1. Effect of dopant density on contact potential difference across n-type GaAs homojunctions using Kelvin Probe force Microscopy
C. Kameni Boumenou1, Z.N Urgessa1, S.R. Tankio Djiokap1, J.M Nel2 and J.R Botha1
1Department of Physics, P.O.Box 77000, Nelson Mandela Metropolitan University, Port Elizabeth 6031, South Africa
2Department of Physics, University of Pretoria, private bag x20, Hatfield, Pretoria 0028, South Africa
Introduction
Many GaAs based III-V semiconductor structures:
operate in the infrared region and have direct band gaps [1-2]
can be grown with almost defect-free heterointerfaces [3]
are used in the manufacture of devices such as infrared-emitting diodes, laser diode and solar cells.
Understanding the nature of the interface and band alignment at the junction is important.
This can be achieved by using Kelvin Probe Force Microscopy (KPFM) that can provide:
surface potential distribution with sub- nanometer resolution from which the interface Contact potential difference (CPD) can be derived.
topography (1 nm in x-y plane and 0.1 nm in z- direction [4] ).
AM-KPFM
AM-KPFM measurements electrostatic forces between the sharp conducting tip and the sample.
Cantilever responds only to force at/or near its resonance frequency.
The essential force is
𝐹 𝑒𝑙 = 𝜕𝐶 𝜕𝑧 𝑉 𝑑𝑐 − 𝑉 𝐶𝑃𝐷 𝑉 𝑎𝑐 sin 𝑤 𝑎𝑐 𝑡
AM-KPFM setup measures the amplitude of the cantilever oscillation caused by this force.
The main objective in the AM-KPFM is then to minimize this oscillation by applying a dc bias.
When 𝑉 𝑑𝑐 = 𝑉 𝐶𝑃𝐷 , 𝐹 𝑒𝑙 becomes 0.
Hence
The system displays the 𝑉 𝑑𝑐 𝑎𝑠 𝑉 𝐶𝑃𝐷
Acknowledgements: This work is based upon research supported by the SA Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation, South Africa. The financial support of the Nelson Mandela Metropolitan University is also appreciated.
Figure 4 summarizes the variation of the CPD across the interface versus dopant density
CPD increases with epilayer the dopant density.
The estimated uncertainties in each CPD value is ~±9 𝑚𝑉
CPD (meV)
Dopant density 𝒄𝒎 −𝟑
𝑛=4.9× 𝑐𝑚 −3
𝑛=6.3× 𝑐𝑚 −3
𝑛=6.5× 𝑐𝑚 −3
𝑛=6.7× 𝑐𝑚 −3
Figure 4: Experimental evolution of the CPD across n-type GaAs/SI-GaAs interface versus dopant density in the layer, using AM-KPFM. Vertical lines are the estimated uncertainties.
Figure 5 shows the theoretical simulation of the CPD a cross the interface versus electron density, using the following equation:
𝑉 𝐶𝑃𝐷 = 𝐸 𝑔 −∆ 𝐸 𝑔 ++𝑘𝑇 𝑙𝑛 𝑛 𝑁 𝑐 × 𝑛 𝑁 𝑐 − 𝑙𝑛 𝑚 ℎ 𝐺𝑎𝐴𝑠 ∗ 𝑚 𝑒 𝐺𝑎𝐴𝑠 ∗ 𝑙𝑛 𝑛 𝑁 𝑐 × 𝑛 𝑁 𝑐 − 𝑙𝑛 𝑚 ℎ 𝐺𝑎𝐴𝑠 ∗ 𝑚 𝑒 𝐺𝑎𝐴𝑠 ∗
𝑇, 𝑘, 𝑁 𝑐, 𝐸 𝑔, ∆𝐸 𝑔 , 𝑚 ℎ 𝐺𝑎𝐴𝑠 ∗ and 𝑚 𝑒 𝐺𝑎𝐴𝑠 ∗ are the temperature, Boltzmann constant, density of states of the conduction band, energy band gap, band gap narrowing, effective mass of holes and effective mass of electrons, respectively.
At room temperature 𝐸 𝑔 = eV, 𝑁 𝐶 = 4.7× 𝑐𝑚 −3 , 𝑚 ℎ 𝐺𝑎𝐴𝑠 ∗ 𝑚 𝑒 𝐺𝑎𝐴𝑠 ∗ =7.07 have been used. ∆ 𝐸 𝑔 is dopant density (n) dependent.
Theoretical increase in CPD with dopant density smaller than experimental change.
The CPD values obtained experimentally are smaller than the theoretical ones.
This is attributed to surface Fermi level modifications caused by the ambient.
Results and discussions
Figure 2 shows the CPD between semi-insulating GaAs substrate and n-type GaAs epilayers with different dopant densities.
Figure 2: Cross-sectional potential imaging of 𝟑𝝁𝒎 n-type GaAs/SI- GaAs. Four samples with same layer thicknesses, grown on the same substrate, but with difference in electron density have been considered for the studies. The electron density and CPD are shown.
Potential image of each presents two main regions, related to the difference in electron density between the substrate and layer.
Figure 2 clearly shows that the CPD changes with dopant density.
Junction
Experimental details
Growth technique: Metalorganic Chemical Vapour Deposition (MOCVD).
Characterization technique: Amplitude Modulation (AM)–KPFM using Bruker Dimension Fastscan SPM.
Potential (mV)
~144 𝑚𝑉
SI-GaAs
n-type GaAs
~179 𝑚𝑉
Position (𝝁𝒎)
~230 𝑚𝑉
~190 𝑚𝑉
𝑛=4.9× 𝑐𝑚 −3
𝑛=6.5× 𝑐𝑚 −3
𝑛=6.3× 𝑐𝑚 −3
𝑛=6.7× 𝑐𝑚 −3
(b)
Background of Kelvin Probe Force Microscopy
When two materials with differences in work function come in contact, as in Fig 1 (a) to (c), electrons flow across the contact until the Fermi level equalizes.
A dc voltage to compensate the 𝑉 𝐶𝑃𝐷 , and is recorded as the CPD between the tip and the sample (Fig 1 (d)).
Mathematically:
The electrostatic force acting between tip and sample can be given by [5]:
𝐹 𝑒𝑙 =− 𝜕𝐶 𝜕𝑍 𝑉 𝑑𝑐 − 𝑉 𝐶𝑃𝐷 𝑉 𝑎𝑐 − 𝜕𝐶 𝜕𝑧 𝑉 𝑑𝑐 − 𝑉 𝐶𝑃𝐷 𝑉 𝑎𝑐 sin 𝑤 𝑎𝑐 𝑡 + 𝜕𝐶 𝜕𝑧 𝑉 𝑎𝑐 cos 2𝑤 𝑎𝑐 𝑡 𝐹 𝑒𝑙 =− 𝜕𝐶 𝜕𝑍 𝑉 𝑑𝑐 − 𝑉 𝐶𝑃𝐷 𝑉 𝑎𝑐 − 𝜕𝐶 𝜕𝑧 𝑉 𝑑𝑐 − 𝑉 𝐶𝑃𝐷 𝑉 𝑎𝑐 sin 𝑤 𝑎𝑐 𝑡 + 𝜕𝐶 𝜕𝑧 𝑉 𝑎𝑐 cos 2𝑤 𝑎𝑐 𝑡
C and z are the capacitance and distance between tip and sample.
(a)
(b)
(d)
(c)
𝜙 𝑠
𝜙 𝑡
E Fs
E Ft
V DC =− 𝑉 𝐶𝑃𝐷
e 𝑉 𝐶𝑃𝐷
tip
sample
CPD (mV)
Electron density 𝒄𝒎 −𝟑
Figure 3 shows the average potential scan lines of the four samples re-plotted simultaneously.
The CPD varies significantly with dopant density.
Figure 1: Theoretical working principle of KPFM; 𝜙 𝑠 and 𝜙 𝑡 are the work function and 𝐸 𝐹𝑠 and 𝐸 𝐹𝑡 are Fermi energy levels of the sample and the tip, respectively.
Position (𝝁𝒎)
Potential (mV)
𝒏=𝟒.𝟗× 𝟏𝟎 𝟏𝟖 𝒄𝒎 −𝟑
𝒏=𝟔.𝟑× 𝟏𝟎 𝟏𝟖 𝒄𝒎 −𝟑
𝒏=𝟔.𝟓× 𝟏𝟎 𝟏𝟖 𝒄𝒎 −𝟑
𝒏=𝟔.𝟕× 𝟏𝟎 𝟏𝟖 𝒄𝒎 −𝟑
Figure 5: Theoretical evolution of the CPD across the n-type GaAs/SI-GaAs interface versus electron density.
Conclusion
AM-KPFM method is able to study the variation of the CPD across homojunction semiconductor structures with electron density, but are strongly influenced by the ambient.
Figure 3: Average potential scan line versus position
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