High‐Temperature and High‐Electron Mobility Metal‐Oxide‐Semiconductor Field‐Effect Transistors Based on N‐Type Diamond

Abstract Diamond holds the highest figure‐of‐merits among all the known semiconductors for next‐generation electronic devices far beyond the performance of conventional semiconductor silicon. To realize diamond integrated circuits, both n‐ and p‐channel conductivity are required for the development of diamond complementary metal‐oxide‐semiconductor (CMOS) devices, as those established for semiconductor silicon. However, diamond CMOS has never been achieved due to the challenge in n‐type channel MOS field‐effect transistors (MOSFETs). Here, electronic‐grade phosphorus‐doped n‐type diamond epilayer with an atomically flat surface based on step‐flow nucleation mode is fabricated. Consequently, n‐channel diamond MOSFETs are demonstrated. The n‐type diamond MOSFETs exhibit a high field‐effect mobility around 150 cm2 V−1 s−1 at 573 K, which is the highest among all the n‐channel MOSFETs based on wide‐bandgap semiconductors. This work enables the development of energy‐efficient and high‐reliability CMOS integrated circuits for high‐power electronics, integrated spintronics, and extreme sensors under harsh environments.


Modeling the transistor properties
Different from the conventional semiconductors in which the dopants are fully ionized at room temperature, phosphorous in diamond forms a deep donor with a thermal activation energy of 0.57 eV.We include the effects of (i) temperature dependent thermal ionization of the phosphorous donor, (ii) series resistance, and (iii) mobility degradation factors (i.e.interface scattering).In the linear region with gate voltage Vgs larger than the threshold voltage Vth, the drain current (Id) can be expressed as [1]   =  6)

S(3)
where M is the donor occupancy factor, reflecting the ionization rate of the donor.In detail, M=Qd/Qn, where Qd is the charge per unit area of occupied donor sites and Qn is the channel charge per unit area [1b].Here, M is described above the threshold voltage.With increasing current, M decreases and approaches zero, i.e. temperature and gate voltage increase.θ and η are the mobility modulation factors through γ.The factor θ affects the drain current and degrades mobility due to conventional carriers scattering in the channel and the effect of series resistance.The parameter η is a factor reflecting the drain volage effect, which is reasonable considering the tiny microscale/nanoscale structures on the edge of the etched mesa.α is the factor lowering the drain current related to the donor concentration, which is around 1.1 in this study.EF is the quasi Femi level energy of electron, EC is the conduction bandgap energy, and (EC-ED) is the ionization energy for the donor.NC is the effective density of states in the conduction band and Nd is the donor concentration.gd is the degeneracy factor of the donor in diamond, which is equal to 2.  0 and  are the dielectric constants of vacuum and diamond (5.57), respectively.  is the dielectric constant of Al2O3, which is 7 here.ni is the intrinsic carrier concentration.kB is the Boltzmann's constant, q is the electron charge, and T is temperature.Cox is the oxide capacitance per unit area.In the present phosphorous doped diamond n-channel MOSFET, Cox is around 1.7x10 -7 F/cm 2 .The thermal ionization of phosphorous in diamond (EC-ED ) is set to be 0.57 eV for simulation.
The intrinsic concentration varying with temperature is expressed as Where MC and MV are the number of equivalent minima in the conduction band and maxima in the valence band, respectively.For diamond MC=6 and MV=1.mn and mp are the effective mass around the conduction minimum and the valence band maximum.Here mn =1.845m0 and mp =0.908m0 .m0 is the mass of electron.In the saturation region at Vgs larger than Vth , the gate length is replaced by an effective length.Here, the effective gate length is taken as the same as the device for simplicity.

Figure S1 .
Figure S1.Atomic force microscopy (AFM) image of the n -diamond epilayer.Terrace structures with atomically smooth surface is observed, indicating the step-flow growth mode.The height difference (ΔZ) is as small as 0.1~0.2nm, which is due to the off-angle of the miscut substate.

Figure S2 .
Figure S2.AFM image of the n -diamond epilayer.The average roughness in the lines region is less than 1 nm despite the steps.

Figure S8 .
Figure S8.Electrical properties of the n-type diamond MOSFET (device No. 1) presented in the main text at 323 K. (A) Drain current vs drain voltage at different gate voltages.(B) transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S9 .
Figure S9.Electrical properties of the n-type diamond MOSFET (device No. 1) presented in the main text at 373 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S10 .
Figure S10.Electrical properties of the n-type diamond MOSFET (device No. 1) presented in the main text at 423 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S11 .
Figure S11.Electrical properties of the n-type diamond MOSFET (device No. 1) presented in the main text at 473 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S12 .Figure S13 .
Figure S12.Electrical properties of the n-type diamond MOSFET (device No. 1) presented in the main text at 523 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S14 .
Figure S14.Electrical properties of the n-type diamond MOSFET (device No. 2) with the same dimensions as those of device No.1 at 300 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S15 .
Figure S15.Electrical properties of the n-type diamond MOSFET (device No. 2) with the same dimensions as those of device No.1 at 573 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S16 .
Figure S16.Electrical properties of the n-type diamond MOSFET (device No. 4) with the circular geometry with a gate length 10 µm, source-gate and drain-gate distance of 10 µm at 300 K. (A) Drain current vs drain voltage at different gate voltages.(B) Transfer properties.(C) Graphic method for extracting the threshold voltage.(D) Transconductance.

Figure S17 .Figure S18 .
Figure S17.Electrical properties of the n-type diamond MOSFET (device No. 4) with the circular geometry with a gate length 10 µm, source-gate and drain-gate distance of 10 µm at 573 K. (A) Drain current vs drain voltage at different gate voltages.(B) transfer properties.(C) graphic method for extracting the threshold voltage.(D) Transconductance.

Table S1 .
Drain currents of the n-type MOSFETs studied in this work.The Id,sat is for the drain current at Vds=20V and Vgs=10V.The source-gate spacing Lsg is equal to gate-drain spacing Ldg.Devices No.1 to No.3 are rectangular type and device No.4 is circular type.