- Email: [email protected]
Electrical measurements of the electron irradiation induced E- and H-traps in GaAs under hydrostatic pressure
Solid State Communications, Printed in Great Britain. ELECTRICAL
Vol. 54, No. 4, pp. 355-359,
MEASUREMENTS
1985.
0038-1098/85 $3.00 + .OO Pergamon Press Ltd.
OF THE ELECTRON IRRADIATION
GaAs UNDER HYDROSTATIC
INDUCED E- AND H-TRAPS IN
PRESSURE
V.N. Brudnyi and V.M. Diamond V.D. Kuznetsov Siberian Physical-Technical
Institute
at Tomsk University,
634050-Tomsk,
USSR
(Received 30 May 1983; revised 11 December 1984) The change of resistivity of the 2.3MeV-electron-irradiated bulk n- and p-GaAs have been measured at hydrostatic pressure up to 5 kbar at RT. Corrections for the changes in free electron and hole mobilities with pressure have been neglected. The resistivity changes are explained by a dependence on pressure of the ionisation energy of the radiation-induced E- and H-traps. The results indicate that most from these radiationinduced levels moves away from the conduction-band edge (I’,-point) at a rate approximately (0.8-1.0) yo, here yo = 11.6 x lo- eV bar-’ is the energy gap pressure coefficient for GaAs at RT. The high changes in ionization energies of E2 to ES-traps upon pressure are to be compared with the lower changes in ionization energies found for the deep-lying impurity levels. In accordance with the theoretical investigation it was suggested that most of the investigated radiation-induced levels in GaAs are>, -states of Ga- and As-vacancies.
THE INFLUENCE OF HYDROSTATIC pressure on gallium arsenide band structure [l-3] and the position of the impurity and defect levels in the gap [4-81 has been widely studied. The hydrostatic pressure dependence of some radiation-unduced levels of so called Eand H-traps in GaAs has been observed recently by Brudnyi et al. [9] and Wallis et al. [lo] , These results have been interpreted to reflect the relative importance of different bands in the level wave function. The high-energy electron irradiation is known to introduce deep-lying E- and H-traps into the gap of GaAs [l l] which compensate the initial conductivity so that the resistivity of the irradiated samples increases with fluence and approaches lo9 Ohm cm at room temperature (RT) [ 121 . A remarkable property of electronirradiated GaAs n-type samples is their high sensitivity to an external hydrostatic pressure, i.e. the resistivity of these samples changes greatly with pressure [9]. In this note we report electrical measurements under hydrostatic pressure, P, up to 5 kbar as a function of the post-irradiation Fermi level position in the forbidden gap performed on 2.3 MeV-electron irradiated bulk n- and p-GaAs crystals grown by Czochralski’s (C) and Bridgman’s (B) techniques. The different kinds of samples used in our experiments are summarized in Table 1. The samples were irradiated at RT by an electron linear accelerator which operates with a pulse duration of 4.5~s having a 250 Hz duty cycle and average electron beam current of (l-9) x 10e6 A cm-‘. The accuracy of the resistivity measurement of irradiated GaAs samples is of the order of (1 to 2)s. The pressure is measured using a manganin wire gauge with the accuracy at about + 50 bar.
Table 1. The initial electrical properties of investigated GaAs samples symbol
initial conductivity type (n, P)
free carriers concentration (cmv3 j
Bridgman’s (B) Czochralski’s (C)
n
n n n I1
1 x lOI (1-2)10’6 (0.8-1.6)10’7 (3-3.9)10”8 1 x 1o’6 (l-5)10’6 (1.2-3.9)1017 (5-9)10’S
B C c c C c C c
n 0 0 A A # l
P P P P
An interpretation of the tensosensibility vs dose data in electron-irradiated GaAs has been attempted based on the Lang’s model of the radiation-induced levels into the gap [ 131. The position of the Fermi level, F, as a function of the dose and of the pressure is determined by the numerical computer solution of the charge neutrality condition with a multi-level model (with chemical impurity levels, seven radiation-induced levels and grown-in defect levels) with the assumption that the energy levels of the radiation-induced and grown-in defects are known from previous researches [ 13- 161. IZ +lv,
355
+f/vij j=1
= p +lv;
+i,v&+iN;, i=l 1=1
(1)
ELECTRICAL
356
MEASUREMENTS
Here, Nd, (resp. A’,) is the chemical impurity donor (Te) (resp. acceptor (Zn, Fe, Cr)) concentration; Noi, (resp. NAj) are the radiation induced donors, (resp. acceptors), where Nni = Vi x D; NAj = 5 x D ; Vi (resp. 5) are the production rates of each induced donor, (resp. acceptor); The energy levels, E,, of the E- and H-traps induced into GaAs by electron bombardment at RT have been measured by Land et al. [I 1, 131 and Pons et al. [14] (see Table 2). We assume that E, varies with hydrostatic pressure P as Eij = Eij(O) + Yij x P with the same pressure coefficient Yij when occupied or not. The energy gap pressure coefficient 7G was taken as 11.6 x 10e6 eV bar-’ at RT [9]. No are grown-in defects in bulk GaAs. Some native defects are observed in bulk GaAs [ 15, 161. One major omnipresent grown-in defect in bulk GaAs is associated with the well-known EL2 donor-deep trap at an energy level between E, - 0.78 to 0.83 eV with concentration in the range (2 x 10” - 3 x defect 1Or6) cme3 which is assigned to a As,,-related [ 161 or to a complex of point defects [ 171. The pressure coefficient of this level with respect to the conduction band (I?,-min.) is equal to 3.8 x 10m6 eV bar-r when it is occupied while the pressure coefficient with respect to the valence band (Fv-max) is equal to 1.7 x 10m6 eVbar_’ when it is empty [5, 81. Since the true EL2-trap concentration in our samples is not known we assumed for our calculation that it is equal to the average value given in published papers, N(EL2) = 15 x 1016 cme3 with energy level E, -0.83 eV. Another trap which we took into consideration is the deep donor-type defect (E, - 0.15 eV) present in concentration of order 10” cmm3 [15, 181. This trap is supposed to involve a lattice defects of unknown nature [18]. We used N(E, -0.15 eV) = 1 x 10” cme3 with a pressure coefficient with respect to F,-point equal to 1 x 10m6 eV bar-’ as forM1 (E, -0.14 eV)-trap [6]. The first part of the analysis considers the p vs D data. The resistivity, p, vs dose, D, of the low doped samples irradiated with 2.3 MeV-electrons are shown in Fig. 1. The resistivity of both n- and P-type samples of GaAs increases with dose which indicates that some radiation-induced defect states act as acceptors and some others as donors. The introduction rates of these donor- and acceptor-type defects are estimated from the condition of charge neutrality by using the measured values of the resistivity as a function of bombardment dose. The experimental p vs D data were quantitatively interpreted by combaining the equation (1) with the resistivity equation taking into account both electrons and holes: p = (enp,
+ ep&-’
here. e is the electronic
(2) charge. n(resn. ZJ) is the free VI \ * ,I
Vol. 54, No. 4
OF E- AND H-TRAPS IN GaAs
I
L
L
loo+ Id2
-7 I
I
IfiS
IIII
I
1o’6
IllI
I
IllI
to” 10’s DOSE, EL./CM’
I
II
10’9
Fig. 1. Variation of the resistivity as a function of 2.3 MeV-electron irradiation flw at room temperature for low doped n-GaAs (a) and p-GaAs (A) samples. The calculated curves (solid lines) are obtained by using the equation (2) with constant carriers mobilities and the parameters of E- and H-traps from Table 2. The grownin defects are not taken into account. electron (resp. hole) concentration, pn (resp. ~~p) is the electron (respectivity hole) mobility. The relationship between n (resp. p) and the incedent electron flux are given from the condition of charge neutrality for the irradiated samples. We ignored the mobilities change as a result of electron bombardment because the mobilities decrease by about (50-80)% only in the flux of up to 1 x lo’* cm-’ while the resistivities simultaneously increase by lo9 to 10” times at RT. This suggest that the calculated p vs D curves are neglectively dependent upon the variation of the mobilities. It is supposed b = /J,,//+ = 20 at RT before and after electron irradiation. Only Vii-parameters have been assumed variable in the fitting procedure for this case. The dichotomy method is used for the numerical solution of equation (1). The fitting of unknown parameters in this equation is performed using the random search method and accurate results have been obtained by using the gradient method. The calculated p - D curves are compared with the experimental p vs D data. To check the reliability of the Vii-values obtained from the numerical analysis of the experimental data in Fig. 1 the fitting of the experimental results was attempted with different versions of donor and acceptortype radiation-induced E- and H-traps. However, a reasonable fit could be obtained within a reasonable range of vii-parameters for the version is presented in Table 2 only. This result supports the correctness of selected version. We have deduced from the resistivity vs D measurements the acceptor-type levels are induced in the upper half of the forbidden gap mainly. The
Vol. 54, No. 4
ELECTRICAL
MEASUREMENTS
Table 2. The parameters
ofE- and H-traps in electron-irradiated bulk GaAs
357
OF E- AND H-TRAPS IN GaAs
Defect
El
E2
E3
E4
E5
HI
HO
energy level (eV) introduction rate (cm-’ )* pressure coefficient (1 0b6 eV/bar)* donor-type (0) acceptor-type (A)
0.08
0.14
0.31
0.71
0.90
0.29
0.10
2.3
2.8
1.1
1 .o
0.60
1.1
1.6
0
9.6
11.0
11.6
11.6
0
0
A
A
A
A
*
D
D
A
with f 10% deviation
analysis of the reverse voltage-current characteristics [19] and of the reverse bias dependence of the capacitance [20] of electron-irradiated GaAs diodes confirm the presence of acceptor-type levels in the upper half of the gap. The results of the p vs D curves fitting are presented in Fig. 1 with the best-fit parameters given in Table 2. In this table we include the published data [13, 141 for the ionisation energies of the radiationinduced E- and H-traps. The Fig. 1 gives an estimate of the deviation of the calculated p vs D curves from the experimental points. The calculated curves tally with the experimental points at fluxes up to 1 x 10’s cm-’ but differ from ones at high doses. The experimental values of p vs D at these high fluxes are independent of the electrical state of the starting material and decrease upon irradiation for both initial n- and p-GaAs samples. Probably, this departure can be cancelled by taking into account a new conduction mechanism appearance in the high dose region. The final Fermi level position evaluated from equation (1) and (2) using the experimental values of p vs D in Fig. 1 is estimated near EC - 0.75 eV at RT. The second part of the analysis considers the conductivity vs pressure. For the same electron-irradiated samples measurements of conductivity was made as a function of hydrostatic pressure up to 5 kbar at RT. These measurements were numerically analysed by adjusting the yijparameters using the introduction rates for radiationinduced E- and H-traps (see Table 2). The experimental values of the pressure coefficients of resistivity (Y= dlnp/ dP are presented in Fig. 2 as a function of cumulative dose. It is shown that pressure coefficient (II increases upon irradiation up to 4.5 x lo4 bar-’ and then drops down to = 0 x 10e4 bar-’ at high electron fluences. In Fig. 3 the pressure coefficient a as a function of the post-irradiation Fermi level position in the gap is shown.
D /Nd, CM Fig. 2. Variation of the pressure coefficient of resistivity in n-GaAs samples as a function of 2.3 MeV-electron irradiation flux at RT. The calculated curves 1, 2, 3 (solid line) are obtained using the equation 3 and data from Table 2 for the samples with initial electron concentration (1, 10, 100) x 1016 crnv3 respectively. The grown-in defects are not taken into account. The pressure induced changes of the traps energies are obtained from these data. Using the equation (2) we can obtain equation (3) for the pressure coefficient of resistivity cr = dln p/dP by a straight forward differentiation dln (enp,J/dP o!=
1 +p/nb
dln (enM,)/dP -
1 +nb/p
(3)
’
We analysed the term dln (enl.c”)/dP in equation dln H, dln (enlu,) = ---+dP dP
-rn
&,
kT
IJL,,
(3)
+
(4)
ELECTRICAL
MEASUREMENTS
TRAPS
fl I
I
0.2
I
I
11’1
I
0.4
0.6 EN
0.0
M
11’
1.0
1’
1.2 1.k
E RGY,eV
Fig. 3. Pressure coefficient of resistivity of various n (open symbol) and p (full symbol) GaAs samples as a function of the post-irradiation Fermi level position in the gap. The calculated curves (solid lines) are obtained using equation 3 and the parameters of Table 2. The curves 1 to 3 are for the samples with initial free carriers concentration (1, 10, 100) x 1016 cme3 respectively. The grown-in defects are not taken into account. The dotted line is obtained for the sample with initial free carriers concentration 1 x 1016 cm- . The grownin defects (EL2 and E, - 0.15 eV, see text) are taken into account in this latter case. The E- and H-levels and their pressure coefficients (X) are also given. Here, N, is the density-of-state factor for the conduction band and yn = d(Ec -F)/dP. The mobility of electrons is determined by lattice scattering mechanism (I*&) and scattering by impurities and defects (pin). These mechanisms are statistically independent and the total mobility /Jn-’ = p-i, + p-A. The pressure coefficient for N, is of the order of 1 x 10d6 bar-’ [21]. This effect is low in magnitude in comparison with the experimentally measured pressure coefficient of resistivity at about of 1 x 10e4 bar-’ . The electron mobility fin in the heavily irradiated samples is decreased to less than 5% of its initial magnitude at the pressure up to 5 kbar at RT. This value is low in comparison with the resistivity increases on (20 to 50)s at P = 5 kbar at RT for (Y= (1 to 4) x 10e4 bar-’ . Therefore we could neglect the pressure coefficient of mobility in equation (4). The same analysis would be made for p-type GaAs. So, we can write the approximate equation (5) +-----
7P
l+nb/p
1’
(5)
The result of analysis of equation (3) indicates that the change in the experimental resistivity with pressure in electron-irradiated samples of GaAs is due to the change in Fermi level position into forbidden gap mainly. In
OF E- AND H-TRAPS IN GaAs
Vol. 54, No. 4
other words when pressure changes the ionization energy of the level the change in carrier density is so large that corrections due to the density -of-state factors and due to the mobilities changes are negligible at RT. The solid lines in Fig. 2, 3 present the results of fitting according to equation (5) with seven fitting parameters yii of E- and H-traps. The pressure deviation of the (El-ES)-levels with respect to the conduction-band minimum, I’,_, are (0;9.6;11;11.6;11.6) x lob6 eVbar_’ respectively at RT (crosses in Fig. 3). The values of y for (E2-E4)-levels are close to these deduced from the measurements on transient capacitance electronirradiated Schottky diodes [lo] In electron-irradiated p-GaAs samples the resistivity is observed to have small hydrostatic-pressure dependence. Moreover, in some p-type samples a negative pressure coefficient of resistivity is observed. The low value of (Yin heavily-electron-irradiated n-GaAs (Fig. 2, 3) confirms our data [12] showing n to p-type conductivity conversion upon electron bombardment in n-GaAs compound. From the results of hydrostatic pressure investigation we infer that the most of radiation-induced levels in GaAs remains essentially fixed with respect to the valence band edge (I’,-potint). This “tying” of these levels to the valence band edge can be understood from the theoretical calculation of hydrostatic-pressure dependence of the ideal-neutral-vacancy levels in GaAs. Osbourn obtained that the anion and cation vacancy levels with f2-symmetry have high pressure deviation band minimum with respect to the Fc conduction irrespective of their position in the gap. This behaviour results from the weak dependence on hydrostatic pressure of the upper valence band and large portions in the reciprocal space of the lowest conduction band, which form the wave functions of these states. It is known the valence band is nearly immobile while the lowest conduction band moves upward under hydrostatic pressure in GaAs compound. The main conclusion of our note is that most of the radiationinduced levels in GaAs move very little with pressure. This results in a strong pressure dependence of the resistivity in electron-irradiated rz-GaAs samples and a weak pressure dependence of the resistivity in electronirradiated p-GaAs samples. The weak pressure dependence of most of the E’- and H-levels in GaAs mdicates that these levels belong to highly localized states. In conclusion it’s necessary to make a note that the use of the parameters listed in Table 2 all the experimental data from Fig. 1 to Fig. 3 are fitted to all points to better than 10% for low doped samples. The overall fit appears to justify the use of the set parameters determined from this work for the radiation-induced level position are borrowed from the published data [ 13, 141. The variation of parameters from values are
Vol. 54, No. 4
ELECTRICAL
presented in Table experimental data.
2 worsens
MEASUREMENTS
the overall
OF E- AND H-TRAPS IN GaAs
fit to the
Acknowledgements - The authors are pleased to express their thanks to V.T. Podlesnuch and S.V. Solnusko for their collaboration in the _ preparation of the computer _ programmes.
5. 6. 7. 8. 9.
APPENDIX Equations
10. n+N,+itVij j=l P
=
CY =
(w-b
+
= p+ht~+~N&+~ht~~
din (en/-M@
__-___-
1 +p/nb
din (en&) dP
1=1
i=l
(1)
11 .
(2)
ewJ1
din (ewp)ldf’ 1 + rib/p
12. (3) 13. 14.
=
15. (4) 16. ------++-
-fP
1 + rib/p
I
’
(5)
REFERENCES 1. 2. 3. 4.
B. Welber, M. Cardona, C.K. Kim & S. Rodriguez, Phys. Rev. B: Solid State 2, 5729 (1975). D. Oiego, M. Cardona & H. Muller, Phys. Rev. B22,894 (1980). H. Neumann, I. Topol, K.R. Schulze & E. Hess, Phys. Status Solidi (b) 56, KS5 (1973). ^ A.M. White, P. Porteous, W.F. Sherman CLrA.A.
17. 18. 19. 2. 21,
37 --‘.
359
Stadtmuller, J. Phys. C: Solid State Phys. 10, L473 (1977). A. Zylbersztejn & R.H. Wallis, Appt. Phys. Lett. 32,764 (1978). 0. Kumagai, K. Wunstell & W. Jantsch, Solid State Commun. 41,89 (1982). A.M. Hennel & G. Martinez, Phys. Rev. B 25, 1029 (1982). P. Dzwig, Solid State Commun. 46,305 (1983). V.N. Brudnyi, A.A. Vilisov, V.M. Diamond& N.P. Krivorotov, Fiz. Tekh. Poluprov. 14, 13 (1980). R.H. Wallis, A. Zylbersztejn & J.M. Besson, Appl. Phys. Lett. 38,698 (198 1). D.V. Lang & L.C. Kimerling, Lattice Defects in Semicond, 1974 (Inst. Phys. Conf. Ser. N23) p.581 (1975). V.N. Brudnyi, M.A. Krivov, A.I. Potapov & V.I. Shahovtsov, Fiz, Tekh. Poluprov. 16,36 (1982). D.V. Lang, Rad. Effects in Semicond. 1976 (Inst. Phys. Conf. Ser. N3 1) p. 70 (1977). D. Pons, P.M. Mooney & J.C. Bourgoin, J. Appl. Phys. 51,2038 (1980). A. Mircea and D. Bois, Defects and Rad. Effects in Semicond. 1978 (Inst. Phys. Conf. Ser.’ N46), p. 82 (1979). M.G. Milvidskii, V.B. Osvenskii & 1.1. Shershakova, Izv. vuzov Fizika 10,5 1 (1983). G.M. Martin & S. Makram-Ebeid, Physica 116B. 371 (1983). D.C. Look, D.C. Walters & J.R. Meyer, Solid State Commun. 42,745 (1982). V.N. Brudnyi, A.A. Vilisov, V.I. Gaman & V.M. Diamond, Solid St. Electron. 26, 699 (1983). J.A. Grimshow, Rad. Damage and Defects in Semicond. 1972 (Inst. Phys. Conf. N16), p. 355 (1973). Solids Under Pressure, ed. by W. Paul and D.M. Warschauer. McGraw-Hill Book Company Inc., N-Y- San Francisco-Toronto-London. 1963. G.C. Osbourn, Phys. Rev. B22,2898 (1980).
Vol. 54, No. 4, pp. 355-359,
MEASUREMENTS
1985.
0038-1098/85 $3.00 + .OO Pergamon Press Ltd.
OF THE ELECTRON IRRADIATION
GaAs UNDER HYDROSTATIC
INDUCED E- AND H-TRAPS IN
PRESSURE
V.N. Brudnyi and V.M. Diamond V.D. Kuznetsov Siberian Physical-Technical
Institute
at Tomsk University,
634050-Tomsk,
USSR
(Received 30 May 1983; revised 11 December 1984) The change of resistivity of the 2.3MeV-electron-irradiated bulk n- and p-GaAs have been measured at hydrostatic pressure up to 5 kbar at RT. Corrections for the changes in free electron and hole mobilities with pressure have been neglected. The resistivity changes are explained by a dependence on pressure of the ionisation energy of the radiation-induced E- and H-traps. The results indicate that most from these radiationinduced levels moves away from the conduction-band edge (I’,-point) at a rate approximately (0.8-1.0) yo, here yo = 11.6 x lo- eV bar-’ is the energy gap pressure coefficient for GaAs at RT. The high changes in ionization energies of E2 to ES-traps upon pressure are to be compared with the lower changes in ionization energies found for the deep-lying impurity levels. In accordance with the theoretical investigation it was suggested that most of the investigated radiation-induced levels in GaAs are>, -states of Ga- and As-vacancies.
THE INFLUENCE OF HYDROSTATIC pressure on gallium arsenide band structure [l-3] and the position of the impurity and defect levels in the gap [4-81 has been widely studied. The hydrostatic pressure dependence of some radiation-unduced levels of so called Eand H-traps in GaAs has been observed recently by Brudnyi et al. [9] and Wallis et al. [lo] , These results have been interpreted to reflect the relative importance of different bands in the level wave function. The high-energy electron irradiation is known to introduce deep-lying E- and H-traps into the gap of GaAs [l l] which compensate the initial conductivity so that the resistivity of the irradiated samples increases with fluence and approaches lo9 Ohm cm at room temperature (RT) [ 121 . A remarkable property of electronirradiated GaAs n-type samples is their high sensitivity to an external hydrostatic pressure, i.e. the resistivity of these samples changes greatly with pressure [9]. In this note we report electrical measurements under hydrostatic pressure, P, up to 5 kbar as a function of the post-irradiation Fermi level position in the forbidden gap performed on 2.3 MeV-electron irradiated bulk n- and p-GaAs crystals grown by Czochralski’s (C) and Bridgman’s (B) techniques. The different kinds of samples used in our experiments are summarized in Table 1. The samples were irradiated at RT by an electron linear accelerator which operates with a pulse duration of 4.5~s having a 250 Hz duty cycle and average electron beam current of (l-9) x 10e6 A cm-‘. The accuracy of the resistivity measurement of irradiated GaAs samples is of the order of (1 to 2)s. The pressure is measured using a manganin wire gauge with the accuracy at about + 50 bar.
Table 1. The initial electrical properties of investigated GaAs samples symbol
initial conductivity type (n, P)
free carriers concentration (cmv3 j
Bridgman’s (B) Czochralski’s (C)
n
n n n I1
1 x lOI (1-2)10’6 (0.8-1.6)10’7 (3-3.9)10”8 1 x 1o’6 (l-5)10’6 (1.2-3.9)1017 (5-9)10’S
B C c c C c C c
n 0 0 A A # l
P P P P
An interpretation of the tensosensibility vs dose data in electron-irradiated GaAs has been attempted based on the Lang’s model of the radiation-induced levels into the gap [ 131. The position of the Fermi level, F, as a function of the dose and of the pressure is determined by the numerical computer solution of the charge neutrality condition with a multi-level model (with chemical impurity levels, seven radiation-induced levels and grown-in defect levels) with the assumption that the energy levels of the radiation-induced and grown-in defects are known from previous researches [ 13- 161. IZ +lv,
355
+f/vij j=1
= p +lv;
+i,v&+iN;, i=l 1=1
(1)
ELECTRICAL
356
MEASUREMENTS
Here, Nd, (resp. A’,) is the chemical impurity donor (Te) (resp. acceptor (Zn, Fe, Cr)) concentration; Noi, (resp. NAj) are the radiation induced donors, (resp. acceptors), where Nni = Vi x D; NAj = 5 x D ; Vi (resp. 5) are the production rates of each induced donor, (resp. acceptor); The energy levels, E,, of the E- and H-traps induced into GaAs by electron bombardment at RT have been measured by Land et al. [I 1, 131 and Pons et al. [14] (see Table 2). We assume that E, varies with hydrostatic pressure P as Eij = Eij(O) + Yij x P with the same pressure coefficient Yij when occupied or not. The energy gap pressure coefficient 7G was taken as 11.6 x 10e6 eV bar-’ at RT [9]. No are grown-in defects in bulk GaAs. Some native defects are observed in bulk GaAs [ 15, 161. One major omnipresent grown-in defect in bulk GaAs is associated with the well-known EL2 donor-deep trap at an energy level between E, - 0.78 to 0.83 eV with concentration in the range (2 x 10” - 3 x defect 1Or6) cme3 which is assigned to a As,,-related [ 161 or to a complex of point defects [ 171. The pressure coefficient of this level with respect to the conduction band (I?,-min.) is equal to 3.8 x 10m6 eV bar-r when it is occupied while the pressure coefficient with respect to the valence band (Fv-max) is equal to 1.7 x 10m6 eVbar_’ when it is empty [5, 81. Since the true EL2-trap concentration in our samples is not known we assumed for our calculation that it is equal to the average value given in published papers, N(EL2) = 15 x 1016 cme3 with energy level E, -0.83 eV. Another trap which we took into consideration is the deep donor-type defect (E, - 0.15 eV) present in concentration of order 10” cmm3 [15, 181. This trap is supposed to involve a lattice defects of unknown nature [18]. We used N(E, -0.15 eV) = 1 x 10” cme3 with a pressure coefficient with respect to F,-point equal to 1 x 10m6 eV bar-’ as forM1 (E, -0.14 eV)-trap [6]. The first part of the analysis considers the p vs D data. The resistivity, p, vs dose, D, of the low doped samples irradiated with 2.3 MeV-electrons are shown in Fig. 1. The resistivity of both n- and P-type samples of GaAs increases with dose which indicates that some radiation-induced defect states act as acceptors and some others as donors. The introduction rates of these donor- and acceptor-type defects are estimated from the condition of charge neutrality by using the measured values of the resistivity as a function of bombardment dose. The experimental p vs D data were quantitatively interpreted by combaining the equation (1) with the resistivity equation taking into account both electrons and holes: p = (enp,
+ ep&-’
here. e is the electronic
(2) charge. n(resn. ZJ) is the free VI \ * ,I
Vol. 54, No. 4
OF E- AND H-TRAPS IN GaAs
I
L
L
loo+ Id2
-7 I
I
IfiS
IIII
I
1o’6
IllI
I
IllI
to” 10’s DOSE, EL./CM’
I
II
10’9
Fig. 1. Variation of the resistivity as a function of 2.3 MeV-electron irradiation flw at room temperature for low doped n-GaAs (a) and p-GaAs (A) samples. The calculated curves (solid lines) are obtained by using the equation (2) with constant carriers mobilities and the parameters of E- and H-traps from Table 2. The grownin defects are not taken into account. electron (resp. hole) concentration, pn (resp. ~~p) is the electron (respectivity hole) mobility. The relationship between n (resp. p) and the incedent electron flux are given from the condition of charge neutrality for the irradiated samples. We ignored the mobilities change as a result of electron bombardment because the mobilities decrease by about (50-80)% only in the flux of up to 1 x lo’* cm-’ while the resistivities simultaneously increase by lo9 to 10” times at RT. This suggest that the calculated p vs D curves are neglectively dependent upon the variation of the mobilities. It is supposed b = /J,,//+ = 20 at RT before and after electron irradiation. Only Vii-parameters have been assumed variable in the fitting procedure for this case. The dichotomy method is used for the numerical solution of equation (1). The fitting of unknown parameters in this equation is performed using the random search method and accurate results have been obtained by using the gradient method. The calculated p - D curves are compared with the experimental p vs D data. To check the reliability of the Vii-values obtained from the numerical analysis of the experimental data in Fig. 1 the fitting of the experimental results was attempted with different versions of donor and acceptortype radiation-induced E- and H-traps. However, a reasonable fit could be obtained within a reasonable range of vii-parameters for the version is presented in Table 2 only. This result supports the correctness of selected version. We have deduced from the resistivity vs D measurements the acceptor-type levels are induced in the upper half of the forbidden gap mainly. The
Vol. 54, No. 4
ELECTRICAL
MEASUREMENTS
Table 2. The parameters
ofE- and H-traps in electron-irradiated bulk GaAs
357
OF E- AND H-TRAPS IN GaAs
Defect
El
E2
E3
E4
E5
HI
HO
energy level (eV) introduction rate (cm-’ )* pressure coefficient (1 0b6 eV/bar)* donor-type (0) acceptor-type (A)
0.08
0.14
0.31
0.71
0.90
0.29
0.10
2.3
2.8
1.1
1 .o
0.60
1.1
1.6
0
9.6
11.0
11.6
11.6
0
0
A
A
A
A
*
D
D
A
with f 10% deviation
analysis of the reverse voltage-current characteristics [19] and of the reverse bias dependence of the capacitance [20] of electron-irradiated GaAs diodes confirm the presence of acceptor-type levels in the upper half of the gap. The results of the p vs D curves fitting are presented in Fig. 1 with the best-fit parameters given in Table 2. In this table we include the published data [13, 141 for the ionisation energies of the radiationinduced E- and H-traps. The Fig. 1 gives an estimate of the deviation of the calculated p vs D curves from the experimental points. The calculated curves tally with the experimental points at fluxes up to 1 x 10’s cm-’ but differ from ones at high doses. The experimental values of p vs D at these high fluxes are independent of the electrical state of the starting material and decrease upon irradiation for both initial n- and p-GaAs samples. Probably, this departure can be cancelled by taking into account a new conduction mechanism appearance in the high dose region. The final Fermi level position evaluated from equation (1) and (2) using the experimental values of p vs D in Fig. 1 is estimated near EC - 0.75 eV at RT. The second part of the analysis considers the conductivity vs pressure. For the same electron-irradiated samples measurements of conductivity was made as a function of hydrostatic pressure up to 5 kbar at RT. These measurements were numerically analysed by adjusting the yijparameters using the introduction rates for radiationinduced E- and H-traps (see Table 2). The experimental values of the pressure coefficients of resistivity (Y= dlnp/ dP are presented in Fig. 2 as a function of cumulative dose. It is shown that pressure coefficient (II increases upon irradiation up to 4.5 x lo4 bar-’ and then drops down to = 0 x 10e4 bar-’ at high electron fluences. In Fig. 3 the pressure coefficient a as a function of the post-irradiation Fermi level position in the gap is shown.
D /Nd, CM Fig. 2. Variation of the pressure coefficient of resistivity in n-GaAs samples as a function of 2.3 MeV-electron irradiation flux at RT. The calculated curves 1, 2, 3 (solid line) are obtained using the equation 3 and data from Table 2 for the samples with initial electron concentration (1, 10, 100) x 1016 crnv3 respectively. The grown-in defects are not taken into account. The pressure induced changes of the traps energies are obtained from these data. Using the equation (2) we can obtain equation (3) for the pressure coefficient of resistivity cr = dln p/dP by a straight forward differentiation dln (enp,J/dP o!=
1 +p/nb
dln (enM,)/dP -
1 +nb/p
(3)
’
We analysed the term dln (enl.c”)/dP in equation dln H, dln (enlu,) = ---+dP dP
-rn
&,
kT
IJL,,
(3)
+
(4)
ELECTRICAL
MEASUREMENTS
TRAPS
fl I
I
0.2
I
I
11’1
I
0.4
0.6 EN
0.0
M
11’
1.0
1’
1.2 1.k
E RGY,eV
Fig. 3. Pressure coefficient of resistivity of various n (open symbol) and p (full symbol) GaAs samples as a function of the post-irradiation Fermi level position in the gap. The calculated curves (solid lines) are obtained using equation 3 and the parameters of Table 2. The curves 1 to 3 are for the samples with initial free carriers concentration (1, 10, 100) x 1016 cme3 respectively. The grown-in defects are not taken into account. The dotted line is obtained for the sample with initial free carriers concentration 1 x 1016 cm- . The grownin defects (EL2 and E, - 0.15 eV, see text) are taken into account in this latter case. The E- and H-levels and their pressure coefficients (X) are also given. Here, N, is the density-of-state factor for the conduction band and yn = d(Ec -F)/dP. The mobility of electrons is determined by lattice scattering mechanism (I*&) and scattering by impurities and defects (pin). These mechanisms are statistically independent and the total mobility /Jn-’ = p-i, + p-A. The pressure coefficient for N, is of the order of 1 x 10d6 bar-’ [21]. This effect is low in magnitude in comparison with the experimentally measured pressure coefficient of resistivity at about of 1 x 10e4 bar-’ . The electron mobility fin in the heavily irradiated samples is decreased to less than 5% of its initial magnitude at the pressure up to 5 kbar at RT. This value is low in comparison with the resistivity increases on (20 to 50)s at P = 5 kbar at RT for (Y= (1 to 4) x 10e4 bar-’ . Therefore we could neglect the pressure coefficient of mobility in equation (4). The same analysis would be made for p-type GaAs. So, we can write the approximate equation (5) +-----
7P
l+nb/p
1’
(5)
The result of analysis of equation (3) indicates that the change in the experimental resistivity with pressure in electron-irradiated samples of GaAs is due to the change in Fermi level position into forbidden gap mainly. In
OF E- AND H-TRAPS IN GaAs
Vol. 54, No. 4
other words when pressure changes the ionization energy of the level the change in carrier density is so large that corrections due to the density -of-state factors and due to the mobilities changes are negligible at RT. The solid lines in Fig. 2, 3 present the results of fitting according to equation (5) with seven fitting parameters yii of E- and H-traps. The pressure deviation of the (El-ES)-levels with respect to the conduction-band minimum, I’,_, are (0;9.6;11;11.6;11.6) x lob6 eVbar_’ respectively at RT (crosses in Fig. 3). The values of y for (E2-E4)-levels are close to these deduced from the measurements on transient capacitance electronirradiated Schottky diodes [lo] In electron-irradiated p-GaAs samples the resistivity is observed to have small hydrostatic-pressure dependence. Moreover, in some p-type samples a negative pressure coefficient of resistivity is observed. The low value of (Yin heavily-electron-irradiated n-GaAs (Fig. 2, 3) confirms our data [12] showing n to p-type conductivity conversion upon electron bombardment in n-GaAs compound. From the results of hydrostatic pressure investigation we infer that the most of radiation-induced levels in GaAs remains essentially fixed with respect to the valence band edge (I’,-potint). This “tying” of these levels to the valence band edge can be understood from the theoretical calculation of hydrostatic-pressure dependence of the ideal-neutral-vacancy levels in GaAs. Osbourn obtained that the anion and cation vacancy levels with f2-symmetry have high pressure deviation band minimum with respect to the Fc conduction irrespective of their position in the gap. This behaviour results from the weak dependence on hydrostatic pressure of the upper valence band and large portions in the reciprocal space of the lowest conduction band, which form the wave functions of these states. It is known the valence band is nearly immobile while the lowest conduction band moves upward under hydrostatic pressure in GaAs compound. The main conclusion of our note is that most of the radiationinduced levels in GaAs move very little with pressure. This results in a strong pressure dependence of the resistivity in electron-irradiated rz-GaAs samples and a weak pressure dependence of the resistivity in electronirradiated p-GaAs samples. The weak pressure dependence of most of the E’- and H-levels in GaAs mdicates that these levels belong to highly localized states. In conclusion it’s necessary to make a note that the use of the parameters listed in Table 2 all the experimental data from Fig. 1 to Fig. 3 are fitted to all points to better than 10% for low doped samples. The overall fit appears to justify the use of the set parameters determined from this work for the radiation-induced level position are borrowed from the published data [ 13, 141. The variation of parameters from values are
Vol. 54, No. 4
ELECTRICAL
presented in Table experimental data.
2 worsens
MEASUREMENTS
the overall
OF E- AND H-TRAPS IN GaAs
fit to the
Acknowledgements - The authors are pleased to express their thanks to V.T. Podlesnuch and S.V. Solnusko for their collaboration in the _ preparation of the computer _ programmes.
5. 6. 7. 8. 9.
APPENDIX Equations
10. n+N,+itVij j=l P
=
CY =
(w-b
+
= p+ht~+~N&+~ht~~
din (en/-M@
__-___-
1 +p/nb
din (en&) dP
1=1
i=l
(1)
11 .
(2)
ewJ1
din (ewp)ldf’ 1 + rib/p
12. (3) 13. 14.
=
15. (4) 16. ------++-
-fP
1 + rib/p
I
’
(5)
REFERENCES 1. 2. 3. 4.
B. Welber, M. Cardona, C.K. Kim & S. Rodriguez, Phys. Rev. B: Solid State 2, 5729 (1975). D. Oiego, M. Cardona & H. Muller, Phys. Rev. B22,894 (1980). H. Neumann, I. Topol, K.R. Schulze & E. Hess, Phys. Status Solidi (b) 56, KS5 (1973). ^ A.M. White, P. Porteous, W.F. Sherman CLrA.A.
17. 18. 19. 2. 21,
37 --‘.
359
Stadtmuller, J. Phys. C: Solid State Phys. 10, L473 (1977). A. Zylbersztejn & R.H. Wallis, Appt. Phys. Lett. 32,764 (1978). 0. Kumagai, K. Wunstell & W. Jantsch, Solid State Commun. 41,89 (1982). A.M. Hennel & G. Martinez, Phys. Rev. B 25, 1029 (1982). P. Dzwig, Solid State Commun. 46,305 (1983). V.N. Brudnyi, A.A. Vilisov, V.M. Diamond& N.P. Krivorotov, Fiz. Tekh. Poluprov. 14, 13 (1980). R.H. Wallis, A. Zylbersztejn & J.M. Besson, Appl. Phys. Lett. 38,698 (198 1). D.V. Lang & L.C. Kimerling, Lattice Defects in Semicond, 1974 (Inst. Phys. Conf. Ser. N23) p.581 (1975). V.N. Brudnyi, M.A. Krivov, A.I. Potapov & V.I. Shahovtsov, Fiz, Tekh. Poluprov. 16,36 (1982). D.V. Lang, Rad. Effects in Semicond. 1976 (Inst. Phys. Conf. Ser. N3 1) p. 70 (1977). D. Pons, P.M. Mooney & J.C. Bourgoin, J. Appl. Phys. 51,2038 (1980). A. Mircea and D. Bois, Defects and Rad. Effects in Semicond. 1978 (Inst. Phys. Conf. Ser.’ N46), p. 82 (1979). M.G. Milvidskii, V.B. Osvenskii & 1.1. Shershakova, Izv. vuzov Fizika 10,5 1 (1983). G.M. Martin & S. Makram-Ebeid, Physica 116B. 371 (1983). D.C. Look, D.C. Walters & J.R. Meyer, Solid State Commun. 42,745 (1982). V.N. Brudnyi, A.A. Vilisov, V.I. Gaman & V.M. Diamond, Solid St. Electron. 26, 699 (1983). J.A. Grimshow, Rad. Damage and Defects in Semicond. 1972 (Inst. Phys. Conf. N16), p. 355 (1973). Solids Under Pressure, ed. by W. Paul and D.M. Warschauer. McGraw-Hill Book Company Inc., N-Y- San Francisco-Toronto-London. 1963. G.C. Osbourn, Phys. Rev. B22,2898 (1980).