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Determination of barrier heights in heterostructures utilising real-space transfer of hot electrons
MATE]UALS SCIENCE & ENGINEERING ELSEVIER
Materials Science and Engineering B35 (1995) 263-266
B
Determination of barrier heights in heterostructures utilising real-space transfer of hot electrons J.P. Williarns, a,1 J.E. A u b r e y , a C.R. Tucker, a D.I. W e s t w o o d , ~ S.M. Zahabi, a C.D.W. Wilkinson b aDepartment of ?hysics and Astronomy, University of Wales College of Cardiff, PO Box 913, Cardiff CF2 3YB, UK bDepartment of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Abstract Preliminary work is reported on electrical transport in a GaAs/A1GaAs heterojunction test structure, aimed primarily at investigating the barrier height at the interface. The structure consisted of an n-GaAs layer in the form of a Hall bar, with an n-A1GaAs mesa standing woud on the upper broad face of the layer. Hot electrons were generated in the n-GaAs by applying a voltage pulse to the Hall bar current contacts, and the transfer of electrons across the junction interface led to the appearance of an open circuit voltage pulse across the junction. Experimental results obtained for a GaAs/A10.a3Ga0.57As structure were analysed using a simple theoretical model to give the value ~b= (0.37 + 0.06) eV for the barrier height at the interface. This preliminary result is shown to be satisfactory, and it is suggested that the experimental procedure described could provide a useful means of measuring small barrier heights at heterojunction interfaces.
Keywords: Heterostructure
1. Introduction We have probed the G a A s / A I G a A s heterojunction by investigating the real-space transfer of hot electrons across the interface in a suitable test structure. The structure consisted of an n-GaAs heater layer in the form of a planar Hall bar, with an AIGaAs mesa standing proud of the layer. The electrons on the G a A s side of the heterojunction were heated electrically by applying a voltage pulse V to the Hall bar current contacts, giving an electric field parallel to the plane of the junction. This led to, the transfer of hot electrons across the junction interface into the A1GaAs mesa, and the resulting open-circuit voltage pulse at the mesa top contact, A V, was recorded, and its magnitude investigated as a function of V~ A simplified theory of the expected behaviour is given in the next section, and indicates that the relationship between A V and V depends upon the barrier ]Present address: Optoelectronics Group, Cavendish Laboratory, Madingley Road, Cambridge CB30HE, UK. 0921-5107/95/$09.50 © 1995 --Elsevier Science S.A. All rights reserved SSDI 0921-5107(95)01323-7
height ~b at the heterojunction interface. Experimental details of the work are presented in Section 3, and results obtained for a GaAs/Alo.43Ga0.57As junction are presented and analysed in Section 4. The value of ~b obtained compares favourably with the value calculated in a self-consistent solution of Poisson's equation for the junction. Comments on the method as a means of determining ~b values are given in Section 5.
2. Theory In the present preliminary theoretical discussion, currents through the heterojunction arising from thermionic emission over the barrier at the interface, only, are taken into account. Fig. 1 shows an energy band diagram of the junction in the absence of an applied voltage. Here, a dynamic equilibrium condition exists in which equal and opposite currents flow from one side of the junction to the other across the interface. We can express this condition by means of the current-balance equation [1]
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J.P. Williams et al. / Materials Science and Engineering B35 (1995) 263-266
A1T2exp - (qVbl + ~ c i -- g v ) / k T = A2T2exp - (qVb2 + ~c2 - g v ) / k T
where (1)
When the heating pulse is applied on the GaAs side of the junction, a new equilibrium condition is rapidly achieved which can be expressed by means of the equation A 1T 2 exp - (q Vbl + 8cl -- g ~ ) / k T
= A2T2exp - (qVbz -}- gc2
-
-
Cv)/kTe
2
,3> where ~b = q Vb2 + 8~.2-- gv
(4)
as indicated in Fig. 1. The open-circuit voltage A V across the junction is now given by
AV= -
(5)
where we measure electron energy in eV. From Eqs. (3) and (5) we obtain the result -
+ 2kTln --~
In order to relate A V given by Eq. (6) to the heating voltage V applied to the sample, we use the following simple carrier-heating model. The energy balance between the electron system and the lattice in the GaAs layer can be expressed by means of the relation [2] q l t E 2 = (3/2)k (Te - T)
(9)
and the voltage V is applied across the distance d between the Hall bar current contacts. Finally we make the approximation that kT<
, (2)
In the left-hand term, representing the AIGaAs side of the junction, we write the new Fermi level as g~, indicating an expected rise due to the transfer of hot electrons from the GaAs side of the junction. These rapidly thermalise and acquire the temperature, T, of the lattice. In the right-hand term, representing the GaAs side of the junction, we have made the approximation that the Fermi level remains at gv owing to the high doping level of the layer (see Sections 3 and 4). The electron temperature, on the other hand, rises to a value Te greater than T, reflecting the elevated kinetic energy of the hot electrons on this side of the junction. Dividing Eqs. (1) and (2) we obtain the result T
2%~q o~ = 3 k d ~
A V - ~b I + ~ V 5
(10)
3. Experimental details Test structures for the experiment were fabricated using growth and processing facilities at the Cardiff I I I - V Compound Semiconductor Centre, and the Glasgow Nanoelectronics Research Centre. Fig. 2(a) shows a schematic diagram of a longitudinal vertical section through the structure, showing the n-GaAs heater layer, the A1GaAs mesa, ohmic contacts to the structure and a SiO: insulating layer. A plan view is shown in Fig. 2(b), where the mesa is seen to be located centrally on the broad upper face of the GaAs Hall bar at the junction with a pair of side arms. During growth, the n-GaAs layer was silicon-doped to 10 TM c m - 3, and the A1GaAs layer which was etched to give the mesa, to 5 × 1016 cm-3. The Hall bar dimensions were approximately 30/zm × 8/zm × 1 pm, and the mesa diameter was 6 pm. In order to access the mesa top contact electrically, it was necessary to encapsulate the structure with the insulating SiO: layer shown in Fig. 2(a), and after opening a window above the mesa, a contacting gold
W I 1
~. . . . . . .
cI)
(7)
Te
where/~ is the electron mobility, E the applied electric field and % an energy relaxation time. The use of Boltzmann statistics here leads to a simple final result, but may lead to error for the high doping levels used in our GaAs layers. Also, although/~ should be treated as a function of E, in the present discussion we shall assign to/~ its constant low-field value. We rewrite Eq. (7) in the form Te = T + ~ V2
(8)
t
%
f A1GaAs
Ef F_c2
GaAs
Fig. 1. Band structure diagram of the heterojunction studied in the present work.
265
J.P. Williams et al. / Materials Science and Engineering B35 (1995) 263-266
(a)
/z = (0.39 + 0.07) m z V - ~ s -~
n-GaAs GaAs Buffer Semi-insulatingGaAs Substrate
(b)
<
2ati°n /
Fig. 2. (a) Schematic vertical section along the test structure. (b) Plan diagram of the Hall bar and mesa.
strip was deposited on top of the SiO2 layer. Chips each carrying two gold wire-bonded test structures were mounted in ceramic packages for ease of handling. In the electrical measurements, pulse operation was necessary in order to avoid excessive Joule heating of the Hall bars. Voltage pulses typically of 200 ns duration and 10 Hz repeat frequency were fed to the sample from a Hewlett-Packard 214B pulse generator. A Philips PM3365A digital storage oscilloscope was used to measure and pre-process the output A V pulses induced between the mesa top contact and a Hall bar side arm. A H M Systems Idinstrel workstation was programmed to control the experiment and to retrieve and process the experimental data.
(12)
for the electron mobility in the GaAs layer. A self-consistent solution of Poisson's equation gave the value 0.36 eV for the conduction band offset for the junction studied in this work [3]. The measured barrier height is expected to differ from this value for the following reasons. First, the interval g F - ~'~c2(see Fig. 1) must be taken into account, which for our sample amounted to 0.04 eV. Secondly, the application of the heating pulse not only raises the electron temperature in the GaAs layer, but also lowers the Fermi level if the electron concentration is to remain constant. A decrease of up to 0.03 eV in the Fermi level occurs at the higher values of heating field used in the present work [4]. Finally, further work has shown that the use of the Hall bar side arm as a reference point for the measurement of A V may be open to question, and may lead to an error amounting to tens of meV at the higher values of heating field [5]. These considerations indicate that further theoretical and experimental work is needed to clarify the details of the behaviour under investigation in the present study. The mobility value (12), although a fraction high, is in reasonably good agreement with the value 0.29 m 2 V - ~ s - ~ given in the literature for GaAs at an electron concentration of 10 ~8 cm 3 [6].
5. Conclusion
We have carried out a preliminary investigation of the real-space transfer of hot electrons across a GaAs/ AIGaAs heterojunction with the aim of investigating features such as the barrier height at the interface. Experimentally, a heating field applied parallel to the interface on the GaAs side of the junction led to an increase in the proportion of conduction electrons 25 20 1/AV 15
4. Results
Fig. 3 shows a typical set of experimental results obtained for a GaAs/Alo.43Gao.s7As heterojunction, plotted in the manner suggested by Eq. (10). The straight line fit is very satisfactory, and the intercept on the A V-1 axis gives the' result ~b = (0.37 _ 0.06) eV
(11)
The slope of the straight line, taken in conjunction with (11) and the value re = 10-12 s [2], leads to the result
10 5 0
0.02
0.04
0.06
0.08
0.10
IN 2 Fig. 3. Experimental data obtained for a GaAs/Alo.a3Gao.57Astest structure with AV-~ plotted as a function of V -2.
266
J.P. Williams et al. / Materials Science and Engineering B35 (1995) 263-266
which were able to surmount the potential barrier at the interface, and to the establishment of an open-circuit voltage, A V, across the junction. The use of elementary theoretical models allowed a simple relationship to be derived between A V and the voltage V applied to the GaAs heater layer. Experimental resuits obtained for a GaAs/Alo.43Gao.57As test structure were analysed to give an acceptable value for the barrier height q5 at the interface. Further theoretical and experimental work is needed to elucidate more fully the details of the behaviour explored in the present work. However, it seems clear that the technique could prove valuable for the determination of barrier heights at heterojunction interfaces, particularly for cases where these are small
( < 0.3 eV) and difficult to measure by other methods [7]. References [1] S.M. Sze, Physics of Semiconductor Devices, 2nd edn., Wiley, New York, 1981, p. 258. [2] S.M. Sze, Physics of" Semiconductor Devices, 2nd edn., Wiley, New York, 1981, p. 647. [3] J.P. Williams, PhD Thesis, University of Wales, 1993, unpublished. [4] J.P. Williams, J.E. Aubrey and P. Rees, to be published. [5] S.M. Zahabi and J.E. Aubrey, to be published. [6] S.M. Sze, Physics of Semiconductor Devices, 2nd edn., Wiley, New York, 1981, p. 29. [7] E.H. Rhoderick and R.H. Williams, Metal Semiconductor Contacts, Second Edition, Clarendon Press, Oxford, 1988, p.38.
Materials Science and Engineering B35 (1995) 263-266
B
Determination of barrier heights in heterostructures utilising real-space transfer of hot electrons J.P. Williarns, a,1 J.E. A u b r e y , a C.R. Tucker, a D.I. W e s t w o o d , ~ S.M. Zahabi, a C.D.W. Wilkinson b aDepartment of ?hysics and Astronomy, University of Wales College of Cardiff, PO Box 913, Cardiff CF2 3YB, UK bDepartment of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8QQ, UK
Abstract Preliminary work is reported on electrical transport in a GaAs/A1GaAs heterojunction test structure, aimed primarily at investigating the barrier height at the interface. The structure consisted of an n-GaAs layer in the form of a Hall bar, with an n-A1GaAs mesa standing woud on the upper broad face of the layer. Hot electrons were generated in the n-GaAs by applying a voltage pulse to the Hall bar current contacts, and the transfer of electrons across the junction interface led to the appearance of an open circuit voltage pulse across the junction. Experimental results obtained for a GaAs/A10.a3Ga0.57As structure were analysed using a simple theoretical model to give the value ~b= (0.37 + 0.06) eV for the barrier height at the interface. This preliminary result is shown to be satisfactory, and it is suggested that the experimental procedure described could provide a useful means of measuring small barrier heights at heterojunction interfaces.
Keywords: Heterostructure
1. Introduction We have probed the G a A s / A I G a A s heterojunction by investigating the real-space transfer of hot electrons across the interface in a suitable test structure. The structure consisted of an n-GaAs heater layer in the form of a planar Hall bar, with an AIGaAs mesa standing proud of the layer. The electrons on the G a A s side of the heterojunction were heated electrically by applying a voltage pulse V to the Hall bar current contacts, giving an electric field parallel to the plane of the junction. This led to, the transfer of hot electrons across the junction interface into the A1GaAs mesa, and the resulting open-circuit voltage pulse at the mesa top contact, A V, was recorded, and its magnitude investigated as a function of V~ A simplified theory of the expected behaviour is given in the next section, and indicates that the relationship between A V and V depends upon the barrier ]Present address: Optoelectronics Group, Cavendish Laboratory, Madingley Road, Cambridge CB30HE, UK. 0921-5107/95/$09.50 © 1995 --Elsevier Science S.A. All rights reserved SSDI 0921-5107(95)01323-7
height ~b at the heterojunction interface. Experimental details of the work are presented in Section 3, and results obtained for a GaAs/Alo.43Ga0.57As junction are presented and analysed in Section 4. The value of ~b obtained compares favourably with the value calculated in a self-consistent solution of Poisson's equation for the junction. Comments on the method as a means of determining ~b values are given in Section 5.
2. Theory In the present preliminary theoretical discussion, currents through the heterojunction arising from thermionic emission over the barrier at the interface, only, are taken into account. Fig. 1 shows an energy band diagram of the junction in the absence of an applied voltage. Here, a dynamic equilibrium condition exists in which equal and opposite currents flow from one side of the junction to the other across the interface. We can express this condition by means of the current-balance equation [1]
264
J.P. Williams et al. / Materials Science and Engineering B35 (1995) 263-266
A1T2exp - (qVbl + ~ c i -- g v ) / k T = A2T2exp - (qVb2 + ~c2 - g v ) / k T
where (1)
When the heating pulse is applied on the GaAs side of the junction, a new equilibrium condition is rapidly achieved which can be expressed by means of the equation A 1T 2 exp - (q Vbl + 8cl -- g ~ ) / k T
= A2T2exp - (qVbz -}- gc2
-
-
Cv)/kTe
2
,3> where ~b = q Vb2 + 8~.2-- gv
(4)
as indicated in Fig. 1. The open-circuit voltage A V across the junction is now given by
AV= -
(5)
where we measure electron energy in eV. From Eqs. (3) and (5) we obtain the result -
+ 2kTln --~
In order to relate A V given by Eq. (6) to the heating voltage V applied to the sample, we use the following simple carrier-heating model. The energy balance between the electron system and the lattice in the GaAs layer can be expressed by means of the relation [2] q l t E 2 = (3/2)k (Te - T)
(9)
and the voltage V is applied across the distance d between the Hall bar current contacts. Finally we make the approximation that kT<
, (2)
In the left-hand term, representing the AIGaAs side of the junction, we write the new Fermi level as g~, indicating an expected rise due to the transfer of hot electrons from the GaAs side of the junction. These rapidly thermalise and acquire the temperature, T, of the lattice. In the right-hand term, representing the GaAs side of the junction, we have made the approximation that the Fermi level remains at gv owing to the high doping level of the layer (see Sections 3 and 4). The electron temperature, on the other hand, rises to a value Te greater than T, reflecting the elevated kinetic energy of the hot electrons on this side of the junction. Dividing Eqs. (1) and (2) we obtain the result T
2%~q o~ = 3 k d ~
A V - ~b I + ~ V 5
(10)
3. Experimental details Test structures for the experiment were fabricated using growth and processing facilities at the Cardiff I I I - V Compound Semiconductor Centre, and the Glasgow Nanoelectronics Research Centre. Fig. 2(a) shows a schematic diagram of a longitudinal vertical section through the structure, showing the n-GaAs heater layer, the A1GaAs mesa, ohmic contacts to the structure and a SiO: insulating layer. A plan view is shown in Fig. 2(b), where the mesa is seen to be located centrally on the broad upper face of the GaAs Hall bar at the junction with a pair of side arms. During growth, the n-GaAs layer was silicon-doped to 10 TM c m - 3, and the A1GaAs layer which was etched to give the mesa, to 5 × 1016 cm-3. The Hall bar dimensions were approximately 30/zm × 8/zm × 1 pm, and the mesa diameter was 6 pm. In order to access the mesa top contact electrically, it was necessary to encapsulate the structure with the insulating SiO: layer shown in Fig. 2(a), and after opening a window above the mesa, a contacting gold
W I 1
~. . . . . . .
cI)
(7)
Te
where/~ is the electron mobility, E the applied electric field and % an energy relaxation time. The use of Boltzmann statistics here leads to a simple final result, but may lead to error for the high doping levels used in our GaAs layers. Also, although/~ should be treated as a function of E, in the present discussion we shall assign to/~ its constant low-field value. We rewrite Eq. (7) in the form Te = T + ~ V2
(8)
t
%
f A1GaAs
Ef F_c2
GaAs
Fig. 1. Band structure diagram of the heterojunction studied in the present work.
265
J.P. Williams et al. / Materials Science and Engineering B35 (1995) 263-266
(a)
/z = (0.39 + 0.07) m z V - ~ s -~
n-GaAs GaAs Buffer Semi-insulatingGaAs Substrate
(b)
<
2ati°n /
Fig. 2. (a) Schematic vertical section along the test structure. (b) Plan diagram of the Hall bar and mesa.
strip was deposited on top of the SiO2 layer. Chips each carrying two gold wire-bonded test structures were mounted in ceramic packages for ease of handling. In the electrical measurements, pulse operation was necessary in order to avoid excessive Joule heating of the Hall bars. Voltage pulses typically of 200 ns duration and 10 Hz repeat frequency were fed to the sample from a Hewlett-Packard 214B pulse generator. A Philips PM3365A digital storage oscilloscope was used to measure and pre-process the output A V pulses induced between the mesa top contact and a Hall bar side arm. A H M Systems Idinstrel workstation was programmed to control the experiment and to retrieve and process the experimental data.
(12)
for the electron mobility in the GaAs layer. A self-consistent solution of Poisson's equation gave the value 0.36 eV for the conduction band offset for the junction studied in this work [3]. The measured barrier height is expected to differ from this value for the following reasons. First, the interval g F - ~'~c2(see Fig. 1) must be taken into account, which for our sample amounted to 0.04 eV. Secondly, the application of the heating pulse not only raises the electron temperature in the GaAs layer, but also lowers the Fermi level if the electron concentration is to remain constant. A decrease of up to 0.03 eV in the Fermi level occurs at the higher values of heating field used in the present work [4]. Finally, further work has shown that the use of the Hall bar side arm as a reference point for the measurement of A V may be open to question, and may lead to an error amounting to tens of meV at the higher values of heating field [5]. These considerations indicate that further theoretical and experimental work is needed to clarify the details of the behaviour under investigation in the present study. The mobility value (12), although a fraction high, is in reasonably good agreement with the value 0.29 m 2 V - ~ s - ~ given in the literature for GaAs at an electron concentration of 10 ~8 cm 3 [6].
5. Conclusion
We have carried out a preliminary investigation of the real-space transfer of hot electrons across a GaAs/ AIGaAs heterojunction with the aim of investigating features such as the barrier height at the interface. Experimentally, a heating field applied parallel to the interface on the GaAs side of the junction led to an increase in the proportion of conduction electrons 25 20 1/AV 15
4. Results
Fig. 3 shows a typical set of experimental results obtained for a GaAs/Alo.43Gao.s7As heterojunction, plotted in the manner suggested by Eq. (10). The straight line fit is very satisfactory, and the intercept on the A V-1 axis gives the' result ~b = (0.37 _ 0.06) eV
(11)
The slope of the straight line, taken in conjunction with (11) and the value re = 10-12 s [2], leads to the result
10 5 0
0.02
0.04
0.06
0.08
0.10
IN 2 Fig. 3. Experimental data obtained for a GaAs/Alo.a3Gao.57Astest structure with AV-~ plotted as a function of V -2.
266
J.P. Williams et al. / Materials Science and Engineering B35 (1995) 263-266
which were able to surmount the potential barrier at the interface, and to the establishment of an open-circuit voltage, A V, across the junction. The use of elementary theoretical models allowed a simple relationship to be derived between A V and the voltage V applied to the GaAs heater layer. Experimental resuits obtained for a GaAs/Alo.43Gao.57As test structure were analysed to give an acceptable value for the barrier height q5 at the interface. Further theoretical and experimental work is needed to elucidate more fully the details of the behaviour explored in the present work. However, it seems clear that the technique could prove valuable for the determination of barrier heights at heterojunction interfaces, particularly for cases where these are small
( < 0.3 eV) and difficult to measure by other methods [7]. References [1] S.M. Sze, Physics of Semiconductor Devices, 2nd edn., Wiley, New York, 1981, p. 258. [2] S.M. Sze, Physics of" Semiconductor Devices, 2nd edn., Wiley, New York, 1981, p. 647. [3] J.P. Williams, PhD Thesis, University of Wales, 1993, unpublished. [4] J.P. Williams, J.E. Aubrey and P. Rees, to be published. [5] S.M. Zahabi and J.E. Aubrey, to be published. [6] S.M. Sze, Physics of Semiconductor Devices, 2nd edn., Wiley, New York, 1981, p. 29. [7] E.H. Rhoderick and R.H. Williams, Metal Semiconductor Contacts, Second Edition, Clarendon Press, Oxford, 1988, p.38.