SPIE Proceedings [SPIE Sixth International Conference on Advanced Optical Materials and Devices -...

Mid-infrared photoluminescence of PbSe film structures up to room

temperature

Zinovi Dashevskya*, Vladimir Kasiyana, Gal Radovskya, Eduard Shufera, Mark Auslenderb

aDepartment of Materials Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel

bDepartment of Electrical Engineering, Ben-Gurion University

ABSTRACT

Lead salt materials are of high interest for midinfrared optical emitters and detectors for molecular spectroscopy. The IV-VI narrow gap semiconductors have a multivalley band structure with band extrema at the L point of the Brillioun zone. Due to the favorable mirrorlike band structure, the nonradiative Auger recombination is reduced by one or two orders of magnitude below that of narrow gap III-V and II-VI semiconductor compounds1. The photoluminescence in the midinfrared range for PbSe film structures, excited by a semiconductor laser diode, is investigated. The PbSe films were prepared by Physical Vapor Deposition (PVD) using an electron gun. A PbSe crystal doped with 0.1 at% Bi was used as a source for the fabrication of thin layers. Starting from the assumption that the rate of nucleation is a predominate factor in determining grain size, thin films were fabricated on substrates that had been maintained at various temperatures of deposition process2. Amorphous glass and Kapton polyimide film was used as substrate. The growth rate was 0.2 nm/s. Films were thermally treated at high oxygen pressure in a heated encapsulated system. Microstructure has been studied using XRD, AFM and HRSEM. For PbSe structures photoluminescence at temperature as high as 300 K is demonstrated. Keywords: Lead Chalcogenides, Polycrystalline Films, Thermal Oxidation, Inversion Layers, IR Photoluminescence

1. INTRODUCTION Lead chalcogenides (LC) is a group of semiconductors which possesses a narrow direct energy band. This makes them attractive for the production of thin film IR-detectors for various applications3-4. It is known that the majority of polycrystalline PbSe films prepared by traditional deposition techniques are characterized by weak photoconductivity. As a rule, the sensitization is performed in an oxygen atmosphere. The oxidation of polycrystalline PbSe films of different compositions was investigated in5-7. It was shown that grains of polycrystalline films consist of PbSe with a nonuniform distribution of electrically active point defects, whereas a layer of high resistance semiconductor is located near garin surface. It was found that the grain surface is covered by a dielectric layer composed PbSeO3

7. Neustroev and Osipov8-11 put forward a model that qualitatively and quantitatively provided explanation for the role of oxygen in determining the photosensitive behavior of the polycrystalline lead chalcogenides films. According to the model oxygen-generated acceptor states are present on the surfaces of n-type grains. The acceptor states are able to capture electrons from the interior of grains. This gives rise to p-type inversion layers at the grain boundaries. According to this model, the current flowing in the thin chalcogenide film is exclusively due to the motion of holes in the inversion channels along grain boundaries (Fig. 1). ___________________________________________ *E-mail: [email protected]; Phone +972-8-6472573; Fax +972-8-6479441

Sixth International Conference on Advanced Optical Materials and Devices (AOMD-6), edited byJanis Spigulis, Andris Krumins, Donats Millers, Andris Sternberg, Inta Muzikante, Andris Ozols, Maris Ozolinsh

Proc. of SPIE Vol. 7142, 71420L · © 2008 SPIE · CCC code: 0277-786X/08/$18 · doi: 10.1117/12.815199

Proc. of SPIE Vol. 7142 71420L-1

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/06/2013 Terms of Use: http://spiedl.org/terms

-PbSe

Figure 1. Schematic view of PbSe film fragment containing n-type grains, and p-type conducting inversion channels. The arrow indicates the direction of the current.

2. METHODOLOGY

PbSe films were prepared by Physical Vapor Deposition (PVD) using an electron gun. The thermal evaporation runs are re carried out at a base pressure of 1×10-7 Torr. A PbSe crystal doped with 0.1 at% Bi (donor in PbSe) was used as a source for the fabrication of thin layers by evaporation unto substrate surfaces hold at temperatures 250 -300oC within ± 1oC accuracy. The amorphous glass and Kapton polyimide film were used as substrates. The growth rate was 0.2 nm/s. Films were thermally treated at high oxygen pressure in a heated encapsulated system. Microstructure has been studied using XRD, AFM and HRSEM The Seebeck effect was measured at 300 K. Gold film contacts on a chromium sub-layer, prepared by a thermal evaporation technique, were used for the electrical contacts. The current-voltage characteristics were found to be linear for all samples over the whole temperature range examined, confirming ohmic nature of the contact. The electrical conductivity and the Hall effect were investigated over the 80-300 K range. The photoluminescence was studied at the same temperature range under excitation with a GaAs light emitting diode (LED), spectrophotometer SPEX-1000 was used. A InSb photodiode served as a photodetector. The variation in the temperature range of 80 – 300 K was maintained using the cold-finger cryostat SH-4-1 closed cycle refrigerator system Janis Research Co. INC, model RDK 101D. Temperature stabilization was maintained by the CryoCon, model 32 BB, cryogenic control system. For the Hall effect measurements, we used instant CoSm magnet with a magnetic field B = 0.8 T mounted inside the cryostat finger. The films reaction to irradiation (photosignal) was also determined in the same temperature range.

3. RESULTS

3.1 Structural properties The XRD spectrum of PbSe film deposited on a polyimide substrate is shown in Fig. 2. The film contains a single face-centered-cubic (FCC) crystalline phase with a rock salt structure. The diffraction peak intensities in the measured spectrum differ from those quoted from the standard PDF card, indicating (100) texture in the film deposited on an amorphous substrate. The texture structure suggests that (100) is the preferred film growth orientation due to its low surface energy. The microstructure of PbSe film on polyimide substrate is shown in Fig. 3a. Annealing of PbSe films in the oxygen atmosphere led to the surface oxidation, which is confirmed by the surface SEM image of annealed films (Fig. 3b).

Figure 4a shows the surface morphology of PbSe film on a polyimide substrate obtained by AFM. PbSe film has a grain size in the range of 200 to 300 nm and rms surface roughness of 10 to 15 nm. According to the SEM results of cleavage PbSe film with a thickness ≈ 1.1 µm possess a columnar structure (Fig. 4b). The microstructural and morphological similarity between PbSe films deposited on different amorphous substrates (polyimide film and glass plates) is not coincidental and is indicative of the texture nature of PbSe polycrystalline films.



0S

20000-

15000-

10000-t=S 5000- 0b ij3 S ij3 :

(1) I0__SL ______________II_______________0-

-5000- I I I

20 30 40 50 50 70 80

25

(a) (b) Figure 3. SEM image of PbSe films (a) - the initial layer. (b) - after the treatment in an oxygen atmospere at T = 400oC for 1 h.

3.2 Electrical properties The initial PbSe films (grown using a bismuth added PbSe target) show n-type conduction and carrier mobility of 80 - 100 cm2/V-s from Hall measurements. The measured carrier concentration is (5 – 10)×1017 cm-3. The conductivity type inversion effect (CTIE) due the oxygen treatment is demonstrated by positive Seebeck coefficient values at 300 K (Fig. 5) measured for originally n-type PbSe films Figure 6 presents the conductivity as a function of temperature for the PbTe films deposited on a polyimide and glass substrates. The conductivity, σ of the initial PbSe film decreases as the temperature increases, due to electron scattering on lattice vibrations. However, the temperature dependence of σ (T) for PbSe film is weaker than σ (T) for bulk PbSe crystals due to additional scattering of carriers on the grain boundaries.12

Figure 2. XRD spectra of PbSe. 1 - film on polyimide substrate (Ts = 2500oC); 2 – standard XRD data of PbSe powder



(a) (b)

Figure 4. (a) - AFM image of PbSe film microstructure on a polyimide substrate. (b) - HRSEM cross-sectional view image of PbSe film microstructure on a polyimide substrate, Ts = 300oC. For PbSe films after the oxygen treatment conductivity in all these films is thermally activated, the activation increases sharply with temperature. The activation energy calculated using the equation )/exp(~ kTEa−σ (1) is about 80 - 100 meV. At temperature below 150 K the conductivity temperature dependence is much weaker. Hopping conductivity and tunneling are two mechanisms which provide weak temperature dependence of conductivity.13

-300

-200

-100

0

100

200

300

400

500

0 0.5 1 1.5 2 2.5 3 3.5

Treatment duration, h

Seeb

eck

coef

ficie

nt S

, µV/

K

Figure. 5. Seebbek coeffcieint for PbSe films measured at 300 K as a function of the treatment duration at 400oC.



•_•.s...

2

yytI,yyyyy V V VA

A .• A

%,A

AA• A • •• A4

+ AI I I

0.002 0.004 0.006 0.008 0.010 0.012

1000ff, K1

3.3 Photosensitivity The photosignal from GaAs LED was observed on PbSe films only after their activation in oxygen atmosphere. The results for photosignal vs. temperature are presented held at different temperatures (Fig. 7). One can observe that the maximum of photo-response is at the temperature T ≈ 220 K.

Figure 7. The photosignal vs. temperature for PbSe films on the polyimide substrate after oxidation.

Figure. 6. Conductivity in PbSe films on polyimide and glass substrates as a function of reciprocal temperature. 1, 2 – the initial PbSe films; 3, 5 – after 1 h oxidation; 4 – after 3 hours, 1, 3, 4 – films on the polyimide substrate. 2, 4 – films on a glass substrate.



25 3 as 4 45 5 5.5 6 asX, jim

3.3 Photoluminescence (PL)

The PL was studied over 170 -300 K temperature ranges. Figure 8 shows that, as the temperature decreases, the PL spectra shifts to the longer wavelengths corresponding to decreasing of the PbSe band gap.11 The maximum of PL is at 270 K.

Figure 9. The photoluminescence (PL) l vs. temperature for PbSe films on the polyimide substrate after oxidation.

4. DISCUSSION

Life time Recombination-generation processes are means provided by nature for restoring a semiconductor to equilibrium by removing the surplus or deficiency of carriers in the material as compared to equilibrium condition. There are mainly three recombination processes in semiconductors (i) direct band-to-band radiative recombination, (ii) indirect phonon-assisted Shockley-Read-Hall (SRH) recombination and (iii) Auger recombination.14 Of these, the first two processes are two-carrier processes, while the third one is a three-carrier process. Once excess electron (n) - hole (p) pairs created, the equilibrium is restored according to celebrated thermal generation-recombination kinetic equation14

ASHRrad2 ),( α+α+α=α−α−== inpn

dtdp

dtdn , (2)



where αrad, αSHR and αA are radiative, Shockley-Read-Hall and Auger recombination-generation coefficients respectively; in is the intrinsic carrier concentration. The factor 2

inpn − represents the deviation of carrier concentration from equilibrium state. For direct band-to-band recombination, the radiative coefficient is proportional to the optical absorption, i.e. joint density of states Jcv(E) 15

( )ωω−−

∝α hh

cvrad1

Jff he , (3)

where fe and fh are non-equilibrium distributions of electrons and holes; Jcv(E) in PbSe was calculated in 16. The Shockley-Read-Hall (SRH) recombination-generation coefficient is given by14

11

SRH cosh2−

− ⎟⎠⎞

⎜⎝⎛ −

++τ=αkT

EEnpn it

it , (4)

where Ei and Et are trap energy level and the intrinsic Fermi level respectively, 1−τ t is a nominal trapping frequency. The recombination rate approaches a maximum as the energy level of the recombination center approaches midgap (i.e. Ei ≈ Et). Thus, the most effective recombination centers are those located in the energy near the middle of the bangap. The Auger recombination-generation coefficient may be presented in a symmetric form

pCnC pn +=αA , (5) where Cn and Cp are the Auger capture coefficients for electrons and holes, respectively; formulas for them are found in17, 18. Actually, in equation (5) only one of the two terms is effective since the Auger processes dominate at moderate and heavy doping, when the semiconductor is of strongly n- or p-type. Under low injection conditions, that is, when the injected carriers are much fewer in number than the equilibrium carriers, when keeping ∆n = ∆p, the recombination process may be characterized by the expression

τ∆

=∆ ndt

nd , (6)

where τ is an effective carrier life time. The effective life time is expressed as the resultant of the above three recombination-generation processes

1A

1SRH

1rad

1 −−−− τ+τ+τ=τ . (7) The life time for the radiative, SRH and Auger processes are given by

[ ] 100radrad )( −+α=τ pn (8)

( ) 10000SRH cosh2 −+⎟

⎠⎞

⎜⎝⎛ −

++τ=τ pnkT

EEnpn itit (9)

[ ] 10000A ))(( −++=τ pnpCnC pn (10)

Note that in equations (8) - (10) the contribution of minority carriers can be safely neglected. Auger recombination is the dominant process in narrow gap semiconductors like InSb based compounds, lead chalcogenides (PbS, PbTe and PbSe) and HgCdTe ternary alloy.19 The band structure in PbSe is characterized by four valence and four conduction band at the centre of the <111> zone faces, the maximum of each valence band is at the same point in k space as the minimum of the corresponding conduction band, and corresponding bands are dominated by a strong kp interaction. The effective masses



are therefore proportional to the band gap, and the conduction and valence bands are very similar to each other in structure and effective mass. Each band is an ellipsoid of revolution whose heavy mass is along <111> axis.17,18 For scattering within a single ellipsoidal pair of such bands it is really shown that for the case µ = mc/mv = 1 (mc and mv are effective mass in the conduction and valence bands respectively) the capture coefficient for Auger process satisfies

⎟⎟⎠

⎞⎜⎜⎝

⎛−∝

kTE

C gpn exp, , (11)

where Eg is the band gap, k is Boltzmann’s constant, T is the absolute temperature. However, when interactions between electrons in different ellipsoids are taken into account, life time is characterized by expression17

⎟⎟⎠

⎞⎜⎜⎝

⎛−∝

kTrE

C gpn exp, (12)

where r = ml/mt is the ratio of transverse to longitudinal effective masses. The above recombination parameters can be determined when combining small and high level optical pumping approaches. In strongly non-linear regime, when n ≈ p >> n0, p0, equations (2) - (4) result in 16

32 CnBnAn

dtdn

−−−= , (13)

where A = (2τt)

−1 for Ei ∼ Et, B = αrad and the effective Auger coefficient C is given by

pn CCC += . (14) Due to the favorable mirror-like band structure (r ≈ 1.75 – 2 for the conduction and valence bands respectively11), Auger recombination rate in PbSe is reduced by one or two orders of magnitude compared to that in narrow gap III-V and II-VI materials. Figure 10 illustrates the value of C for two types of compounds: PbSe and Hg1-xCdxTe obtained in.16 One of the clear differences between the two systems is in the dependence of Auger coefficient C on temperature. Both PbSe and Hg1-xCdxTe are anomalous in that the band gap decreases with lowering temperature. However, in the case of Hg1-

xCdxTe, because of the low ratio of electrons to heavy-hole effective mass, the mass decreases further with decreasing band gap. By a contrast, the electron to hole effective mass ratio for PbSe is approximately unity over the whole range of values of band gap. Graded gap semiconductor In the framework of model put forward by Neustroev and Osipov8-11 described above, absorbed oxygen lead to formation of acceptor states in the grain boundaries. According to this model, oxygen-derived acceptor states are present on the interfaces between the grains, which interior is of n-type. The acceptor states may capture electrons from the interior and so acquire a negative charge. At sufficiently large surface density of charged acceptors, the emerging built-in potential becomes strong enough to give rise to a p-type inversion layer at a grain boundary (see Fig. 11). The photo-response time τp determined by the bulk recombination processes (Eq. 7) and band-bending potential near the grain surface. In the τp theory, there are different recombination regimes depending on possible interplays between parameters, which in turn depend on details of the acceptors distribution inside the grain boundary and mutual position of the Fermi and the acceptor energy level. We consider the regime, when the acceptors are inactive as regards capturing photo-generated carriers; thus the photo-holes and electrons emerging in the quasi neutral region recombine immediately due to short recombination time in crystalline lead chalcogenides dominated by Auger processes at room temperature, while the carriers generated in the inversion and space charge regions spatially separate due to built-in electric field and should overcome the potential barrier in order to recombine (see Fig. 12).



CL]TL ( 11pm at lOOK)

_-,——____Hg !...Cd,!:... ] c

7LLnl at (0(1K)

AIII - -C -

PbSc (. — 7pm at LOOK)A,/

NPAThwPA TheoryK(ann eta'. (1995)

0 5(1 15(1

Temperature (Ic)

Fv

1

Figure 10. Auger coefficient C as a function of temperature for n-type PbSe and Hg1-xCdxTe. The energy gap for PbSe and Hg0.744Cd0.256Te is the same (~ 7 µm) at T = 100 K.18

This regime in 1D geometry approximation results in the following formula for photo-response time 9,10

1

1 1p rad Aexp 2s

s s

kT L L kTkT a a

−

− −⎡ ⎤⎛ ⎞⎛ ⎞ϕ π⎢ ⎥τ = τ + − + τ⎜ ⎟⎜ ⎟ ⎜ ⎟ϕ ϕ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

, (15)

where )()0( Ls ϕ=ϕ=ϕ is the value of the built-in electrostatic potential, 0)( <ϕ x , at the grain boundaries, L is the grain width, a is the space charge region width which, on neglect of the grain boundary finiteness, is equal to

2 2s sD

da L

kTqN +

ε ϕ ϕ= = . (16)

where ε and +

dN are the dielectric permittivity and charged donors density, respectively, and LD is the Debye screening length

Figure 11. Schematic energy band diagram of a system consisting of 1 - bulk grains and 2 - surface interlayers. ES is the maximum energy of the ground state of acceptors in the interlayer measured from the top of the valence band on the surface of the grain; FS and FV are the energy gaps between the Fermi level and the top of the valence band on the surface of a grain, and the bottom of the conduction band in a grain, respectively.11



2D

d

kTLq N +ε

= . (17)

It is quite clear that Eq. 15 has a sense only for kTs >>ϕ and L >> a. At L >> LD, which is well satisfied, the built-in potential inside the grain satisfies the Poisson equation

22

2 exp 2 sinh 1d i

d

qN nd q qkT kTdx N

+

+

⎡ ⎤⎛ ⎞ϕ ϕ ϕ⎛ ⎞ ⎛ ⎞⎢ ⎥= + −⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎢ ⎥ε ⎝ ⎠ ⎝ ⎠⎝ ⎠⎣ ⎦

. (18)

The solution of this equation, on account of screening the surface acceptors charge, leads to the following transcendental equation

( )22

exp 1 2 cosh 18

ss s si

d d

qNnkT kT kTN N kT

−

+ +

⎛ ⎞⎛ ⎞ ⎛ ⎞ϕ ϕ ϕ− − + + − =⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ε⎝ ⎠ ⎝ ⎠⎝ ⎠

, (19)

where −sN is the concentration of charged acceptors given by the textbook formula

kTEE

ss Fs

e

NN −−

+=

21, (20)

in which Ns is the total acceptors concentration, Es is the acceptor energy and Es is the Fermi level. Note that the inversion occurs when the last term in the left hand side of Eq.19 is large in spite of smallness of +

di Nn / .

In a case where the electron concentration in grains of polycrystalline PbSe film equals += dNn ≈ 5×1017 cm-3 the radiative life time equals11

61712rad

1rad 100.2105104 ×=×××=α=τ −+−

dN s−1. (21) For Auger life time τA (Eq. 10), we use a coefficient C = 8×10−28 cm6 s−1 obtained for PbSe over temperature range 100 – 300 K in16. Assuming Cn ~ Cp we get from Eq.10 due to Eqs.13 and 14

82172821A 100.1)105(104)(

2×=××==τ −+−

dNC s−1 (22)

Thus with these estimations, we obtain from Eqs. 15 and 17

Figure 12. Schematics of electron-hole recombination in graded gap lead chalcogenide films11.



S MeasuredCalculted

SS

S

15

S

ID

.

5

S

U I I

140 160 180 200 220 240 260 280 300

Temperature T. K

1

p 212

02.1)exp(

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

ψ⎟⎟⎠

⎞⎜⎜⎝

⎛π+

ψψ

=τsDs

s

LL ×10-8 s−1 (23)

where kTq ss /ϕ=ψ . For PbSe, ε = 250 11 therefore atfor +

dN =5×1017 cm-3 we have LD ≈ 0.03µm at T = 300 K. In this case

1

230087.9)exp(−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

ψψψ

=τTss

sp ×10-8 s−1. (23)

Presently, in Eq.23 we have only the only free parameter sψ . Given −

sN at given temperature, one can solve equation

for sψ (Eq.19). Figure 13a shows an analysis of the photo-response time versus the temperature. The measured results of τp for photo-detectors based on graded gap PbSe films are also shown. We can notice that qualitative agreement between experimental and calculated results is observed.

Figure 13. Comparison of calculated and experimental photo-response time τp in the graded gap PbSe films.

5. CONCLUSIONS

The experimental results confirm the physical model put forward by Neustroev and Osipov8-11 regarding the creation of inversion channels (p-type conductivity) in polycrystalline lead chalcogenides films after activating annealing in the oxygen atmosphere. In the present case, these inversion channels appear on account of the acceptor states that had been generated at the grain boundaries. The graded gap PbSe films on the polyimide substrates display photosensitivity and photoluminescence that is enhanced and its temperature range is extended almost to room temperature.



REFERENCES [1] Boberl, M., Heiss, W., Schwarzl, T., Wiesauer, K., Springholz, G., “Midinfrared continuous phtoluminiscence of lead-salt structures up to temperature of 190oC”, Appl. Phys. Lett. 82, 4065-4067 (2003). [2] Dashevsky, Z., Kreizman, R., Dariel, M., “Physical properties and inversion of conductivity type in nanocrystalline PbTe films”, J. of Appl. Physics 98, 094309-1-5 (2005). [3] Arnold, M., Zimin, D., Zogg, H., “Resonant-cavity-enhanced photodetectors for mid-infrared”, Appl. Phys. Lett. 87, 141103-1-3 (2005). [4] Zhao, F., Wu, H., Majumbar, A., Shi, Z., “Continuous wave optically pumped lead salt mid-infrared quantum-well vertical-cavity surface-emitting lasers”, Appl. Phys. Lett. 83, 5133-5135 (2003). [5] Zhao, F., Mukherjee, S., Ma, J., Li, D., Elizondo, S.L., Shi, Z. “Influence of oxygen passivation on optical properties of PbSe thin films”, Appl. Phys. Lett. 92, 211110-1-3 (2008). [6] Golubchenko, N.V., Moshnikov, V.A., Chesnokova, D.B., “Investigation into the microstructure and phase composition of polycrystalline lead selenide films in the course of thermal oxidation”, Glass physics and chemistry 32, 337-345 (2006). [7] Popov, V.P., Tikhonov, P.A., Tomaev, V.V., “Investigation into the mechanism of oxidation on the surface of lead selenide semiconsuctor structures”, Glass physics and chemistry 29, 494-500 2003. [8] Neustroev, L.N. and Osipov, V.V., “Theory of physical properties of photosensitive polycrystalline PbS-type films. I. Model, conductivity, and Hall effect”, Sov. Phys. Semicond. 20, 34-38 (1986). [9] Neustroev, L.N. and Osipov, V.V., “Theory of physical properties of photosensitive polycrystalline PbS-type films. II. Photoconductivity. Comparison with experimental results”, Sov. Phys. Semicond. 20, 38-42 (1986). [10] Neustroev, L.N., Onarkulov, K. E. and Osipov, V.V., “Photoconductivity and anomalous Hall effect in polycrystalline PbSe films”, Sov. Phys. Semicond. 21, 1352-1353 (1987). [11] Dashevsky, Z. , “High photosensitive films of lead chalcogenides”, chapter 11 in Handbook of Semiconductor Nanostructures and Devices, edited by A. A. Balandin and K. L. Wang, American Scientific Publishers, Los Angelis, 335-359 (2006). [12] Dashevsky, Z, “Influence of potential barriers on the thermoelectric properties of PbTe thin films”, Proceedings of XVI Int. Conf. on Thermoelectrics, Dresden, Germany, 255-258 (1997). [13] Komissarova, T., Khokhlov, D., Ryabova, L., Dashevsky, Z., Kasiyan, V., “Impedance of photosensitive nanocrystalline PbTe(In) films”, Phys. Rev. B 75, 195326-1-5 (2007). [14] Khanna, V.K., “Physical understanding and technological control of carrier life times in semiconductor materials and devices”, Progress in Quantum Electronics 29, 59-163 (2005). [15] Dresselhaus, M., [Optical properties of solids], American Scientific Publishers, New York, 110-130 (1980). [16] Findlay, P.C., Pidgeon, C.R., Kotitschke, R., et al., “Auger recombination dynamics of lead salts under picosecond free-electron-laser excitation,” Phys. Rev. 58, 12908-12915 (1998). [17] Emtage, P.R., “Auger recombination and junction resistance in lead-tin telluride”, J. Appl. Phys. 48, 2565-2568 (1976) [18] Ziep, O., Mocker, M., Genzow, D. and Herrmann, K.H., “Auger recombination in PbSnTe-like semiconductors,” Phys. Stat. Sol. (b) 90, 197-205 (1978). [19] Rogalski, A., “Infrared detectors: status and trends”, Progress in Quantum Electronics 27, 59-210 (2003).



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