, PHYSICAL REVIEW B, VOLUME 63, 165321 Electronic structure and vertical transport in random dimer GaAs-Al xGa1ÀxAs superlattices A. Parisini and L. Tarricone Istituto Nazionale per la Fisica della Materia-Dipartimento di Fisica, Universita` di Parma, I-43100 Parma, Italy V. Bellani and G. B. Parravicini Istituto Nazionale per la Fisica della Materia-Dipartimento di Fisica ‘‘A. Volta,’’ Universita` di Pavia, I-27100 Pavia, Italy E. Diez and F. Domı´nguez-Adame Grupo Interdisciplinar de Sistemas Complicados, Departamento de Fı´sica de Materiales, Universidad Complutense, E-20840 Madrid Spain R. Hey Paul Drude Institut fu¨r Festkörperelektronik, Hausvogteiplatz 5-7, D-10117 Berlin, Germany ~Received 25 July 2000; published 5 April 2001! We report a systematic study of several GaAs-AlxGa12xAs semiconductor superlattices grown by molecular-beam epitaxy specifically designed to explore the existence of extended states in random dimer superlattices. We have confirmed our previous results@V. Bellani et al., Phys. Rev. Lett.82, 2159~1999!# with much additional evidence that allows us to lay claim to a clear-cut experimental verification of the presence of extended states in random dimer superlattices due to the short-range correlations~dimers! that inhibit the localization effects of the disorder. DOI: 10.1103/PhysRevB.63.165321 PACS number~s!: 73.21.2b, 78.66.2w, 78.55.2m, 73.20.Jc rin pe ict e p th o an e ta n ha s ep i- le re d si je ss s- te t r the h c- b- he vi- like - nts p- e- s en- sys- r- is s ex- that ms. re and ur - I. INTRODUCTION Spatial overlap between electronic states of neighbo quantum wells~QW’s! in a semiconductor superlattice~SL! shifts the degenerate energy levels and leads to the ap ance of minibands separated by minigaps, as was pred long ago by Esaki and Tsu.1 In their seminal paper, thes authors speculated that a periodic modulation of the com sition of a semiconductor at a length scale smaller than electron mean free path would result in the occurrence negative differential conductance.2 Furthermore, if the length of the SL is shorter than the mean free path, coherent tr mission through an ideal SL is to be expected.3 Subsequent advances in semiconductor research made it possibl firmly establish these predictions on solid experimen grounds.4 Successful experimental validation of former predictio arising from purely theoretical investigation suggests t SL’s are ideal candidates to carry out research project basic physics. Advances achieved in molecular-beam taxy, which allow the production of high-quality SL’s ta lored with the desired conduction- and valence-band profi support the feasibility of this belief. In recent years, the have been remarkable examples of this appealing tren solid state physics. More than 70 years ago, Bloch con ered the motion of electron wave packets in crystals sub to an external applied electric field.5 Work by Bloch was further clarified and elaborated by Zener,6 who pointed out that an electron that is not subjected to scattering proce will perform an oscillatory motion, the so-called Bloch o cillations. Clear evidence of such oscillations was repor by Feldmannet al.7 and Leoet al.8 Moreover, 40 years ago i was proposed that a Stark-Wannier ladder should appea periodic solids subject to an applied electrical field9 although 0163-1829/2001/63~16!/165321~7!/$20.00 63 1653 g ar- ed o- e f s- to l s t in i- s, in d- ct es d in it could not be observed until the end of the 1980s, after advent of SL’s.10 More recently, intentionally disordered SL’s, in whic disordering is artificially created by random thickness flu tuations, have received much attention.11–30These intention- ally disordered SL’s were grown with the main aim of o serving Anderson localization and mobility edges. T reported enhancement of photoluminescence~PL! was attrib- uted to electron and hole localization due to disorder. E dence of the existence of extended states in impurity SL’s ~namely, two ordered SL’s joined by a wide QW! were reported by Lorussoet al.31 It is thus apparent that semicon ductor SL’s are suitable systems for controllable experime on localization or delocalization and related electronic pro erties. An ideal semiconductor superlattice forms a on dimensional~1D! structure in the growth direction that ha been used successfully to study theoretically or experim tally the electronic properties of 1D systems.32,33 In this con- text, some authors proposed that SL’s arephysically realiz- able systemsthat allow for a clear-cut validation of the existence of extended states in low-dimensional random tems with correlated disorder.34–37 These systems are cha acterized by the key ingredient that structural disorder short-rangecorrelated. A number of tight-binding38–40 and continuous41 models of correlated disordered 1D system predicted theoretically at the beginning of the 1990s the istence of extended states, in contrast to the earlier belief all the eigenstates are localized in 1D disordered syste But, owing to the lack of experimental confirmation, the was some controversy as to the relevance of these results their implications for transport properties. Recently, o group presented clearexperimental evidenceof this phenom- enon in semiconductor SL’s.42 To be specific, the experimen ©2001 The American Physical Society21-1 lcu f r S e th u te es v is o po w tic d v e di ra lo rm th e si L er p lo in- s or se t ss n h k rin o ed is is n a ral- th sent - n pt ffi- ists ero nt and te A. PARISINI et al. PHYSICAL REVIEW B 63 165321 tal PL energies were in very good agreement with the ca lated electronic states,36 suggesting the formation o delocalized extended states. Most important, vertical dc sistance of both correlated disordered SL and ordered were very similar, showing no temperature dependenc low temperature, as should be expected for transport in presence of extended states. These measurements led conclude that Anderson localization is inhibited in correla disordered SL’s. In this work, we report further progress along the lin given in the preceding paragraph. We provide further e dence of the existence of extended states in correlated d dered SL’s, and we study carefully the physical nature such states as well as their effects on optical and trans phenomena. The paper is organized as follows. In Sec. II present our model and summarize our previous theore work,34–37which we find convenient for a better understan ing of the present paper, specifically as regards the beha of the transmission coefficient and dc conductance. To ch the relevance of theoretical predictions, we grew three ferent types of GaAs-Al0.35Ga0.65As SL’s, namely ordered SL ~OSL!, random SL~RSL! without spatial correlation, and random dimer SL~DSL! with dimerlike correlation. Section III describes these samples in detail as well as their x- characterization. In Sec. IV we present PL spectra at temperature from the various SL’s. This allows us to perfo the analysis of the experimental transition energies and ascertainment of the localization and delocalization prop ties of the SL’s from comparison with calculations.36 The body of the paper is Sec. V where we present an exten discussion of transport properties of the three types of S determined by a variety of techniques: dc conductivity v sus temperature,I -V characteristic, photovoltage~PV!, and short circuit photocurrent~PC!. Finally, in Sec. VI, we dis- cuss our results and, from the comparison between trans properties of RSL and DSL, we conclude that Anderson calization is inhibited when correlations are intentionally troduced in the sample. II. MODEL AND BACKGROUND We summarize in this section previous results of our36 for correlated disordered GaAs-AlxGa12xAs SL’s, which will be useful for the discussion of optical and transp properties, addressed in the next sections. For our pre purposes, it is enough to focus on electron states close to band gap withk'50 and use the one-band effective-ma framework to calculate the envelope function. The electro states were calculated using a Kronig-Penney model that been shown to hold in the range of well and barrier thic nesses we used.45 Let us assumedw anddb to be the width of QW’s ~GaAs layers! and barriers (AlxGa12xAs layers!, re- spectively. The thickness of barriers separating neighbo QW’s is assumed to be the same in the whole SL,db5b. OSL’s are constructed by also assuming the thickness QW’s to be the same in the whole SL,dw5a. In our model of RSL, we consider thatdw takes at random one of tw values,a and a8. Finally, a DSL is built by imposing the additional constraint that QW’s of thicknessa8 appear only 16532 - e- L at e s to d i- or- f rt e al - ior ck f- y w e r- ve ’s - ort - t nt he ic as - g of in pairs, called hereafter a dimer QW~DQW!, as shown in Fig. 1. We now consider a single DQW in an otherwise order SL. The condition for an electron to move in the OSL given by34 Ucos~ka!cosh~hb!2 k22h2 2kh sin~ka!sinh~hb!U<1, ~1! where k252m* E/\2 and h252m* (DEc2E)/\2. Here DEc is the conduction-band offset. The origin of energies taken at the GaAs conduction-band edge. We have take constant effective massm* at theG valley, but this is not a serious limitation as our description can be easily gene ized to include two different effective masses. For the grow parameters corresponding to the SL’s used in the pre work ~see Sec. III!, there is only one allowed miniband be low the barrier, ranging from 0.1 up to 0.2 eV. Any electro moving in the SL will be reflected back at the DQW exce if its energy matches a resonant energyEr obtained from the following condition34 cos~ka8!cosh~hb!2 k22h2 2kh sin~ka8!sinh~hb!50. ~2! In our DSL this energy isEr50.15 eV and thus it lies within the allowed miniband. This means that the reflection coe cient at the DQW vanishes and, consequently, there ex complete transparency at the resonant energyEr . In the vi- cinity of the resonance, the reflection coefficient is nonz but rather small. Choosinga8 appropriately is important in allowing us to locate the resonant energyEr within an al- lowed miniband of the periodic SL, that is, the resona FIG. 1. Schematic diagram of the conduction- and valence-b profiles of the three SL’s considered in this work. Arrows indica the center of narrow QW’s for clarity. 1-2 h gy te ed ho s sp or n th rs e th e fo is lso per- he L is sm. th c- u- e for us a val- ing sis- rves s. that f the el ns er, nce , 00 sis- ex- . ELECTRONIC STRUCTURE AND VERTICAL TRANSPORT . . . PHYSICAL REVIEW B 63 165321 energy in the range of energies given by Eq.~1!. When sev- eral DQW’s are introduced at random to build up a DSL, t transmission coefficient is still unity at the resonant ener as can be easily demonstrated,34 and the corresponding sta is delocalized in spite of the fact that the SL is disorder Close to this resonance there are a number of states w localization length is larger than the system size and, con quently, they behave like extended ones as regards tran properties. We now turn to the problem of transport across dis dered SL’s. The extended or localized nature of electro states close to the Fermi level can be elucidated from dependence of the dc conductance on the number of laye the SL. The states are extended~localized! when the dc con- ductance is constant~decays exponentially! as the SL size increases, thus leading to an Ohmic~non-Ohmic! behavior of the sample. In Fig. 2 we can see the dependence of th conductance at 77 K on the number of barriers when Fermi level matches the resonant energyEr for both RSL and DSL. Notice that the behavior is Ohmic only for th DSL. We have obtained the dc conductance through the lowing expression, earlier discussed in detail by Engqu and Anderson:46 G~T,m!5 e2 h E S 2 ] f ]ED t~E!dE E S 2 ] f ]ED @12t~E!#dE , ~3! FIG. 2. dc conductance, in units ofe2/h, at 77 K as a function of the number N of barriers in intentionally disordered GaAs-Al0.35Ga0.65As SL’s when the chemical potential is 0.15 eV i.e., it matches the resonant energy. Upper~lower! curve corre- sponds to DSL~RSL!. We present results of averages over 1 different SL’s for each case. 16532 e , . se e- ort - ic e in dc e l- t where integrations are extended over the allowed bands,t is the transmission coefficient,f is the Fermi-Dirac distribution, andm denotes the chemical potential of the sample. We a studied the temperature dependence of the transport pro ties. The current density can be calculated within t stationary-state model47,48 by the expression j ~V!5 m* ekBT 2p2\3 E 0 ` t~E,V!N~E,V!dE, ~4! whereT is the temperature,V the applied bias, andkB the Boltzmann constant; the electron transport through the S described through the resonant tunneling mechani N(E,V,T) accounts for the occupation of states on bo sides of the device, according to the Fermi distribution fun tion, and it is given by N~E,V!5 lnS 11exp@~EF2E!/kBT# 11exp@~EF2E2eV!/kBT# D , ~5! EF being the Fermi level. In this framework we have calc lated the dependence of the resistance on the temperatur a constant electric potentialof 0.1 V. The data are plotted in Fig. 3. We compare the numerical results with our previo measurements,42 which are shown in the inset. There is reasonable qualitative agreement with the experimental ues for the three types of SL’s. We can note that by lower the temperature, both the calculated and experimental re tances increase and, at the lower temperatures, the cu flatten, in agreement with experiments by other author43 This behavior can be roughly understood by considering as the temperature decreases, the broadening in energy o Fermi-Dirac distribution function around the Fermi lev shrinks, by making more and more restrictive the conditio for the electron tunnelling between adjacent wells. Howev when this broadening becomes comparable with the dista FIG. 3. Computed temperature dependence of the vertical re tance for the RSL, DSL, and OSL. In the inset are shown the perimental measurements for the three SL’s in the same order 1-3 be th lt ew - ca b n d he he m ic f a at si a c ve i- o ed a e is th a 5 de n n th s i f t r d w , i tion this he el, se the wo by e ons ing be ak ers vi- of s of our lly re K. emi- sed f 2 nge as nse and ed ch n PL kes a of A. PARISINI et al. PHYSICAL REVIEW B 63 165321 between the intraminiband levels of the SL, the current comes temperature independent. We will come back to point later. III. SAMPLES AND X-RAY CHARACTERIZATION Now let us turn the attention to our experimental resu and how they compare with theory. To this end, we gr several GaAs-Al0.35Ga0.65As SL’s, and we studied their elec tronic properties by PL at low temperature and dc verti transport. The samples are three undoped SL’s grown molecular-beam epitaxy . All the SL’s have 200 periods a Al0.35Ga0.65As barriers 3.2 nm thick. The conduction-ban offset is DEc50.25 eV and the effective mass ism* 50.067m, m being the electron mass. In the OSL, all t 200 wells are identical with a thickness of 3.2 nm. In t RSL, 58 wells are replaced by wells of a thickness of 2.6 n and this replacement is done randomly. The DSL is ident to the RSL, with the additional constraint that the wells o thickness of 2.6 nm appear only in pairs.36 In the latter sample, the disorder exhibits the desired short-range sp correlations. In each sample, the SL is cladded on each by 100 nm of n-type Al0.3Ga0.7As, Si doped to 4 31018 cm23, with a 50 nmn-type GaAs buffer layer~doped to 431018 cm23) on the substrate and a 3 nmn-type GaAs cap layer~doped to 631018 cm23). We measured x-ray diffraction spectra of the SL’s with double-crystal diffractometer, in order to check their stru tural parameters. This technique has been shown to be powerful for the study of periodicity and disorder in sem conductor superlattices.44,49,50The diffraction curve at~004! symmetric reflections for the two disordered samples sh satellite peaks of the order of61 lying close to60.8° with respect to the GaAs peak. These satellite peaks are locat identical positions for the two disordered SL’s, showing th the random SL’s have identical periods. Therefore, the dim constraint intentionally introduced during sample growth the only difference between RSL and DSL. IV. PHOTOLUMINESCENCE CHARACTERIZATION PL has proved to be a good technique in the study of electronic properties of SL’s,11,12 giving transition energies between confined electron states. PL spectra were taken function of the temperature in the 4–300 K range~light power density on the sample of about 2.5 W/cm2). The ex- citing source was an argon laser (l5514.5 nm); the light emitted by the samples was analyzed by means of a 0. Jobin Yvon-Spex HR 460 single monochromator and tected by a cooled PbS detector through a conventio lock-in technique. The spectral resolution was better tha meV. Figure 4 shows the PL spectra at low temperatures of three SL’s; in the inset, a sketch of the radiative transition the three SL’s is drawn. The temperature dependence o energy of the near-band edge peaks is different for the th samples, but the energy shift between them is almost in pendent of temperature on a wide range. The lo temperature PL peak for the OSL, which lies at 1.69 eV 16532 - is s l y d , al ial de - ry w at t r e s a m - al 1 e n he ee e- - s due to recombination between electrons in the conduc band and heavy holes in the valence band. The energy of transition is in good agreement with the calculation of t miniband structure performed using a Kronig-Penney mod the calculated lower energy of the miniband being very clo to the energy at which PL intensity rises. The PL peak of RSL is at higher energies with respect to the other t samples. In this SL, the intentional disorder introduced the random distribution of wells 2.6 nm thick localizes th electronic states.36 The energy blueshift is of 20 meV with respect to the OSL and compares well with the calculati of the transition energy, assuming that the exciton bind energy is the same in the SL’s. The PL peak of the DSL is close to 1.70 eV and, as can clearly seen in Fig. 4, redshifted with respect to the PL pe for the RSL. According to Fujiwara45 this redshift is due to the formation of a miniband with a tunnel process for carri between the GaAs wells. This result strongly supports pre ous theoretical predictions of the occurrence of a band extended states in correlated disordered SL’s. The value the transition energies agree with the values predicted by models,42 indicating that the predictions were fundamenta correct. V. TRANSPORT MEASUREMENTS PV at open-circuit and short-circuit PC experiments we performed in the temperature range between 10 and 80 These techniques have been used widely to investigate s conductor quantum heterostructures.30,51–59The light source was a white light produced by a halogen lamp pas through a monochromator, with a spectral resolution o meV. The spectra were measured in the photon energy ra between 1.5 eV and 2.1 eV. The photoelectrical signal w revealed by using a lock-in technique. The spectral respo of the optical system was measured in the whole range used to normalize the spectra. The PV spectrum taken atT510 K confirms the PL re- sults. Moreover, practically coincident spectra were obtain by measuring the short-circuit PC signal. In fact, for ea sample the excitonic peaks are at the same energies as i spectra, with a slight difference that could be due to a Sto shift. It is worth noting that generally a photovoltaic or photocurrent signal is the result of the light modulation FIG. 4. PL spectra atT54 K of the OSL, DSL, and RSL. 1-4 te e ta o an a c d n te rd : i na s , m k t a a s ra e le c o a . O ir s ke st e 1 a r ffi- e ure the the be- es o rly r- ted mi- r- b- wer . In ble he ne ce e is . L. ELECTRONIC STRUCTURE AND VERTICAL TRANSPORT . . . PHYSICAL REVIEW B 63 165321 the barrier potential or the collection of the photogenera minority carriers, both requiring the presence of an inn junction. Moreover, as confirmed by recent experimen results,55,59 the energetic position of the peaks depends the optical absorption process, whereas their intensity line shape are also related to the transport mechanism therefore, indirectly, to the potential profile along the dire tion of the electric field. In the present case, we measure open-circuit PV signal despite the absence of any intentio junction. In effect, in our structure low~weak! potential bar- riers are present between then1 andn regions. As proof of this fact we observed a clear correlation between the in sity of the PV signal and a significant asymmetry of forwa and reverseI -V characteristics taken at each temperature other words, the photovoltaic effect rises for an unintentio non-Ohmic behavior of then-i -n structure. At temperature above 80 K the nonlinearity of theI -V curves disappears and the possibility to monitor the PV signal at higher te peratures is prevented. In addition, the lowest-energy pea the PV spectrum appears to be better resolved when asymmetry of theI -V curve is maximum, and this happens a temperature of'30 K, even if the PV signal shows strong monotonic reduction with the temperature increa Figure 5 shows the PV spectra of the SL’s at this tempe ture. The above observation also suggests that the temp ture evolution of the peaks is dominated by uncontrol factors such as the accidental presence of an internal ele field, in addition to the generation rate and the transp mechanism of the carriers. Therefore, in the present c a line shape analysis of the peaks becomes unreliable the contrary, the significant information is given by the position. I -V characteristics were taken at different temperature the range between 10 K and 300 K. The curves were ta by setting the current values and measuring the steady- voltages in a two-point geometry. The measurements w performed in the dark, by increasing the temperature from K to room temperature, after the sample was illuminated the lowest temperature with white light. This latter procedu FIG. 5. Photovoltage spectra of the OSL~circles!, DSL ~crosses!, and RSL~squares! at T530 K. 16532 d r l n d nd - an al n- n l - in he t e. - ra- d tric rt se n in n ate re 0 t e proved useful to contrast the reduction of the injection e ciency of carriers from then1-doped contact layers into th SL structure due to the electron trapping into theDX centers: this deep level is introduced in then-type Al0.3Ga0.7As material by the donor atoms themselves.60,61 Owing to the thermally activated electron capture cross section of theDX center, the photoionization of the latter at a low temperat actually increases persistently the free electron density in conduction band until it reaches a saturated value~persistent photoconductivity effect!. The electron capture into theDX centers becomes appreciable above'70 K; the equilibrium occupancy of the deep level is restored above'150 K. The sample resistance was calculated as a function of temperature,R(T), from the linear region of I -V curves. Since at low temperatures (T<100 K) the linear regime is restricted to a very narrow range and the curves tend to come nonsymmetrical with respect toV50, in these condi- tions theR(T) values were obtained by averaging the slop of the forward and reverseI -V data around zero. In order t compareR(T) values taken in the same way, and in a nea Ohmic regime, the calculation of this quantity was pe formed at a very low field~1–10 V/cm!. The resistance data thus obtained are slightly different from those we presen recently42 ~see the inset of Fig. 3! since in that work we measuredR(T) by applying aconstant currentof 1 mA and reading the voltage drop across the sample, without illu nation. Figure 6 reports the ‘‘Ohmic’’ resistance of the SL’s ve sus 1000/T. The qualitative behavior of theR(T) curves agrees with the results of Fig. 3; in particular, we can o serve that the resistance of the OSL is systematically lo than the other two at all the temperatures, as expected addition, the Arrhenius plot of the data reveals a possi regime of activated transport. When theI -V curves were taken without the low-temperature photoionization of t DX centers, a behavior on the whole similar to the o shown in Fig. 6 was obtained forR(T), but with higher FIG. 6. Arrhenius plot of the experimental electrical resistan of the OSL, DSL, and RSL. The diameter of the mesa structur 160 mm in the case of the OSL and 200mm in both the other cases The interpolation in the region of linearity is reported for the RS 1-5 w d su S is s- b is e bu na fr n rv , at b nt id n re r, S th ti en s ca e ent ties nd e SL ex- the of ed- the the and ion te- on est ing In al ab- der ve cter- ens s ssi- no- ns tti, ir ted t- A. PARISINI et al. PHYSICAL REVIEW B 63 165321 absolute values of the sample resistance; also, the narro of the linear range of theI -V curves at a low temperature an their nonsymmetry were in any case observed. This re confirms that the low-temperature photoionization of theDX centers does not modify the probability of crossing the region by the carriers, but it reduces the ‘‘external res tance’’ in series to it (Rext) and, above all, restores persi tently the highest free carrier density that can be supplied the contact layers. Returning to Fig. 6, four temperature regions can be d tinguished. (1) High temperatures (150 K< T < 300 K). The DX center occupancy is at equilibrium, and the SL resistanc in series with the resistance of the contacts, which is low appreciable; in addition, a contribution due to the exter circuit ~bonding, wires, etc.! cannot be excluded. (2) Intermediate temperature (70 K< T < 150 K). The data are scarcely meaningful because the density of the carriers supplied by then-doped Al0.3Ga0.7As layers, and also theI -V curves, evolves in time, owing to the activatio of the process of electron capture intoDX centers. This phe- nomenon is more and more evident as the temperature creases, and it is responsible for the weak shoulder obse in the R(T) curves in this range. (3) Middle-low temperatures (25 K< T < 70 K). For all the samples the resistance shows an activated regime activation energies increasing from the OSL ('20 meV) and DSL ('23 meV) to the RSL ('29 meV). As regards the transport mechanism responsible for such an activ regime,~i! the thermoionic emission over the barriers can excluded as a dominant mechanism, because the SL qua level ~or miniband! in the well is over 100 meV below the barrier top;~ii ! the phonon-assisted hopping could be cons ered;~iii ! moreover, it can be observed that the SL regio are '1 mm thick, and therefore a bowing of the structu can be expected in all the SL’s;~iv! also, the spike in the conduction-band profile at the interface with then-doped Al0.3Ga0.7As layers could play a significant role. Howeve we notice that in this range the absolute value of the O resistance is close to an order of magnitude lower than for the other samples, and we can observe that the activa energy increases from the OSL, DSL, to the RSL: this t tatively points to the relating of the region of activated tran port to the SL structure itself~more than toRext). This point will be further investigated in the future. (4) Low temperatures (10 K< T < 25 K). The R(T) curves are weakly dependent on temperature, as in the m 16532 ing lt L - y - is t l ee in- ed the ed e um - s L at on - - se of transport by tunneling.43,62 In this temperature region, th resistance of the DSL approaches the OSL, in agreem with our expectations. VI. CONCLUSIONS We studied the structural, optical, and transport proper of ordered and intentionally disordered superlattices with a without correlation of the disorder. It was found that th introduction of a short-range correlation in a disordered leads to the formation of extended states, theoretically pected. The PL experiment shows that the correlation of disorder in a semiconductor SL leads to the delocalization the electronic states, with tunneling of the electrons and r shift of the electronic transition energies. The values of electrical resistances at a low temperature shows that RSL has the highest values of resistance, while the OSL the DSL have comparable values, confirming the format of bands of extended states in the DSL. In an intermedia temperature range (25 K