Characterization of Trapping Levels by Photon Stimulated Current Measurements

Indian J. Phys. <S7A (4), 311 -3 1 8 (1993)

Characterization of trapping levels by photon stimulated current measurements

T Pal, S L Sharma and H N Acharya

D c p a i t m e n t o f P h y s i c s a n d M e t e o r o l o g y , I n d ia n I n s t i t u t e o f T e c h n o l o g y , K h a r a g p u r - 7 2 1 3 0 2 , W e s t B e n g a l , I n d ia

Received4 February 1993, accepted 2 March 1993

A b s t r a c t : l l i i s p a p e r p r e s e n t s th e d e t a i l e d t h e o r y a n d p r o c e d u r e f o r d e t e r m i n i n g th e t r a p p i n g l e v e l p a r a m e t e r s ( e n e r g y , c a p t u r e c r o s s s e c t i o n a n d d e n s i t y ) in w i d c - b a n d - g a p s e m i c o n d u c io r s a n d in s u la to r s u s in g p h o to n s tim u la te d c u r r e n t m e a s u r e m e n ts . I h c p r o c e d u r e h a s b e e n s u c c e s s f u l l y a p p l i e d t o d e t e r m i n e th e s e p a r a m e t e r s in r e d m e r c u r ic io d i d e s in g le c r y s ta l s g r o w n in o u r la b o r a t o r y u s in g p o l y m e r c o n tr o lle d g r o w th te c h n i q u e in v a p o u r p h a s e .

K e y w o r d s : R e d m e r c u r i c i o d i d e , p o l y m e r c o n t r o l l e d g r o w t h , t r a p p i n g l e v e l s , p h o t o n s d m u la ie d c u r r e n t.

PACS N os. : 71.55.-1, 72.20.Jv, 72.40.+(d

1. Introduction

The electrical properlies of wide-band-gap semiconduciors and insulators arc greatly involved with the mechanism of charge transport as well as of charge storage in these materials.

Localized levels in the forbidden energy gaps of such materials play an important role in the transport of charge carriers and storage of charge and therefore the characterization of these localized levels, called trapping levels, is of prime importance in the study of these materials.

These trapping levels have been characterized by a variety of experiments such as the study of luminescence [11, capacitance variation of voltage [1], space-charge limited currents [2], Poolc-Frenkel currents [3], isothermal currents [2,3], thermally stimulated currents [4-6] and the study of photon stimulated currents [7].

This paper presents the detailed procedure for determining the trapping level parameters (energy, capture cross section and density) from the photon stimulated current (PSC) measurements. The procedure is applied to the red mercuric iodide single crystals grown in our laboratory using polymer controlled growth (PCG) technique in vapour phase [8]. Red mercuric iodide (a -H g l2) has been successfully used as room temperature operable X-ray and low-energy gamma ray detectors [9]. Due to the poor charge collection in the presence of trapping centres, however, this material has found limited use in medium and high-energy gamma ray detection [10].

© 1993 lACS

2. T heory

In PSC measurements, the sample under investigation is cooled to a very low temperature and then excited by means of some external sumulus in order to generate a very large amount of non-equilibrium charge carriers within the delocalized states. This excitation results into a large proportion of the traps being filled. Because of the low temperature, which inhibits thermal release of the charge carriers from the traps, the traps remain filled even after the external stimulus is removed. The sample is then irradiated with near monochromatic light and the sample current is monitored as a function of wavelength which is varied from far infrared to the band gap energy of the material under investigation. Thus one obtains a current-wavelength spectrum from which the energy distribution of the traps can be obtained.

For wide-band materials the trap depth £, corresponds to the long wavelength cut-off of the peak, whereas, in narrow-band materials the peak of the spectrum corresponds very closely to the trap depth. In order to obtain the density and the capture cross section of a particular b'apping level, one needs to examine the current-time transient curve (see Figure 1) as th e.

trapping centres are optically emptied. Different transient curves arc obtained for different degrees of trap-filling. The following analysis shows as to how it is possible to evaluate the trap density and cross section from these U'ansient curves.

Figure 1. Typical variation of the ficc-charge-carricr density with time dunng trap-emptying process.

At sufficiently low temperature, the equations for the rale ofehangeof the free carrier density and the trapped charge density with a single level of election U'apping centres are,

dn^ _ dn, n, dt

dt

d t

= -gn, + {N ,-n,)n^vS,

0

(2⁾

Characterization o f trapping levels etc.

313

where

we have

He = frec-canier density in the conduction band,

n, = instantaneous density of the occupied traps,

T = effective lifetime of the carriers in the conduction band,

g = product of the irradiating intensity (pholons/cmVsecond) and the effective cross section of the photons and the trapped electrons,

N, = density of the trapping ccnu’cs, V = thermal velocity and

S , = capture cross section of the trapping centres.

For the decaying portion of the transient curve far away from the peak (see Figure 1),

dn^ dn,

— — « ■ — ~ and dn^

----E - « -- £-

d t T

d t dt

Therefore eq. (1) gives

dn, I f ' .

n^ = - T--- and n, = n,„---n^dt

d t T Jo

From eq. (2) and eq. (3), we obtain

Jo

(3)

(4) If wc consider ihc system at limes i\ and ti (sec Figure 1), the corresponding values of will be and and the corresponding values of the integral in eq. (3) will be and A2, Then eq. (4) will give

Subtracting eq. (5) form eq. (6) and then rcairanging, wc get

where

Y = {A2- Ai ) / ( n ,2- n , , ) and X = (/Ij/i.z - A,n,,)/(n,2- n , , ) . For the trap-filling process, wc can write

dn,. dn, n^

dt dt T

(5)

(.6)

(7)

(8)

T Pal, S L Sharma and H N Acharya

dn,

dt • ~ n^{Ni — R|)v5f (

9

where/is the generation rate. As n, is negligibly small as compared to /a n d (njt ), the solution of cq. (9) gives

«c = /T [l-ex p (-//T )].

Substituting this into eq. (8) and then integrating, we get fl, =yv,[l-exp{-/TvS,[t + T(exp(-«/T)-l)]}]

For /^{» X,} the above equation simplifies to n^=JV,[l-exp^-n,vS,t

(10⁾

(11⁾

(12⁾ where

I* = duration of the trap-filling excitation,

hk) = density of the occupied traps at the end of trap-filling and

= /t .

Substituting from eq. (12) into cq. (7), we get X — + vS,N, exp(-n’vS,r*)

8 m8

= Y + - ^ X .

8 (13)

A set of values of X and Y are obtained by varying I2 (sec Figure 1). A plot of Y against X gives a straight line with the slope = -{vS,/g). The intercept / of the linckwith the ordinate is given by

I = “ + vS,N, cxp(-/i*vS,t*)

J? L T (14)

For different values of the product (riet*), different intercepts are obtained. The value of the intercept / versus the product (nj/*) graph shows a saturation to (-1/g). Substituting this value of the intercept (= -1/g) into the slope of Y versus X curve, one may evaluate

the capture cross section S,. 6

From cq. (14), we get

Inr , 1 = ln■ vS,N,t '

1+—

8 . 8 . ⁽¹⁵⁾

The plot of In / - . - L 8

ln[(vS,/g)A^ir]. Using the determined value of [vS,/g) and known value of x, one can

\

versus r* yields a straight line with the intercept equal to

Characterization o f trapping levels etc. 315 3. Experiment

Commercially available a - H g l2 powder (E-MERCK : 98%) was purified by repealed sublimation and repeated crystallization [11]. Single crystals were then grown using polymer controlled growth (PCG) technique in vapour phase [8]. The platelet shaped crystals, thus obtained, were etched in 10% aqueous KI solution before making electrical contacts. The contacts were made by painting aquadag on both the faces of the platelets. After cooling the sample to liquid nitrogen temperature, the traps were filled by exciting the sample with near- band'gap light ( - 560 nm) obtained from ORIEL lamp-monochromator assembly (Models : 7340 and 77250 respectively). After certain trap-filling excitation time r*. the sample current was allowed to decay to the value of dark current. Keeping the sample temperature unchanged, the sample current was monitored as a function of the trap-emptying radiation wavelength which was varied from 16 iim to 0.8 M,m. For the purpose, a KEITHLEY electrometer amplifier (Model : 610C) was used. The energies of the trapping levels were evaluated directly from the peak-wavelengths in the PSC spectrum.

For determining the densities and capture cross sections of different trapping levels, the current-time transient curves for each trapping level were recorded at the C values of 10, 60,90, 180 and 240 seconds.

4. Results and discussion

Figure 2 shows the current-wavelength spectrum. It consists of four peaks giving four discrete trapping levels. The energies of these trapping levels are found to be 0.1,0.15,0.31 and 0.54 eV. By changing the polarity, the level at 0.31 eV was confirmed to be due to electron trapping centres. The capture cross section and density of this level were also determined. These results are presented and discussed below.

ENERGY ( « V ) -

Figure 2, Typical PSC spectrum for PCG grown Or-Hgla single crysials.

Figure 3 shows the decay curves for trap-filling excitation, limes of 10, 60, 90, 180 and 240 seconds. Figure 4 shows the plots of Y versus X for C versus oi 10, 60, 90, 180

67A-(4)3

and 240

The

the Y versus X straight line

t*is

shown in Figure 5. From the saturated value of the intercept, the value of 'g' was calculated and was found to be 4.9 x 10-^ From the slopes of the

Y versus X

Tifvurc 3. Current density transient curves for Figure 4. Y versus X graphs for different irap- diffcrcni trap-filling times (T). filling times (/*). (Expressions for Y and X arc given

in the text).

Figure 6 shows the plot of ln(|/ + l/g|) versus t*. The straight line was fitted using method of least square error. From the intercept on the ordinate, we obtained the trap density N, = 4.24 ^X

'Hie value of cross section for this trapping centre obtained by others [4,12] using TSC technique arc quite different from each otlier. However, our value of cross section is in good agreement with the value reported by Mohammed-Brahim et al [4]. The results obtained

Characterization o f trapping levels etc. 317 depend upon any model. So the value of cross section obtained by us should be considered more appropriate. The value of the density is very low as compared to that obtained by

Figure 5. Variation of intercept ( /) with trap-filling times (/*).

Gelbart et a/ [12] for this trapping level. If we assume that ihc trapping centres are solely due to the impurities present in ihc crystals, then the crystals grown in our laboratory seem to be much purer than the crystals used by Gelbart et al. The crystals used by us are expected to be much purer because of the superiority of PCG technique over other techniques [8]. Since the temperature is kept constant throughout the experiment, the environment of the traps arc not changed and thus there are very few sources of error in the evaluation of the density of traps and their capture cross section.

Figure 6. Variation of ln[|/ 4* l/g |] with trap-filling limes (/*). The straight line is filled using the method of least square error.

Acknowledgm ent

Wc are grateful to the Department of Atomic Energy, Govt, of India, for giving us the financial assistance in the form of a research scheme.

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318

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