Semiconducting Diamond

Short Introduction on Semiconducting Diamond

Physical features of diamond

Diamond lattice

Carbon allotropes consist of several formations, individually distinguished by how carbon atoms bonded to their neighbors. Electrons orbiting the carbon atom in the configuration of (1s)2(2s)2(2p)2 possibly possess up to four covalent bonds. Figure 1 visualizes electron configuration of a single carbon atom.

Figure 1. Structure of a single carbon atom. It has two core electrons surrounding the nucleus in an s orbital and four valence electrons, two in an s orbital and two in p orbitals.

A production of graphene is caused by the sp2 bonding of carbon atoms, in which each carbon atom is connected to its three closest neighbors. This graphene is described as a two-dimensional material. Because of the graphene formation remaining one electron left and extremely flat dimension, the graphene is thus superconductive. The stacking of many graphene layers, attracted with each other using Van der Waals force (weak force) in the c-axis direction, creates graphite, which is well known as a nonmetallic conductor. Figure 2(top) depicts the formation of graphite created by several graphene layers. Unlike graphite, sp3 carbon bonding forms a diamond lattice configuration. Each carbon atom in diamond site connects to four closest neighboring atoms (All electrons in 2s22p2 are used) with a bonding length of 0.154 nm, forming tetrahedral covalent bonds. Due to high strength of covalent bond arisen from a short distance between each atom in diamond lattice, diamond, therefore, possesses an extreme physical robustness. Diamond shows a great dielectric property as no free electrons remained in lattice site. Figure 2(bottom) depicts a diamond primitive cell which the structure is equivalent to a face-centered cubic (FCC) with a side length of 3.567 Å (lattice constant a0 = 3.567 Å). The diamond primitive cell has 8 atoms of carbon and tiny lattice site, making it has the highest atomic number density (~1023 cm-3) of any material on earth.

Figure 2 Graphite formed stacking graphene layers (top) and diamond primitive cell (bottom).

Energy band structure

As we discussed in the previous section, the tiny size of carbon atoms allows them to locate close to each other in the diamond lattice, resulting in an extremely short C-C bond length. This unique structure causes an overlap of electron orbitals between adjacent C atoms in the C-C covalent bond, creating a large energy separation between the occupied bonding orbitals and the unoccupied antibonding orbitals. Hence, an electronic band structure of diamond owns a huge forbidden energy gap between valence band (VB) and conduction band (CB) states. Painter et al calculated the electronic band structure of diamond using the discrete variational method in an ab initio approach, found that the minimal bandgap of diamond was indirect bandgap with a value of 5.47 eV at 300 K. Therefore, if diamond is not considered as an insulator, it is well known as a wide bandgap semiconductor.

Figure 3 Electronic band structure of diamond calculated ab initio. Red lines show the energy difference between valence band maximum (VBM) and conduction band minimum (CBM) at 300 K. Indirect and direct band gaps of diamond are 5.47 eV and 7.3 eV, respectively. (Adapted from G. S. Painter, D. E. Ellis, A. R. Lubinsky, Phys. Rev. B 1971, 4, 3610.)

Charge carrier mobility and saturation velocity

Natural (IIa-type) diamond owns electron and hole mobilities of 2300 cm2V-1s-1 and 1800 cm2V-1s-1 at 300 K, respectively. Previous studies, as shown in Figure 4, indicated that these mobilities were dominated by acoustic phonon scattering at temperature below 400 K, and were predominated by inter-valley (for electron) or optical (for hole) phonon scattering at temperature above 400 K. Because of high and nearly equal mobilities of electron and hole, diamond, therefore, is suitable for applications in high-speed devices as well as particles sensors.

For single crystal (SC) - CVD diamond, the charge mobilities are superior rather than the natural one. An intrinsic SC-CVD diamond owns electron and hole mobilities of 4500 cm2V-1s-1 and 3800 cm2V-1s-1 at 300 K, respectively, which are the highest values among wide bandgap semiconductors. The previous study of temperature dependence of hole mobility in the intrinsic diamond, as shown in Figure 5, indicated that acoustic phonon scattering mainly disrupted charge movement in a high crystallinity of diamond networks at temperature range of 300 - 400 K. For impurity diamond, this reduced mobility at the same temperature range were observed, and possibly due to charge scattering from incomplete ionization of impurity atoms reported by Somogyi (K. Somogyi, Diam. Relat. Mater. 2002, 11, 686.). Namely, impurity deteriorates carrier mobilities of diamond. At temperatures above about 400 K, this hole mobility was reduced rapidly due to optical phonon scattering. However, this mobilities of > 1000 cm2V-1s-1 could be obtained at temperature ~500 K, making diamond suitable for high-temperature devices application.

Figure 4 Temperature dependence of electron and hole mobilities in IIa diamond. Data symbols represent measurement approaches as triangle and black circle: Hall mobility and white circle: drift mobility. (A. G. Redfield, Phys. Rev. 1954, 94, 526, E. C. Lightowlers, A. T. Collins, Phys. Rev. 1966, 151, 685, L. Reggiani, S. Bosi, C. Canali, F. Nava, S. F. Kozlov, Phys. Rev. B 1981, 23, 3050, and F. Nava, C. Canali, C. Jacoboni, L. Reggiani, S. F. Kozlov, Solid State Commun. 1980, 33, 475.)

Figure 5 Temperature dependence of hole mobility in intrinsic single crystalline diamond, analyzed and reported by Isberg et al. (Science (80). 2002, 297, 1670.)

The conductivity in semiconductor under high electric fields is determined by a saturation velocity rather than mobility. This is because the moving carriers rapidly lose energy to the crystal lattice by emission of optical phonons associated with other scattering events, limiting the maximum carrier velocity. So, the optical phonon energy in a material is a crucial factor to determine the saturation velocity of charge carriers. Diamond has the largest optical phonon energy (Eopt = 160 meV) compared with other semiconductors. it, therefore, possesses high saturation velocity of ~107 cm s-1 for both electron and hole. Higher saturation velocity is higher profitable for high-speed field-effect transistors (FETs) performance. Figure 6 shows a comparison of carrier mobility of diamond and other common semiconductor materials.

Figure 6 Carrier mobility of diamond and other common semiconductor materials (data taken form Pierson, Handb. Carbon, Graph. Diamonds Fullerenes 1993, 226).

Power handling versus operating frequency for various groups of semiconductor materials. Source: AKHAN Semiconductor

Dielectric constant and dielectric breakdown strength

Ia diamond shows a dielectric constant of 5.7 (εdia = 5.7ε0), which is the lowest value of wide bandgap semiconductors. This dielectric constant and the device geometry can determine capacitance of switching-sensing devices. Low dielectric constant values are preferred for high frequency or power applications to minimize electric power loss. Moreover, diamond exhibits remarkable a loss tangent below ~3×10-6 at 170 GHz at 300 K, making it suitable for application in high-frequencies high-power transmission devices. Intrinsic CVD diamond theoretically exhibits a high dielectric strength of 10 MV/cm, which is the highest value of any semiconductors before occurrence of avalanche breakdown. A high dielectric breakdown strength enhances not only capability of voltage blocking in diodes but also tolerance of high frequency operation in FETs. However, this dielectric strength is greatly impacted by impurities, dopants, and crystal defects in material.

Thermal conductivity of semiconducting diamond

Diamond is a wide bandgap semiconductor. Literately, there are almost no free electrons (intrinsic diamond) up to high temperatures in the Debye temperature range (ΘD = 2240 K for diamond). So, the heat in diamond crystal is mostly transferred using phonon. As of the stiffness of the lattice and very short distance of bond length, diamond can rapidly transfer phonon through the periodic carbon network. This phenomenon makes diamond known as the highest thermal conductivity (22 Wcm–1K–1 at room temperature) of any rigid materials. Figure 7 shows room temperature thermal conductivities of different materials vs their electronic bandgaps. Due to this high thermal conductivity, heat dissipation during operation of diamond device is effective. Hence, diamond electronics requires smaller area for cooling system when compared with Si, SiC or GaN-based electronics.

Displacement energy

Due to high strength of covalent bond arisen from a short distance between each atom, an extreme physical robustness can be expected for diamond. Diamond has the highest displacement energy (Ed = 47.6 eV for IIa diamond) of any semiconductors, as shown in Figure 8. However, the Ed of diamond is anisotropic, which were found to be 37.5, 45.0 and 47.6 eV for crystal direction of [100], [111] and [110], respectively. With this property, diamond, therefore, is perfectly suitable for application in radiation-hardened electronics.

Figure 7 Room temperature thermal conductivities of different materials vs their electronic bandgaps (Data taken from Xu et al, J. Appl. Phys. 2019, 126, 185105)

Figure 8 Threshold displacement energy (Ed) with the lattice parameter of various semiconductors (data summarized by Khanal et al, J. Appl. Phys. 2018, 124, 215702.)

Electromagnetic absorption spectrum

Absorption spectrum of intrinsic diamond is depicted in Figure 9. Strong absorption edge was found at wavelength of 225 nm corresponding to the indirect bandgap of diamond (Eg = 5.47 eV). This indicated that the corresponding absorption is resulted from the electron transition between valence and conduction bands of diamond. An complex infrared (IR) absorption was found at wavelength of 2.5 - 6.5 μm, originated from the creation of phonons and multi-phonon absorption. Ideally, diamond is a purely covalent crystal possessing, consequently, no dipole moment. Due to this the ideal diamond lattice does not absorb light in the one-phonon spectral region. Consequently, no observation of IR cut-off for diamond is obtained. Because of visible-light transparency in the intrinsic diamond, particle and solar-blind detectors on diamond do not need for external light filter or screening systems.

Figure 9 Absorption spectrum of intrinsic diamond (taken from A. M. Bennett, B. J. Wickham, H. K. Dhillon, Y. Chen, S. Webster, G. Turri, M. Bass, (Eds.: Clarkson, W. A.; Shori, R. K.), 2014, p. 89590R.

Growth and Wafer

Growth of diamond

Natural diamond

Almost of natural diamonds are used as jewelry, making high-luxury accessories. Natural diamonds might be formed in at least four completely different ways, such as (I) deep in the earth, (II) tectonic plate movement, (III) meteorite impact and (IV) meteorites in space. However, almost of the diamonds in jewelry market are possibly formed by only (I) and (II) ways. Literately, natural diamonds were formed deep below the earth surface at depths of over 120 km, through intense heat of ~900 - 1300°C and pressures of > 45 kbar. However, theses formed diamonds need to be released from the intense pressure and heat under which they are formed in order to embark upon their voyage to the earth surface by using chaos events such as volcanic eruption and tectonic plate movement (earthquake). Figure 10 visualizes where the natural diamond formed and how they came out to the earth surface.

Figure 10 Drawing image depicts natural diamond formation and how they could come up to the earth surface (visualized by Craig Husar Fine Diamonds & Jewelry Designs company). Insertion (right bottom) is a natural uncut-rough diamond (taken from https://sciencing.com/identify-uncut-rough-diamond-7627586.html).

As mentioned in the previous section, the natural diamonds are mostly used in jewelry industry due to its beauty, limit of crystal size, quality and limited number. These make the natural diamonds as the most expensive jewel. In order to reduce the cost and increase availability of diamond for electronic industry, a synthetic diamond must be established and developed. There are currently two major processes for synthesis of diamond, which are (I) high-temperature high pressure (HPHT) and (II) chemical vapor deposition (CVD).

HPHT technique

HPHT technique was first invented in 1955 by the General Electric (GE) Research Laboratories in Schenectady, New York. HPHT synthesis uses an amount of graphite and a metal as catalyzer placed into a large press. The two main press technologies used today are the BELT press (hydraulic) and the cubic press. The graphite is simultaneously heated to around ∼ 1727ºC and pressed under pressure > 5 GPa. With the assistance of the metallic catalyzer, which acts as a solvent, the graphite is converted over a period of several hours/days into single crystal diamonds. Figure 11 illustrate the cutaway diagram of the origin belt-press invented by GE company and a modern cubic press for HPHT diamond synthesis. The HPHT technique permits us to achieve high purity diamond with a low defect density. Still, their total domain size is limited (~2-10 mm each side for IIa), making back-end process of application device difficult. However, because of their low dislocation density (~105 cm-2) and low cost, type Ib HPHT diamond substrates are usually employed for electronic applications. The lower dislocation density (<103 cm-2) could be achieved in IIa substrates but they are much more expensive due to the complex and difficult process of synthesis.

Figure 11 A cutaway diagram of the origin belt-press (left) invented by GE company, taken from US patent 2,947,608, and a modern cubic press (right) for HPHT diamond synthesis.

CVD technique

The idea to synthesize diamond from gas phase was born in the 1950s but it took about 30 years until first diamond layers directly grown from the gas phase on substrates were shown in Japan by Matsumoto and co-workers. As its name, as chemical vapor deposition, CVD technique is on the basis of a gas phase chemical reaction above a substance, then condensed into a solid phase on top of the solid surface. This technique needs an energy supplier (heat, microwave, or radio frequency) to activate gas phase carbon-containing precursor molecules. The mechanism of diamond formation will be discussed in detail later. In fact, CVD technique usually produces polycrystalline diamond, but it is now possible to find single-crystal CVD (SC-CVD) diamond of high quality by optimization of growth conditions. There are various kinds of CVD technique, for example, hot filament CVD (HFCVD), microwave plasma CVD (MWCVD), direct-current plasma assisted CVD (DCPCVD), combustion flame, radio frequency plasma CVD (RFCVD) and plasma jet CVD. However, only HFCVD and MWCVD techniques are now the most popular technique for fabrication of diamond due to their reliability, reproducibility and industrial purposes. Therefore, this section focuses on the HFCVD and MWCVD techniques.

HFCVD technique

The hot filament process employs a metallic filament (tungsten, rhenium or tantalum) heated up to ∼>2000ºC to thermally activate the molecules of the gas mixture. Methane (CH4) and hydrogen (H2) are typically used as the reactant-mixed gas, in which the amount of CH4 is diluted < 1% of the mixed gas at pressure range between 10 - 50 torr. A substrate is usually heated up in temperature range of 700 - 1000ºC during growing diamond. Figure 12 illustrates the growing mechanism of diamond using HFCVD technique, which can be simplified the mechanism as:

I. The precursor gases, methane (CH4) and hydrogen (H2) are mixed in determined portions.

II. Thermal activation of the mixed gas by hot filament

Dissociation of the mixed gas and then creation of atomic hydrogen and different carbon species (i.e., CH2, CH3, ...). The gas temperature could be reached to a few thousand degrees Celsius.

III. Interaction between the reactive flux and the substrate surface

Condensation of reactive flux to solid phase of diamond and graphite

Simultaneous termination of the graphite by hydrogen atoms.

Diamond nuclei formed and then diamond is grown.

IV. Removal of residual gas species by evacuation.

Figure 12 The growing mechanism of diamond using HFCVD technique.

Although HFCVD technique has great advantages such as simple system and capability of large area coating, but the inconveniences are the low growth rate (0.1-10 µm/hr), the contamination with the metallic impurities due to the deterioration of the filament during the process and small area of uniform coating.

MWCVD technique

This technique is the most widely used technique for fabrication of diamond. Unlike HFCVD, it requires microwave power, instead of heat, to activate the gas reactants. Typically, MWCVD reactor, shown in Figure 13, uses a microwave generator coupled to a vacuum chamber which supplies energy to electrons of gas phase. Rapid change of electron momentum transfers the energy by colliding with the gas reactants, generating high intensity of plasma. The reactants molecules are dissociated by plasma temperature (a few thousand Kelvin), yielding reactive species. These reactive species (i.e., CH2, CH3, ...) will be condensed as diamond and graphite at the surface of a substrate where it is immersed in the plasma. The mechanism of diamond formation on the substrate via MWCVD is almost the same one via HFCVD. Due to no need of metallic filament, diamond synthesized using MWCVD is higher purity and crystallinity compared to those one using HFCVD. HFCVD technique is, hence, reliable, and reproducible, an important factor for industrial purposes.

Figure 13 A typical schematic of MWCVD for diamond formation, adapted from Schwander et al, Diam. Relat. Mater. 2011, 20, 1287.

Diamond wafer

Regularly, types of diamond crystals are distinguished by impurity concentrations which are nitrogen and boron impurities. By using this distinction, types of both natural and synthetic diamonds (including HPHT and CVD wafers) are summarized in table 1. Type I diamonds contain a distinct amount of nitrogen (~0.3-0.5 %), in which type Ia is usually colorless and visible-light transparent and most of natural diamonds are in this type. Type Ib has nitrogen atom more than type Ia. The nitrogen atom separately replaces the carbon atom in diamond lattice, remaining one unbonded electron. This electron is thought to be a cause of yellow color for type Ib diamond. Most of HPHT diamonds belong to type Ib. Type II diamonds contain very less nitrogen (0-10 ppm). Type IIa diamonds are insulators and extremely high-thermal conductive due to highest purity and high crystallinity. Type IIb has low impurity but boron concentration is higher than nitrogen concentration, showing semiconducting properties (p-type). Arrangement of impurities atom for each diamond type are visualized in Figure 14.

Table 1. Classification of diamond wafers (taken from C. Breeding, J. Shigley, Gems Gemol. 2009, 45, 96.).

Page updated

Report abuse