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Universit¨ at Ulm Fakult¨at f¨ ur Ingenieurwissenschaften und Informatik Institut f¨ ur Optoelektronik Albert-Einstein-Allee 45 89081 Ulm
Chemical sensors based on GaN heterostructures Submitted by: Paulette Hatem Hanna Iskander 29.08.2017
1st Referee: Prof. Dr. Ferdinand Scholz Supervisor: M.Sc. Martin Schneidereit
Declaration Hereby, I confirm that I have prepared this bachelor thesis independently by myself. All information taken from other sources and being reproduced in this thesis are clearly referenced.
Contents 1 Abstract
3 Theoretical background 3.1 Crystal structure of GaN . . . . . . . . 3.2 InGaN quantum wells . . . . . . . . . . 3.2.1 Spontaneous polarization . . . . 3.2.2 Piezoelectric polarization . . . . 3.3 Quantum confined Stark effect (QCSE) 3.4 (Bio)chemical sensing principle . . . . .
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4 Code Implementation
5 Performed simulations and results 5.1 Variable doping concentration . . 5.2 Variable QW thickness . . . . . . 5.3 Variable cap layer thickness . . . 5.4 Variable indium concentration . . 5.5 Variable undoped QW thickness
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6 Experimental verification
7 Conclusion and outlook
List of tables
List of figures
1 Abstract In this work, the optimization of indium gallium nitride quantum well heterostructures towards high biosensitivity is presented. In contrast to the conventional electrical read-out of III-nitride sensors, a purely optical photoluminescence read-out is performed. Indium gallium nitride quantum wells provide a much more stable luminescence signal in contrast to conventional fluorescent labels, and hence, are promising candidates for next generation bioanalytical sensor structures. The externally induced quantum confined Stark effect due to potential changes on the surface of the semiconductor caused by the adsorbed species deposited on the quantum well surface induce a spectral photoluminescence shift. This redshift is due to the upward near-surface band bending which alters the semiconductor’s optical properties. The aim of this thesis is to increase the quantum well’s emission wavelength shift and signal intensity in order to achieve maximum sensitivity in detecting biomolecules on the surface. The semiconductor software nextnano is used to simulate various parameters to find the ideal quantum well thickness, doping concentration, cap layer thickness and indium content within the quantum well. It has been concluded from the results that the presence of n-type dopants increases the wavelength shift due to the accumulation of the free electrons on the quantum well boundary, therefore increasing the band bending. Hence, high background doping concentration (5 · 1018 cm−3 ≤ ND ≤ 1 · 1019 cm−3 ) is proposed for such structures. Thin cap layers and quantum wells exhibit higher signal intensity but lower redshift. Therefore, a trade-off has to be met between sensitivity i.e. the amount of wavelength shift on one hand, and signal-to-noise ratio, which is related to the recombination rate, on the other. Intermediate indium concentrations are also desirable. The final purpose is that with both simulations and experiments, further quantum well samples will be improved to come closer to our final goal of realising medical sensors for biomolecules.
2 Introduction One-dimensional nanomaterials, such as thin films and engineered surfaces have been developed and used for decades in fields such as electronic device manufacturing, chemistry, biology and engineering . Nanostructures allow completely new device concepts which are not possible for structures with macroscopic dimensions. The world of nanomaterials starts with a characteristic length of about 100 nm and extends down to about 1 nm . Today, even structures of smaller dimensions can be realized such as mono-layers which have a thickness of one atom or molecule. Such monolayers enable the functionalization of surfaces which can be subsequently applied for biological engineering . Examples for nanomaterials include quantum dots (QD), nanowires, nanorods and quantum wells (QW). Thin films behave differently than bulk materials, as they have different electrical, optical, and thermal properties. At the nanometer scale, the surface-to-volume ratio becomes an important factor because it affects the nanostructures’ sensitivity to their surroundings, i.e. by introducing some functional groups or adsorption of molecules on the surface results in an overall change of the semiconductor properties. Possible materials utilized for fabricating nanostructures include group III nitrides. Group III nitride semiconductors have a direct bandgap which cover the ultraviolet to infrared energy range. Gallium nitride (GaN) is the most commonly used binary material within this group. Owing to its wide bandgap, GaN is favorable for short-wavelength light emitting devices and high-power devices . In addition to being a direct bandgap semiconductor, GaN is also chemically inert, thermally stable, and bio-compatible in comparison to Silicon, with very good optoelectronic properties . Hence, it can be used in the fabrication of (bio)chemical sensors. In this work, GaN layers with indium gallium nitride (InGaN) QWs close to the surface are used as optochemical transducers for biosensing. The basic idea is that the presence of adsorbates on the semiconductor surface translates in a surface band bending without the need for electrical contacts. The photoluminescence (PL) signal of InGaN QW heterostructures is sensitive to the electrical fields inside the QW. The varying fields present in the QW due to the surface band bending induce a shift in the wavelength emission as well as an intensity change, which is used to detect surface potential changes . The motivation of this thesis is to improve optical sensing by optimizing the GaN/InGaN heterostructures. The semiconductor software nextnano is used to simulate various parameters to find the optimum QW thickness, cap layer thickness, background doping and indium content within the QW. Live sensing on biomolecules is then performed using a horizontal sample positioning setup in order to verify the simulatory results.
3 Theoretical background 3.1 Crystal structure of GaN Group III-V compound semiconductors, and particularly group III nitrides are used in many applications including short wavelength lasers and LEDs which operate in the visible spectral range (450 nm − 700 nm)  due to their wide and direct band gaps (Figure 3.1). Group III nitrides include GaN, AlN and InN.
Figure 3.1: Direct (left) and indirect (right) band structures of group III nitrides . GaN exists in many crystalline structures such as wurtzite (Wz), zinc blende (ZB) and rocksalt . The most thermodynamically stable crystal structure for GaN under ambient conditions is wurtzite. The difference between Wz and ZB crystal structures is in the atoms stacking sequence. The most appropriate unit cell illustrating the Wz crystal structure is a hexagonal prisma with an in-plane lattice constant a and an out-of-plane lattice constant c  as shown in Figure 3.2. The Wz structure consists of alternating biatomic close-packed (0001) planes of Ga and N p pairs . The crystal lattice constants a and c are related as follows where c/a = 8/3 = 1.633, and internal parameter u = 3/8 = 0.375, where uc represents the anion-cation bond length parallel to the  direction . The Wz GaN can be grown along different crystal orientations. Some of the most important GaN polar, non-polar and semi-polar crystal growth planes are given in Figure 3.3. The polar growth orientation is along the (0001) c plane with the c axis normal to the layer
3 Theoretical background
Figure 3.2: Wurtzite crystal unit cell. The green balls represent N atoms, while the red balls represent Ga atoms . surface. Non-polar growth planes include the (1120) a plane and the (1100) m plane with the c axis parallel to the layer surface. Semi-polar growth planes include the (1122) plane with the c axis inclined with respect to the layer surface. The above mentioned polarizations caused by different crystal orientations affect the electrical and optical properties of GaN .
3.2 InGaN quantum wells A quantum well structure is formed when a lower band gap material is sandwiched between two layers of a material with a higher band gap, with a restriction that the QW thickness Lz ≤ 10 nm. Since InN has a lower band gap than GaN (see Table 3.1), Inx Ga1−x N active regions (QWs) are formed as shown in Figure 3.4, where x denotes the alloy content incorporated. Depending on the indium content and the QW thickness, the emission wavelength can be tuned. Table 3.1: Band gap energies and lattice constants group III nitrides . GaN AlN Eg (eV) 3.510 6.25 a (˚ A) 3.189 3.112
a for wurtzite structures of some InN 0.78 3.545
Within the QW, both electrons and holes have lower energies than the barriers, therefore it is also called a potential well; where the carriers are trapped and their motion is confined in this thin layer. This causes the energy to be quantized along the direction perpendicular to the heterojunction. By solving the general time-
3.2 InGaN quantum wells
Figure 3.3: Crystallography and orientation of group III nitride layers growth . independant Schr¨ odinger equation, the wavefunctions ψ(x) of the carriers confined in the QW can be obtained as illustrated in Equation 3.1 [12, 13] ~2 2 − ∗ ∇ + V (x) ψn (x) = En ψn (x) 2m
where ~ is the reduced Planck’s constant, m∗ is the particle’s effective mass, V (x) is the potential energy and En are the quantized energy eigenstates (Equation 3.2). This Schr¨ odinger equation, along with the Poisson equation (to be shortly explained in chapter 4), is solved numerically in our QW model by nextnano. En =
~2 π 2 n2 2m∗ L2z
where n = 0, 1, 2, ...
Figure 3.4: GaN/InGaN heterostructure. Cross section for a grown sample (left) and band edges of the heterostructure (right).
3 Theoretical background
Table 3.2: Bowing parameter b for wurtzite type III nitrides . b (eV) AlGaN 0.7 InGaN 1.4 AlInN 2.5 Table 3.3: Spontaneous polarization coefficients for wurtzite GaN and InN . GaN InN Psp (C m−2 ) -0.074 -0.05 The band gap of the Inx Ga1−x N ternary alloy is interpolated by the following quadratic relation : Eg,Inx Ga1−x N = x · Eg,InN + (1 − x) · Eg,GaN − bx · (1 − x)
where b is the bowing parameter (see Table 3.2 for reference). The lattice mismatch (see Table 3.1) between the QW and the barrier induces strain in the QW which causes a piezoelectric field. This phenomenon will be explained shortly in subsection 3.2.2.
3.2.1 Spontaneous polarization Due to the small ionic radius of nitrogen compared to gallium and indium, GaN and InN are considered to be extremely polar . N has a higher electronegativity than Ga, thus N atoms are able to attract more electrons than Ga atoms due to this difference in electronegativity. Hence, a polarization occurs which is refered to as spontaneous polarization (Psp ) i.e. polarization at zero strain. This results in a permanent dipole moment. The intrinsic dipole moment is neutralized by free electric charge that builds up on the surface by internal conduction or from the ambient atmosphere. For GaN and InN, the spontaneous polarization coefficients are almost equal (see Table 3.3 for reference). The spontaneous polarization coefficient of Inx Ga1−x N deviates from linearity i.e. Vegard’s law and is interpolated by the following second-order polynomial of the alloy composition [15, 16] Psp,Inx Ga1−x N = x · Psp,InN + Psp,GaN (1 − x) + bInGaN · x · (1 − x).
3.2.2 Piezoelectric polarization If a thin layer of a different lattice constant is grown on a bulk, it grows with a relatively low defect density, however, it gets biaxially strained. Since aInN > aGaN , therefore the InGaN QW is compressively strained (see Figure 3.5). The in-plane strain for epitaxial growth is defined in Equation 3.5 as − al εa = (3.5) al
3.2 InGaN quantum wells
Figure 3.5: Schematic of a pseudomorphically strained lattice mismatched layer .
where as is the in-plane lattice constant of the substrate (GaN), and al is the inplane lattice constant of the unstrained (relaxed) epitaxial layer (InGaN) . Strain is can be used for altering and optimizing the electronic and optical properties of QWs by varying both the energy levels and the spatial extent of the wavefunctions, as will be explained in chapter 5. Due to this asymmetric deformation, charge redistribution occurs which causes piezoelectric fields. The piezoelectric polarization field (Ppz ) is evaluated as follows  X Ppz,i = eij εj (3.6) j
where εj are the strain components and the parameter eij is a tensor consisting of piezoelectric stress coefficients. The piezoelectricity gives rise to an electric field pointing from the substrate side (N face) to the surface side (Ga face) as shown in Figure 3.6. The electric field (Ez ) along the  direction in strained InGaN is given by  Ez =
Ppz εr · εo
where εr is the dielectric constant of the material for which the electric field is calculated and εo is the permittivity of free space. The elctric field is dependent on the indium concentration x such that Ez ≈ x · 10 MV cm . The total polarization in a strained material (Ptot ) is considered to be the sum of both the spontaneous and piezoelectric polarizations  Ptot = Psp + Ppz .
However, since Ppz Psp , the spontaneous polarization is typically neglected.
3 Theoretical background
Figure 3.6: Crystal structure, spontaneous polarization fields (Psp ) and piezoelectric polarization fields (Ppz ) for Inx Ga1−x N coherently strained to GaN (0001) .
3.3 Quantum confined Stark effect (QCSE) The electric field arised due to the piezoelectricity causes an inclination of the conduction and valence band edges in the quantum well, respectively (see Figure 3.7). This leads to a redistribution of the carriers; the electrons are driven towards the upper boundary of the QW, while the holes are confined at the lower boundary . Hence, the polarization induced electric field leads to spatial separation of the electron and hole wavefunctions, i.e., their reduced overlap (radiative efficiency) . Moreover, the effective band gap shrinks causing a red shift in the QW wavelength emission. This effect is named quantum confined Stark effect (QCSE). It may also be generated by an externally applied electric field e.g. surface band bending.
3.4 (Bio)chemical sensing principle Besides group III nitride semiconductors applications in general lighting and lasing, they can also be used in the field of (bio)chemical sensing. Group III nitrides provide a very stable and biocompatible material system with excellent optoelectronic properties [23, 24]. Currently, (bio)chemical sensing methods are often based on fluorescent labels which enable optical investigations down to the microscopic scale . However, fluorescent labels often suffer from photobleaching effects and weak light intensity which limits applications in biosensing . Moreover, the signal-to-noise ratio (intensity) is significantly limited and the fluorescent antibodies are not selective to specific molecular properties such as the iron-load of fer-
3.4 (Bio)chemical sensing principle
Figure 3.7: Quantum confined Stark effect: electron and hole wavefunctions without (left) and with electric field (right) within the QW . ritin molecules . Hence, label-free sensing approaches are of interest for optical biosensing. In this work, GaN/InGaN heterostructures are used as optochemical transducers for (bio)chemical sensors, the optical sensing principle is based on the study of the changes in the photoluminescence (PL) intensity due to the presence of different adsorbates on the semiconductor surface. The adsorbed biomolecules, in our case ferritin and apoferritin, immobilize onto the GaN semiconductor surface causing spectral shifts of the polar InGaN QW photoluminescence. These spectral shifts are associated to changes of the QCSE present in the InGaN QW. The near-surface band bending induced by the potential difference between the surface and the biomolecules causes a tilt of the QW band structure, and hence, a separation of the electron and hole wavefunctions. As illustrated in Figure 3.8, for an undisturbed/virgin surface (left), the slight tilt of the surface potential is only due to the presence of piezoelectric field inside the QW. On the other hand, for adsorbed molecules (right), the surface potential is shifted, resulting in a near surface band bending which leads to shift in the effective QW recombination energy. This surface potential change is translated into QW wavelength emission shift. In order to maximize the spectral luminescence shift, and also maintaining a high signal-to-noise ratio, nextnano software is used to simulate various parameters in order to find the optimum dimensions.
3 Theoretical background
Figure 3.8: Sensor principle schematic: virgin surface (left), and the presence of adsorbed (bio)molecules on the surface (right) which induce a near surface band bending .
4 Code Implementation In order to improve the optical sensing, various parameters have to be adjusted; including the background doping concentration, QW thickness, cap layer thickness and lastly the indium concentration within the QW. The tool used for these simulations is nextnano; which is an advanced software for simulating electronic and optoelectronic semiconductor nanodevices. Before presenting the results, a brief introduction to the software will be given. The following list includes the classes used in order to simulate our sensor model on nextnano. 1. numeric control: This class is responsible for controlling all the numerical methods and input parameters when solving strain, current equations, Schr¨odinger-Poisson equation and evaluation of Fermi functions. For these simulations, the following parameters were changed: • simulation dimension : The simulation dimension parameter sets the complexity of the simulated system. For planar QW structures, one dimension is sufficient (along the crystal c-direction). • varshni parameters on : The varshni parameters on is included in our model in order to have temperature dependent energy gaps using the Varshni formula Eg (T ) = Eg (0) −
αT 2 T +β
where α and β are material constants. In an alloy composed of two binary materials, the Varshi parameters are not interpolated linearly. For the first material, the conduction band energy is calculated taking into account the Varshni parameters for the first material, then the conduction band energy for the second material is calculated taking into account the Varshni parameters for the second material. Finally the conduction band energy for the ternary is calculated by interpolating between the conduction band energies of the first and second materials including the bowing parameter for the conduction band energy . • piezo constants : The piezo constants parameter is included in our model in order to set the piezoelectric constants from nextnano database. This option is necessary for studying the effects of piezoelectric charges in wurtzite structures, it
4 Code Implementation is also useful for understanding the influence of strain in semiconductor materials. • pyro constants : The pyro constants parameter is included in our model in order to set the pyro polarization from nextnano database. This is important because GaN and InGaN are naturally elertically polarized, and as a result contain large electric fields. 2. simulation flow control: This class controls the simulation flow and thus tells the program which method to use in order to calculate certain values, for example; strain, eigenstates and wavefunctions within a potential well. In the simulation, the following two parameters were changed: • flow scheme: By choosing the flow scheme, you can tell the program which flow algorithm should be executed. Each flow scheme has a different algorithm. In all cases, the strain is calculated before any of the flow schemes is applied unless strain calculation is switched off. Then the classical (i.e. without quantum mechanics) Poisson equation is solved once to determine the electrostatic potential using the following formula  ∇ · [ε0 εr (x)∇φ(x)] = −ρ(x)
where φ is the electrostatic potential, ε0 is the vacuum permittivity, the tensor εr is the dielectric constant for the material at position x and ρ(x) is the charge density distribution within a semiconductor and is calculated as follows  ρ(x) = e[−n(x) + p(x) + ND+ (x) − NA− (x) + ρfix (x)]
where e is the electron charge, n and p are the electron and hole densities, and ND+ and NA− are the ionized donor and acceptor concentrations respectively. In this work, the flow scheme is set to number 2, which solves the self-consistent Schr¨odinger-Poisson current equation after the above mentioned steps. • strain calculation: The strain calculation used in our model is homogeneous strain, which determines the material strain in the system due to the lattice mismatch between the GaN and the InGaN QW. The strain tensor is a 3x3 matrix and its components are defined as δuj 1 δui i,j = + (4.4) 2 δxj δxi where i, j = 1, 2, 3. The vector u(x) describes the displacement due to lattice deformations. The strain tensor is symmetric for the (001) substrate orientation. The diagonal elements of measure the extensions
per unit length along the coordinate axes (positive values mean tensile strain while negative values mean compressive strain); which means that the lengths which form the volume change while the angles remain constant. The off-diagonal elements measure the shear deformations where the angles change but the volume remains constant . 3. domain coordinates: In this class, the orientation of the crystal relative to the simulation coordinate system is specified. Additionally, some information about a substrate for pseudomorphic growth must be given. • growth coordinate axis: The growth coordinate axis is set to , which means it is grown on the z-axis. The growth direction is only important for the calculation of pseudomorphic strain as it enters the equation to calculate the strain tensor. • xyz-coordinates: The xyz-coordinates parameter specifies the boundaries of the whole simulated area. • pseudomorphic on: The pseudomorphic on parameter specifies on which material all layers are grown pseudomorphically. In our simulations, GaN is included as the substrate. GaN is a predefined binary material in the nextnano database, having a default crystal structure of wurtzite. In our simulations, we choose GaN to be the layer on which the whole structure is grown pseudomorphically so that GaN is not strained. On the other hand, if the whole model is built pseudomorphically on sapphire (Al2 O3 ), GaN will grow strained which affects the QW’s optical properties. In the simulations, nextnano does not consider the crystal defects (dislocations) and assumes perfect crystal growth, thus the strain is the main factor which affects the photoluminescence and intensity. • hkil z-direction: These are the Miller indices which define a crystal plane. The orientation of the crystal with respect to the general three-dimensional simulation coordinate system is fixed by specifying the Miller direction indices of two simulation coordinate axes. In this case, both the hkil z-direction and hkil x-direction Miller indices are specified. The hkil z-direction parameter is equals to (0001); which is the polar c-plane (Ga-face) growth plane, while the hkil x-direction is equals to (10-10). 4. regions: This class is for building up the structure. There are various basic geometry elements available, which are specified within the keyword regions and can be clustered to a bigger object later on.
4 Code Implementation
Figure 4.1: Schematic of the QW heterostructure. The InGaN QW layer (thickness 2-10 nm) is grown on a GaN buffer layer of 2 µm, followed by a GaN capping layer of 3-10 nm. Lastly, an air interface of 10 nm is added in order to model the sensor surface. • region number: The region number parameter is an integer number ≥ 1. Each region has a unique number, such that all region numbers together form a dense set 1,2,3,...maxnumber. • region priority: The region priority parameter is an integer number ≥ 1. In case of overlapping regions, the region with higher priority (i.e. higher numerical value) overwrites the region with lower priority. • base geometry: The base geometry parameter is for specifying the geometric shape of the object. In our model, planar QW structures are simulated, therefore, we use the line option. • z-coordinates: The z-coordinates; zmin and zmax for each region are specified. The default unit for all dimensions is nanometers. The following code which produces the structure above (see Figure 4.1 for reference) is taken from the input file for the performed simulations:
$regions region-number = region-priority base-geometry = z-coordinates =
1 = 1 line 0 2000
region-number = region-priority base-geometry = z-coordinates =
2 = 1 line 2000 2003
region-number = region-priority base-geometry = z-coordinates =
3 = 1 line 2003 2006
region-number = region-priority base-geometry = z-coordinates = $end_regions
4 = 1 line 2006 2016
5. material: This class assigns a material to each region. All materials used in these simulations are known to the nextnano database. • material number: Each material used needs to have a unique integer number. • cluster numbers: These are the region numbers already defined in the regions class. • material name: The material name parameter is the type of semiconductor material or metal used to build up a structure. It can be an element, a binary or a ternary compound. Most materials are known to the nextnano database, however, if the material is not predefined in the database, the user must enter its parameters to the software manually. • alloy function: The alloy function parameter fixes the function used to generate the alloy profile within the material, this is typically used for ternary alloys. In the simulations, the alloy function is set to constant; for constant alloy concentration. The following code is taken from the input file for the performed simulations: $material material-number = 1 material-name = GaN cluster-numbers = 1 material-number = 2 material-name = In(x)Ga(1-x)N cluster-numbers = 2 alloy-function = constant material number = 3 material-name = GaN cluster-numbers = 3
4 Code Implementation material-number = 4 material-name = Air-wz cluster-numbers = 4 $end_material 6. alloy function: This class is necessary for ternary materials. The name of the alloy function must be provided in the material specification. The parameters for various built-in functions which generate the alloy profile have to be specified within this class. • material number: The material number parameter is a unique integer number used to refer to a ternary material to which the alloy function should be applied. • function name: The function name parameter generates the alloy profile within the ternary material. • xalloy: The xalloy parameter is the alloy concentration within the ternary material. The x is the constant in Inx Ga1−x N (0 < x < 1). The following code is taken from the input file for the performed simulations; below, the alloy content is 0.12 (12% of indium) and is applied to material number 2, which is the Inx Ga1−x N QW. $alloy-function material-number = 2 function-name = constant xalloy = 0.12 $end_alloy-function 7. doping function: This class is responsible for defining the doping profile functions. There can exist a total of n functions, n is the dimension of the simulation, (i.e. n = 1, 2 or 3). Each function depends only on one coordinate. • doping function number: The doping function number parameter is an integer number. At the very end, the doping function numbers must be given in a way, that a dense ascending series starting at 1 is formed. • impurity number: The impurity number is an integer number which is a reference to an impurity dopant and its parameters which will be specified below. • doping concentration: The doping concentration specifies the concentration of the semiconductor dopant atoms, it is normalized to the order of 1018 cm−3 .
• only region: The only region parameter specifies the region where the doping should be applied, therefore, the zmin and zmax coordinates should be specified by the user. • base function: The base function parameter specifies the function implemented to introduce the impurity atoms. For 1D simulations, the default is a constant doping profile. The following code is taken from the simulations performed. The doping concentration ND = 0.01 · 1018 cm−3 (= 1 · 1016 cm−3 ), and the doped region goes up to the GaN capping layer. $doping-function function-number = 1 impurity-number = 1 doping-concentration = 0.01 only-region = 0 2006 base-function = constant $end_doping-function 8. impurity parameters: This class is for specifying the properties of impurities used in the simulation. • impurity number: The impurity number is the unique integer number, already defined in the doping function class, for which the doping is applied to. • impurity name: The impurity name parameter is used to read the parameters of the dopant material from the database. • impurity type: The impurity type parameter specifies the type of impurity, n-type means that the impurity is treated as a donor, while p-type is treated as an acceptor. • number of energy levels: The number of energy levels parameter specifies the number of energy levels for this impurity. • energy levels relative: The energy levels relative parameter defines the impurities’ energy levels separation from the nearest bandedge in eV. For n-type dopants the conduction band is the nearest band edge, while for p-type dopants the valence band is the nearest bandedge. These energies are meant as ionization energies, e.g. a donor with an energy level right below the conduction band edge would be specified by a small positive energy level in units of eV. Each dopant material has its own relative energy level value, which
4 Code Implementation is predefined in the nextnano database. To calculate the energies of the neutral donor impurities, the following equation is used  ion ED,i (x) = Ec (x) − ED,i (x)
ion is the ionization where Ec is the bulk conduction band edge and ED,i energy (= 27 meV for Si ). When impurity levels are relatively deep compared to the thermal energy KB T (25 meV) at room temperature, incomplete ionization must be considered. The ionization process of impurity atoms in the semiconductor has a significant effect on the freecarrier concentrations, hence the properties of the semiconductor . The degree of incomplete ionization depends on the type of impurity, the temperature and the type of semiconductor. The conventional assumption of 100% ionization at room temperature is questionable, particularly for doping densities which reach higher than 1 · 1018 cm−3 .
• degeneracy of energy levels: The degeneracy of energy levels parameter considers the different transition rates from the impurity into the conduction or valence band and vice versa. For donors, the degeneracy level is 2 because the outer s orbital is half occupied in the neutral state, so there is one possibility to lose an electron but two possibilities to incorporate an electron (spin up ↑, spin down ↓) . The following code is taken from the simulations performed: $impurity-parameters impurity-number = 1 impurity-name = Silicon impurity-type = n-type number-of-energy-levels = 1 energy-levels-relative = 0.12 degeneracy-of-energy-levels = 2 $end_impurity-parameters 9. poisson boundary conditions: This class is responsible for defining which Poisson’s boundary conditions will be assumed at the interface. • poisson cluster number: The poisson cluster number parameter is a unique integer number to refer to the Poisson cluster. • region cluster number: The region cluster number parameter is the region to which the Poisson boundary conditions should be applied. • boundary condition type: The boundary condition type used in our model is a Schottky contact,
Figure 4.2: The Schottky barrier height between n-doped GaN and an air surface. The conduction band edge is pinned at eφB above the Fermi level. which requires the specification of a Schottky barrier. A Schottky contact implies Dirichlet boudary conditions for the electrostatic potential (Φ(z)|boundary = constant), and Dirichlet boundary conditions for the Fermi levels. • contact control: The contact control parameter specifies whether the Schottky contact is current or voltage controlled. • applied voltage: If the contact control is included as a voltage control, then the applied voltage parameter is used to define how much voltage is applied to the contact. • schottky barrier: The schottky barrier parameter is the value of the Schottky barrier height from the Fermi level to the conduction band (see Figure 4.2 for reference). The Schottky barrier model in nextnano is a Fermi level pinning, where we assume that the conduction band edge Ec is pinned with respect to the Fermi level EF due to surface states (interface states). The Schottky
4 Code Implementation barrier height is related to the work functions of the semiconductor, and to the electron affinities of the insulator and the semiconductor. The barrier height can thus be adjusted manually to take into account the dependence on electron affinities, doping concentrations or surface charge . In our model, the Schottky barrier is applied at the interface between the GaN cap layer and air; thus it is applied to region number 4. The following code is taken from the simulation input file: $poisson-boundary-conditions poisson-cluster-number = 1 region-cluster-number = 4 boundary-condition-type = Schottky contact-control = voltage applied-voltage = 0 schottky-barrier = 0.7 $end_poisson-boundary-conditions
5 Performed simulations and results In order to find the ideal parameters for the sensor model, different simulations are carried out to investigate the effect of each variable on the wavelength shift (∆λ), and signal intensity. This is achieved by performing a parametric sweep on each of the following four variables using nextnano, to reduce time and cost for the growth series. A brief explanation of the implementation of the sensor heterostructure on nextnano software has been given in chapter 4. In order to investigate the wavelength shift and the PL intensity, the change in the surface potential due to the adsorption of biomolecules on the semiconductor surface is modeled by a change in the Schottky barrier height φB between the GaN cap layer and the surrounding (air region). For each simulation file, two samples are considered; a virgin sample and a sensor sample. If the electron affinity χe of GaN in air is ≈ 4.1 eV and the band alignment ∆Ec : ∆Ev = 80 : 20, then the bare surface barrier height of n-GaN/air is deduced to be ≈ 0.7 eV using the formula below  φB,GaN/air = φGaN − χe,GaN
where φGaN is the work function of GaN. While for the sensor structure which represents having the biomolecules adsorbed on the surface, φB is assumed to be 0.4 eV. Thus, the potential shift is chosen to be −0.3 eV as this is the order of magnitude that can be expected from biomolecules.
5.1 Variable doping concentration As a first means, the background doping is varied from ND = 1 · 1016 cm−3 up to ND = 1 · 1019 cm−3 . The n-Si doping is applied to the whole structure, i.e. including the QW. The QW and cap layer have fixed dimensions of 3 nm each, and the indium content is 0.12 (12%). The presence of more free carriers increases the electric field inside the material which subsequently makes the sensor model more sensitive to surface potential shifts. The excess electrons accumulate on the QW edge. Thus, increasing the band bending between the GaN/InGaN interface which, in turn, compensates the near surface band bending, decreasing the overall electric field inside the QW. As a result, the QCSE decreases. This band bending translates into a larger wavelength shift (Figure 5.1). However, as the doping exceeds 7 · 1018 cm−3 , the internal field starts to compensate the potential difference on the surface as the carriers drift into the QW and decrease the tiltling which results in a flatter bandstructure resulting in a smaller shift. The wavelength shift is calculated
5 Performed simulations and results
Figure 5.1: Wavelength shift vs. doping concentration. As the impurity density increases, the wavelength shift increases up to ND = 7 · 1018 cm−3 , then the shift slightly decreases. as the difference between the emitted wavelength from the sensor sample and the virgin sample. ∆λ = λsensor − λvirgin (5.2) Another feature which is also investigated, is the overlap between the electron and hole wavefunctions within the InGaN QW (Figure 5.2). This overlap (recombination) probability ψ 2 (z) indicates the intensity of the signal. The higher the recombination probability of the exciton, the higher the luminescence signal. Increasing the doping concentration results in an increase in the recombiation probability due to the presence of excess donor electrons. Moreover, it is observed from Figure 5.2 that overlapvirgin > overlapsensor because the virgin sample has a higher surface band bending (Schottky barrier height), thus the wavefunctions tend to be more confined inside the QW leading to a higher recombination probability. It is concluded from these results that an n-doping concentration ND = 6 · 1018 cm−3 exhibits the best wavelength shift and a high recombination probability.
5.2 Variable QW thickness
Figure 5.2: Overlap between electron and hole wavefunctions vs. doping concentration for both sensor and virgin samples. Increasing the impurity concentration level results in higher wavefunctions overlap percentages.
5.2 Variable QW thickness The second parameter which has been varied is the InGaN QW thickness, with various background doping concentrations. The QW is varied from 2 nm up to 10 nm in steps of 0.5 nm. The cap layer thickness is fixed at 3 nm, and the indium content is 12%. It is expected that for a thicker QW, QCSE increases due to an increase in the internal potential difference. As a result, the wavelength shift increases and thus the sensitivity of the sensor heterostructure. The results are indicated in Figure 5.3. However, for very high doping concentrations (ND ≥ 5 · 1018 cm−3 ), the heterostructure’s sensitivity seems to be reduced due to the over compensation of the internal electric field by the excess donors which fall into the QW. On the other hand, as the QW thickness increases, the separation between electron and hole wavefunctions increases linearly which reduces their overlap exponentially as shown in Figure 5.4. This leads to a deterioration in the PL signal by a huge factor (up to a 106 reduced recombination rate). Therefore, a compromise
5 Performed simulations and results
Figure 5.3: Wavelength shift vs. QW thickness. The colored curves represent different n-doping concentrations. Thicker QWs exhibit an increased shift.
between the sensitivity (∆λ) and the signal intensity has to be made. It is deduced from these results that thin QW layers in the range of 3 nm to 4nm with high background doping concentrations in the range of 5 · 1018 cm−3 to 1 · 1019 cm−3 are desirable.
5.3 Variable cap layer thickness The third parameter considered in the simulations is the positioning of the QW relative to the surface, again with various background doping concentrations. This barrier between the surface and the QW is called the cap layer. The GaN cap layer is varied from 3 nm to 10 nm with steps of 0.5 nm (see Figure 5.5). The QW thickness is fixed at 3 nm, and the indium content is 12%. Depending on the doping concentration, the penetration of the surface band bending into the material happens within a few to hundreds of nanometers. This changes the QCSE within the QW. Therefore, for thin cap layers and for maximum local fields, the QW is most sensitive to these potential changes. It is clear from the results that the maximum wavelength shift is achieved by having a thin cap layer and a high doping concentration due to
5.3 Variable cap layer thickness
Figure 5.4: Overlap between electron and hole wavefunctions vs. QW thickness for the sensor sample. The colored curves represent different n-doping concentrations. Thicker QWs show less wavefunctions overlap percentages.
the strong near surface band bending which compensates the internal piezoelectric polarization effects. While for QWs positioned deep into the material i.e. thick cap layers, and high doping concentrations (5 · 1018 cm−3 ≤ ND ≤ 1 · 1019 cm−3 ), the potential gradient in the QW region is small, thus the sensor suffers from less sensitivity to surface changes. Unfortunatly, for intermediate doping concentrations (5 · 1017 cm−3 ≤ ND ≤ 1 · 1018 cm−3 ), it is obvious that the curves have some fluctuations due to simulatory errors. This might be due to the grid specification in nextnano, as the grid points cannot be treated as a variable, therefore as the cap layer increases, the grid points are less, resulting in the wavefunctions not being precisely computed and the values do not seem to converge. As shown in Figure 5.6, the recombination probability only slightly decreases as the cap layer increases; as the positioning of the QW within the GaN bulk (i.e. thickness of the capping layer) doesn’t have a strong effect on the electron-hole recombination. However, the most prominent factor for the intensity change is the doping concentration. High background doping concentrations show the best overlap integral due to partial compensation of the piezofield in the QW. These results are consistent with the ones obtained from varying the doping concentration
5 Performed simulations and results in section 5.1. However, having a thin cap layer increases the risk of the carriers tunneling out of the QW and non-radiatively recombining at the surface or in the bulk. Hence, this could potentially lead to a loss in the PL intensity, but only for very thin layers (< 3 nm). Under these circumstances, a trade-off between high sensitivity and high signal-to-noise ratio has to be made for such a sensor. However, for now the signal intensity of the 3 nm cap layer is enough for detection as the tunneling is still almost negligible. Therefore, it is concluded that having a high background doping (ND = 1 · 1019 cm−3 ) and a 3 nm cap layer exhibits the best combination of both wavelength shift and recombination probability.
Figure 5.5: Wavelength shift vs. cap layer thickness for various n-doping concentrations. Thin cap layers with dense doping profiles are desirable.
5.4 Variable indium concentration The last parameter considered in the simulations is the indium content within the InGaN QW, also for different background doping concentrations. The indium content is varied from 6% up to 15%, keeping the QW and cap layer thicknesses both fixed at 3 nm. As shown in Figure 5.7, low doping concentrations show a weak
5.4 Variable indium concentration
Figure 5.6: Overlap between electron and hole wavefunctions for the sensor sample vs. cap layer thickness. The recombination probability slightly decreases as the cap layer thickness increases linearly. The decrease in recombination probability is weak compared to the overlap response for variable QW thickness. response for the wavelength shift even for high indium content. For high background doping (ND ≥ 5 · 1018 cm−3 ), the wavelength shift is high even for low indium contents. It is also observed from the results that for ND = 1 · 1019 cm−3 , as the indium content reaches a value of 11%, the wavelength shift starts to decrease. This reduced spectral shift is due to the excess dopant electrons being trapped in the QW, relieving the strain resulting from the high alloy content which results in a flatter band structure. With increasing the indium concentration within the QW, clustering behavior is stronger. When indium is clustered, a non-uniform distribution of pinning sites on the surface occurs. As a result, non-uniformities in the surface potential are also anticipated. Such non-uniform surface potentials complicate the interpretation of band bending measurements. Hence, it is not recommended to have a high indium concentration within the QW.
5 Performed simulations and results On the other hand, as the indium content increases, the overlap integral decreases because the strain within the QW is stronger (similar to higher QW thicknesses). Results are shown in Figure 5.8. Therefore, the electron and hole wavefunctions are more spatially separated. It is concluded from the previously shown results that for intermediate indium concentrations (9% ≤ x ≤ 12%) and high background doping (ND ≥ 5 · 1018 cm−3 ), the sensitivity and the signal intensity are acceptable.
Figure 5.7: Wavelength shift vs. indium content within the QW for various n-doping concentrations. Higher doping concentrations have a much stronger effect even for low indium contents.
5.5 Variable undoped QW thickness Further simulations have been performed to study the effect of having the QW and the cap layer undoped. Therefore, for these simulations, only the buffer layer is n-doped. This effect is considered due to the fact that having dopants in the InGaN QW increases the crystal defects and deformation. Hence, for the metal organic vapor phase epitaxy (MOVPE) growth procedure (samples fabrication process), it is not recommended to introduce dopants in addition to the deformation problems
5.5 Variable undoped QW thickness
Figure 5.8: Overlap between electron and hole wavefunctions for the sensor sample vs. indium content. The recombination probability decreases exponentially with increasing the indium content linearly.
which arise due to the indium content within the QW (strain). Thus, the simulations were done in order to compare them later on to the experimental PL measurements. Only doping the buffer layer still introduces many carriers within the active region due to their diffusion. In the simulations, the doping stops at 5 nm before the QW region in order to control the dopants within the QW. It is obvious from Figure 5.9, that the same trend appears as the simulations performed in section 5.2. As the QW thickness increases, the redshift increases. Howevever, since the doping is only defined for the buffer layer, the excess electrons donot compensate the field (band tilt) in the QW region, therefore, the shift increases even at high doping concentrations for the thick QWs; which is not the case in the results presented in section 5.2. For low doping concentrations and for high doping concentrations but thin QWs, both figures have the same behavior. On the other hand, as shown in Figure 5.10, the recombination probabillity decreases with thicker QWs by a factor up to ≈ 108 , which is 100 times more than the overlap decrease observed in section 5.2. However, for high doping concentrations
5 Performed simulations and results
Figure 5.9: Wavelength shift vs. QW thickness for various n-doping concentrations in the GaN buffer layer. Increasing the QW thickness results in a higher wavelength shift. and thin QWs, the reombination probabilty matches the earlier obtained results. Therefore, it is concluded from these simulations that only doping the buffer layer has a better outcome for the wavelength shift, especially for high doping concentrations. It is still desirable to have thin QWs for highest sensitivity and detectable signal intensities.
5.5 Variable undoped QW thickness
Figure 5.10: Overlap percentage between electron and hole wavefunctions for the sensor sample vs. QW thicknness. The overlap integral is reduced exponentially as the QW thickness increases.
6 Experimental verification Doped InGaN QW structures have been grown by metal organic vapor phase epitaxy (MOVPE). However, upon measuring them with the Photoluminescence (PL) setup, the results were incosistent. Therefore, the following results have been provided by . PL spectroscopy is a powerful method to study the characteristics of a semiconductor material. In a typical PL setup, the sample semiconductor is excited by a strong laser diode. The exciting energy is larger than the band gap of the sample material and hence they are absorbed by the material and free carriers are generated. After certain time known as relaxation time (order of few nanoseconds), the carriers recombine spontaneously and produce luminescence. The
Figure 6.1: Wavelength shift obtained from different samples after the adsorption of ferritin and apoferritin biomolecules .
6 Experimental verification measured cap layer series is undoped, however, we assume an unintentional doping of ≈ 1 · 1018 cm−3 . The results measured experimentally for the cap layer series shows a higher wavelength shift than the simulatory results from section 5.3. This might be due to the assumption of the surface potential on nextnano for both the virgin sample and the sensor sample. The actual near-surface band bending due to the adsorption of ferritin and apoferritin is more than what has ben assumed in the software, however, it is challenging to measure the potential difference experimentally. The cap layer thicknesses used iin the experimental measurements are shown below Table 6.1. Table 6.1: Cap layer series consisting of 5 samples of different thicknesses. Sample Cap layer thickness (nm) Y1966 3 Y1967 6 Y1968 9 Y1960 15 Y1970 30
7 Conclusion and outlook Optochemical transducers based on GaN/InGaN heterostructures are used for the detection of biomolecules. Simulations on nextnano have been performed in order to optimize the heterostructure design parameters to achieve maximum biosensitivity. Two samples are considered in each of the simulations; a virgin sample and a sensor sample, having a potential difference of -0.3 eV. The difference in their wavelength emission is calculated, which indicates the sensitivity of the sensor. In order to conclude the results, having high n-doping concentrations for the sensor in the range of 5 · 1018 cm−3 up to 1 · 1019 cm−3 exhibit high sensitivity and overlap integral. Thin cap layers in the range of 3 nm to 4 nm, and thin QWs in the range of 3 nm to 4 nm also exhibit a high redshift and overlap integral. Intermediate indium concentrations in the range of 9% to 12% are recommended as they show a high shift and recombination probability. Further simulations were done on variable QW thicknesses having only the buffer layer n-doped. Doping only the buffer layer, and leaving the QW and cap layer undoped results in more redshift but less overlap of the electron-hole wavefunctions. Experimental results have been compared to the simulatory results for the cap layer series, and an huge error magnitude is observed. Experimental results show a higher redshift than the simulatory results. The proposed sample parameters are; a cap layer thickness of 3 nm, QW thickness of 3 nm, n-doping concentration of 1 · 1019 cm−3 and indium concentration of 11%. The proposed sample has an emission wavelength λvirgin ≈ 403 nm for the virgin surface, and an emission wavelength λsensor ≈ 408 nm for the surface with adsorbed molecules. Therefore, the wavelength shift is around 5 nm. For future work, it is proposed to perform PL measurements for n-doped samples for a cap layer series, a QW series and an indium content series in order to verify the simulatory results. The PL measurements should be performed for both the virgin samples and the samples having (bio)chemicals adsorbed on the surface. It is also suggested to perform Hall measurements for the samples in order to confirm the exact doping concentration. Moreover, it is recommended to investigate the points which exhibit a strange behavior in the simulations of the cap layer thickness as the fluctuations are of huge magnitude. Also, different compounds can be used for the cap layer e.g. AlGaN due to its wide bandgap. Lastly, growing N-polar heterostructures instead of Ga-polar might improve the sensitivity as the nitrogen bonds are more reactive to surface changes.
Acknowledgment I would like to express my deep gratitude for all people who helped me finish my bachelor thesis project. • I would like to acknowledge my referee Prof. Dr. Ferdinand Scholz for giving me the opportunity to do my bachelor thesis in this interesting field. I am honored to have been his student. Without his timely advice, I would not have been able to finish my project. • I would like to thank my supervisor, Martin Schneidereit for his friendly guidance and assistance. I am grateful for the time he spent teaching me and helping me get a better understanding of this topic. • I would like to thank Abdelrahman Said and Yujia Liao for teaching me how to perform PL measurements. • I would like to thank Jan Patrick Scholz for growing the series of doped samples, and teaching me how the MOVPE machine operates. • I am grateful for Oliver Rettig for teaching me how to perform Hall measurements. • Last but not least, I am thankful for my family and friends for their kind support.
List of Tables 3.1 3.2 3.3
Band gap energies and lattice constants a for wurtzite structures of some group III nitrides . . . . . . . . . . . . . . . . . . . . . . . . Bowing parameter b for wurtzite type III nitrides . . . . . . . . . Spontaneous polarization coefficients for wurtzite GaN and InN .
6 8 8
Cap layer series consisting of 5 samples of different thicknesses. . . .
List of Figures 3.1 3.2 3.3 3.4 3.5 3.6
Direct (left) and indirect (right) band structures of group III nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Wurtzite crystal unit cell. The green balls represent N atoms, while the red balls represent Ga atoms . . . . . . . . . . . . . . . . . . . 6 Crystallography and orientation of group III nitride layers growth . 7 GaN/InGaN heterostructure. Cross section for a grown sample (left) and band edges of the heterostructure (right). . . . . . . . . . . . . . 7 Schematic of a pseudomorphically strained lattice mismatched layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Crystal structure, spontaneous polarization fields (Psp ) and piezoelectric polarization fields (Ppz ) for Inx Ga1−x N coherently strained to GaN (0001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Quantum confined Stark effect: electron and hole wavefunctions without (left) and with electric field (right) within the QW . . . . . . 11 Sensor principle schematic: virgin surface (left), and the presence of adsorbed (bio)molecules on the surface (right) which induce a near surface band bending . . . . . . . . . . . . . . . . . . . . . . . . . 12 Schematic of the QW heterostructure. The InGaN QW layer (thickness 2-10 nm) is grown on a GaN buffer layer of 2 µm, followed by a GaN capping layer of 3-10 nm. Lastly, an air interface of 10 nm is added in order to model the sensor surface. . . . . . . . . . . . . . . The Schottky barrier height between n-doped GaN and an air surface. The conduction band edge is pinned at eφB above the Fermi level. .
Wavelength shift vs. doping concentration. As the impurity density increases, the wavelength shift increases up to ND = 7 · 1018 cm−3 , then the shift slightly decreases. . . . . . . . . . . . . . . . . . . . . . 24 Overlap between electron and hole wavefunctions vs. doping concentration for both sensor and virgin samples. Increasing the impurity concentration level results in higher wavefunctions overlap percentages. 25 Wavelength shift vs. QW thickness. The colored curves represent different n-doping concentrations. Thicker QWs exhibit an increased shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
List of Figures 5.4
Overlap between electron and hole wavefunctions vs. QW thickness for the sensor sample. The colored curves represent different n-doping concentrations. Thicker QWs show less wavefunctions overlap percentages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Wavelength shift vs. cap layer thickness for various n-doping concentrations. Thin cap layers with dense doping profiles are desirable. . . 5.6 Overlap between electron and hole wavefunctions for the sensor sample vs. cap layer thickness. The recombination probability slightly decreases as the cap layer thickness increases linearly. The decrease in recombination probability is weak compared to the overlap response for variable QW thickness. . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Wavelength shift vs. indium content within the QW for various ndoping concentrations. Higher doping concentrations have a much stronger effect even for low indium contents. . . . . . . . . . . . . . . 5.8 Overlap between electron and hole wavefunctions for the sensor sample vs. indium content. The recombination probability decreases exponentially with increasing the indium content linearly. . . . . . . 5.9 Wavelength shift vs. QW thickness for various n-doping concentrations in the GaN buffer layer. Increasing the QW thickness results in a higher wavelength shift. . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Overlap percentage between electron and hole wavefunctions for the sensor sample vs. QW thicknness. The overlap integral is reduced exponentially as the QW thickness increases. . . . . . . . . . . . . . 6.1
Wavelength shift obtained from different samples after the adsorption of ferritin and apoferritin biomolecules . . . . . . . . . . . . . . .
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