그래핀(Graphene) 디랙 페르미온 클라인 터널링 & 1,000Hz 0-Alloc C# 탄도 수송(Ballistic Transport) 게이트 서보 제어기

using System;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;

namespace ZeliDesk.Defense.QuantumTransport
{
    /// <summary>
    /// 그래핀 소자 드레인 전류 및 채널 컨덕턴스 센서 프레임
    /// </summary>
    [StructLayout(LayoutKind.Sequential, Pack = 8)]
    public readonly struct GrapheneSensorFrame
    {
        public readonly double TimestampSeconds;
        public readonly double DrainCurrentMicroamps;   // 드레인 전류 I_d (uA)
        public readonly double SourceDrainVoltageVolts; // 바이어스 전압 V_ds (V)
        public readonly double TopGateVoltageVolts;     // 현재 Top 게이트 전압 (V)
        public readonly double BackGateVoltageVolts;    // 현재 Back 게이트 전압 (V)

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public GrapheneSensorFrame(double timestamp, double id, double vds, double vtg, double vbg)
        {
            TimestampSeconds = timestamp;
            DrainCurrentMicroamps = id;
            SourceDrainVoltageVolts = vds;
            TopGateVoltageVolts = vtg;
            BackGateVoltageVolts = vbg;
        }
    }

    /// <summary>
    /// 듀얼 게이트 전압 제어 출력 프레임
    /// </summary>
    [StructLayout(LayoutKind.Sequential, Pack = 8)]
    public readonly struct GrapheneGateControlOutput
    {
        public readonly double CommandedTopGateVolts;   // 지령 Top 게이트 전압 (V)
        public readonly double CommandedBackGateVolts;  // 지령 Back 게이트 전압 (V)
        public readonly double EstimatedFermiEnergyEv;  // 추정 페르미 에너지 E_F (eV)
        public readonly double CurrentOnOffRatio;       // 추정 온/오프 전류비
        public readonly bool IsKleinLeakageSuppressed;  // 클라인 누설 억제 플래그

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public GrapheneGateControlOutput(double vtg, double vbg, double ef, double ratio, bool isSuppressed)
        {
            CommandedTopGateVolts = vtg;
            CommandedBackGateVolts = vbg;
            EstimatedFermiEnergyEv = ef;
            CurrentOnOffRatio = ratio;
            IsKleinLeakageSuppressed = isSuppressed;
        }
    }

    /// <summary>
    /// 1,000Hz 0-Alloc C# 그래핀 디랙 페르미온 탄도 수송 서보 엔진
    /// </summary>
    public ref struct GrapheneKleinTunnelingServoEngine
    {
        private const double QuantumOfConductance = 7.7480917e-5; // 2e^2/h (S)
        private const double FermiVelocity = 1e6;                 // 10^6 m/s
        private const double TargetOffCurrentMicroamps = 0.05;   // 목표 오프 전류 50nA

        private double _accumulatedError;
        private double _lastTimestamp;
        private double _currentTopGate;
        private double _currentBackGate;
        private bool _isInitialized;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Initialize(double initialVtg, double initialVbg)
        {
            _accumulatedError = 0.0;
            _lastTimestamp = 0.0;
            _currentTopGate = initialVtg;
            _currentBackGate = initialVbg;
            _isInitialized = true;
        }

        /// <summary>
        /// 1,000Hz(1ms 주기) 채널 전류 기반 듀얼 게이트 전위 최적화 틱
        /// </summary>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public GrapheneGateControlOutput ProcessTick(in GrapheneSensorFrame frame)
        {
            if (!_isInitialized)
            {
                Initialize(frame.TopGateVoltageVolts, frame.BackGateVoltageVolts);
            }

            double dt = frame.TimestampSeconds - _lastTimestamp;
            if (dt <= 0.0 || dt > 0.01) dt = 0.001; // 1ms 기본 주기
            _lastTimestamp = frame.TimestampSeconds;

            // 1. 컨덕턴스 계산: G = I_d / V_ds
            double conductance = (frame.DrainCurrentMicroamps * 1e-6) / Math.Max(frame.SourceDrainVoltageVolts, 1e-4);

            // 2. 백 게이트 전압으로부터 페르미 에너지 E_F 추정: E_F ~ hbar * v_F * sqrt(pi * alpha * V_bg)
            double carrierDensity = 7.2e14 * Math.Abs(frame.BackGateVoltageVolts); // m^-2
            double kFermi = Math.Sqrt(Math.PI * carrierDensity);
            double fermiEnergyEv = (1.0545718e-34 * FermiVelocity * kFermi) / 1.602176634e-19;

            // 3. 클라인 터널링 누설 전류 차단을 위한 비대칭 장벽 피드백 (PI 제어)
            double currentError = frame.DrainCurrentMicroamps - TargetOffCurrentMicroamps;
            _accumulatedError += currentError * dt;
            _accumulatedError = Math.Clamp(_accumulatedError, -10.0, 10.0);

            // 게이트 차동 보정: Top 게이트를 음의 방향으로, Back 게이트를 양의 방향으로 분할 가변
            double deltaV = 0.8 * currentError + 0.15 * _accumulatedError;
            _currentTopGate -= deltaV * 0.05;
            _currentBackGate += deltaV * 0.02;

            _currentTopGate = Math.Clamp(_currentTopGate, -5.0, 5.0);
            _currentBackGate = Math.Clamp(_currentBackGate, -10.0, 10.0);

            // 4. 온/오프 비 산출 및 누설 억제 여부 판정
            double onOffRatio = 100.0 / Math.Max(frame.DrainCurrentMicroamps, 0.01);
            bool isSuppressed = frame.DrainCurrentMicroamps < 0.1;

            return new GrapheneGateControlOutput(
                vtg: _currentTopGate,
                vbg: _currentBackGate,
                ef: fermiEnergyEv,
                ratio: onOffRatio,
                isSuppressed: isSuppressed
            );
        }
    }
}