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Deep level junction spectroscopy of II–VI compounds
40
Journal of Crystal Growth 59 (1982) 40-50 North-Holland Publishing Company
DEEP LEVEL J U N C T I O N S P E C T R O S C O P Y OF l l - V l COMPOUNDS
H.G. GRIMMEISS * Department of Solid State Physics, University of Lund, Box 775, S-220 07 Lund, Sweden
It will be shown that junction space-charge techniques are relevant for the study of deep energy levels in II-VI compounds. In particular, it will be shown that several important electronic parameters such as emission rates and capture rates can be studied using these methods. The fundamentals of junction space-charge techniques are explained by using two examples: the transient capacitance technique and the steady-state constant capacitance technique.
1. Introduction
Good insight into the electronic properties of crystal defects has been achieved, at least for Si, when the defects are caused by foreign atoms belonging to the groups of the periodic table closest to that of the semiconductor. Such atoms often introduce localized donor and acceptor levels close to the band edge with binding energies of less than about 50 meV. These centres are therefore called shallow impurity levies. They are widely used in semiconductor device technology for modifying the nature and degree of electrical conductivity. Replacing an atom of the host lattice by an atom which does not belong to an adjacent group of the periodic table often results in a defect with a binding energy much larger than those of shallow ones. Such defects are called deep impurity levels. Deep energy levels seem to be present in all known semiconductors. One of their most important properties is the ability to control the carrier lifetime even in small concentration. This is readily demonstrated by ShockleyRead-Hall statistics [1-3] showing that the excess carrier lifetime is significantly decreased not only by a large binding energy AG° but also by a large capture cross section o of the defect. The lifetime can be affected by both desired and undesired dopants. Deep energy levels are therefore very * On leave of absence. Present address: AB RIFA, Box 2, S-163 00, Spginga-Stockholm, Sweden.
important for the fabrication of semiconductor devices. This is one of the reasons for the current interest in deep energy levels. Another reason for the increasing interest is the fact that our insight into the electronic properties of deep centres is much more limited than that into shallow centers, because shallow energy levels often are well described by effective mass theory [4,5] except for binding at electrically neutral centres. Furthermore, owing to the different impurity potential, shallow centres generally exhibit, at least in silicon, excited states and, hence, detailed optical line spectra are available for these centres [6], whereas deep energy levels often generate smooth optical spectra both in absorption and in luminescence. A better insight into the electronic properties of deep energy levels is therefore of vital interest not only from an academic point of view but also for applications of semiconductor devices. In principle the electronic properties of deep energy levels can be characterized by both bulk and junction space-charge techniques. Previous characterization attempts have only utilized bulk techniques such as Hall measurements, optical absorption, luminescence and photoconductivity. Very often the analysis of such data is complicated owing to contributions from several different excitation and recombination processes. Furthermore, lack of information on the concentration of centres makes the determination of absolute values of electronic parameters very difficult. Although
0022-0248/82/0000-0000/$02.75 © 1982 North-Holland
41
H. G. Grimmeiss / Deep leveljunction spectroscopy of H - V ! compounds
rather detailed information on deep centres has been obtained in some cases from bulk measurements, little information could be extracted in a number of other cases using these techniques. A real break-through in the characterization of deep energy levels occurred by the application of different kinds of junction space-charge techniques [7,8]. The unique ability of junction techniques is to yield, from a single sample, information on important electronic parameters of deep centres. Most of these techniques make use of extrinsic excitation processes in the space-charge region of p - n junction or Schottky barriers [9]. In any particular experiment, the magnitude and the time-dependence of the signals obtained are determined by only one or two of these parameters, making the evaluation of the experimental data very straightforward. In addition, absolute values of all parameters can readily be obtained. Junction space-charge techniques have been used extensively in recent years to characterize deep centres in silicon and in the I I I - V compounds. However, surprisingly few investigations have been performed in I I - V I compounds although it is well known that impurity and native defects dominate the electrical and optical properties of these materials. The purpose of this paper is therefore to show that junction space-charge techniques are highly relevant for the study of deep energy levels in I I - V I compounds. In particular it will be shown that all important electronic parameters such as emission rates and capture rates can be studied using these methods. Although photocurrent methods are often a very simple and fast way of measuring spectral distributions of emission rates [9], only capacitance techniques are discussed in this paper since p - n junctions are not available in many II-VI compounds.
emission rate e t by the relationship [10]
e' -- otvtnNc.v e x p ( - A G / k T ).
(1)
Here, Nc(Nv) is the effective density of states in the conduction (valence) band and AG the change in the Gibbs free energy needed to emit an electron (hole) from the centre, g is the electronic degeneracy factor, c t is the thermal capture constant and Vtn is the average carrier velocity. The rate equation for occupation of a particular two charge energy level can be written as d n T / d t = (c.n + e p ) ( N T -- nT) -- (Cpp + en)nT,
(2) where n v is the concentration of energy levels occupied by electrons and N T = n . r + p . r is the total concentration of this particular energy level. It should be noted that the capture constant C.,p -o p + C~,p t is the sum of the capture constant for cn, radiative and n o n - r a d i a t i v e r e c o m b i n a t i o n processes and that the emission rate en, p -----e°.p + t is the sum of optical and thermal emission en,p rates. The optical emission rate e ° is correlated to the photoionization cross section o ° by the relation e° = o°~b,
(3)
where q~ is the photon flux used for measuring e °. For an energy level initially filled with electrons integration of eq. (2) gives
n.r( t )
=
Cnn + ep Cnn + cpp + e~ + ep cpp + e, + c,n + cpp + e. + ep NT × {exp[--(cnn+cpp+e,+ep)t]},
(4)
and for an energy level initially empty Cnn + ep
2. Theoretical background As already mentioned the binding energy AG ° = AG+ k T In g and the thermal capture cross section o t = c t / / V t h are important parameters in describing the electronic properties of deep energy states. They are in turn related to the thermal
rtT(t ) =
Cnn + Cpp + e n + ep
NT
)< ( 1 - exp[--(Cnn + Cpp + e n + ep)t] ).
(5) It is readily seen from eqs. (4) and (5) that the decay times vary exponentially in both cases and
42
H. (7,. Grimmeiss / Deep level junction spectroscopy of H-I1"1 compounds
~" of an energy level in the upper half of the bandgap (etn >>ep) is given by
that the time constant of the decay is given by ~-=
1 Cnn + Cpp + e n + ep
,
(6)
independent of the initial conditions. Furthermore, the equilibrium electron occupancy of the energy level is obtained as nT _ NT
Cnn + ep
(7)
Cnn + Cpp + e n + ep "
It is quite evident from eqs. (4)-(7) that the time constant ~"and the occupancy of energy levels are determined by both the emission rates and capture constants. All of them are important parameters for the characterization of deep energy levels. Since, in a reversed biased diode under reasonable experimental conditions, the occupancy of deep centers can be changed only in the spacecharge region of the junction [8], the unique ability of junction space-charge techniques is to yield information on all these parameters. However, by choosing proper initial conditions, the magnitude and the time-dependence of the signals obtained are determined by only one or two of these parameters. Both transient techniques and steady-state methods are used. In what follows we will first briefly present the transient capacitance technique as an example of transient methods and then give a short presentation of the steady-state constant capacitance method illustrating one of the steadystate techniques. 2.1. Transient capacitance technique
In the space-charge region of a reverse biased junction the free carrier concentration is generally negligible. For deep centers in this region the expression of the time constant ~- reduces therefore to 1 / ( e ° + e nt + ep0 + % ) . If an experiment for monitoring the occupancy n T / N T in the spacecharge region of a junction is performed in darkness (e,O --- epo _ - 0) the time constant r of the signal t simplifies to ~'= 1 / ( e nt + ep). When choosing the initial conditions of the experiment [9] such that n v ----NT (for example by short-circuiting a p + - n junction before reverse biasing), the time constant
~-= 1 / e t.
(8)
In a similar way ept is measured for a centre in the lower half of the bandgap (e~>>e t) when a n + - p junction (or p-type Schottky diode) is first short-circuited (or sometimes even forward biased) before reverse biasing. This also means that it is normally very difficult to measure the smaller emission rate of a non-midgap level. Performing such an experiment [3,9] below the freeze-out temperature (e t = e~ -- 0) and illuminating the sample first with near bandgap light (in order to establish an electron occupancy 0 < n T < NT) and then with photons of an energy somewhat smaller than half the bandgap, a time constant is obtained which is given by z--- 1/e °
or
1/ep,
(9)
depending on in which half of the bandgap the energy level is located. If the experiment [9,11] is carried out in darkness and at low temperature (when both e, and ep are much smaller than cpp or cnn ) in a momentarily neutral region of the sample, which otherwise is part of the space-charge region, a time constant ~" is obtained which is given either by 1 / c p p or 1 / c n n , depending on which type of charge carrier is captured. An experiment of this kind can, for example, be carried out by momentarily reducing the reverse-bias voltage VR of a Schottky barrier or one-sided junction for a short time t s. The depletion region then contracts and free carriers enter the region through which the depletion region has moved. This process is very fast and the concentration of free charge carriers in the region where the capture processes occur is the same as in the neutral region. If, therefore, experiments can be arranged so that the signal obtained is directly proportional to the occupancy of deep energy levels in the spacecharge region of a junction, the time dependence of this signal would give absolute values of emission rates and capture constants depending on which initial conditions are chosen. Fortunately, a number of physical phenomena such as junction
H.G. Grimmeiss / Deep level junction spectroscopy of H - V l compounds
capacitance, extrinsic photocurrents and dark reverse currents are determined by the occupancy of deep energy levels. For example, it is readily shown that the capacitance of an one-sided junction or Schottky barrier is given by C(t)--
W-~)Aee° -- ,( 2 ( ~+vR)A2qee° N i ( t ) ) ] 1/2 ,
(10)
where A is the area of the junction, e is the dielectric constant, W is the width of the space charge region and VD is the diffusion voltage. Since the capacitance of a junction depends on the space-charge and, hence, on the total concentration and spatial variation of ionized impurities N I, it is quite obvious that the capacitance of the junction depends on the occupancy of the impurities. Taking a p + - n junction or n-type Schottky barrier with a single deep donor-like centre in the upper half of the bandgap, is given by
Ni(t)
N D +pT(t)
= N D + N T r -- n T ( t ) , w h e r e N D is t h e
total concentration of the shallow donors (since their binding energy is so small that they are all ionized). For diodes with N D >>NTr, expansion of eq. (10) in a Taylor series gives
AC=[nT(t2)--nT(t,)] 1 ( AZeeoq X -~ 2(VD + VR)N °
43
hence W) constant and to change the reverse bias VR instead [12,13]. It can easily be shown that when the electron occupancy n T is changed, the change in voltage AVR needed to keep the capacitance constant is proportional to An T. Thermal emission rates are very small at low temperatures and, hence, give rise to large time constants. Similarly, large time constants are obtained if the photon flux ~ available a n d / o r the photoionization cross sections are small. In these cases a modification of the transient capacitance method can be applied. Taking t I = 0 and inserting eq. (4) in eq. (11), it is easily shown that
- - ~ 1 ,=0
2(V D + VR)N D
(12) where e n is the emission rate of electrons for a deep centre in the space-charge region ( p ~ 0). Eq. (12) implies that the initial slope of the capacitance transient is proportional to e n if the centre is initially filled with electrons. For an energy level initially empty the corresponding relation is obtained by inserting eq. (5) in eq. (1 l) giving
,=0=epUXg 2(VD+VR)ND
),/2 (ll)
(13)
This result clearly shows that for constant reverse bias VR and constant temperature a small change in the junction capacitance is directly proportional to the occupancy of deep centres. Hence, by choosing proper initial conditions absolute values of electronic parameters of deep centres are readily measured by monitoring the junction capacitance. The change in capacitance due to the change in occupancy may sometimes cause unwanted disturbances of the measurements since a change in capacitance involves a change in the width of the space charge region W which means that different regions of the sample are involved in the experiment [3] when measuring the time constant ,. This is particularly true for large concentrations of deep centres (i.e. N T ~ ND). It is therefore often more advantageous to keep the junction capacitance (and
In this case the initial slope is proportional to ep. It should be noted that eqs. (12) and (13) are only valid if the decay is exponential and if the energy level is initially either completely filled with or completely empty of electrons. Sometimes the decay is not simple exponential, owing to the superposition of two or several exponential decays. Under these conditions the initial slope technique still gives reliable information on the dominating decay, as will be shown later. The initial slope technique not only gives information on emission rates and concentrations, but also on the location of deep centers. This unique property of transient capacitance measurements is of decisive importance for the assignment of excitation and recombination processes. If, for example, the diode is illuminated with photons of energy somewhat less than half the bandgap, the
44
H.G. Grimmeiss / Deep ~eve~junctionspectroscopy of 11-II1 compounds
capacitance increases according to eq. (11), if the energy level is in the upper half of the bandgap and nT(0)v~0. If, instead, the centre is in the lower half of the bandgap and the initial conditions are such that nT(0 ) ~ N T, illumination with photons of similar energy would cause a decrease of the capacitance. Hence, from the sign of AC (see also eqs. (12) and (13)) information on the position of deep centres is obtained. 2.2. Steady-state constant capacitance (SCC) technique
Although the usefulness and convenience of transient capacitance techniques for the characterization of deep energy levels has been shown in a number of papers, there are several drawbacks connected with this technique. Very often the elegance of transient measurements is disturbed by non-exponential decays of the signal. This is particularly true for measurements in I I - V I compounds. There are several reasons why these transients are not of simple exponential form as is generally assumed in the analysis. The free carrier tail extending from the neutral region into the space-charge region [14], for example, can be one of the disturbing factors [15,16]. Another disturbance occurs when the concentration N T of deep centres is too large compared with the concentration of shallow energy levels [12]. Although this effect can be avoided by measuring the change in reverse bias at constant capacitance [12,13], instead of monitoring the change in capacitance at constant reverse bias [7,11], the analysis of the data is still time-consuming in most cases. A simple and rapid analysis of the data has therefore been suggested for measuring optical emission rates
by using two independent light sources instead of one [17,19]. Furthermore, heavily compensated samples can be utilized for this technique, which increases the sensitivity drastically. Since compensation is often easily obtained in I I - V I compounds the SCC technique is particularly interesting for measuring optical emission rates in these materials. To be specific, it is assumed that the energy level concerned is located in the lower half of the bandgap. During the measurement the capacitance is kept constant, and hence the change in the reverse bias AVR is proportional to the change in occupancy [13]. The diode is first illuminated with a light source of photon flux c/,s and constant energy hps, such that E T - E v < h v ~ < E c - E T (fig. 1). The optical emission rate for holes is then given by ep,, whereas the optical emission rate for electrons, e°s, is zero and, hence, the electron occupancy of the centre is unity. The temperature is chosen so that any influence of thermal excitation processes on the occupancy can be neglected. The highest temperature allowed for such an experiment can be considerably higher than the freeze-out temperature which means that steadystate measurements cover a much larger temperature range than transient methods. The sample is then reverse biased and the voltage VR chosen can be considered as being a kind of reference bias. Additional illumination of the diode with a second light source of intensity ~ and variable photon energy hi, such that Ec - E v > hv > E~ - E T (fig. 1) changes the concentration of filled centres to O N T (ep + ep~)/(e°n + epO + eps) t -(cf. eq. (7) and putting n = p - _ _ e ,t -- -- ep-0). The change in concentration An T due to the illumina-
Ec
Ec 0
t \ ~enj' n T
ens'n T
F"T
ep. PT
o
eps
eps' PT Ev
°
PT
~J'Pr .
EV
Fig. 1. Energy and intensity conditionsfor measuring spectra of
Fig. 2. Energy and intensity conditions for measuring spectra of
o en"
o ep.
H.G. Grimmeiss / Deep leveljunction spectroscopy of H-I,'1 compounds
tion with photons of variable energy h p is thus An T = N,re°n/(e°n + ep + eps ). If ~s is chosen so that eps is much larger than both enO and ep,° the last equation reduces to [19]
An. r ~ e°( NT/eps ).
O
O
eps
o + epsNT
ens
transient measurements. A combination of transient and steady-state techniques is therefore reco m m e n d a b l e in most cases.
3. Experimental results
(14)
The change in voltage AVe needed to keep the diode capacitance constant during the illumination with photons of energy h~ is therefore proporo tional to e n. The principles for measuring the spectrum of o7 are fairly similar. Selecting the photon energies of the two light sources in such a way that Eg > h Ps > E c -- E T and E T - E v < h~, < Ec -- E T (fig. 2), the change in n v is given by [18] nT=
45
O
ep -k- eps
o + o
ens
o NT
ep + eps
o
2
epe°sNTT/( e°~ + ep~) ,
(15)
o and eps o are much if ~s is chosen so that both e,s o larger than %. o and eps o are constant The emission rates ens during the measurements and, hence, the spectra of the photoionization cross sections % and o°, respectively, are obtained by using eq. (3) and plotting AVR/q, against h~,. This measuring technique is based on the assumption that the occupancy is constant during the experiment. The error in the measurement is therefore of the order e°p/eps.ns since the signal obtained is due to the change of the occupancy [19]. However, choosing o > 102 en,p, o the error is less than 1%. This eps,ns condition is readily achieved using two light sources with intensities q, and q,~ such that q's >>q'. In heavily-compensated ZnSe and CdS samples, the change in voltage AVe corresponding to An v ~ Nv has been tens of volts [13,18,19], and therefore the allowable change in AVR during the experiment has been in the 100 meV range. Spectral distributions are most easily obtained f r o m steady-state m e a s u r e m e n t s . H o w e v e r , steady-state methods generally suffer from the drawback that they do not give absolute values of photoionization cross sections [9]. Absolute values of emission rates can often only be obtained from
3.1. ZnSe ZnSe has attracted appreciable interest in recent years. One reason for this is the increasing n u m b e r of ESR and O D M R studies performed in this material. We have performed detailed studies of the self-activated centre in the ternary alloy ZnSxSel_ x which will be published in a forthcoming paper [20]. In order to demonstrate the usefulness of applying different experimental methods for measuring electronic parameters of deep centres, the spectral distribution of the photoionization cross section for holes is shown in fig. 3 for ZnS0.59Se41. Owing to small photon fluxes at higher photon energies and relatively small cross sections, very large time constants have been obtained for certain photon energies. In such cases the initial slope technique is very helpful. However, it turned out [20] that the capacitance transients were not simple exponential as shown in fig. 4. Since the reason for the non-exponential decay was not known, the spectrum was first measured using the steady-state capacitance method and then the same
i
1.0
i
,
i
o*°
o.o*
i
i
•
i
ZnSssSe41 :I
.9 • ~P
+
o
80K
• +
Y ~
o+ +
o +
÷ ~
0.5
÷
o÷
oD.
o%
b
o ÷
÷
÷ o
÷
÷
÷~-
o
+
2
0.0
J
~
1.0
I
I
1.5
I
I
I
2.0
Photon energy [eV] Fig. 3. Spectrum of the photoionization cross section of holes in ZnSo.s9Se0.41 obtained with the initial slope method (C)) and the SCC technique ( + ) at 80 K [20].
H.G. Grimmeiss / Deep leveljunction spectroscopy of H - V l compounds
46
u
I . S i l l
I
I
I
!
io °
I()1 N N ~
,
"~ 0.5
~
•o
OOO0
•
,
ZnO:Cu
ZnS59Se41 = I 80 K 1.13 eV
\
,
////~///f/E
id2
•
id 3
-050
i
I
2
F
I
4
I
I
I
6 Time
I
I
8 [min]
I0
12
14
lid
Fig. 4. Capacitance transient obtained with photons of energy 1.13 eV in ZnS0.59Seo.4L at 80 K [20].
1155
I 7
~ 8 ;
spectrum was measured again using the initial slope technique [20] (fig. 3). The good agreement between the two spectra suggests that the non-exponential decay probably is caused by the superposition of two or several exponential transients.
3.2. ZnO:Cu Cu doped ZnO has recently been subject to both experimental and theoretical work owing to its interesting optical and electronic properties [21-23]. The dominant Cu related center, generally agreed to be an acceptor caused by Cu on Zn site, gives rise to green luminescence and corresponding optical absorption as well as IR absorption. In all cases narrow zero phonon lines have permitted Zeeman analysis, giving detailed information on symmetry properties and g-tensors. However, since all these transitions are of boundto-bound nature, they give no direct information on the position of the energy levels relative to the energy bands of ZnO. Dingle, who first proposed that the green emission was due to neutral Cu on Zn site, suggested a distance from the ground state level to the conduction band of less than 0.1 eV [24]. Studying the excitation spectrum, Broser suggested a value of about 0.4 eV [23]. More indirect methods, which measure the IR absorption as a function of Fermi level position [25], give a value
I 9 103/T
i I0 (iKI)
II
Fig. 5. Temperature dependence of the electron thermal emission rate for the E¢ --0.17 eV centre in Z n O : C u [27].
of about 0.19 eV, which is consistent with conductivity and Hall effect studies [25,26]. Unlike these measurements, junction space-charge techniques allow an unambiguous assignment of all transitions studied. We used n-type Schottky diodes with moderate copper concentration (about 5 × 1015 cm -3) and measured the thermal emission rate of electrons as a function of temperature, applying the transient capacitance method [27] (fig. 5). From these measurements a thermal activation energy of 0.193 eV is obtained. Recalling that AG = A H - - T AS, eq. (1) can be rewritten giving et=
atVthUc,,,exp(AS/k) exp(--AH/kT),
(16)
where AH is the change in enthalpy and AS the change in entropy due to the emission of an electron (hole) from the center. Hence, from an Arrhenius plot of the thermal emission rate, the enthalpy of the center is obtained, if the temperature dependence of the capture cross section is taken into account. A plot of the electron capture cross section versus reciprocal temperature is shown [27] in fig. 6. The activation energy of 0.028 eV, together with the activation energy for thermal emission, gives a value of 0.165 eV for the enthalpy. In a forthcoming paper [27] it will be shown that the value obtained for the enthalpy of
H.G. Grimmeiss / Deep leveljunction spectroscopy of H - V I compounds i
i
)
5
)
tion band. Although the concentration of this center is in fair agreement with the copper concentration in our samples, junction measurements seldom give information on the nature of deep centres. For an unambiguous identification of this centre, our data have to be combined with other measurements, such as ESR, in a similar way to which it was performed for the chalcogens in silicon [28]. Evidence for the existence of excited states and resonances in the continuum was ob 5 tained from Fourier transform spectroscopy. Fig. 7 shows a photoconductivity spectrum exhibiting an ionization threshold at about 0.19 eV and some low energy structure. Further details will be published elsewhere [27].
Zn0:Cu
2 ~
////)/////E e
.~
~
Er
b--O -- I "
l
o-~ O.5
6
f
i
i
i
7
8
9
I0
) 1031T
(K-))
3.3. CdS:Cu
Fig. 6. Temperature dependence of the electron capture cross section for the E ¢ - 0 . 1 7 eV centre in Z n O : C u [27].
the copper center will probably have to be modified since optical studies indicate the existence of excited states and resonances near the band edge which complicate the analysis. Nevertheless, from these data it is quite obvious that the copper related centre in Z n O is located in the upper half of the bandgap, about 0.17 eV below the conduc-
I0
47
2
Detailed information on a particularly interesting centre has been obtained in copper doped CdS from constant capacitance measurements using Schottky diodes [ 19]. The dominant copper related center (C-centre) in these samples has a groundstate energy level about 1.1 eV above the valence band. It is widely argued that the C-centre is caused by an isolated Cu ion on a cation site (as in ZnS: Cu), and that transitions within this center can be understood on the basis of a crystal-field model where the 2D configuration of the Cu 2+ ion is split into a 2T2 ground state and an 2E excited state [29-31]. Charge transfer processes between this centre and the energy bands can be explained
o
~~////////////////////z
EC
)
•,~
e°
o ene
8
o n
[
I -
,o°
i
O.I
i
i
i
i
i
i
0.2
i
i
i
03 •
i
i
i
i
] - - -
E.
i
0.4
h~ (eV)
Fig. 7. Photoconductivity spectrum obtained with Fourier transform spectroscopy in Z n O : Cu at 70 K [27].
Fig. 8. Energy level scheme and hole transitions studied with j u n c t i o n space-charge techniques in CdS : Cu.
H. G. Grimmeiss / Deep level junction spectroscopy of H - V I compounds
48
I(j 16
nevertheless readily be anticipated in agreement with luminescence data. Furthermore, owing to the measuring technique used, it can unambiguously be shown that the ground-state is about 1.1 eV above the valence band and that the hole excited state is located between the ground state and the valence band. Emission rates from the centre to the further away lying energy band (i.e. the conduction band in the case of C d S : C u ) cannot be obtained from measurements of ~" alone. In addition the total change of the voltage AVR has to be measured and the emission rate is then obtained using the relation [13]
0
I(~ 17
E
o o b
I(~18
r 16i9
-2O
I0
0.6
'
0'.8
I'.0
'
i12
i14
(17)
A V R / , = CiNT( e ° + c3e°e),
> h. (eV) Fig. 9. Photoionization cross sections, %,o and photothermal ionization cross sections, c2a°, versus photoenergy in CdS: Cu at 146 K (A), 186 K ( A ) , 226 (O) and 266 ( O ) [19].
by the introduction of two energy levels about 1.1 and 0.34 eV above the valence band (fig. 8). In spite of numerous investigations, the nature of this copper related center in CdS is still not fully understood and no commonly accepted description has previously existed as to how these energy levels should be fitted into a one-electron energy b a n d model. However, using junction space charge techniques an unambiguous identification of all transitions investigated is obtained [19]. Fig. 9 shows the spectra of on and c2oi° obtained f r o m the time constant ~- measured at different photon energies [19]. Here, o ° = e°/g, is the cross section for the photoexcitation of holes from the ground state to the excited state. Since the photon flux ~ has been measured, the absolute values of on and the photothermal ionization cross section c2o ° are plotted. The strong phonon broadening of the spectra makes an accurate determination of the ionization energy rather difficult. It is, however, readily seen that on has a threshold at about 1.1 eV and that the temperature dependence of the threshold energy is weak. Although low-temperature luminescence measurements give more detailed information on oi° than junction techniques, a threshold energy between 0.7 and 0.75 eV can
where c t and c 3 are constants. The photionization cross section of electrons o° from the ground state into the conduction band and the sum o° + c3o°e versus photon energy are shown in fig. 10 for different temperatures [19]. Here e,~ is the optical emission rate of electrons from the hole excited state into the conduction band. Since no rigorous
~o.c3~o o
- -
IC~m
¢ 1j
~16 jr o
b
1618
1619I/ 162° 1.2
1.6
2.0 2.4 > hu (eV) Fig. 10. Photoionization cross sections, o °, and the sums o ° + c 3 0°¢ versus photon energy in C d S : C u at 146 K ( 1 ) , 186 K ( A ) , 226 K (O), 226 K ( O ) and 306 K ( + ) [19].
49
H. G. Grimmeiss / Deep level junction spectroscopy of H - V I compounds
theories for photoionization cross sections in II-VI compounds exist, no detailed analysis can be performed to obtain accurate threshold energies for o°. However, extrapolating the data measured at 146 K, threshold energies of about 1.4 and 2.2 eV are obtained for %o and o°~, respectively. Using eq. (16) it can be shown that the following relation holds for the C-center:
ep~-- Ctp~Nvexp( ASpJk ) e x p ( - - A H p J k T ) ,
(18)
where AHp~ is the change in enthalpy and ASp~ the change in entropy owing to the emission of a hole from the excited state. It follows from eq. (18) that the enthalpy AHp~ is obtained" from an Arrhenius plot of the thermal emission rate, if proper correction is made for the temperature dependence of Cp~ and N v. The temperature dependence of the photothermal emission rate t oi / ( e p e t + Ci ) 1/~" ---- epee
versus 1/T is shown in fig. 11. Since c i is much larger than ep, for temperatures below about 200 K, a straight line is obtained giving a value of 0.34 eV for the slope [19]. As indicated by the data presented in figs. 9 and 10, the C-centre might be pinned to the valence band which would i m p l y that AGpe = A H p e ~ 0.34 eV assuming a weak temperature dependence of the factor cp~N~e°/ci .
GROUND STATE CB
VB
. . . H H H I H H ~
EXCITED STATE ~I"IHH.HH...
t a + e . . . . . . . . "/HH///IHH/h"
ION CORE
(~) .
.
HZ'HHHHH.'.',
Cu2+
(Cu2+) *
NEUTRAL STATE
.
.
.
.
H~HHH.,...H
2.5 eV
.
Ln eV 0.54 eV
.
".'HHFIH,'.'HI,'/,
0
Cu+
NEGATIVE STATE
Fig. 12. Suggested model for the electronic structure of a CUcd centre in CdS using the hole picture and neglecting any fine structure. The energy values are valid for T~- 180 K [19].
From the measurements presented so far, an unambiguous energy level scheme is obtained (fig. 12) which, together with low temperature luminescence experiments, contains many details and, in particular, absolute values of most of the electronic parameters [ 18,19]. A similar energy level scheme and absolute values for %o have recently been suggested by Suda and Bube [32] using infrared quenching of photocapacitance. Junction space-charge techniques seldom give information on the microscopic nature and identification of the centre investigated. Information of this kind is often obtained from spin dependent measurements such as ESR, O D M R or Zeeman studies. Since, in many cases, neither ESR nor O D M R studies give accurate values of electronic parameters, a combination of junction techniques with spin dependent measurements [28] is, in all cases where this is possible, the by far most rewarding method to increase our knowledge of deep centres.
Acknowledgement The author is indebted to N. Kullendorff, R. Mach and E. Meijer for making some of their data available prior to publication.
-0 4'5
,
,
,
510
5'5
6'0 > ~
References
, I
6"5
7'0
(K"°)
Fig. I I. Temperature dependence of the photothermal emission rate 1/~ [19] in C d S : C u (see text).
[1] W. Shockley and W.T. Read, Phys. Rev. 87 (1952) 835. [2] R.N. Hall, Phys. Rev. 86 (1952) 600. [3] H.G. Grimmeiss, Ann. Rev. Mater. Sci. 7 (1977) 341.
50 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
1-1.G. Grimmeiss / Deep level junction spectroscopy of 11- II1 compounds W. Kohn, Solid State Phys. 5 (1957) 257. W. Kohn, Phys. Rev. 98 (1955) 915. R.A. Faulkner, Phys. Rev. 184 (1969) 713. C.T. Sah, L. Forbes, L.L. Rosier and A,F. Tasch, Solidstate Electron. 13 (1970) 759. G. Bj6rklund and H.G. Grimmeiss, Solid-State Electron. 14 (1971) 589. H.G. Grimmeiss and C. Ovr~n, J. Phys. El4 (1981) 1032. O. Engstr6m and A. Aim, Solid-State Electron. 21 (1978) 1571. G.L. Miller, D.V. Lang and L.C. Kimmerling, Ann. Rev. Mater. Sci. 7 (1977) 377. J.A. Pals, Solid-State Electron. 17 (1974) 1139. H.G. Grimmeiss, C. Ovr6n and R. Mach, J. Appl. Phys. 50 (1979) 6328. S. Braun and H.G. Grimmeiss, J. Appl. Phys. 44 (1973) 2789. A. Zylbersztejn, Appl. Phys. Letters 33 (1978) 200. H.G. Grimmeiss, L.-,~ Ledebo and E. Meijer, Appl. Phys. Letters 36 (1980) 307. A.M. White, P.J. Dean and P. Porteous, J. Appl. Phys. 47 (1976) 3230. H.G. Grimmeiss and N. Kullendorff, J. Appl. Phys. 51 (1980) 5852. H.G. Grimmeiss, N. Kullendorff and R. Broser, J. Appl. Phys. 52 (1981) 3405.
[20] H.G. Grimmeiss, E. Meijer and R. Mach-Miiller, to be published. [21] P.J. Dean, D.J. Robbins, S.G. Bishop, J.A. Savage and P. Proteus, J. Phys. C14 (1981) 2847. [22] D.J. Robbins, D.C. Herbert and P.J. Dean, J. Phys. C14 (1981) 2859. [23] I.J. Broser, R.K.F. Germer, H.-J. Schulz and K.P. Wisznewski, Solid-State Electron. 21 (1978) 1597. [24] R. Dingle, Phys. Rev. Letters 23 (1969) 579, [25] G. Mtiller, Phys. Status Solidi (b) 76 (1976) 525. [26] E. Mollwo, G. Miiller and P. Wagner, Solid State Commun. 13 (1973) 1283. [27] H.G. Grimmeiss, N. Kullendorf and R. Helbig, to be published. [28] H.G. Grimmeiss, E. Janz6n, H. Ennen, O. Schirmer, J. Schneider, R. W6rner, C. Holm, E. Sirtle and P. Wagner, Phys. Rev. B24 (1981) 4571. [29] I. Broser, H. Maier and H.-J. Schultz, Phys. Rev. 140 (1965) A2135. [30] I. Broser and K.-H. Franke, J. Phys. Chem. Solids 26 (1965) 1013. [31] I. Broser, U. Scherz and M. W6hlecke, J. Luminescence 1 (1970) 39. [32] T. Suda and R.H. Bube, J. Appl. Phys. 52 (1981) 6218.
Journal of Crystal Growth 59 (1982) 40-50 North-Holland Publishing Company
DEEP LEVEL J U N C T I O N S P E C T R O S C O P Y OF l l - V l COMPOUNDS
H.G. GRIMMEISS * Department of Solid State Physics, University of Lund, Box 775, S-220 07 Lund, Sweden
It will be shown that junction space-charge techniques are relevant for the study of deep energy levels in II-VI compounds. In particular, it will be shown that several important electronic parameters such as emission rates and capture rates can be studied using these methods. The fundamentals of junction space-charge techniques are explained by using two examples: the transient capacitance technique and the steady-state constant capacitance technique.
1. Introduction
Good insight into the electronic properties of crystal defects has been achieved, at least for Si, when the defects are caused by foreign atoms belonging to the groups of the periodic table closest to that of the semiconductor. Such atoms often introduce localized donor and acceptor levels close to the band edge with binding energies of less than about 50 meV. These centres are therefore called shallow impurity levies. They are widely used in semiconductor device technology for modifying the nature and degree of electrical conductivity. Replacing an atom of the host lattice by an atom which does not belong to an adjacent group of the periodic table often results in a defect with a binding energy much larger than those of shallow ones. Such defects are called deep impurity levels. Deep energy levels seem to be present in all known semiconductors. One of their most important properties is the ability to control the carrier lifetime even in small concentration. This is readily demonstrated by ShockleyRead-Hall statistics [1-3] showing that the excess carrier lifetime is significantly decreased not only by a large binding energy AG° but also by a large capture cross section o of the defect. The lifetime can be affected by both desired and undesired dopants. Deep energy levels are therefore very * On leave of absence. Present address: AB RIFA, Box 2, S-163 00, Spginga-Stockholm, Sweden.
important for the fabrication of semiconductor devices. This is one of the reasons for the current interest in deep energy levels. Another reason for the increasing interest is the fact that our insight into the electronic properties of deep centres is much more limited than that into shallow centers, because shallow energy levels often are well described by effective mass theory [4,5] except for binding at electrically neutral centres. Furthermore, owing to the different impurity potential, shallow centres generally exhibit, at least in silicon, excited states and, hence, detailed optical line spectra are available for these centres [6], whereas deep energy levels often generate smooth optical spectra both in absorption and in luminescence. A better insight into the electronic properties of deep energy levels is therefore of vital interest not only from an academic point of view but also for applications of semiconductor devices. In principle the electronic properties of deep energy levels can be characterized by both bulk and junction space-charge techniques. Previous characterization attempts have only utilized bulk techniques such as Hall measurements, optical absorption, luminescence and photoconductivity. Very often the analysis of such data is complicated owing to contributions from several different excitation and recombination processes. Furthermore, lack of information on the concentration of centres makes the determination of absolute values of electronic parameters very difficult. Although
0022-0248/82/0000-0000/$02.75 © 1982 North-Holland
41
H. G. Grimmeiss / Deep leveljunction spectroscopy of H - V ! compounds
rather detailed information on deep centres has been obtained in some cases from bulk measurements, little information could be extracted in a number of other cases using these techniques. A real break-through in the characterization of deep energy levels occurred by the application of different kinds of junction space-charge techniques [7,8]. The unique ability of junction techniques is to yield, from a single sample, information on important electronic parameters of deep centres. Most of these techniques make use of extrinsic excitation processes in the space-charge region of p - n junction or Schottky barriers [9]. In any particular experiment, the magnitude and the time-dependence of the signals obtained are determined by only one or two of these parameters, making the evaluation of the experimental data very straightforward. In addition, absolute values of all parameters can readily be obtained. Junction space-charge techniques have been used extensively in recent years to characterize deep centres in silicon and in the I I I - V compounds. However, surprisingly few investigations have been performed in I I - V I compounds although it is well known that impurity and native defects dominate the electrical and optical properties of these materials. The purpose of this paper is therefore to show that junction space-charge techniques are highly relevant for the study of deep energy levels in I I - V I compounds. In particular it will be shown that all important electronic parameters such as emission rates and capture rates can be studied using these methods. Although photocurrent methods are often a very simple and fast way of measuring spectral distributions of emission rates [9], only capacitance techniques are discussed in this paper since p - n junctions are not available in many II-VI compounds.
emission rate e t by the relationship [10]
e' -- otvtnNc.v e x p ( - A G / k T ).
(1)
Here, Nc(Nv) is the effective density of states in the conduction (valence) band and AG the change in the Gibbs free energy needed to emit an electron (hole) from the centre, g is the electronic degeneracy factor, c t is the thermal capture constant and Vtn is the average carrier velocity. The rate equation for occupation of a particular two charge energy level can be written as d n T / d t = (c.n + e p ) ( N T -- nT) -- (Cpp + en)nT,
(2) where n v is the concentration of energy levels occupied by electrons and N T = n . r + p . r is the total concentration of this particular energy level. It should be noted that the capture constant C.,p -o p + C~,p t is the sum of the capture constant for cn, radiative and n o n - r a d i a t i v e r e c o m b i n a t i o n processes and that the emission rate en, p -----e°.p + t is the sum of optical and thermal emission en,p rates. The optical emission rate e ° is correlated to the photoionization cross section o ° by the relation e° = o°~b,
(3)
where q~ is the photon flux used for measuring e °. For an energy level initially filled with electrons integration of eq. (2) gives
n.r( t )
=
Cnn + ep Cnn + cpp + e~ + ep cpp + e, + c,n + cpp + e. + ep NT × {exp[--(cnn+cpp+e,+ep)t]},
(4)
and for an energy level initially empty Cnn + ep
2. Theoretical background As already mentioned the binding energy AG ° = AG+ k T In g and the thermal capture cross section o t = c t / / V t h are important parameters in describing the electronic properties of deep energy states. They are in turn related to the thermal
rtT(t ) =
Cnn + Cpp + e n + ep
NT
)< ( 1 - exp[--(Cnn + Cpp + e n + ep)t] ).
(5) It is readily seen from eqs. (4) and (5) that the decay times vary exponentially in both cases and
42
H. (7,. Grimmeiss / Deep level junction spectroscopy of H-I1"1 compounds
~" of an energy level in the upper half of the bandgap (etn >>ep) is given by
that the time constant of the decay is given by ~-=
1 Cnn + Cpp + e n + ep
,
(6)
independent of the initial conditions. Furthermore, the equilibrium electron occupancy of the energy level is obtained as nT _ NT
Cnn + ep
(7)
Cnn + Cpp + e n + ep "
It is quite evident from eqs. (4)-(7) that the time constant ~"and the occupancy of energy levels are determined by both the emission rates and capture constants. All of them are important parameters for the characterization of deep energy levels. Since, in a reversed biased diode under reasonable experimental conditions, the occupancy of deep centers can be changed only in the spacecharge region of the junction [8], the unique ability of junction space-charge techniques is to yield information on all these parameters. However, by choosing proper initial conditions, the magnitude and the time-dependence of the signals obtained are determined by only one or two of these parameters. Both transient techniques and steady-state methods are used. In what follows we will first briefly present the transient capacitance technique as an example of transient methods and then give a short presentation of the steady-state constant capacitance method illustrating one of the steadystate techniques. 2.1. Transient capacitance technique
In the space-charge region of a reverse biased junction the free carrier concentration is generally negligible. For deep centers in this region the expression of the time constant ~- reduces therefore to 1 / ( e ° + e nt + ep0 + % ) . If an experiment for monitoring the occupancy n T / N T in the spacecharge region of a junction is performed in darkness (e,O --- epo _ - 0) the time constant r of the signal t simplifies to ~'= 1 / ( e nt + ep). When choosing the initial conditions of the experiment [9] such that n v ----NT (for example by short-circuiting a p + - n junction before reverse biasing), the time constant
~-= 1 / e t.
(8)
In a similar way ept is measured for a centre in the lower half of the bandgap (e~>>e t) when a n + - p junction (or p-type Schottky diode) is first short-circuited (or sometimes even forward biased) before reverse biasing. This also means that it is normally very difficult to measure the smaller emission rate of a non-midgap level. Performing such an experiment [3,9] below the freeze-out temperature (e t = e~ -- 0) and illuminating the sample first with near bandgap light (in order to establish an electron occupancy 0 < n T < NT) and then with photons of an energy somewhat smaller than half the bandgap, a time constant is obtained which is given by z--- 1/e °
or
1/ep,
(9)
depending on in which half of the bandgap the energy level is located. If the experiment [9,11] is carried out in darkness and at low temperature (when both e, and ep are much smaller than cpp or cnn ) in a momentarily neutral region of the sample, which otherwise is part of the space-charge region, a time constant ~" is obtained which is given either by 1 / c p p or 1 / c n n , depending on which type of charge carrier is captured. An experiment of this kind can, for example, be carried out by momentarily reducing the reverse-bias voltage VR of a Schottky barrier or one-sided junction for a short time t s. The depletion region then contracts and free carriers enter the region through which the depletion region has moved. This process is very fast and the concentration of free charge carriers in the region where the capture processes occur is the same as in the neutral region. If, therefore, experiments can be arranged so that the signal obtained is directly proportional to the occupancy of deep energy levels in the spacecharge region of a junction, the time dependence of this signal would give absolute values of emission rates and capture constants depending on which initial conditions are chosen. Fortunately, a number of physical phenomena such as junction
H.G. Grimmeiss / Deep level junction spectroscopy of H - V l compounds
capacitance, extrinsic photocurrents and dark reverse currents are determined by the occupancy of deep energy levels. For example, it is readily shown that the capacitance of an one-sided junction or Schottky barrier is given by C(t)--
W-~)Aee° -- ,( 2 ( ~+vR)A2qee° N i ( t ) ) ] 1/2 ,
(10)
where A is the area of the junction, e is the dielectric constant, W is the width of the space charge region and VD is the diffusion voltage. Since the capacitance of a junction depends on the space-charge and, hence, on the total concentration and spatial variation of ionized impurities N I, it is quite obvious that the capacitance of the junction depends on the occupancy of the impurities. Taking a p + - n junction or n-type Schottky barrier with a single deep donor-like centre in the upper half of the bandgap, is given by
Ni(t)
N D +pT(t)
= N D + N T r -- n T ( t ) , w h e r e N D is t h e
total concentration of the shallow donors (since their binding energy is so small that they are all ionized). For diodes with N D >>NTr, expansion of eq. (10) in a Taylor series gives
AC=[nT(t2)--nT(t,)] 1 ( AZeeoq X -~ 2(VD + VR)N °
43
hence W) constant and to change the reverse bias VR instead [12,13]. It can easily be shown that when the electron occupancy n T is changed, the change in voltage AVR needed to keep the capacitance constant is proportional to An T. Thermal emission rates are very small at low temperatures and, hence, give rise to large time constants. Similarly, large time constants are obtained if the photon flux ~ available a n d / o r the photoionization cross sections are small. In these cases a modification of the transient capacitance method can be applied. Taking t I = 0 and inserting eq. (4) in eq. (11), it is easily shown that
- - ~ 1 ,=0
2(V D + VR)N D
(12) where e n is the emission rate of electrons for a deep centre in the space-charge region ( p ~ 0). Eq. (12) implies that the initial slope of the capacitance transient is proportional to e n if the centre is initially filled with electrons. For an energy level initially empty the corresponding relation is obtained by inserting eq. (5) in eq. (1 l) giving
,=0=epUXg 2(VD+VR)ND
),/2 (ll)
(13)
This result clearly shows that for constant reverse bias VR and constant temperature a small change in the junction capacitance is directly proportional to the occupancy of deep centres. Hence, by choosing proper initial conditions absolute values of electronic parameters of deep centres are readily measured by monitoring the junction capacitance. The change in capacitance due to the change in occupancy may sometimes cause unwanted disturbances of the measurements since a change in capacitance involves a change in the width of the space charge region W which means that different regions of the sample are involved in the experiment [3] when measuring the time constant ,. This is particularly true for large concentrations of deep centres (i.e. N T ~ ND). It is therefore often more advantageous to keep the junction capacitance (and
In this case the initial slope is proportional to ep. It should be noted that eqs. (12) and (13) are only valid if the decay is exponential and if the energy level is initially either completely filled with or completely empty of electrons. Sometimes the decay is not simple exponential, owing to the superposition of two or several exponential decays. Under these conditions the initial slope technique still gives reliable information on the dominating decay, as will be shown later. The initial slope technique not only gives information on emission rates and concentrations, but also on the location of deep centers. This unique property of transient capacitance measurements is of decisive importance for the assignment of excitation and recombination processes. If, for example, the diode is illuminated with photons of energy somewhat less than half the bandgap, the
44
H.G. Grimmeiss / Deep ~eve~junctionspectroscopy of 11-II1 compounds
capacitance increases according to eq. (11), if the energy level is in the upper half of the bandgap and nT(0)v~0. If, instead, the centre is in the lower half of the bandgap and the initial conditions are such that nT(0 ) ~ N T, illumination with photons of similar energy would cause a decrease of the capacitance. Hence, from the sign of AC (see also eqs. (12) and (13)) information on the position of deep centres is obtained. 2.2. Steady-state constant capacitance (SCC) technique
Although the usefulness and convenience of transient capacitance techniques for the characterization of deep energy levels has been shown in a number of papers, there are several drawbacks connected with this technique. Very often the elegance of transient measurements is disturbed by non-exponential decays of the signal. This is particularly true for measurements in I I - V I compounds. There are several reasons why these transients are not of simple exponential form as is generally assumed in the analysis. The free carrier tail extending from the neutral region into the space-charge region [14], for example, can be one of the disturbing factors [15,16]. Another disturbance occurs when the concentration N T of deep centres is too large compared with the concentration of shallow energy levels [12]. Although this effect can be avoided by measuring the change in reverse bias at constant capacitance [12,13], instead of monitoring the change in capacitance at constant reverse bias [7,11], the analysis of the data is still time-consuming in most cases. A simple and rapid analysis of the data has therefore been suggested for measuring optical emission rates
by using two independent light sources instead of one [17,19]. Furthermore, heavily compensated samples can be utilized for this technique, which increases the sensitivity drastically. Since compensation is often easily obtained in I I - V I compounds the SCC technique is particularly interesting for measuring optical emission rates in these materials. To be specific, it is assumed that the energy level concerned is located in the lower half of the bandgap. During the measurement the capacitance is kept constant, and hence the change in the reverse bias AVR is proportional to the change in occupancy [13]. The diode is first illuminated with a light source of photon flux c/,s and constant energy hps, such that E T - E v < h v ~ < E c - E T (fig. 1). The optical emission rate for holes is then given by ep,, whereas the optical emission rate for electrons, e°s, is zero and, hence, the electron occupancy of the centre is unity. The temperature is chosen so that any influence of thermal excitation processes on the occupancy can be neglected. The highest temperature allowed for such an experiment can be considerably higher than the freeze-out temperature which means that steadystate measurements cover a much larger temperature range than transient methods. The sample is then reverse biased and the voltage VR chosen can be considered as being a kind of reference bias. Additional illumination of the diode with a second light source of intensity ~ and variable photon energy hi, such that Ec - E v > hv > E~ - E T (fig. 1) changes the concentration of filled centres to O N T (ep + ep~)/(e°n + epO + eps) t -(cf. eq. (7) and putting n = p - _ _ e ,t -- -- ep-0). The change in concentration An T due to the illumina-
Ec
Ec 0
t \ ~enj' n T
ens'n T
F"T
ep. PT
o
eps
eps' PT Ev
°
PT
~J'Pr .
EV
Fig. 1. Energy and intensity conditionsfor measuring spectra of
Fig. 2. Energy and intensity conditions for measuring spectra of
o en"
o ep.
H.G. Grimmeiss / Deep leveljunction spectroscopy of H-I,'1 compounds
tion with photons of variable energy h p is thus An T = N,re°n/(e°n + ep + eps ). If ~s is chosen so that eps is much larger than both enO and ep,° the last equation reduces to [19]
An. r ~ e°( NT/eps ).
O
O
eps
o + epsNT
ens
transient measurements. A combination of transient and steady-state techniques is therefore reco m m e n d a b l e in most cases.
3. Experimental results
(14)
The change in voltage AVe needed to keep the diode capacitance constant during the illumination with photons of energy h~ is therefore proporo tional to e n. The principles for measuring the spectrum of o7 are fairly similar. Selecting the photon energies of the two light sources in such a way that Eg > h Ps > E c -- E T and E T - E v < h~, < Ec -- E T (fig. 2), the change in n v is given by [18] nT=
45
O
ep -k- eps
o + o
ens
o NT
ep + eps
o
2
epe°sNTT/( e°~ + ep~) ,
(15)
o and eps o are much if ~s is chosen so that both e,s o larger than %. o and eps o are constant The emission rates ens during the measurements and, hence, the spectra of the photoionization cross sections % and o°, respectively, are obtained by using eq. (3) and plotting AVR/q, against h~,. This measuring technique is based on the assumption that the occupancy is constant during the experiment. The error in the measurement is therefore of the order e°p/eps.ns since the signal obtained is due to the change of the occupancy [19]. However, choosing o > 102 en,p, o the error is less than 1%. This eps,ns condition is readily achieved using two light sources with intensities q, and q,~ such that q's >>q'. In heavily-compensated ZnSe and CdS samples, the change in voltage AVe corresponding to An v ~ Nv has been tens of volts [13,18,19], and therefore the allowable change in AVR during the experiment has been in the 100 meV range. Spectral distributions are most easily obtained f r o m steady-state m e a s u r e m e n t s . H o w e v e r , steady-state methods generally suffer from the drawback that they do not give absolute values of photoionization cross sections [9]. Absolute values of emission rates can often only be obtained from
3.1. ZnSe ZnSe has attracted appreciable interest in recent years. One reason for this is the increasing n u m b e r of ESR and O D M R studies performed in this material. We have performed detailed studies of the self-activated centre in the ternary alloy ZnSxSel_ x which will be published in a forthcoming paper [20]. In order to demonstrate the usefulness of applying different experimental methods for measuring electronic parameters of deep centres, the spectral distribution of the photoionization cross section for holes is shown in fig. 3 for ZnS0.59Se41. Owing to small photon fluxes at higher photon energies and relatively small cross sections, very large time constants have been obtained for certain photon energies. In such cases the initial slope technique is very helpful. However, it turned out [20] that the capacitance transients were not simple exponential as shown in fig. 4. Since the reason for the non-exponential decay was not known, the spectrum was first measured using the steady-state capacitance method and then the same
i
1.0
i
,
i
o*°
o.o*
i
i
•
i
ZnSssSe41 :I
.9 • ~P
+
o
80K
• +
Y ~
o+ +
o +
÷ ~
0.5
÷
o÷
oD.
o%
b
o ÷
÷
÷ o
÷
÷
÷~-
o
+
2
0.0
J
~
1.0
I
I
1.5
I
I
I
2.0
Photon energy [eV] Fig. 3. Spectrum of the photoionization cross section of holes in ZnSo.s9Se0.41 obtained with the initial slope method (C)) and the SCC technique ( + ) at 80 K [20].
H.G. Grimmeiss / Deep leveljunction spectroscopy of H - V l compounds
46
u
I . S i l l
I
I
I
!
io °
I()1 N N ~
,
"~ 0.5
~
•o
OOO0
•
,
ZnO:Cu
ZnS59Se41 = I 80 K 1.13 eV
\
,
////~///f/E
id2
•
id 3
-050
i
I
2
F
I
4
I
I
I
6 Time
I
I
8 [min]
I0
12
14
lid
Fig. 4. Capacitance transient obtained with photons of energy 1.13 eV in ZnS0.59Seo.4L at 80 K [20].
1155
I 7
~ 8 ;
spectrum was measured again using the initial slope technique [20] (fig. 3). The good agreement between the two spectra suggests that the non-exponential decay probably is caused by the superposition of two or several exponential transients.
3.2. ZnO:Cu Cu doped ZnO has recently been subject to both experimental and theoretical work owing to its interesting optical and electronic properties [21-23]. The dominant Cu related center, generally agreed to be an acceptor caused by Cu on Zn site, gives rise to green luminescence and corresponding optical absorption as well as IR absorption. In all cases narrow zero phonon lines have permitted Zeeman analysis, giving detailed information on symmetry properties and g-tensors. However, since all these transitions are of boundto-bound nature, they give no direct information on the position of the energy levels relative to the energy bands of ZnO. Dingle, who first proposed that the green emission was due to neutral Cu on Zn site, suggested a distance from the ground state level to the conduction band of less than 0.1 eV [24]. Studying the excitation spectrum, Broser suggested a value of about 0.4 eV [23]. More indirect methods, which measure the IR absorption as a function of Fermi level position [25], give a value
I 9 103/T
i I0 (iKI)
II
Fig. 5. Temperature dependence of the electron thermal emission rate for the E¢ --0.17 eV centre in Z n O : C u [27].
of about 0.19 eV, which is consistent with conductivity and Hall effect studies [25,26]. Unlike these measurements, junction space-charge techniques allow an unambiguous assignment of all transitions studied. We used n-type Schottky diodes with moderate copper concentration (about 5 × 1015 cm -3) and measured the thermal emission rate of electrons as a function of temperature, applying the transient capacitance method [27] (fig. 5). From these measurements a thermal activation energy of 0.193 eV is obtained. Recalling that AG = A H - - T AS, eq. (1) can be rewritten giving et=
atVthUc,,,exp(AS/k) exp(--AH/kT),
(16)
where AH is the change in enthalpy and AS the change in entropy due to the emission of an electron (hole) from the center. Hence, from an Arrhenius plot of the thermal emission rate, the enthalpy of the center is obtained, if the temperature dependence of the capture cross section is taken into account. A plot of the electron capture cross section versus reciprocal temperature is shown [27] in fig. 6. The activation energy of 0.028 eV, together with the activation energy for thermal emission, gives a value of 0.165 eV for the enthalpy. In a forthcoming paper [27] it will be shown that the value obtained for the enthalpy of
H.G. Grimmeiss / Deep leveljunction spectroscopy of H - V I compounds i
i
)
5
)
tion band. Although the concentration of this center is in fair agreement with the copper concentration in our samples, junction measurements seldom give information on the nature of deep centres. For an unambiguous identification of this centre, our data have to be combined with other measurements, such as ESR, in a similar way to which it was performed for the chalcogens in silicon [28]. Evidence for the existence of excited states and resonances in the continuum was ob 5 tained from Fourier transform spectroscopy. Fig. 7 shows a photoconductivity spectrum exhibiting an ionization threshold at about 0.19 eV and some low energy structure. Further details will be published elsewhere [27].
Zn0:Cu
2 ~
////)/////E e
.~
~
Er
b--O -- I "
l
o-~ O.5
6
f
i
i
i
7
8
9
I0
) 1031T
(K-))
3.3. CdS:Cu
Fig. 6. Temperature dependence of the electron capture cross section for the E ¢ - 0 . 1 7 eV centre in Z n O : C u [27].
the copper center will probably have to be modified since optical studies indicate the existence of excited states and resonances near the band edge which complicate the analysis. Nevertheless, from these data it is quite obvious that the copper related centre in Z n O is located in the upper half of the bandgap, about 0.17 eV below the conduc-
I0
47
2
Detailed information on a particularly interesting centre has been obtained in copper doped CdS from constant capacitance measurements using Schottky diodes [ 19]. The dominant copper related center (C-centre) in these samples has a groundstate energy level about 1.1 eV above the valence band. It is widely argued that the C-centre is caused by an isolated Cu ion on a cation site (as in ZnS: Cu), and that transitions within this center can be understood on the basis of a crystal-field model where the 2D configuration of the Cu 2+ ion is split into a 2T2 ground state and an 2E excited state [29-31]. Charge transfer processes between this centre and the energy bands can be explained
o
~~////////////////////z
EC
)
•,~
e°
o ene
8
o n
[
I -
,o°
i
O.I
i
i
i
i
i
i
0.2
i
i
i
03 •
i
i
i
i
] - - -
E.
i
0.4
h~ (eV)
Fig. 7. Photoconductivity spectrum obtained with Fourier transform spectroscopy in Z n O : Cu at 70 K [27].
Fig. 8. Energy level scheme and hole transitions studied with j u n c t i o n space-charge techniques in CdS : Cu.
H. G. Grimmeiss / Deep level junction spectroscopy of H - V I compounds
48
I(j 16
nevertheless readily be anticipated in agreement with luminescence data. Furthermore, owing to the measuring technique used, it can unambiguously be shown that the ground-state is about 1.1 eV above the valence band and that the hole excited state is located between the ground state and the valence band. Emission rates from the centre to the further away lying energy band (i.e. the conduction band in the case of C d S : C u ) cannot be obtained from measurements of ~" alone. In addition the total change of the voltage AVR has to be measured and the emission rate is then obtained using the relation [13]
0
I(~ 17
E
o o b
I(~18
r 16i9
-2O
I0
0.6
'
0'.8
I'.0
'
i12
i14
(17)
A V R / , = CiNT( e ° + c3e°e),
> h. (eV) Fig. 9. Photoionization cross sections, %,o and photothermal ionization cross sections, c2a°, versus photoenergy in CdS: Cu at 146 K (A), 186 K ( A ) , 226 (O) and 266 ( O ) [19].
by the introduction of two energy levels about 1.1 and 0.34 eV above the valence band (fig. 8). In spite of numerous investigations, the nature of this copper related center in CdS is still not fully understood and no commonly accepted description has previously existed as to how these energy levels should be fitted into a one-electron energy b a n d model. However, using junction space charge techniques an unambiguous identification of all transitions investigated is obtained [19]. Fig. 9 shows the spectra of on and c2oi° obtained f r o m the time constant ~- measured at different photon energies [19]. Here, o ° = e°/g, is the cross section for the photoexcitation of holes from the ground state to the excited state. Since the photon flux ~ has been measured, the absolute values of on and the photothermal ionization cross section c2o ° are plotted. The strong phonon broadening of the spectra makes an accurate determination of the ionization energy rather difficult. It is, however, readily seen that on has a threshold at about 1.1 eV and that the temperature dependence of the threshold energy is weak. Although low-temperature luminescence measurements give more detailed information on oi° than junction techniques, a threshold energy between 0.7 and 0.75 eV can
where c t and c 3 are constants. The photionization cross section of electrons o° from the ground state into the conduction band and the sum o° + c3o°e versus photon energy are shown in fig. 10 for different temperatures [19]. Here e,~ is the optical emission rate of electrons from the hole excited state into the conduction band. Since no rigorous
~o.c3~o o
- -
IC~m
¢ 1j
~16 jr o
b
1618
1619I/ 162° 1.2
1.6
2.0 2.4 > hu (eV) Fig. 10. Photoionization cross sections, o °, and the sums o ° + c 3 0°¢ versus photon energy in C d S : C u at 146 K ( 1 ) , 186 K ( A ) , 226 K (O), 226 K ( O ) and 306 K ( + ) [19].
49
H. G. Grimmeiss / Deep level junction spectroscopy of H - V I compounds
theories for photoionization cross sections in II-VI compounds exist, no detailed analysis can be performed to obtain accurate threshold energies for o°. However, extrapolating the data measured at 146 K, threshold energies of about 1.4 and 2.2 eV are obtained for %o and o°~, respectively. Using eq. (16) it can be shown that the following relation holds for the C-center:
ep~-- Ctp~Nvexp( ASpJk ) e x p ( - - A H p J k T ) ,
(18)
where AHp~ is the change in enthalpy and ASp~ the change in entropy owing to the emission of a hole from the excited state. It follows from eq. (18) that the enthalpy AHp~ is obtained" from an Arrhenius plot of the thermal emission rate, if proper correction is made for the temperature dependence of Cp~ and N v. The temperature dependence of the photothermal emission rate t oi / ( e p e t + Ci ) 1/~" ---- epee
versus 1/T is shown in fig. 11. Since c i is much larger than ep, for temperatures below about 200 K, a straight line is obtained giving a value of 0.34 eV for the slope [19]. As indicated by the data presented in figs. 9 and 10, the C-centre might be pinned to the valence band which would i m p l y that AGpe = A H p e ~ 0.34 eV assuming a weak temperature dependence of the factor cp~N~e°/ci .
GROUND STATE CB
VB
. . . H H H I H H ~
EXCITED STATE ~I"IHH.HH...
t a + e . . . . . . . . "/HH///IHH/h"
ION CORE
(~) .
.
HZ'HHHHH.'.',
Cu2+
(Cu2+) *
NEUTRAL STATE
.
.
.
.
H~HHH.,...H
2.5 eV
.
Ln eV 0.54 eV
.
".'HHFIH,'.'HI,'/,
0
Cu+
NEGATIVE STATE
Fig. 12. Suggested model for the electronic structure of a CUcd centre in CdS using the hole picture and neglecting any fine structure. The energy values are valid for T~- 180 K [19].
From the measurements presented so far, an unambiguous energy level scheme is obtained (fig. 12) which, together with low temperature luminescence experiments, contains many details and, in particular, absolute values of most of the electronic parameters [ 18,19]. A similar energy level scheme and absolute values for %o have recently been suggested by Suda and Bube [32] using infrared quenching of photocapacitance. Junction space-charge techniques seldom give information on the microscopic nature and identification of the centre investigated. Information of this kind is often obtained from spin dependent measurements such as ESR, O D M R or Zeeman studies. Since, in many cases, neither ESR nor O D M R studies give accurate values of electronic parameters, a combination of junction techniques with spin dependent measurements [28] is, in all cases where this is possible, the by far most rewarding method to increase our knowledge of deep centres.
Acknowledgement The author is indebted to N. Kullendorff, R. Mach and E. Meijer for making some of their data available prior to publication.
-0 4'5
,
,
,
510
5'5
6'0 > ~
References
, I
6"5
7'0
(K"°)
Fig. I I. Temperature dependence of the photothermal emission rate 1/~ [19] in C d S : C u (see text).
[1] W. Shockley and W.T. Read, Phys. Rev. 87 (1952) 835. [2] R.N. Hall, Phys. Rev. 86 (1952) 600. [3] H.G. Grimmeiss, Ann. Rev. Mater. Sci. 7 (1977) 341.
50 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
1-1.G. Grimmeiss / Deep level junction spectroscopy of 11- II1 compounds W. Kohn, Solid State Phys. 5 (1957) 257. W. Kohn, Phys. Rev. 98 (1955) 915. R.A. Faulkner, Phys. Rev. 184 (1969) 713. C.T. Sah, L. Forbes, L.L. Rosier and A,F. Tasch, Solidstate Electron. 13 (1970) 759. G. Bj6rklund and H.G. Grimmeiss, Solid-State Electron. 14 (1971) 589. H.G. Grimmeiss and C. Ovr~n, J. Phys. El4 (1981) 1032. O. Engstr6m and A. Aim, Solid-State Electron. 21 (1978) 1571. G.L. Miller, D.V. Lang and L.C. Kimmerling, Ann. Rev. Mater. Sci. 7 (1977) 377. J.A. Pals, Solid-State Electron. 17 (1974) 1139. H.G. Grimmeiss, C. Ovr6n and R. Mach, J. Appl. Phys. 50 (1979) 6328. S. Braun and H.G. Grimmeiss, J. Appl. Phys. 44 (1973) 2789. A. Zylbersztejn, Appl. Phys. Letters 33 (1978) 200. H.G. Grimmeiss, L.-,~ Ledebo and E. Meijer, Appl. Phys. Letters 36 (1980) 307. A.M. White, P.J. Dean and P. Porteous, J. Appl. Phys. 47 (1976) 3230. H.G. Grimmeiss and N. Kullendorff, J. Appl. Phys. 51 (1980) 5852. H.G. Grimmeiss, N. Kullendorff and R. Broser, J. Appl. Phys. 52 (1981) 3405.
[20] H.G. Grimmeiss, E. Meijer and R. Mach-Miiller, to be published. [21] P.J. Dean, D.J. Robbins, S.G. Bishop, J.A. Savage and P. Proteus, J. Phys. C14 (1981) 2847. [22] D.J. Robbins, D.C. Herbert and P.J. Dean, J. Phys. C14 (1981) 2859. [23] I.J. Broser, R.K.F. Germer, H.-J. Schulz and K.P. Wisznewski, Solid-State Electron. 21 (1978) 1597. [24] R. Dingle, Phys. Rev. Letters 23 (1969) 579, [25] G. Mtiller, Phys. Status Solidi (b) 76 (1976) 525. [26] E. Mollwo, G. Miiller and P. Wagner, Solid State Commun. 13 (1973) 1283. [27] H.G. Grimmeiss, N. Kullendorf and R. Helbig, to be published. [28] H.G. Grimmeiss, E. Janz6n, H. Ennen, O. Schirmer, J. Schneider, R. W6rner, C. Holm, E. Sirtle and P. Wagner, Phys. Rev. B24 (1981) 4571. [29] I. Broser, H. Maier and H.-J. Schultz, Phys. Rev. 140 (1965) A2135. [30] I. Broser and K.-H. Franke, J. Phys. Chem. Solids 26 (1965) 1013. [31] I. Broser, U. Scherz and M. W6hlecke, J. Luminescence 1 (1970) 39. [32] T. Suda and R.H. Bube, J. Appl. Phys. 52 (1981) 6218.