- Inis this given case by the trap-limited mobility nential band tail DOS, who identified features in thedefects, and spectrum demonstrated associated that with correlation oftra MPC spec- at different temperatures was substantiallywhen improved variations in thetaken into bandgap account. with temperature are energy range of localizedsemiconductor gap amorphous states zinc in tin oxide theconfirmed (ZTO). transparent that They thesteep conduction (10 meV), band consistent with the tail known highmobility is electron in ZTO extremely despite its amorphous structure. to Detailed behavior dependsand recombination on coefficients. In some the instancesshoot over- ratio of the ofbeen steady-state trapping observed. value is Althoughswitch-on predicted, as the a and possibility more has detailedcombination of probe of has utilizing trapping been and re- identified [7. little further work has since taken place. ear increase in switch-onorder photocurrent of at 100 times ns, of in the the chalcogenide glass As D  solid ,and 0 ]ana- (eV) E 68 ). In the –E = 9 c [7. T E ,where B  k G ), (ii) after light Annealed 66 h (420 K) + 139 h (460 K) D / Street ˛ ph  are nonzero. However is constant and the pho- G gray dots R ], and 67 and [7. G ] model, coined from the initials ), (iii) annealed for 66 h at 420 K (tri- ) 70 –1 , ]) eV 69 62 Monroe is the characteristic energy of the expo- –3 0 As depos. Light soaked Ann. 66 h (420 K) T , the dispersion parameter and B brown dots DOS below the CB edge of a polymorphous sil- 1 E) (cm k (  ), (iv) annealed for further 139 h at 460 K ( N D ˛/ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 The switch-on regime has not been greatly studied 0 ). (After [7. 16 15 19 18 17  E 10 10 10 10 10 1 . Immediately after switch-on, 7.5 Switch-on and Switch-off Transients 7.5.1 Switch-on Transient Fig. 7.11  icon sample depositedas at follows: 423 K (i) and as-deposited measured ( by MPC soaking ( line angles tocarrier density evolves withemission, time, and recombination. through This may trapping, beplex, highly com- depending onconditions material of intensity properties and temperature.may and However be there external circumstances whereplified, the for example situation through an can assumption be ofDOS a sim- profile, specific or ifdominate certain over a processes particular are time considered interval. to in comparison to SSPC,ered or in the the following switch-off subsection, regime dueintroduced to cov- the if complexity both Kastner lyzed switch-on assuming an exponentiallytail distributed of states.the They TROK [7. followed what is referred to as of the authors,steady-state which photoconductivity in wasdered a successful semiconductors, number in and ofphotoconductivity other explaining disor- addressed aspects of later transient (Chap. steady state, it is predicted that Fundamental Properties Part A

164 Part A | 7.5 Photoconductivity in Materials Research 7.5 Switch-on and Switch-off Transients 165

a) Photocurrent (μA) b) Mobility (cm2/(Vs)) 12 10–1 Electric field (V/cm) 4 × 103 10 4 × 104 1.4 × 105

8 10–2

6 Photocurrent

4 10–3

2

Laser pulse 0 10–4

–2 0 100 200 300 400 3 456 7 8 9 Time (ns) 1000/T (K–1)

Fig. 7.12 (a) Switch-on measurement on an As2Te3 sample. The photocurrent increases approximately linearly over the duration of the pulse. (b) The rate of current increase is interpreted to yield a shallow-trap limited mobility that is temperature- and electric field-dependent. (After [7.71])

AsshowninFig.7.12b eff is thermally activated, with forms. Main et al. [7.72] reviewed this topic by means an activation energy related to the reservoir depth. This of analysis supported by computer simulation. For par- may be compared with the well-established procedure ity with existing work they assumed an exponential for measuring trap-limited mobility, the time-of-flight band tail and examined the current decay under strong (TOF) or Spear method described later. The switch-on or weak retrapping conditions, governed by the relative method could be used as an alternative if the dielec- probabilities of free carrier capture by traps and recom- tric relaxation time is short relative to the TOF drift bination centers. These conditions may be selected by time, where the uniform field assumption is invalidated. the value of G prior to switch-off. It was shown that 7.5 | A Part However, TOF has the advantage that it can also be used even for this relatively simple DOS, the initial rate of to measure both electron and hole mobilities separately. decay of current need not involve emission from or mul- titrapping in states near the quasi-Fermi energy, and 7.5.2 Switch-off Transient thus any analysis making such an assumption will be limited in its range of validity. This demonstrates the At switch-off the generation term is eliminated from value of computer modeling in supporting interpreta- the rate equation that describes the nonequilibrium car- tion of photocurrent behavior. rier distribution, but the recombination kinetics are In a different context, the switch-off photocurrent not immediately altered. Consequently, the initial pho- decay in (usually crystalline or polycrystalline) semi- tocurrent decay is governed by whatever recombination conductors with relatively well-defined deep trap(s) mode existed under SSPC conditions. Because of the has yielded a mainstream tool, in use for some 40 presence of traps, the initial decay is not directly re- years; it is often termed photoinduced current tran- lated to the free carrier lifetime, since carriers trapped sient spectroscopy (PICTS), [7.73]. PICTS involves at the instant the light is switched off must be emit- measurement of the quasi-exponential decay of pho- ted to the band at least once to become free, and in tocurrent associated with emission from discrete or general may be trapped and emitted many times before narrow bands of traps at a given energy depth, using they recombine. Given that in addition, recombination the rate-window concept. Trap density and trapping co- may be a monomolecular or a bimolecular process, the efficients are obtained from a series of measurements switch-off current is expected to exhibit a rich variety of versus temperature, often in conjunction with addi- is A = V 5ns. V C 9  Scope 10 cryostat Sample in Sample  7.17, 5 Pre-amp V + limitations mean RC Trigger IEEE488 PC Laser s e.g., by means of a reel of optical fiber  Typical coplanar TPC measurement system. 1  being a common choice, but 1 : Control At short times the transient current may be recorded The current transient can contain useful information  A similar arrangementple is is used a for sandwich TOF structure except as shown the in sam- Fig. a bias step ratherfor than 0 DC, and the laser pulse is delayed Fig. 7.13 Performance may alsointerference be from limited the byscreening laser, electromagnetic which and/or can byRepetitive be averaging use reduced is highly of by effectivecorrelated in a noise. reducing un- fiber-optic delay line. as the volt-drop across50 a low-value sampling resistor, a larger value of resistor is oftentimes unsatisfactory at and longer a fast transimpedance pre-amplifieroption. is A a suitable better unit provides a gain of 10 the influence ofcombination strong and mechanisms weakcases. is retrapping of and re- importance in both constants and impedance matching, to around 1 with a rise time offully 100 ns–1 ms. possess The a pre-amp maycurrent DC use- to offset be optionis nulled. to often At imposed enable long bya the times stable the cryostat dark a is drift desirable. recording It ofsufficient is time limit dark important should to be current, note allowed between that andable pulses to so the en- system tootherwise return close deep to traps thermalduring may equilibrium, repetitive averaging. become significantly filled out to some 100 s,orders thus of a magnitude dynamic range innecessary. of both To around achieve time this ten and necessitates the current transient may be- be and F E 7.13.Car- of charge to progressively 0 by a short pulse of uniformly D are empty, and photogenerated car- t F E thermalization The TPC experiment is carried out in secondary 1 s at 300 K. However this does not correspond to the for holes below The TPC experimental setup is shown inriers may Fig. be generated by means ofin a duration, typically pulse from of a order nitrogen-pumped 1 dye ns laser. Longer pulses fromused. an Peak overdriven laser powers LED of may thebe attenuated, order typically also of by a 100 be kW factor of needurating 1000, to to the avoid sat- traps onecurrent wishes decay to is measure. recorded The using aan transient fast analogue oscilloscope, bandwidth with of aroundtransferred 1 GHz, to signals a being PCtransient for further fidelity processing. at The short current times is limited by RC time 7.6.2 TPC Experiment 7.6.1 TPC Principles In the transientfree photoconductivity carriers (TPC) are excited experiment, into the bandstor of sample a semiconduc- at time 7.6 Transient Photocurrent Spectroscopy (TPC) tional complementary measurements, enablingof species traps to bethe identified. broadly This distributed is DOS a different discussed scenario above, to though absorbed above-gap light. Since the carrierare distributions in thermal equilibriumperiment, the at trapping the sites beginning for electrons of above the ex- riers are not excluded from anyis of dependent those sites. on Trapping resulting the in density a ofcomes rapid states, trapping a trapped rate. high ittime When density later, is in a a immobilized carrier thermallydepth activated until be- process being with emitted the the trap some activationrelease energy. trapped As carriers shallower sooner, retrapping states increased will occupation lead of to theceeds, deeper and states a asdensity. consequent time This pro- reduction in the free carrier deeper energies continues until recombination setswhich in, point at charge is stripped away.as This is a manifested steeper fall in> the measured current, oftenfree at carrier times recombination time,spend as far on more time average in carriers traps than in the band. photocurrent mode, making use of thegain. photoconductive The current, measured overas as possible, wide will a contain timelocalized information range on states the and density theirmight of depth. reliably How be extracted that to information yieldergy the is DOS considered shortly. versus en- Fundamental Properties Part A

166 Part A | 7.6 Photoconductivity in Materials Research 7.6 Transient Photocurrent Spectroscopy (TPC) 167

example, if in addition to the band tail there is a bump Current (A) in the DOS at deeper energies due to a species of de- –3 10 fects, capture into this bump will commence at a time when the thermalizing charge has reached a depth in the tail at which the bump DOS equals the band tail 10 –5 Raw data DOS (assuming both have the same capture coefficient). This may abruptly reduce the measured current, but it does not signify anything unusual existing in the DOS 10 –7 at E . Edited data th To enable TPC to be applied reliably as a DOS spectroscopy requires circumstances such as these to be 10 –9 interpreted correctly, and the fact that both trapping and emission may in general contribute to the measured cur- rent throughout the time range requires a more holistic 10–11 treatment. This has been a topic of interest for several 10 –10 10 –8 10 –6 10 –4 10 –2 100 Time (s) decades, and a variety of techniques for inverting the I.t/ curve have emerged [7.75–77]. The more enduring Fig. 7.14 Sections of TPC decays obtained from an a-Si:H of these involve either Fourier [7.78] or Laplace [7.79, sample at room temperature, recorded at progressively 80] transformations. As the impulse response and the longer times (and with greater current amplification). By HF-MPC response constitute a Fourier transform pair, overlapping the sections and then removing obvious instru- a discrete Fourier transformation of the entire TPC time mental artifacts, a generally smooth and consistent curve series may be carried out to obtain the frequency do- extending over some ten orders of magnitude of time may main response be obtained X I.!n/ D i.tk/Œcos.!nt/  jsin.!nt/tk ing recorded in 46 sections, overlapped and edited to k give a single log-log trace for subsequent processing, as D ip  jiq : (7.19) illustrated in Fig. 7.14. Several such traces are measured over the temperature range 100400 K to give broad The in-phase ip and quadrature iq components define energy coverage. the amplitude and phase terms input to the HF-MPC ex- pressions (7.12)–(7.14) presented earlier. This pathway 7.6.3 TPC Density-of-States Analysis to extracting the DOS makes no a priori assumptions as to its form, though it includes some mathematical Central to the TROK model introduced earlier is the approximations, and may suffer from artifacts due to concept of the thermalization energy short-time data restrictions. The DFT approach [7.78] 7.6 | A Part has proved to be robust, and is applicable to both pre- Eth D kBT ln.t/: (7.18) and post-recombination regimes. Its performance has been characterized rigorously by inverting computer- This is the energy at which traps will, on average, have simulated i.t/ curves generated from model DOS dis- released once after a time t. In the case of a purely tributions, and then comparing the result with the exponential tail of states, the traps that control the in- model [7.78–80]. Figure 7.15 shows an example of two stantaneous current are located at this energy depth. FT DOS methods, of lower and higher resolution, ap- Provided the experimental temperature is less than plied to the study of band tails and defects in a-Si:H. the band tail temperature (T < T0) the TROK analysis Experimentally, the main advantage of the TPC ap- yields I.t/ / t.1˛/, i. e., the current decays according proach over MPC as a DOS spectroscopy is that the to a power law that is related directly to the DOS slope. high-frequency limit is somewhat extended. At a given Essentially exponential distributions have been shown temperature, this may result in improved definition of to dominate the valence band tail of equilibrated amor- shallow states. There may be discrepancies [7.81]be- phous As2Se3 samples over a wide energy range [7.74], tween the two techniques regarding the recovery of but there are few other examples of extensive feature- deep levels, since the DC optical bias inherent in HF- less decays. MPC alters the occupancy of these states whereas TPC In general, the instantaneous current is the outcome either does not do so, or does so rather differently. of a range of kinetic interactions, and I.t/ versus t can- Strictly speaking, HF-MPC should be compared to TPC not be mapped to the DOS in such a simple way. For with the addition of optical bias. ] ], 87 1 85 gear 10 A respec- 0.7 E (eV) - –1 C Time (s) Time 3 E 10  –3 cm 0.6 10 15 ) were both poor 3 –5 10  10  5 : cm –7 0.5 10 15 ]. 10 –9 88  10 –5 –7 –9 ], crystalline CdTe:Sn [7. –11 0.4 10 10 10 Current (A) 10 86 ]. A further benefit of the copla- [7. 7.13, there are key differences: 83 3 illustrates how TPC has assisted in 0.3 shows current-time curves ISB4 A549 7.16 ]. mthick. single crystals [7. Comparison of DOS in two samples of a-Si:H. 84 0.2 2 Inset 100  7.17. Thin metal films forming Schottky contacts While the experimental setup is similar to that of 1 Figure A typical TOF sample configuration is shown in 22 21 20 19 18 17 16 15 DOS (rel) DOS 10 10 10 10 10 10 10 10 TPC shown in Fig. 1. The sample is in sandwich configuration, typically tively). compared with sample A549 University of Dundee PECVD material (24 meV and 1 Sample ISB4Falling is solar-cell efficiency was from traced to aity a number control of issues. qual- commercial The conductionand band PECVD tail deep slope reactor. (35 defect meV) density (7 and band tailbeen profile identified in [7. microcrystalline silicon have Fig. 7.16 identifying a qualityamorphous control silicon problem PECVD in reactor.not an The reader industrial however should surmisestricted that to thin practical silicon films. Similarly applicationbeen to MPC, used is TPC to has re- studyterials, transport including in short-chain a organic diverse molecules range [7. of ma- nar technique is thatversus it bulk defect is densities possible byuniformly to comparing absorbed results and estimate strongly using surface absorbed lighttively respec- [7. spray-coated WO 2. The contacts3. must be blocking At to least carriers. one contact is semitransparent. Fig. and TiO 7.12). ]. The (eV) 77 E – c E ]. 90 [7. method, was devel- uses the analysis of ( Bronger ]. However TPC has the ]. A recent review of the omewhat by accident – in Spear 82 FT 89 FT HFT , at the expense of somewhat increased noise DOS below the conduction band edge in a-Si:H, DOS (relative) is a high-resolution analysis described in [7. bump 0.2 0.3 0.4 0.5 0.6 0.7 15 20 19 18 17 16 10 10 10 10 10 10 latter offers improved resolution offect both band-tail and de- HFT obtained through Fourier transformationdecays. of The identical curve TPC marked 7.7 Time-of-Flight (TOF) and Related Techniques 7.7.1 TOF Mobility and DOS Measurements The time-of-flight (TOF) measurementtially technique, ini- referred to as the 7.6.4 TPC Applications Unlike the time-of-flight (TOF) technique discussed be- low, TPC has theto disadvantage that measure it carrier cannotIn mobility, be addition, used or thetransport at current-time of majority least curve carriers, and not istroscopy thus directly. TPC determined is DOS spec- by restrictedwith to which probing majority carrierssionally the possible interact. localized to It states probe isof the only the DOS occa- bandgap, on and the this other s side Fig. 7.15 n-type amorphous silicon,mediate the times current is decay controlledthe by at emission inter- valence of holes band from tail [7. advantage of simplicity; therewith dielectric are relaxation time, normally space-chargecontacts, or no difficult and issues the currentnation region measured is in generally comfortably the large. Asis prerecombi- current traveling inful the to compare plane results of withto the the the TOF film technique same applied the it material, film. may where In be current this use- travels way, through anisotropies in defect density oped in the 1960sment from as the a Haynes–Shockley meanslow-mobility, experi- of high-resistivity measuring semiconductors transport suchchalcogenide properties as in glasses [7. technique has been given by Fundamental Properties Part A

168 Part A | 7.7 Photoconductivity in Materials Research 7.7 Time-of-Flight (TOF) and Related Techniques 169

Photocurrent (a.u.) Pulsed laser 2.0 Me R R' Me R R'

+++++++ n 1.5 R' Me R R' L Sample Va R: n-decyl Pulsed v(t) R': n-hexyl tT bias I(t) 1.0 R

0.5 Fig. 7.17 TOF measurement sample arrangement, shown for the case of holes drifting through length L under a pos- itive applied voltage Va. Transit time is tT 0.0 (Chap. 8), or a p-i-n or other solar cell type structure, 0123 are commonly employed. The measurement procedure t/ttr is as follows. A reverse-bias voltage step is applied, Fig. 7.18 Time-of-flight transients measured at 243 K establishing a uniform electric field F D .Va C Vbi/=L, in methyl-substituted ladder-type poly(para)phenylene where L is the sample length and Vbi the built-in volt- (MeLPPP) with 60 kV=cm (line) and 300 kV=cm (dot)ap- age. Following a brief settling time, a strongly absorbed plied, and normalized to a transit time set to 90% of the (laser) light pulse generates a sheet of carriers close pretransit current. The inset shows the chemical structure to one or other contact. In hole TOF for example, the of MeLPPP. (After [7.91]) laser is directed at the positive contact; excess electrons are removed rapidly, and excess holes drift across the curve on a log-log scale. Figure 7.19 shows a tem- sample to be extracted at the negative contact. Neither perature series of hole transits in amorphous silicon carrier is replenished, as the contacts are blocking. This (Chap. 25) deposited by the expanding thermal plasma primary photocurrent is recorded as an equivalent dis- technique [7.92], as an illustration. A geometric con- placement current in the external circuit. What may be struction may be made to define the transit time, or seen is a period of relatively constant drift mobility, alternatively, the time at which a proportion (say 50%) as carriers traverse the sample, followed by a period of the total charge has been collected may be adopted. where the current falls more rapidly, as carriers are ex- In dispersive transport the mobility is not a constant tracted. This is illustrated in Fig. 7.18 for the organic for a given material, since charge remaining in the 7.7 | A Part semiconductor MeLPPP [7.91]. The changeover in be- sample for longer will have an opportunity to become havior denotes the transit time tT, the average time taken more deeply trapped, which further delays its progress. for carriers to cross the sample, and the resulting drift Thus a TOF experiment performed at low electric field mobility is D D L=.FtT/. The experiment may be car- will yield a lower mobility than that at high field. It ried out by directing the laser at either side, so that in is thus important to report sample details and experi- principle both electron and hole drift mobilities may mental conditions when comparing data from sample be determined from separate experiments on the same to sample, and from lab to lab [7.93]. Figure 7.19 illus- sample. It should be noted that the electric field remains trates that as the experimental temperature is decreased constant for a period somewhat less than the dielec- at constant electric field, the current is reduced and the tric relaxation time, which thus defines the maximum transit is lengthened. The total collected charge how- timescale of the experiment. The photocharge must be ever remains constant. limited to a fraction of the product CVa,whereC is the A complication in the TOF experiment is that if sample capacitance, to avoid distortion of the field. deep trapping occurs it may produce an artifact similar Many materials exhibit dispersive transport [7.75], in appearance to a transit [7.94], but is distinguishable due to capture and subsequent emission of carriers by its field independence. A high density of deep traps from traps distributed at various energy depths, rather will thus curtail the useful TOF time range. than conventional diffusion of the charge sheet. In such While majority carriers dominate photocurrents in cases it is often more revealing to plot the current-time TPC, TOF allows independent measurements of ma- 37) ]) Kasap 102 ]. TOF has , enables the 96 i t ] Time (5 µs/Div) ' 1 T 98 .(After[7. 2 i t 97] T , ] ] ]. 83 2 99 j 100 101 i )[7. t 20 A/Div) TiO μ a sample with carriers of one polarity IFTOF experiments. The electric field is 12 1 for a length of time j ) ) b 7.20, a lower current intensity is measured b ( Comparison of current traces obtained in 1 ( ] differs from the time-of-flight experiment T 102 O for transit times to liedow. within the measurement win- A wide range of organic semiconductors (Chap. Microcrystalline silicon [7. Crystalline CdTe and CdZnTe [7. Single-crystal diamond [7. Polycrystalline CIGS [7. Sillenite (Bi precharging TOF, and b) a) Photocurrent (100 ) a 2. Suitable blocking contacts3. must be established. A sample of appropriate thickness must be prepared also been applied successfullyrange of in inorganic semiconductors, the including: study of a wide satisfy these criteria,complementary techniques and has supported TOF thement advance- in of transport combination models with in this field [7. Fig. 7.20a,b The IFTOFet al. [7. experiment pioneered by      7.7.2 Interrupted Field TOF (IFTOF) described inplied the field that previous drives the photogeneratedthrough section, carrier the sample packet is in turned off forbefore that some the period carriers of have the time completed theirtrated transit. ap- in As illus- Fig. when the field iscarriers turned have on again, become signaling immobilizedfall that in in some deep current traps. versus The interruption time ( deep-trapping lifetime ofBy the carriers to be evaluated. turned off in (s) t m-thick 10V  may thus –3 6 : 10 7.19 ]. –4 , respectively. Since 95 10 ]) ˛/ ]. Specific procedures C 92 94 1 .  t –5 / 10 . / 10 V applied across a 5 t . C) I C substrate temperature, sandwiched  ı 70] in the case of purely exponential 5 –6 , 48 24 and –13 –30 10 , the conduction band tail slope is ob- 69 0 ˛/ E  1 time constant Example of TOF hole transients measured at sev- . s and 250 = Temperature ( Temperature = –7  T (A) t B 10 I k / TOF is now a well-established characterization long to allow atained over constant the electric transit. field to be main- In the post-transit regime, current arises from emis- –7 –8 –4 –5 –6 / D t 85 nm 10 10 10 10 10 : . offering higher energytions resolution have also under been developed these [7. condi- technique, used in the study ofporary a thin-film wide electronic range materials. of The contem- concerning main its criteria applicability are that: 1. The dielectric relaxation time must be sufficiently sion of carriersthan that to be are retrapped assis more need deeply consider likely again. only Here to a DOSsimplifying distribution analy- be of interpretation emission extracted times, [7. band tails, pre- andI post-transit currents take the form tained from electronslope TOF, from hole and TOF. The the curves in valence Fig. band tail be interpreted in terms oftail, an at least exponential valence to band firsttime order. curves Just may as be with analyzed TPC,a spectroscopically the less to current- yield prescriptive DOS,Fourier using transformation procedures method. such The asfor approach the is both valid recombinationof (TPC) carriers, since and analyticallya extraction both generic are (TOF) represented by between Mo contacts. (After [7. ˛ jority and minoritystates, carrier and separate interactions examinations of with thevalence conduction localized band and sides of theing bandgap TROK is [7. possible. Follow- Fig. 7.19 eral temperatures, with a-Si:H sample grown in0 an expanding thermal plasma at Fundamental Properties Part A

170 Part A | 7.7 Photoconductivity in Materials Research 7.8 Other Photoconductivity-Related Techniques 171 before performing an IFTOF experiment that drifts est amorphous semiconductors to be studied in detail, carriers of the opposite polarity through the sample, driven by its application at that time in xerography. recombination parameters can also be studied [7.103]. While selenium is no longer used in this role, it re- Another modification involves generating free car- mains an important x-ray photoconductor in flat-panel riers through one contact and drifting the slower carrier medical x-ray imaging (Chap. 45). A combination of into the sample, followed by a second pulse through the TOF and IFTOF has been used to study the relaxation other contact, which sends faster carrier in the oppo- of arsenic-stabilized a-Se, following deposition, anneal- site direction. The two packets will cross, and some will ing and cooling to room temperature [7.105], and the recombine, affecting the observed currents and provid- influence of the stabilizer on the properties of oxygen ing a way to study recombination. An example of this and chlorine doped a-Se [7.106]. Both electron and technique applied to amorphous selenium is given in hole mobilities may be studied independently in this Haugen and Kasap [7.104]. a-Se was one of the earli- way.

7.8 Other Photoconductivity-Related Techniques

This chapter has for the most part addressed how pho- between tip and semiconductor is adjusted to zero by toconductivity may be used as a tool in the detection, application of a bias potential, whose value is plotted identification and measurement of electronic and/or op- versus position to yield a surface map. tical properties of photoconductors. We conclude with brief descriptions of three techniques, related directly to 7.8.2 Spin-Dependent Recombination photoconductivity, that do not feature elsewhere in this handbook but which readers may find relevant to their As was discussed in Sect. 7.1, recombination is in- fields of interest. fluenced both by material properties and by external parameters. A further external variable, alongside tem- 7.8.1 Surface Photovoltage (SPV) perature and light intensity, is afforded by the pos- sibility of altering recombination kinetics by means This technique involves the detection of changes in con- of spin flipping. For a recombination event to occur, tact potential between a semiconductor and an electrode both electron and hole must form a singlet spin state. (Kelvin probe) placed close to its surface, under varying Recombination via the more probable triplet state is illumination conditions. A space-charge region forms excluded, but may be enabled by flipping one of the in the bulk close to the surface, balanced by charge spins by spin resonance. Thus by shining light on residing in surface states. Light incident on the semi- a photoconductive sample and scanning in an electron conductor generates free charge, which redistributes spin resonance (ESR) system, the resonance condition 7.8 | A Part under the built-in field. The steady-state charge dis- may be detected as a decrease in photoconductiv- tribution is sensitive to the semiconductor ambipolar ity [7.109]. This detection method, termed electrically diffusion length L, which in turn is reflected in the SPV. detected magnetic resonance or EDMR, is is many or- Details may be found in [7.107]. ders of magnitude more sensitive than a standard ESR Measurement of L involves stepping the wavelength experiment, which measures absorbed power using of the incident light, and adjusting its intensity after a microwave bridge. When combined with measured g- each step so as to maintain a constant SPV. Each wave- values and conductivity changes, spin-dependent pho- length corresponds to a specific absorption depth 1=˛ toconductivity provides detailed information on recom- in the semiconductor, and the value of L is obtained as bination pathways, and may be applied to devices the intercept of a plot of light intensity versus absorp- such as solar cells and LEDs as well as to material tion depth. SPV is a popular technique for measuring L, samples. particularly in bulk materials, although inaccuracies are claimed to arise when used on thin films. 7.8.3 Time-Resolved Microwave SPV is versatile and may be configured to measure Conductivity (TRMC) surface state density, and charge separation lengths in materials such as molecular clusters and quantum dots. TRMC consists of measuring changes in microwave It also forms the basis of a surface potential microscopy reflectivity of a photoconductor when excess photogen- (Kelvin probe force microscopy) [7.108] when com- erated carriers are created by a short flash of light. The bined with an AFM system. The electrostatic force reflectivity is proportional to the free carrier density, , 77 ,719 ,1675 ,7499 80 352 515 , 336 (1986) 34,541(1994) 57 ,1301(1990) 76 , 5138 (1993) tenschappelijk Onder- 74 ,263(1996) 198 ,141 123 (1992) ,49(2005) , 964 (2013) , 1199 (1981) ,24(1984) 13 89 , 228 (2004) 39 44,1423(1982) The authors are grateful to the 120 , 453 (2010) 338 19 ,6203(1995) 78 ,316(1989) , 2260 (1994) 085202 (2010) J. Non-Cryst. Solids J. Non-Cryst. Solids S. Nakano: Sol. Energy Mater. Sol. Cells State Commun. Phys. 547 (1985) (2002) G.J. Adriaenssens: J.(2006) Non-Cryst. Solids Curr. Appl. Phys. Cryst. Solids K. Inoue, H. Shishido, K.properties Kato, and S. evaluation Yamazaki: of Optical localizedof level In-Ga-Zn-O in thin gap film,Active-MatrixProc. Flatpanel 19th Disp. Int. Devices (2012) Workshop p. 143 State Commun. Mater. Sol. Cells (2007) AIP Conf. Proc. 114 76 lat. Mater. 26 C. Main, S. Reynolds, I. Zrinscak, A. Merazga: J. Non- 7.17 C. Main, F. Dick, S. Reynolds, W. Gao, R.A.G. Gibson: 7.18 H. Fritzsche, B.-G. Yoon, D.-Z. Chi, M.Q. Tran: 7.24 K. Pierz, H. Mell, J. Terjukov: J. Non-Cryst. Solids 7.19 R.H. Bube: J. Appl. Phys. 7.23 D. Ritter, K. Weiser: Optics Commun. 7.22 M. Sasaki, S. Okamoto, Y. Hishikawa, S. Tsuda, 7.20 M. Vaněček, J. Kočka, J. Stuchlík, A. Tříska: Solid 7.21 M. Vaněček, J. Kočka, A. Poruba, A. Fejfar: J. Appl. 7.25 P. Jensen: Solid State Commun. 7. 7.28 J. Willekens, M. Brinza, T. Aernouts,7.29 J. Poortmans, K. Sharma, A.S. Al-Kabbi, G.S.S. Saini, S.K. Tripathi: 7.30 N. Ishihara, M. Tsubuku, Y. Nonaka, R. Watanabe, 7.31 C. Wronski, B. Abeles, T. Tiedje, G.D. Cody: Solid 7.27 A. Bacioglu, A.O. Kodolbas, O. Oktu: Sol. Energy 7.36 T. Inushima, M.H. Brodsky, J. Kanicki, R.J. Serino: 7.35 M. Vaněček, A. Poruba: Thin Solid Films 7.32 S. Lee, S. Kumar, C.R. Wronski: J. Non-Cryst. Solids 7.37 M. Vaněček, A. Poruba: Appl. Phys. Lett. 7.33 M. Günes, C.7.34 Wronski, T.J. McMahon: J. Appl. Phys. Z. Remes, T. Izak, A. Kromka, M. Vanecek: Diam. Re- Acknowledgments. Engineering and Physicalcil, Sciences and Researchzoek the Coun- – Fonds Vlaanderenthis for voor work. financial Particular We supportand thanks Dr. of A.C. are Reynolds, parts for duemanuscript of their and to constructive critical comments. reading Finally, Dr. we ofindebted are C. the to Main colleagues andand students to past the and numerousand present, academic Leuven visitors labs, toand from the share whom Dundee many fond we memories. have learned much , ], 81 110 ,ed.by [7. Advanced 2 (Wiley, New Proceedings 7, 3051 (1974) ,79(1990) 62 , 2540 (2002) Proceedings of the 92 Proceedings of the Sixth Electronic and Structural dye-sensitized solar cells (last accessed Jan 2016) , ed. by N. Kirov, A. Vavrék , 3306 (1998) 72 , ed. by J.M. Marshall, N. Kirov, A. 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