AIDT 온디바이스 STEM 양전자 소멸 수명 분광(PALS) 원자 결함 서보 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.Pals
{
    public readonly ref struct PalsDefectState
    {
        public readonly double BulkLifetimePs;       // 자유 양전자 수명 tau_2 (ps)
        public readonly double OPsLifetimeNs;        // o-Ps 픽오프 소멸 수명 tau_3 (ns)
        public readonly double DefectRadiusNm;       // 타오-엘드럽 기공 반경 R (nm)
        public readonly double FreeVolumeAngstrom3;  // 자유 체적 Vf (Å^3)
        public readonly double DefectIntensityPercent;// 결함 강도 I_3 (%)
        public readonly double VacancyConcentrationPpm;// 추정 점결함 농도 (ppm)

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public PalsDefectState(double tau2, double tau3, double radius, double vf, double i3, double ppm)
        {
            BulkLifetimePs = tau2;
            OPsLifetimeNs = tau3;
            DefectRadiusNm = radius;
            FreeVolumeAngstrom3 = vf;
            DefectIntensityPercent = i3;
            VacancyConcentrationPpm = ppm;
        }
    }

    public ref struct PalsAnalyzerEngine
    {
        private const double DeltaRNm = 0.1656; // Tao-Eldrup 경계층 두께 (nm)

        private double _cfdThresholdV;          // CFD弁별기 임계 전압 (V)

        public PalsAnalyzerEngine(double thresholdV = -0.15)
        {
            _cfdThresholdV = thresholdV;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public PalsDefectState StepServo(double measuredTau2Ps, double measuredTau3Ns, double measuredI3Percent, double dtSec)
        {
            double tau3 = Math.Clamp(measuredTau3Ns, 0.6, 20.0);

            // 1. 뉴턴-랩슨 반복법을 통한 타오-엘드럽 수명 방정식 역산
            // f(R) = 0.5 / (1 - R/(R+dR) + (1/2pi)*sin(2pi*R/(R+dR))) - tau3 = 0
            double rEst = 0.25; // 초기 추정 반경 (nm)
            for (int iter = 0; iter < 6; iter++)
            {
                double rTotal = rEst + DeltaRNm;
                double xi = rEst / rTotal;
                double sinTerm = Math.Sin(2.0 * Math.PI * xi);
                double invBracket = 1.0 - xi + (1.0 / (2.0 * Math.PI)) * sinTerm;
                double calcTau = 0.5 / Math.Max(invBracket, 1e-4);

                double fVal = calcTau - tau3;
                if (Math.Abs(fVal) < 1e-4) break;

                // 근사 도함수
                double dxiDr = DeltaRNm / (rTotal * rTotal);
                double dBracketDr = -dxiDr * (1.0 - Math.Cos(2.0 * Math.PI * xi));
                double dTauDr = -0.5 * dBracketDr / Math.Max(invBracket * invBracket, 1e-6);

                rEst -= fVal / Math.Max(dTauDr, 1e-4);
                rEst = Math.Clamp(rEst, 0.05, 5.0);
            }

            // 2. 구형 기공 자유 체적 V_f (Å^3) 계산
            double rAngstrom = rEst * 10.0;
            double freeVolume = (4.0 / 3.0) * Math.PI * Math.Pow(rAngstrom, 3.0);

            // 3. 점결함(단원자 공공) 농도 추정 (금속 격자 포획 모델 근사)
            // C_v = (1 / mu_v) * (tau2 - tau_bulk) / (tau_bulk * (tau_v - tau2))
            double vacancyPpm = Math.Clamp(measuredI3Percent * 15.0 * (measuredTau2Ps / 200.0), 1.0, 5000.0);

            return new PalsDefectState(
                tau2: measuredTau2Ps,
                tau3: tau3,
                defectRadiusNm: rEst,
                vf: freeVolume,
                i3: measuredI3Percent,
                ppm: vacancyPpm
            );
        }
    }
}